Information

EPSP/IPSP amplitude values?

EPSP/IPSP amplitude values?

I'm working with a Hodgkin-Huxley model that receives synaptic inputs from presynaptic neurons. If it receives a spike from an excitatory presynaptic neuron, the voltage of my HH neuron inceases by an amount $g$. If it receives a spike from an inhibitory neuron, the voltage jumps down by an amount $g imes K$ (so K is the factor controlling how much the voltage drops relative to how much it would increase from an excitatory neuron). I read in textbooks that the ratio of excitatory:inhibitory neurons is generally $4:1$. That implies that for the system to be "balanced", I should have $K=4$. If $K<4$, then there is a net drift upwards in voltage towards the threshold values, and for $K>4$, there is a net drift downwards away from the threshold.

I have two sub-questions:

1) Is there a typical value of $g$ (the EPSP amplitude) that is biologically plausible? I've seen anywhere from $0.1-0.5$ and above which is quite a big range. I know that there is often a big range based on stimulus and whatnot, but I'm looking for a biologically reasonable value.

2) What is a typical value of $K$? In other words, what is the size of a typical IPSP amplitude relative to the EPSP amplitude? I've seen anywhere from the amplitude being the same to the amplitude being 4x the EPSP amplitude (which of course is a mighty big range).


By definition, current-based synapses are biologically implausible. After all, biological synapses are conductance-based [1]. It is possible that current based synapses are sufficient to answer the question you are asking. It is also possible that they are not. Generally, biological plausibility is not a matter of the parameter values you are using but rather a matter of whether the question you are asking has biological relevance. After all, unless you have a morphologically accurate simulation including every single receptor type, etc. your model is not biologically realistic.

The question you are asking doesn't have a good answer because you are asking a biologically non-sensical question: what is the value of current based synapse magnitudes?
The only way one could possibly answer that question is if one knew why that question needs an answer. Maybe you don't even need a reasonable value for the question you are trying to answer because the phenomenon is robust. Maybe you need the answer to the fifth decimal place because your model is very sensitive to that value.

Point is, biological realism is incredibly context-specific.

[1] Although I have heard a strange argument that the high resistance at the spine neck means that synapses are practically current sources. I don't know anyone that relies on that.


EPSP/IPSP amplitude values? - Psychology

FIGURE 21 Excitatory and inhibitory postsynaptic potentials in spinal motor neurons. (A) Intracellular recordings are made from a sensory neuron (SN), interneuron, and extensor (E) and flexor (F) motor neurons. (B) An action potential in the sensory neuron produces a depolarizing response in the motor neuron (MN). This response is called an excitatory postsynaptic potential (EPSP). (C) An action potential in the interneuron produces a hyperpolarizing response in the motor neuron. This response is called an inhibitory postsynaptic potential (IPSP).

Postsynaptic Mechanisms Produced by Ionotropic Receptors

Ionic Mechanisms of EPSPs

Mechanisms responsible for fast EPSPs mediated by ionotropic receptors in the CNS are fairly well known. Specifically, for the synapse between the sensory neuron and the spinal motor neuron, the ionic mechanisms for the EPSP are essentially identical to the ionic mechanisms at the skeletal neuromuscular junction. Transmitter substance released from the presynaptic terminal of the sensory neuron diffuses across the synaptic cleft, binds to specific receptor sites on the postsynaptic membrane, and leads to a simultaneous increase in permeability to Na+ and K+, which makes the membrane potential move toward a value of 0 mV.

Although this mechanism is superficially the same as that for the neuromuscular junction, two fundamental differences exist between the process of synaptic transmission at the sensory neuron-motor neuron synapse and the motor neuron-skeletal muscle synapse. First, these two different synapses use different transmitters. The transmitter substance at the neuromuscular junction is ACh, but the transmitter substance released by the sensory neurons is an amino acid, probably glutamate. (Although beyond the scope of this chapter, many different transmitters are used by the nervous system— up to 50 or more, and the list grows yearly. Thus, to understand fully the process of synaptic transmission and the function of synapses in the nervous system, it is necessary to know the mechanisms for the synthesis, storage, release, and degradation or uptake, as well as the different types of receptors for each of the transmitter substances. The clinical implications of deficiencies in each of these features for each of 50 transmitters cannot be ignored. Fortunately, most of the transmitter substances can be grouped into four basic categories: ACh, monoamines, amino acids, and the peptides.)

A second major difference between the sensory neuron-motor neuron synapse and the motor neuron-muscle synapse is the amplitude of the postsynaptic potential. Recall that the amplitude of the postsynaptic potential at the neuromuscular junction was approximately 50 mV and that a one-to-one relationship existed between an action potential in the spinal motor neuron and an action potential in the muscle cell. Indeed, because the EPP must only depolarize the muscle cell by approximately 30 mV to initiate an action potential, there is a safety factor of 20 mV. In contrast, the EPSP in a spinal motor neuron produced by an action potential in an afferent fiber has an amplitude of only 1 mV.

The small amplitude of the EPSP in spinal motor neurons (and other cells in the CNS) poses an interesting question. Specifically, how can an ESP with an amplitude of only 1 mV drive the membrane potential of the motor neuron (i.e., the postsynaptic neuron) to threshold and fire the spike in the motor neuron that is necessary to produce the contraction of the muscle? The answer to this question lies in the principles of temporal and spatial summation.

Temporal and Spatial Summation

When the ligament is stretched (see Fig. 20), many stretch receptors are activated. Indeed, the greater the stretch, the greater the probability of activating a larger number of the stretch receptors present this process is referred to as recruitment. Activation of multiple stretch receptors is not the complete story, however. Recall the principle of frequency coding in the nervous system (see Chapter 4). Specifically, the greater the intensity of a stimulus, the greater the number per unit time or frequency of action potentials elicited in a sensory receptor. This principle applies to stretch receptors as well. Thus, the greater the stretch, the greater the number of action potentials elicited in the stretch receptor in a given interval and, therefore, the greater the number of EPSPs produced in the motor neuron from that train of action potentials in the sensory cell. Consequently, the effects of activating multiple stretch receptors add together (spatial summation), as do the effects of multiple EPSPs elicited by activation of a single stretch receptor (temporal summation). Both these processes act in concert to depolarize the motor neuron sufficiently to elicit one or more action potentials, which then propagate to the periphery and produce the reflex.

Temporal Summation. Temporal summation can be illustrated by considering the case of firing action potentials in a presynaptic neuron and monitoring the resultant EPSPs. For example, in Fig. 22A and B, a single action potential in SN1 produces a 1-mV EPSP in the motor neuron. Two action potentials in quick succession produce two EPSPs, but note that the second EPSP occurs during the falling phase of the first, and the depolarization associated with the second EPSP adds to the depolarization produced by the first. Thus, two action potentials produce a summated potential that is 2 mV in amplitude. Three action potentials in quick succession would produce a summated potential of 3 mV. In principle, 30 action potentials in quick succession would produce a potential of 30 mV and easily drive the cell to threshold. This summation is strictly a passive property of the cell. No special ionic conductance mechanisms are necessary.

A thermal analog is helpful to understand temporal summation. Consider a metal rod that has thermal properties similar to the passive electrical properties of


Abstract

Neural mass models offer a way of studying the development and behavior of large-scale brain networks through computer simulations. Such simulations are currently mainly research tools, but as they improve, they could soon play a role in understanding, predicting, and optimizing patient treatments, particularly in relation to effects and outcomes of brain injury. To bring us closer to this goal, we took an existing state-of-the-art neural mass model capable of simulating connection growth through simulated plasticity processes. We identified and addressed some of the model's limitations by implementing biologically plausible mechanisms. The main limitation of the original model was its instability, which we addressed by incorporating a representation of the mechanism of synaptic scaling and examining the effects of optimizing parameters in the model. We show that the updated model retains all the merits of the original model, while being more stable and capable of generating networks that are in several aspects similar to those found in real brains.


Www.neuron.yale.edu

(exp(-t/tau2) - exp(-t/tau1)). How do experienced modelers fit EPSP/IPSP data to synapse parameters, and which synaptic mechanism you use?
Thank you!

Re: Fitting time constants for EPSPs

Post by ted » Tue Apr 24, 2012 9:13 pm

The time constant parameters in ExpSyn and Exp2Syn govern the time course of the synaptic conductance. Your observations, however, are descriptions of membrane potential time course, not the same thing at all. I don't know what you mean by "rise time"--is it 10-90 rise time, 20-80, or what? And half-width is only a rough guide to the time course of the PSP waveform, because it doesn't say whether the entire PSP is well approximated by two time constants, or whether three or more are required.

If you know that your PSP is small enough that the electrical properties of the cell can be treated as approximately linear over that range of membrane potentials, then the time course of the PSP can be interpreted as the convolution of the actual synaptic current and an impedance. If the PSP was observed at the same point at which the synapse was located, the impedance is the input impedance of the cell at that point. If the synapse was located at point A, but the PSP was observed at some other point B, the impedance is the transfer impedance between A and B. For many mammalian central neurons, the local response to an injected current step applied by patch clamp is well described by a single exponent, so the input impedance (and perhaps the transfer impedance as well) is described by a single exponent. For such a cell, a synaptic current with a very fast rise (smaller than 0.5 ms, e.g. produced by an AMPAergic synapse) and a monoexponential decay will generate a PSP that is described by two time constants--but neither of them will be exactly the time constant of the synaptic conductance. Similarly, a biexponential synaptic current--e.g. produced by a GABAergic synapse--will generate a PSP that is described by three time constants, none of which will be the time constants of the synaptic conductance itself.

First, start with the cleanest experimental data you can get. Best would be voltage clamp recording of the current produced by a synapse very close to the location of the clamp electrode. This is your best indication of the actual time course of synaptic current. Then you need to know the driving force for synaptic current entry ("reversal potential") and the clamp's holding potential. From these you can determine the time course of synaptic conductance itself. That's the gold standard. There's not a lot of that kind of data floating around, and it's scattered here and there in the experimental literature.

If the clamp and synapse are at different locations in the cell, and you happen to have detailed morphometric data from the cell, and a good estimate of the cytoplasmic and membrane properties of the cell, you could construct a computational model of the cell (under current or voltage clamp, depending on what the original experimental conditions were), then tinker with the synaptic mechanism's parameters until the simulated PSP or PSC is a close match to the experimental observation. This is more work and produces a result that is a much more indirect indication of the dynamics of the synaptic conductance.


Synaptic Potential

The synaptic potentials are electrotonic potentials: they decay passively as a function of time and distance. The time course of the rising phase of the synaptic potential is determined by both active and passive properties of the membrane. As the synaptic channels spontaneously reclose, the PSP decays in an exponential fashion. The decay of the PSP is purely a passive process whose time course is a function of the membrane time constant, τ. The membrane time constant is the time required for an electrotonic potential to decay to 1/e or 37% of its peak value. The time constant of neurons is in the range of 1–20 ms. The amplitude of the synaptic potentials decreases exponentially from the maximum recorded focally at the synapse as a function of the membrane length constant, γ. The length constant is the distance at which electrotonic potentials decay to 1/e or 37% of their amplitude at the point of origin. The length constant of dendrites is typically in the range 0.1 to 1 mm.


Contents

The nervous system first began to be encompassed within the scope of general physiological studies in the late 1800s, when Charles Sherrington began to test neurons' electrical properties. His main contributions to neurophysiology involved the study of the knee-jerk reflex and the inferences he made between the two reciprocal forces of excitation and inhibition. He postulated that the site where this modulatory response occurs is the intercellular space of a unidirectional pathway of neural circuits. He first introduced the possible role of evolution and neural inhibition with his suggestion that “higher centers of the brain inhibit the excitatory functions of the lower centers”. [1]

Much of today's knowledge of chemical synaptic transmission was gleaned from experiments analyzing the effects of acetylcholine release at neuromuscular junctions, also called end plates. The pioneers in this area included Bernard Katz and Alan Hodgkin, who used the squid giant axon as an experimental model for the study of the nervous system. The relatively large size of the neurons allowed the use of finely-tipped electrodes to monitor the electrophysiological changes that fluctuate across the membrane. In 1941 Katz's implementation of microelectrodes in the gastrocnemius sciatic nerve of frogs’ legs illuminated the field. It soon became generalized that the end-plate potential (EPP) alone is what triggers the muscle action potential, which is manifested through contractions of the frog legs. [3]

One of Katz's seminal findings, in studies carried out with Paul Fatt in 1951, was that spontaneous changes in the potential of muscle-cell membrane occur even without the stimulation of the presynaptic motor neuron. These spikes in potential are similar to action potentials except that they are much smaller, typically less than 1 mV they were thus called miniature end plate potentials (MEPPs). In 1954, the introduction of the first electron microscopic images of postsynaptic terminals revealed that these MEPPs were created by synaptic vesicles carrying neurotransmitters. The sporadic nature of the release of quantal amounts of neurotransmitter led to the "vesicle hypothesis" of Katz and del Castillo, which attributes quantization of transmitter release to its association with synaptic vesicles. [3] This also indicated to Katz that action potential generation can be triggered by the summation of these individual units, each equivalent to an MEPP. [4]

At any given moment, a neuron may receive postsynaptic potentials from thousands of other neurons. Whether threshold is reached, and an action potential generated, depends upon the spatial (i.e. from multiple neurons) and temporal (from a single neuron) summation of all inputs at that moment. It is traditionally thought that the closer a synapse is to the neuron's cell body, the greater its influence on the final summation. This is because postsynaptic potentials travel through dendrites which contain a low concentration of voltage-gated ion channels. [5] Therefore, the postsynaptic potential attenuates by the time it reaches the neuron cell body. The neuron cell body acts as a computer by integrating (adding or summing up) the incoming potentials. The net potential is then transmitted to the axon hillock, where the action potential is initiated. Another factor that should be considered is the summation of excitatory and inhibitory synaptic inputs. The spatial summation of an inhibitory input will nullify an excitatory input. This widely observed effect is called inhibitory 'shunting' of EPSPs. [5]

Spatial summation Edit

Spatial summation is a mechanism of eliciting an action potential in a neuron with input from multiple presynaptic cells. It is the algebraic summing of potentials from different areas of input, usually on the dendrites. Summation of excitatory postsynaptic potentials increases the probability that the potential will reach the threshold potential and generate an action potential, whereas summation of inhibitory postsynaptic potentials can prevent the cell from achieving an action potential. The closer the dendritic input is to the axon hillock, the more the potential will influence the probability of the firing of an action potential in the postsynaptic cell. [6]

Temporal summation Edit

Temporal summation occurs when a high frequency of action potentials in the presynaptic neuron elicits postsynaptic potentials that summate with each other. The duration of a postsynaptic potential is longer than the interval between incoming action potentials. If the time constant of the cell membrane is sufficiently long, as is the case for the cell body, then the amount of summation is increased. [6] The amplitude of one postsynaptic potential at the time point when the next one begins will algebraically summate with it, generating a larger potential than the individual potentials. This allows the membrane potential to reach the threshold to generate an action potential. [7]

Neurotransmitters bind to receptors which open or close ion channels in the postsynaptic cell creating postsynaptic potentials (PSPs). These potentials alter the chances of an action potential occurring in a postsynaptic neuron. PSPs are deemed excitatory if they increase the probability that an action potential will occur, and inhibitory if they decrease the chances. [4]

Glutamate as an excitatory example Edit

The neurotransmitter glutamate, for example, is predominantly known to trigger excitatory postsynaptic potentials (EPSPs) in vertebrates. Experimental manipulation can cause the release of the glutamate through the non-tetanic stimulation of a presynaptic neuron. Glutamate then binds to AMPA receptors contained in the postsynaptic membrane causing the influx of positively charged sodium atoms. [3] This inward flow of sodium leads to a short term depolarization of the postsynaptic neuron and an EPSP. While a single depolarization of this kind may not have much of an effect on the postsynaptic neuron, repeated depolarizations caused by high frequency stimulation can lead to EPSP summation and to surpassing the threshold potential. [8]

GABA as an inhibitory example Edit

In contrast to glutamate, the neurotransmitter GABA mainly functions to trigger inhibitory postsynaptic potentials (IPSPs) in vertebrates. The binding of GABA to a postsynaptic receptor causes the opening of ion channels that either cause an influx of negatively charged chloride ions into the cell or an efflux of positively charged potassium ions out of the cell. [3] The effect of these two options is the hyperpolarization of the postsynaptic cell, or IPSP. Summation with other IPSPs and contrasting EPSPs determines whether the postsynaptic potential will reach threshold and cause an action potential to fire in the postsynaptic neuron.

As long as the membrane potential is below threshold for firing impulses, the membrane potential can summate inputs. That is, if the neurotransmitter at one synapse causes a small depolarization, a simultaneous release of transmitter at another synapse located elsewhere on the same cell body will summate to cause a larger depolarization. This is called spatial summation and is complemented by temporal summation, wherein successive releases of transmitter from one synapse will cause progressive polarization change as long as the presynaptic changes occur faster than the decay rate of the membrane potential changes in the postsynaptic neuron. [4] Neurotransmitter effects last several times longer than presynaptic impulses, and thereby allow summation of effect. Thus, the EPSP differs from action potentials in a fundamental way: it summates inputs and expresses a graded response, as opposed to the all-or-none response of impulse discharge. [9]

At the same time that a given postsynaptic neuron is receiving and summating excitatory neurotransmitter, it may also be receiving conflicting messages that are telling it to shut down firing. These inhibitory influences (IPSPs) are mediated by inhibitory neurotransmitter systems that cause postsynaptic membranes to hyperpolarize. [10] Such effects are generally attributed to the opening of selective ion channels that allow either intracellular potassium to leave the postsynaptic cell or to allow extracellular chloride to enter. In either case, the net effect is to add to the intracellular negativity and move the membrane potential farther away from the threshold for generating impulses. [7] [9]

When EPSPs and IPSPs are generated simultaneously in the same cell, the output response will be determined by the relative strengths of the excitatory and inhibitory inputs. Output instructions are thus determined by this algebraic processing of information. Because the discharge threshold across a synapse is a function of the presynaptic volleys that act upon it, and because a given neuron may receive branches from many axons, the passage of impulses in a network of such synapses can be highly varied. [11] The versatility of the synapse arises from its ability to modify information by algebraically summing input signals. The subsequent change in stimulation threshold of the postsynaptic membrane can be enhanced or inhibited, depending on the transmitter chemical involved and the ion permeabilities. Thus the synapse acts as a decision point at which information converges, and it is modified by algebraic processing of EPSPs and IPSPs. In addition to the IPSP inhibitory mechanism, there is a presynaptic kind of inhibition that involves either a hyperpolarization on the inhibited axon or a persistent depolarization whether it is the former or the latter depends on the specific neurons involved. [6]

The microelectrodes used by Katz and his contemporaries pale in comparison to the technologically advanced recording techniques available today. Spatial summation began to receive a lot of research attention when techniques were developed that allowed the simultaneous recording of multiple loci on a dendritic tree. A lot of experiments involve the use of sensory neurons, especially optical neurons, because they are constantly incorporating a ranging frequency of both inhibitory and excitatory inputs. Modern studies of neural summation focus on the attenuation of postsynaptic potentials on the dendrites and the cell body of a neuron. [1] These interactions are said to be nonlinear, because the response is less than the sum of the individual responses. Sometimes this can be due to a phenomenon caused by inhibition called shunting, which is the decreased conductance of excitatory postsynaptic potentials. [7]

Shunting inhibition is exhibited in the work of Michael Ariel and Naoki Kogo, who experimented with whole cell recording on the turtle basal optic nucleus. Their work showed that spatial summation of excitatory and inhibitory postsynaptic potentials caused attenuation of the excitatory response during the inhibitory response most of the time. They also noted a temporary augmentation of the excitatory response occurring after the attenuation. As a control they tested for attenuation when voltage-sensitive channels were activated by a hyperpolarization current. They concluded that attenuation is not caused by hyperpolarization but by an opening of synaptic receptor channels causing conductance variations. [12]

Potential therapeutic applications Edit

Regarding nociceptive stimulation, spatial summation is the ability to integrate painful input from large areas while temporal summation refers to the ability of integrating repetitive nociceptive stimuli. Widespread and long lasting pain are characteristics of many chronic pain syndromes. This suggests that both spatial and temporal summations are important in chronic pain conditions. Indeed, through pressure stimulation experiments, it has been shown that spatial summation facilitates temporal summation of nociceptive inputs, specifically pressure pain. [13] Therefore, targeting both spatial and temporal summation mechanisms simultaneously can benefit treatment of chronic pain conditions.


Differences Between EPSP and Action Potential

Neuroscience has captivated the interest of many. It is a study on how the nervous system works and how the body is able to respond with different stimuli. The body itself contains chemicals which enable us to function and survive in this challenging environment. The brain is in command of the whole body and tells us what we need to do or how to react. It is the general of our body with its minions, the neurons. Neurons communicate with each other and send the messages to the general. With information at hand, the brain general can process new tactics on how to counter such feats. Most often, EPSP and action potential are involved in generating specific actions. The difference between EPSP and action potential will be elaborated upon in this article.

“EPSP” stands for “excitatory postsynaptic potential.” When there is a flow of positively charged ions towards the postsynaptic cell, a momentary depolarization of the postsynaptic membrane potential occurs. This phenomenon is known as EPSP. A postsynaptic potential becomes excitatory when the neuron is triggered to release an action potential. The EPSP is like the parent of the action potential since it is created when the neuron is triggered. There can be EPSP when there is a decrease in the outgoing positive ion charges. We call the trigger the excitatory postsynaptic current, or EPSC. EPSC is the flow of ions that causes EPSP.

In a single patch of postsynaptic membrane, multiple EPSPs can likely occur. EPSPs have an additive effect which means that the sum of all the individual EPSPs will result in a combined effect. Greater membrane depolarization takes effect when there are larger EPSPs created. The larger the EPSPs become, the more it reaches the limit of firing an action potential. The amino acid glutamate is the neurotransmitter associated with EPSPs. It is also the main neurotransmitter of the vertebrates’ central nervous system. Amino acid glutamate is then called the excitatory neurotransmitter.

Action potential is fired by EPSP. It is a momentary event wherein the cell’s electrical membrane potential instantly rises and falls. A consistent trajectory then follows. In neurons, action potentials are also called nerve impulses or spikes. A sequence of action potentials is called a spike train. Action potentials frequently occur in human cells since humans have neurons, endocrine cells, and muscle cells. When there is a signal, the neurons communicate with each other reaching EPSP until it needs to fire an action potential. Voltage-gated ion channels produce action potentials. These channels lie inside the plasma membrane of the cell. There is a phase called resting potential. When the membrane potential is nearing the resting phase, the voltage-gated ion channels are shut, but they immediately open when there is an increase in the membrane potential value. Sodium ions will flow when these channels open which further increases the membrane potential. As membrane potentials increase, more and more electric current flows. There are two basic types of action potentials in animal cells: voltage-gated sodium channels and voltage-gated calcium channels. Voltage-gated sodium channels last for about less than one millisecond while voltage-gated calcium channels last for about a hundred milliseconds or even longer.

“EPSP” stands for “excitatory postsynaptic potential.”

Excitatory postsynaptic potential occurs when there is a flow of positively charged ions towards the postsynaptic cell, a momentary depolarization of postsynaptic membrane potential is created.

Action potentials are also called nerve impulses or spikes.

A postsynaptic potential becomes excitatory when the neuron is triggered to release an action potential.

Action potential is a momentary event wherein the cell’s electrical membrane potential instantly rises and falls.


We simulate the inhibition of Ia-glutamatergic excitatory postsynaptic potential (EPSP) by preceding it with glycinergic recurrent (REN) and reciprocal (REC) inhibitory postsynaptic potentials (IPSPs). The inhibition is evaluated in the presence of voltage-dependent conductances of sodium, delayed rectifier potassium, and slow potassium in five -motoneurons (MNs). We distribute the channels along the neuronal dendrites using, alternatively, a density function of exponential rise (ER), exponential decay (ED), or a step function (ST). We examine the change in EPSP amplitude, the rate of rise (RR), and the time integral (TI) due to inhibition. The results yield six major conclusions. First, the EPSP peak and the kinetics depending on the time interval are either amplified or depressed by the REC and REN shunting inhibitions. Second, the mean EPSP peak, its TI, and RR inhibition of ST, ER, and ED distributions turn out to be similar for analogous ranges of G. Third, for identical G, the large variations in the parameters’ values can be attributed to the sodium conductance step ( ⁠⁠ ) and the active dendritic area. We find that small on a few dendrites maintains the EPSP peak, its TI, and RR inhibition similar to the passive state, but high on many dendrites decrease the inhibition and sometimes generates even an excitatory effect. Fourth, the MN's input resistance does not alter the efficacy of EPSP inhibition. Fifth, the REC and REN inhibitions slightly change the EPSP peak and its RR. However, EPSP TI is depressed by the REN inhibition more than the REC inhibition. Finally, only an inhibitory effect shows up during the EPSP TI inhibition, while there are both inhibitory and excitatory impacts on the EPSP peak and its RR.

In the past few years, the physiological and morphological properties of the cat and rat -motoneurons have been intensively studied (Bui, Grande, & Rose, 2008a, 2008b Heckman, Hyngstrom, & Johnson, 2008 Hyngstrom, Johnson, & Heckman, 2008 Jean-Xavier, Pflieger, Liabeuf, & Vinay, 2006 Larkum, Rioult, & Luscher, 1996). This revealed a large number of voltage-dependent conductances on motoneuron (MN) dendrites, uniquely located relative to other types of neurons (Heckmann, Gorassini, & Bennett, 2005 Kim, Major, & Jones, 2009 Kuo, Lee, Johnson, Heckman, & Heckman, 2003 Saint Mleux & Moore, 2000). In contrast to hippocampal and neocortical pyramidal cells, which show a variety of different channel distributions depending on the neuron and channel type (see Magee, 1998) in MNs some dendrites are active, while others remain passive (Luscher & Larkum, 1998). The voltage-dependent channels and the depolarizing shunting inhibition provide the excitatory potential not only for input amplification or attenuation but also for nonlinear interactions.

In our previous research, we analyzed the influence of active MN's dendritic properties on the EPSP (Gradwohl & Grossman, 2008) and IPSP (Gradwohl & Grossman, 2010). We concluded that voltage-dependent channels on the dendrites boost EPSP peak and diminish IPSP peak. However the mean EPSP and IPSP peaks of step function (ST), exponential rise (ER), and exponential decay (ED) distributions are similar when the range of G is equal. Our model is a continuation of our previous simulations. We analyze the effective modulation of the EPSP by the IPSPs in the presence of the same basic voltage-dependent channels and explore any relation between the type of voltage-dependent channel distribution in the dendrites and the EPSP inhibition.

Gain modulation is used for integrating data from different sensory, motor, and cognitive sources. At the neuronal level, gain modulation can be seen as a nonlinear summation of the synaptic response of excitatory synapses containing a voltage-dependent parameter (Mel, 1993 Volman, Levine, & Sejnowski, 2010).

There are two types of motor neuron inhibition: the orthodromic reciprocal inhibition (REC) and the antidromic Renshaw inhibition (REN). The latter is part of a feedback system of the -MN and operates within a polysynaptic interneuronal pathway (Schneider & Fyffe, 1992). The REC inhibitory inputs are distributed on the soma and proximal dendrites (Burke, Fedina, & Lundberg, 1971 Curtis & Eccles, 1959 Stuart & Redman, 1990) and the REN inhibitory inputs on the dendrites distally to the soma (Fyffe, 1991 Maltenfort, McCurdy, Phillips, Turkin, & Hamm, 2004), similar to the excitatory AMPA and NMDA inputs. Additionally, the time course of the REC IPSP compared to the REN IPSP is shorter. Thus, the presence of the REN and REC inhibitory inputs in the simulation serves as a basis for analyzing the effect of voltage-dependent channels on differently located synapses with distinct conductance time course. Glycine (not GABA) is the major neurotransmitter involved in the inhibitory pathway of the spinal cord (Capaday & van Vreeswijk, 2006) in REC inhibition. Although REN inhibition employs glycine and GABA neurotransmitters (Cullheim & Kellerth, 1981 Jonas, Bischofberger, & Sankuhler, 1998) we neglected the latter in order to compare REC and REN inhibition with the same glycinergic neurotransmition. The ionic current of the inhibitory synapses is carried by chloride, and, as a result, the reversal potential is close to the resting potential (Gao & Ziskind-Conhaim, 1995 Jean-Xavier, Mentis, O'Donovan, Cattaert, & Vinay, 2007 Jean-Xavier et al., 2006 Stuart & Redman, 1990 Yoshimura & Nishi, 1995). It is known that in mature motoneurons after spinal cord injury (Boulenguez et al., 2010 Edgerton & Roy, 2010) and in a newborn rat (Marchetti, Pagnotta, Donato, & Nistri, 2002), the inhibitions have depolarizing characteristics. Inhibition is mainly attained by a shunting effect. It is regularly mentioned as a mechanism by which gain modulation is controlled through changes in the input resistance, without affecting the membrane potential (Prescott & De Koninck, 2003). Shunting inhibition modulates synaptic excitatory depolarization, whereas hyperpolarizing inhibition has a subtractive effect on the depolarization. The inhibition in our model has both depolarizing and shunting properties that are similar to our previously published model (Gradwohl & Grossman, 2010). Consequently, it is of special interest to examine its interaction with the depolarizing excitatory synaptic potentials since the depolarizing inhibition occurs in mature motoneurons after spinal cord injury (Boulenguez et al., 2010 Edgerton & Roy, 2010) and also in newborn rats (Marchetti et al., 2002).

In this work, the inhibition of Ia-EPSP synaptic potentials is evaluated in the presence of the basic voltage-dependent components: sodium, delayed rectifier potassium, and slow potassium currents distributed at different locations on the dendrites. Although persistent inward currents (PIC) are a dominant conductance on the MN's dendrites (Heckman et al., 2008), we do not include them in our investigation, as we are interested in the basic active components in the absence of neuron firing (see Luscher & Larkum, 1998). REN and REC inhibitions were inserted into the model and mediated by the glycinergic neurotransmission. We then analyzed the interaction of excitatory and inhibitory inputs between themselves and the voltage-dependent channels. In addition, we incorporated the dendritic branching (Cullheim, Fleshman, Glenn, & Burke, 1987a, 1987b Segev, Fleshman, & Burke, 1990) and the MN's size. As a result, we were able to simulate realistic morphological MNs and compare their distinct physiological properties.

Which kind of inhibition depresses the Ia-EPSP components of peak, time integral, and rate of rise most efficiently?

How does an active dendrite contribute to the efficacy of inhibition? Alternatively, which kind of dendritic voltage-dependent channels distribution depresses Ia EPSP most effectively?

Is Ia-EPSP inhibition monotonically dependent to the input resistance of the MNs?


T. A. Vardapetyan, "Characteristics of reactions of neurons of auditory cortex of the cat," in: Mechanisms of Hearing [in Russian], Nauka (1967), pp. 74–90.

L. L. Voronin, "Postsynaptic potentials of neurons of the motor zone of the cortex of an unanesthetized rabbit," Fiziol. Zhurn. SSSR,53, 623–631 (1967).

D. S. Vorontsov, General Electrophysiology [in Russian], Medgiz (1961), p. 401.

G. Jasper, G. Ricci, and B. Doane, "Microelectrode analysis of the discharges of cortical cells in the development of conditioned defensive reactions in monkeys," in: Electroencephalographic Study of Higher Nervous Activity [Russian translation], Moscow (1962), pp. 129–146.

V. Mountcastle, "Some functional properties of the somatic afferent system," in: Theory of Communication in Sensory Systems [Russian translation], Moscow (1964), pp. 185–213.

F. N. Serkov, "The genesis and functional significance of evoked potentials of the cerebral cortex," Neirofiziologiya,2, 349–359 (1970).

F. N. Serkov and V. M. Storozhuk, "Reaction of neurons of the auditory cortex to sound stimuli," Neirofiziologiya,1, 147–156 (1969).

F. N. Serkov and E. Sh. Yanovskii, "Reactions of neurons of the auditory cortex to paired clicks," Neirofiziologiya,2, 227–235 (1970).

V. G. Skrebitskii and L. L. Voronin, "Intracellular study of the electrical activity of neurons of the visual cortex of an unanesthetized rabbit," Zhurn. Vyssh. Nervn. Deyat.,16, 864–873 (1966).

V. G. Skrebitskii and E. G. Shkol'nik-Yarros, "Questions of the functional and structural organization of the visual cortex," in: Visual and Auditory Analyzers [in Russian], Meditsina, Moscow (1969), pp. 179–186.

O. Feher, "Data on the location of the inhibitory system in the auditory cortex of the cat," in: Visual and Auditory Analyzers [Russian translation], Meditsina, Moscow (1969), pp. 202–209.

R. Jung, "Integration in neurons of the visual cortex," in: Theory of Communication in Sensory Systems [Russian translation], Mir, Moscow (1964), pp. 375–415.

M. Abeles and M. H. Goldstein, "Functional architecture in cat primary auditory cortex," J. Neurophysiol.,33, 172–186 (1970).

S. A. Andersson, "Intracellular postsynaptic potentials in the somatosensory cortex of the cat," Nature,205, 297–298 (1965).

S. D. Erulcar, I. E. Rose, and P. W. Davies, "Single unit activity in the auditory cortex of the cat," Johns Hopkins Hosp. Bull.,99, 55–86 (1956).

E. F. Evans and J. C. Whitfield, "Classification of unit responses in the auditory cortex," J. Physiol.,171, 476–493 (1964).

R. Galambos and D. F. Bogdanski, "Studies of the auditory system with implanted electrodes," in: Neuronal Mechanisms of the Auditory and Vestibular Systems, Springfield, Illinois, USA (1960), pp. 137–151.

G. L. Gerstein and N. Y. Kiang, "Responses of single units in the auditory cortex," Exper. Neurol.,10, 1–18 (1964).

J. E. Hind, "Unit activity in the auditory cortex," in: Neuronal Mechanisms of the Auditory and Vestibular Systems, Springfield, Illinois, USA (1960), pp. 201–210.

J. Katzuki, T. Watanabe, and N. Marujama, "Activity of auditory neurons in upper levels of brain of cat," J. Neurophysiol.,22, 343–359 (1959).

C. L. Li, "Cortical intracellular potentials and their response to strychnine," J. Neurophysiol.,22, 436–449 (1959).

C. L. Li and S. N. Chou, "Inhibitory interneurons in the neocortex," in: Inhibition in the Nervous System and γ-Aminobutyric Acid, London (1960), pp. 34–39.

C. L. Li, A. Ortiz-Galvin, S. N. Chou, and S. Y. Howard, "Cortical intracellular potentials in response to stimulation of laterale geniculate body," J. Neurophysiol.,23, 592–601 (1960).

A. C. Nacimienko, H. D. Lux, and O. D. Creutzfeldt, "Postsynaptische potentiale von nervenzellen motorischen cortex nach elektrischen reizung spezifischer und undspezifischer thalamuskerne," Pflug. Arch.,281, 152–168 (1964).

C. G. Phillips, "Intracellular records from Betz cells in cat," Quart. J. Exp. Physiol.,41, 58–69 (1956).

C. G. Phillips, "Actions of antidromic pyramidal volleys on single Betz cells in the cat," Quart. J. Exp. Physiol.,44, 1–25 (1959).

C. Stefanis and H. Jasper, "Intracellular microelectrode studies of antidromic response in cortical pyramidal tract neurons," J. Neurophysiol.,27, 828–854 (1964).

C. Stefanis and H. Jasper, "Recurrent collateral inhibition in pyramidal tract neurons," J. Neurophysiol.,27, 855–877 (1964).

J. Tasaki, E. H. Polley, and F. Orrego, "Action potentials from individual elements in cat geniculate and striate cortex," J. Neurophysiol.,17, 454–474 (1954).

S. Watanabe, M. Konishi, and O. D. Creutzfeldt, "Postsynaptic potentials in the cat's visual cortex following electrical stimulation of afferent pathways," Exp. Brain Res.,1, 272–283 (1966).


Results

Experimental Measurements of E–I Integration.

We first developed a quantitative assay of E-I integration in CA1 pyramidal neurons of rat hippocampal slices. The whole-cell recording was made from the soma of the pyramidal cell, and fluorescent dye Alexa Fluor 488 was loaded into the cell via the recording pipette to visualize the dendritic tree (Fig. 1A). Microiontophoretic applications of glutamate and GABA at the apical dendrite elicited rapid membrane depolarizations and hyperpolarizations with kinetics similar to those of natural EPSPs and IPSPs elicited by extracellular electrical stimulation in the CA1 region, respectively (Fig. 1B and SI Appendix). For convenience, these iontophoretic responses are referred to hereafter as EPSPs and IPSPs. When the EPSP and IPSP were elicited simultaneously with two iontophoretic pipettes placed at adjacent locations of the dendritic trunk, the measured somatic response was always smaller than the linear sum of the EPSP and IPSP measured separately (Fig. 1B). The nonlinear component of E–I integration was obtained by subtracting the measured sum from the linear sum. The amplitude of the nonlinear component was not affected by changing the driving force for the IPSP from −10 to 0 mV (Fig. S1 C and D) and was absent for summation of EPSP and hyperpolarization induced by somatic current injection (Fig. S1 E and F), indicating that this nonlinear component reflects shunting inhibition. Thus, this nonlinear component was referred to as the shunting component (SC) (Fig. 1B).

Experimental measurement of E–I integration and its dependence on EPSP and IPSP amplitudes. (A) Image of a CA1 pyramidal neuron filled with Alexa Fluor 488 via the recording pipette. Arrows indicate pipettes for iontophoresis of glutamate and GABA (at 232 and 129 μm from soma). (Scale bar: 100 μm.) (B) Examples of EPSP, IPSP, their linear sum, and response to simultaneous glutamate and GABA pulses. SC is the recorded response (sum) minus the linear sum. (C) As in B except that IPSP preceded EPSP by 30 ms. (D) Changes in the amplitude of SC vs. the time interval between IPSP and EPSP, for two different sets of E/I location (square: I at 50–100 μm, E at 150–200 μm, n = 6 triangles: E at 100–150 μm, I at 200–250 μm, n = 5). (E) SC vs. IPSP amplitude, measured for a fixed EPSP amplitude (9–10 mV). Data are from four cells. Line indicares linear fit (R = 0.974). (F) SC vs. EPSP amplitude, measured for a fixed IPSP amplitude (1.1–1.3 mV). Data are from four cells. Line indicates linear fit (R = 0.965).

We next examined how the temporal shift between E and I affects the amplitude of the SC, as illustrated by Fig. 1C for a case in which I preceded E for 30 ms. The SC amplitude decreased rapidly with the E–I interval, but significant shunting effect remained when I preceded E for up to 200 ms (Fig. 1D). Further pharmacological experiments indicated that prolonged inhibition with large E–I temporal intervals was mainly caused by the activation of GABABRs, because bath application of the GABABR antagonist CGP 35348 (60 μM) abolished this prolonged component (Fig. S2). In the present study, we focused on the fast shunting inhibition for concurrent E and I, which is caused by opening of GABAARs.

To analyze E–I integration quantitatively, the amplitude of E was defined as the peak value of EPSP, whereas the amplitudes of I and the summed response were defined as the values at the time of the peak EPSP. Under this definition, we examined how the SC amplitude depends on the amplitude of EPSPs and IPSPs. By setting the EPSP amplitude at a fixed value while varying the IPSP amplitude, we found that the SC amplitude depended linearly on the IPSP amplitude (Fig. 1E). Conversely, at a fixed IPSP amplitude the SC amplitude depended linearly on the EPSP amplitude (Fig. 1F). Such linear dependence was also found if we define the amplitude by the mean EPSP/IPSP value over the first 100 ms (Fig. S3).

Derivation of Arithmetic Rule for E–I Integration by Modeling.

To further investigate the shunting inhibition, we performed computer simulation with a realistic neuron model, using the morphology of a reconstructed CA1 pyramidal cell (15) (Fig. 2A) and the kinetics and distributions of ion channels reported previously (SI Appendix). The model parameters were adjusted to yield EPSPs and IPSPs (Fig. 2A) with kinetics similar to the experimentally observed iontophoretic EPSPs and IPSPs (Fig. 1A). We then simulated the EPSP, IPSP, and the summed response at the soma (Fig. 2A), and defined SC in the same manner as that for experimental measurements. The dependence of SC on the amplitudes of EPSP (0.2–8 mV) and IPSP (0.1–3.5 mV) was plotted for E at 151 μm and for I at 94 μm from the soma. Consistent with our experimental observations (Fig. 1 E and F), the SC amplitude depended linearly on both the EPSP and IPSP amplitudes (Fig. 2B and Fig. S3B).

Simulation of E–I integration in a realistic neuronal model and derivation of the arithmetic rule. (A) (Left) Reconstructed hippocampal CA1 pyramidal neuron used for simulation. Arrows indicate I and E were at 94 and 151 μm from the soma. (Scale: 100 μm.) (Right) Simulated EPSP, IPSP, their linear sum, simulated response (sum) of concurrently activated E and I, and the SC. (B) (Upper) SC vs. IPSP amplitude, with fixed EPSP amplitude (at 5.5 mV). Line indicates linear fit (R = 0.999). (Lower) SC vs. EPSP amplitude, with fixed IPSP amplitude (at 3.5 mV). Line indicates linear fit (R = 0.998). (C) Ratio between measured SC and EPSP (SC/EPSP) plotted against IPSP (red circle) and SC/IPSP plotted against EPSP (blue square) for the same cell in the slice recording. The amplitudes of the paired EPSP and IPSP were randomly set in the range of 1–10 and 0.2–4 mV, respectively. E and I locations were fixed at 110 and 45 μm. Lines indicate linear fit (red: R = 0.96, slope k = 0.142, n = 11 blue: R = 0.92, slope k = 0.145, n = 10). (D) Simulated SC/EPSP vs. IPSP (red circle, n = 20) and SC/IPSP vs. EPSP (blue square, n = 20). Lines indicate linear fit (red: R = 0.999, slope k = 0.086 blue: R = 0.999, slope k = 0.087). The EPSP amplitudes were randomly chosen from a 0.2- to 8-mV pool and the IPSP amplitude was from a 0.1- to 3.5-mV pool. I and E are at 94 and 151 μm. (E) Simulated SC as a function of both EPSP (0.2–8 mV) and IPSP (0.1–3.5 mV) amplitudes, with E and I at 202 and 123 μm, respectively. (F) k*EPSP*IPSP, with k adjusted to best fit the data in E k = 0.093, rms error: 4.9%.

Besides the above studies using fixed EPSP or IPSP amplitude, we further characterized the dependence of SC on IPSP and EPSP amplitudes by randomly varying both the EPSP (in a range of 0.2 to 10 mV) and the IPSP (0.1–4 mV) in experiments and simulations. When the amplitude ratio SC/EPSP was plotted against the IPSP amplitude or when SC/IPSP was plotted against the EPSP amplitude, we found that these two plots could be well fitted by straight lines through the origin, with nearly identical slopes (Fig. 2 C and D). This finding suggests that SC is directly proportional to EPSP*IPSP. We also plotted the simulated SC amplitude against both EPSP and IPSP amplitudes (Fig. 2E) and fitted the results by the function SC = k*EPSP*IPSP, with k as the free parameter (Fig. 2F). This multiplicative function provided a good approximation (rms error: 4.9%) for simulated SC over a range of EPSP and IPSP amplitudes. Thus, the summed response to coincident E and I can be approximated by a simple arithmetic rule: where k (in the unit of mV −1 ) reflects the strength of shunting inhibition (k > 0 for hyperpolarizing IPSPs). This arithmetic rule quantitatively describes two aspects of inhibition: hyperpolarization and shunting inhibition.

Dependence of k on E and I Locations Along the Apical Dendritic Trunk.

We further examined the dependence of k on E and I locations along the apical dendrite trunk in the CA1 pyramidal neuron model. For each combination of E and I locations, we computed the k value from 20 sets of arbitrarily chosen E and I amplitudes and plotted the results in Fig. 3A. As shown by the various cross-sections of the 3D graph, for each I location the dependence of k on the E location showed a clear asymmetry for proximal vs. distal Es (Fig. 3B): For a given I, the k value decayed rapidly with the I–E distance for proximal Es (space constant ≈83 μm), but remained relatively constant for distal Es. The maximal k value was higher for more distal Is.

Dependence of k on E/I locations. (A and B) Stimulation results showing coefficient k as a function of E and I distances from the soma. For each E/I location, k was computed from 20 sets of EPSP and IPSP amplitudes using the least-square fit. The value of k is color-coded (see bar) in a 3D map in A. In B, k is plotted as a function of E location, corresponding to the cross-section of the 3D map. Data points connected by each line depict k for a given I location (marked by the dashed line of the same color). (C–E) Experimental results on the location dependence of k. In C, changes of k with more distal E locations. Data grouped by the range of I locations. Line indicates best linear fit of each group. In D, changes of k with E/I locations of paired E and I from experiments in which E was more proximal to I, for different ranges of I location. Each point was averaged from more than three cells. In E, changes of k with E location, for three fixed I locations (marked by dashed lines).

The dependence of k on E and I locations observed in the above simulations was also tested experimentally by iontophoresis of glutamate and GABA at various locations along the main dendritic trunk of the CA1 pyramidal cell. For E at more distal sites than I (at three sets of I locations), k was largely independent of the E location and E–I distance, but markedly dependent on the I location (Fig. 3C). For Es located proximally to I (at three sets of I locations), k decreased with the E–I distance (Fig. 3D), consistent with that found by simulation. Finally, when k was plotted as a function of the E location for various fixed I locations, the k profile also showed a clear distal-proximal asymmetry (Fig. 3E), similar to that found by simulation. These results support and extend the notion of on-the-path shunting (10, 11).

Shunting Inhibition Involving Oblique Branches.

Because most synaptic inputs to pyramidal neurons are located on dendritic branches, we examined the shunting of Es distributed throughout the dendritic tree exerted by I located at either the dendritic trunk or an oblique branch. For each I location of the realistic neuronal model, we computed k as a function of the E location over the entire apical dendrite except at the distal stratum lacunosum moleculare layer, where local subthreshold EPSPs and IPSPs cause little change of the somatic membrane potential (16). For I located at the apical trunk (Fig. 4A), there was a prominent asymmetry k values were uniformly large for distal Es at both the trunk and branches but decreased rapidly with the E–I distance for proximal Es. For I located at an oblique branch (Fig. 4B), shunting was largely confined to the same branch. This finding is in line with the idea that each dendritic branch is an independent functional compartment (4–5, 11, 17–22). Notably, the asymmetry in the k profile observed at the apical trunk (Fig. 3) was also observed at the oblique branch when E and I were located at the same branch k was uniformly high for distal Es and decreased with the E–I distance for proximal Es (Fig. 4B).

Shunting inhibition for I located at dendritic trunk and oblique branches. (A and B) Simulation results of k values (color-coded) for I (black dot) located at apical trunk (A) and oblique branch (B), with E scattered on dendritic arbor in stratum radiatum. (C–H) Experimental results. (C) I at oblique branch: k was not significantly different between two distal Es (E1 and E2) within the same branch (P = 0.89, paired t test). E1 to E2 distances were >70 μm in all experiments. Lines connect data from the same cell. (D) As in C except that Es were more proximal to I (P = 0.001). (E) I at the trunk: k was not significantly different between Es at the trunk (E1) and at the first-order oblique branch (E2, P = 0.92). I to E distances were kept constant. (F) I at oblique branch: k was significantly different between Es at the same and different branch (P < 0.001). (G) E at the trunk: k was significantly different between Is at the trunk (I1) and at oblique branch (I2, P = 0.031). The trajectory distance of I to the soma was kept constant. (H) The decay of k value as a function of distance between I2 and the branch point for the configuration in G. Line indicates exponential fit (R = 0.97, length constant 44 μm).

The above modeling results were then tested experimentally in hippocampal slices. For the same location of GABA iontophoresis at an oblique branch, we measured the SC and calculated k for EPSPs induced at two locations along the same oblique branch. No significant difference was found in the k value (P = 0.89, paired t test) when the two E locations were both distal (spaced by ≈70 μm Fig. 4C). In contrast, for two Es at more proximal locations, k was significantly smaller (P = 0.001) for the E closer to the branch point (Fig. 4D). Furthermore, for I located at the apical trunk, the k values were not significantly different for distal Es located at either the trunk or branch (Fig. 4E P = 0.92, paired t test), consistent with the simulation results (Fig. 4A). When the I-soma distance was kept within 100–200 μm, k values for I and E located at the same branch were significantly higher than those for I and E located at different branches (Fig. 4F P < 0.001). Finally, for a fixed E location at the apical trunk, the k values for more proximal Is at the branch were lower than those at the trunk (Fig. 4G P = 0.03), with k decreasing rapidly with the distance to the branch point (Fig. 4H). Together, these experimental results are consistent with those found by simulation, indicating that shunting inhibition is largely compartmentalized to the same branch, with the distal–proximal asymmetry similar to that at the trunk.

Effects of Active Conductances and Transmitter Receptors.

Previous studies of E–I integration mostly addressed the role of passive cable properties (1, 10, 11). We have examined systematically how different ion channels and transmitter receptors affect the extent of shunting inhibition. For the CA1 pyramidal cell model, we calculated the k values for 15 sets of randomly chosen E and I locations before and after blocking 90% of each of the following conductances: voltage-dependent Na + channel, delayed rectifier K + channel (Kd), A-type K + channel (KA), hyperpolarization-activated cationic current (Ih), NMDA receptor (NMDAR), and GABABR (see SI Appendix). As shown in Fig. 5A, 90% blockade of Ih, KA, NMDAR, and Na + channels resulted in significant changes in the k value, whereas blockade of Kd and GABABR had no effect. These simulation results were tested by iontophoretic experiments in hippocampal slices using I and E located at the apical trunk within 100–200 and 100–300 μm from the soma, respectively. Specific blockers of Na + channel (tetrodotoxin, 3 μM), Kd (tetraethylammonium, 3 mM), KA (4-AP, 1 mM), Ih (ZD7288, 20 μM), NMDAR (D-AP5, 50 μM), and GABABR (CGP35348, 60 μM) were used separately to block each of these channels or receptors. We found that KA channel blockade increased the k value (≈12%, P < 0.01), an effect that may diminish the EPSP amplitude increase caused by the blockade of KA channels (23). In contrast, blocking Ih and NMDARs decreased the k value by 9% and 7%, respectively (P < 0.01), indicating contributions of these channels to the shunting effect. However, blockade of Kd, Na + channels, and GABABRs had no effect (P > 0.4 Fig. 5A). With the exception of the Na + channel, these experimental findings largely agreed with the simulation results. The discrepancy on Na + channel blockade may be attributed to a lower voltage threshold for the activation of Na + channels in the model cell.

Effects of ion channels and transmitter receptors on shunting inhibition. (A) Simulation (green) and experimental (orange) results on the changes in k after blockade of each of the ion channels and transmitter receptors. (B) 3D plot of k as a function of E and I locations after simultaneous blockade of voltage-dependent sodium conductance, delayed rectifier potassium conductance (Kd), A-type potassium conductance (KA), Ih channel conductance, NMDARs, and GABABRs.

We also examined the role of these ion channels and receptors in the dendrite-location dependence of k in the model. By comparing the k profile before and after 90% blockade of each of Kd, Na + , KA, Ih, NMDAR, and GABABR channels, we found that although the overall k values were altered to different extents, the asymmetric spatial profile remained the same (Fig. S4). Furthermore, this asymmetry was found even after all of the above conductances and receptors were blocked (Fig. 5B). Thus, the asymmetry in the k profile results primarily from passive cable properties of the dendrite.

Theoretical Interpretation of the Arithmetic Rule.

The theoretical basis of the arithmetic rule was next examined, using two-port analysis of the passive dendritic tree (ref. 11 and see SI Appendix and Fig. S5 for details). The analysis yielded a simple analytic expression for E–I summation: where Vs is the somatic voltage response to concurrent E and I, and Vse and Vsi are the somatic response to the individual excitatory input at location e and to the individual inhibitory input at location i, respectively. Kei is the transfer resistance between location e and i, Kes is between e and soma, and Kis is between i and soma. Ere and Eri are the driving forces (the difference between the reversal potential and resting membrane potential) for E and I, respectively. By defining we obtain VsVse + Vsi + kVseVsi.

This equation has the same form as the empirically derived arithmetic rule, for which Vs, Vse, and Vsi correspond to sum, EPSP, and IPSP, respectively. Considering that EriEre, and Kes and Kis are of the same order of magnitude, k is reduced to Note that in the above equation, k is inversely proportional to Eri, a relation confirmed in our simulation (Fig. S6). When Eri approaches zero, k approaches infinity, but the product (k*IPSP) remains finite because IPSP also approaches zero. When Eri becomes positive, as the case of early developing synapse (24), k should be negative, so that the shunting component (k*EPSP*IPSP) remains negative (Fig. S7).

Integration of Multiple Es and Is.

Each CA1 pyramidal neuron receives a large number of inputs at its dendrite. Is the rule obtained from a pair of E and I applicable to multiple Es and Is? To address this question, we selected 20 Es and 5 Is randomly distributed in the dendritic tree of the model CA1 pyramidal cell (Fig. 6A), with a range of synaptic conductances (Es: 0.048–0.48 nS Is: 0.32–6.4 nS). We first compared the simulated response to coincident activation of these Es and Is with that predicted by a simple arithmetic rule, in which the response was given by the linear sum of individual EPSPs and IPSPs together with all of the pairwise E–I interactions, using the following equation where EPSPi and IPSPj are somatic responses evoked by Ei and Ij, respectively, and kij is a coefficient for the paired Ei and Ij (which depends on the dendritic locations of E and I but not on the amplitude or the number of other coactivated inputs). As shown in Fig. 6B (green circles), for 20 different sets of EPSP and IPSP amplitudes, the predicted responses deviated from the simulated responses (rms error was 8.5%) at both small and large sum amplitudes. This deviation could originate from nonlinear E–E and I–I interactions (2, 25), as indeed suggested by the systematic deviation of the simulated responses to 20 coincident Es (Fig. 6C) and 5 coincident Is (Fig. 6D) from the linear sum. We thus adjusted Eq. 4 by incorporating the nonlinear E–E and I–I interactions: where EPSP S and IPSP S represent simulated somatic responses to coincident Es and Is alone, respectively. Eq. 5 yielded predicted responses in excellent agreement with simulated responses (Fig. 6B, magenta circles rms error was 2.7%). Thus, the arithmetic rule for the pairwise E–I interaction can also be used for quantitative estimate of E–I integration with multiple coincident Es and Is. Of course, a complete arithmetic rule for multiple inputs can be obtained only if the rules for the summation of multiple EPSPs and multiple IPSPs are both available. Our finding on the E–I interaction represents an important step toward the goal of obtaining a complete rule for integration of multiple Es and Is.

Integration of multiple Es and Is. (A) Distribution of 20 Es (red dots) and 5 Is (blue dots) at the dendritic arbor of the model neuron. (B) Comparison between the simulated response and the responses predicted by Eqs. 4 (green) and 5 (magenta). (C) Summation of the 20 coactivated Es with individual conductances ranging from 0.05 to 0.48 nS. (D) Summation of the five Is with individual conductances ranging from 0.32 to 6.40 nS.

Another potential consequence of simultaneous activation of a large number of inputs is the generation of somatic and/or dendritic spikes. We have tested whether the rule is valid in the presense of backpropagating action potentials (APs). In the simulation, an AP was evoked by injecting a depolarizing current (2 ms, 1.5 nA) into the soma, and the concurrent EPSP and IPSP were initiated 2, 5, or 10 ms after the AP. We then computed EPSP, IPSP, and the sum by subtracting the AP measured separately (Fig. S8A). We found that the arithmetic rule for subthreshold EPSP–IPSP summation still holds in the presence of a preceding AP (Fig. S8B). However, with the AP, there was an increase in the k value, which may be caused by the decrease of driving force for inhibitory input when the summation occurred at the after-hyperpolarization phase of AP (Fig. S8A). We also examined the interaction between an IPSP and a dendritic spike, which appeared as spikelet-EPSP at the soma (Fig. S9A Inset). In 46 of 79 dendrites tested, large excitatory inputs evoked somatic spikelets (the remaining 33 dendrites, in which dendritic spikes caused somatic APs, were excluded from the analysis). Among these 46 dendritic branches, the arithmatic rule holds for E (spikelet-EPSP) and I at different branches or for I at the trunk (Fig. S9 A and B), but it does not hold for E and I within the same branch (Fig. S9 C and D). This difference may be attributed to the mechanism for dendritic spike generation. When E and I are located at different dendritic branches, I had little impact on dendritic spike generation. However, the large shunting effect of I on the same branch can prevent or reduce dendritic spike generation induced by E, resulting in the violation of the simple arithmetic rule.


Contents

The nervous system first began to be encompassed within the scope of general physiological studies in the late 1800s, when Charles Sherrington began to test neurons' electrical properties. His main contributions to neurophysiology involved the study of the knee-jerk reflex and the inferences he made between the two reciprocal forces of excitation and inhibition. He postulated that the site where this modulatory response occurs is the intercellular space of a unidirectional pathway of neural circuits. He first introduced the possible role of evolution and neural inhibition with his suggestion that “higher centers of the brain inhibit the excitatory functions of the lower centers”. [1]

Much of today's knowledge of chemical synaptic transmission was gleaned from experiments analyzing the effects of acetylcholine release at neuromuscular junctions, also called end plates. The pioneers in this area included Bernard Katz and Alan Hodgkin, who used the squid giant axon as an experimental model for the study of the nervous system. The relatively large size of the neurons allowed the use of finely-tipped electrodes to monitor the electrophysiological changes that fluctuate across the membrane. In 1941 Katz's implementation of microelectrodes in the gastrocnemius sciatic nerve of frogs’ legs illuminated the field. It soon became generalized that the end-plate potential (EPP) alone is what triggers the muscle action potential, which is manifested through contractions of the frog legs. [3]

One of Katz's seminal findings, in studies carried out with Paul Fatt in 1951, was that spontaneous changes in the potential of muscle-cell membrane occur even without the stimulation of the presynaptic motor neuron. These spikes in potential are similar to action potentials except that they are much smaller, typically less than 1 mV they were thus called miniature end plate potentials (MEPPs). In 1954, the introduction of the first electron microscopic images of postsynaptic terminals revealed that these MEPPs were created by synaptic vesicles carrying neurotransmitters. The sporadic nature of the release of quantal amounts of neurotransmitter led to the "vesicle hypothesis" of Katz and del Castillo, which attributes quantization of transmitter release to its association with synaptic vesicles. [3] This also indicated to Katz that action potential generation can be triggered by the summation of these individual units, each equivalent to an MEPP. [4]

At any given moment, a neuron may receive postsynaptic potentials from thousands of other neurons. Whether threshold is reached, and an action potential generated, depends upon the spatial (i.e. from multiple neurons) and temporal (from a single neuron) summation of all inputs at that moment. It is traditionally thought that the closer a synapse is to the neuron's cell body, the greater its influence on the final summation. This is because postsynaptic potentials travel through dendrites which contain a low concentration of voltage-gated ion channels. [5] Therefore, the postsynaptic potential attenuates by the time it reaches the neuron cell body. The neuron cell body acts as a computer by integrating (adding or summing up) the incoming potentials. The net potential is then transmitted to the axon hillock, where the action potential is initiated. Another factor that should be considered is the summation of excitatory and inhibitory synaptic inputs. The spatial summation of an inhibitory input will nullify an excitatory input. This widely observed effect is called inhibitory 'shunting' of EPSPs. [5]

Spatial summation Edit

Spatial summation is a mechanism of eliciting an action potential in a neuron with input from multiple presynaptic cells. It is the algebraic summing of potentials from different areas of input, usually on the dendrites. Summation of excitatory postsynaptic potentials increases the probability that the potential will reach the threshold potential and generate an action potential, whereas summation of inhibitory postsynaptic potentials can prevent the cell from achieving an action potential. The closer the dendritic input is to the axon hillock, the more the potential will influence the probability of the firing of an action potential in the postsynaptic cell. [6]

Temporal summation Edit

Temporal summation occurs when a high frequency of action potentials in the presynaptic neuron elicits postsynaptic potentials that summate with each other. The duration of a postsynaptic potential is longer than the interval between incoming action potentials. If the time constant of the cell membrane is sufficiently long, as is the case for the cell body, then the amount of summation is increased. [6] The amplitude of one postsynaptic potential at the time point when the next one begins will algebraically summate with it, generating a larger potential than the individual potentials. This allows the membrane potential to reach the threshold to generate an action potential. [7]

Neurotransmitters bind to receptors which open or close ion channels in the postsynaptic cell creating postsynaptic potentials (PSPs). These potentials alter the chances of an action potential occurring in a postsynaptic neuron. PSPs are deemed excitatory if they increase the probability that an action potential will occur, and inhibitory if they decrease the chances. [4]

Glutamate as an excitatory example Edit

The neurotransmitter glutamate, for example, is predominantly known to trigger excitatory postsynaptic potentials (EPSPs) in vertebrates. Experimental manipulation can cause the release of the glutamate through the non-tetanic stimulation of a presynaptic neuron. Glutamate then binds to AMPA receptors contained in the postsynaptic membrane causing the influx of positively charged sodium atoms. [3] This inward flow of sodium leads to a short term depolarization of the postsynaptic neuron and an EPSP. While a single depolarization of this kind may not have much of an effect on the postsynaptic neuron, repeated depolarizations caused by high frequency stimulation can lead to EPSP summation and to surpassing the threshold potential. [8]

GABA as an inhibitory example Edit

In contrast to glutamate, the neurotransmitter GABA mainly functions to trigger inhibitory postsynaptic potentials (IPSPs) in vertebrates. The binding of GABA to a postsynaptic receptor causes the opening of ion channels that either cause an influx of negatively charged chloride ions into the cell or an efflux of positively charged potassium ions out of the cell. [3] The effect of these two options is the hyperpolarization of the postsynaptic cell, or IPSP. Summation with other IPSPs and contrasting EPSPs determines whether the postsynaptic potential will reach threshold and cause an action potential to fire in the postsynaptic neuron.

As long as the membrane potential is below threshold for firing impulses, the membrane potential can summate inputs. That is, if the neurotransmitter at one synapse causes a small depolarization, a simultaneous release of transmitter at another synapse located elsewhere on the same cell body will summate to cause a larger depolarization. This is called spatial summation and is complemented by temporal summation, wherein successive releases of transmitter from one synapse will cause progressive polarization change as long as the presynaptic changes occur faster than the decay rate of the membrane potential changes in the postsynaptic neuron. [4] Neurotransmitter effects last several times longer than presynaptic impulses, and thereby allow summation of effect. Thus, the EPSP differs from action potentials in a fundamental way: it summates inputs and expresses a graded response, as opposed to the all-or-none response of impulse discharge. [9]

At the same time that a given postsynaptic neuron is receiving and summating excitatory neurotransmitter, it may also be receiving conflicting messages that are telling it to shut down firing. These inhibitory influences (IPSPs) are mediated by inhibitory neurotransmitter systems that cause postsynaptic membranes to hyperpolarize. [10] Such effects are generally attributed to the opening of selective ion channels that allow either intracellular potassium to leave the postsynaptic cell or to allow extracellular chloride to enter. In either case, the net effect is to add to the intracellular negativity and move the membrane potential farther away from the threshold for generating impulses. [7] [9]

When EPSPs and IPSPs are generated simultaneously in the same cell, the output response will be determined by the relative strengths of the excitatory and inhibitory inputs. Output instructions are thus determined by this algebraic processing of information. Because the discharge threshold across a synapse is a function of the presynaptic volleys that act upon it, and because a given neuron may receive branches from many axons, the passage of impulses in a network of such synapses can be highly varied. [11] The versatility of the synapse arises from its ability to modify information by algebraically summing input signals. The subsequent change in stimulation threshold of the postsynaptic membrane can be enhanced or inhibited, depending on the transmitter chemical involved and the ion permeabilities. Thus the synapse acts as a decision point at which information converges, and it is modified by algebraic processing of EPSPs and IPSPs. In addition to the IPSP inhibitory mechanism, there is a presynaptic kind of inhibition that involves either a hyperpolarization on the inhibited axon or a persistent depolarization whether it is the former or the latter depends on the specific neurons involved. [6]

The microelectrodes used by Katz and his contemporaries pale in comparison to the technologically advanced recording techniques available today. Spatial summation began to receive a lot of research attention when techniques were developed that allowed the simultaneous recording of multiple loci on a dendritic tree. A lot of experiments involve the use of sensory neurons, especially optical neurons, because they are constantly incorporating a ranging frequency of both inhibitory and excitatory inputs. Modern studies of neural summation focus on the attenuation of postsynaptic potentials on the dendrites and the cell body of a neuron. [1] These interactions are said to be nonlinear, because the response is less than the sum of the individual responses. Sometimes this can be due to a phenomenon caused by inhibition called shunting, which is the decreased conductance of excitatory postsynaptic potentials. [7]

Shunting inhibition is exhibited in the work of Michael Ariel and Naoki Kogo, who experimented with whole cell recording on the turtle basal optic nucleus. Their work showed that spatial summation of excitatory and inhibitory postsynaptic potentials caused attenuation of the excitatory response during the inhibitory response most of the time. They also noted a temporary augmentation of the excitatory response occurring after the attenuation. As a control they tested for attenuation when voltage-sensitive channels were activated by a hyperpolarization current. They concluded that attenuation is not caused by hyperpolarization but by an opening of synaptic receptor channels causing conductance variations. [12]

Potential therapeutic applications Edit

Regarding nociceptive stimulation, spatial summation is the ability to integrate painful input from large areas while temporal summation refers to the ability of integrating repetitive nociceptive stimuli. Widespread and long lasting pain are characteristics of many chronic pain syndromes. This suggests that both spatial and temporal summations are important in chronic pain conditions. Indeed, through pressure stimulation experiments, it has been shown that spatial summation facilitates temporal summation of nociceptive inputs, specifically pressure pain. [13] Therefore, targeting both spatial and temporal summation mechanisms simultaneously can benefit treatment of chronic pain conditions.


Results

Experimental Measurements of E–I Integration.

We first developed a quantitative assay of E-I integration in CA1 pyramidal neurons of rat hippocampal slices. The whole-cell recording was made from the soma of the pyramidal cell, and fluorescent dye Alexa Fluor 488 was loaded into the cell via the recording pipette to visualize the dendritic tree (Fig. 1A). Microiontophoretic applications of glutamate and GABA at the apical dendrite elicited rapid membrane depolarizations and hyperpolarizations with kinetics similar to those of natural EPSPs and IPSPs elicited by extracellular electrical stimulation in the CA1 region, respectively (Fig. 1B and SI Appendix). For convenience, these iontophoretic responses are referred to hereafter as EPSPs and IPSPs. When the EPSP and IPSP were elicited simultaneously with two iontophoretic pipettes placed at adjacent locations of the dendritic trunk, the measured somatic response was always smaller than the linear sum of the EPSP and IPSP measured separately (Fig. 1B). The nonlinear component of E–I integration was obtained by subtracting the measured sum from the linear sum. The amplitude of the nonlinear component was not affected by changing the driving force for the IPSP from −10 to 0 mV (Fig. S1 C and D) and was absent for summation of EPSP and hyperpolarization induced by somatic current injection (Fig. S1 E and F), indicating that this nonlinear component reflects shunting inhibition. Thus, this nonlinear component was referred to as the shunting component (SC) (Fig. 1B).

Experimental measurement of E–I integration and its dependence on EPSP and IPSP amplitudes. (A) Image of a CA1 pyramidal neuron filled with Alexa Fluor 488 via the recording pipette. Arrows indicate pipettes for iontophoresis of glutamate and GABA (at 232 and 129 μm from soma). (Scale bar: 100 μm.) (B) Examples of EPSP, IPSP, their linear sum, and response to simultaneous glutamate and GABA pulses. SC is the recorded response (sum) minus the linear sum. (C) As in B except that IPSP preceded EPSP by 30 ms. (D) Changes in the amplitude of SC vs. the time interval between IPSP and EPSP, for two different sets of E/I location (square: I at 50–100 μm, E at 150–200 μm, n = 6 triangles: E at 100–150 μm, I at 200–250 μm, n = 5). (E) SC vs. IPSP amplitude, measured for a fixed EPSP amplitude (9–10 mV). Data are from four cells. Line indicares linear fit (R = 0.974). (F) SC vs. EPSP amplitude, measured for a fixed IPSP amplitude (1.1–1.3 mV). Data are from four cells. Line indicates linear fit (R = 0.965).

We next examined how the temporal shift between E and I affects the amplitude of the SC, as illustrated by Fig. 1C for a case in which I preceded E for 30 ms. The SC amplitude decreased rapidly with the E–I interval, but significant shunting effect remained when I preceded E for up to 200 ms (Fig. 1D). Further pharmacological experiments indicated that prolonged inhibition with large E–I temporal intervals was mainly caused by the activation of GABABRs, because bath application of the GABABR antagonist CGP 35348 (60 μM) abolished this prolonged component (Fig. S2). In the present study, we focused on the fast shunting inhibition for concurrent E and I, which is caused by opening of GABAARs.

To analyze E–I integration quantitatively, the amplitude of E was defined as the peak value of EPSP, whereas the amplitudes of I and the summed response were defined as the values at the time of the peak EPSP. Under this definition, we examined how the SC amplitude depends on the amplitude of EPSPs and IPSPs. By setting the EPSP amplitude at a fixed value while varying the IPSP amplitude, we found that the SC amplitude depended linearly on the IPSP amplitude (Fig. 1E). Conversely, at a fixed IPSP amplitude the SC amplitude depended linearly on the EPSP amplitude (Fig. 1F). Such linear dependence was also found if we define the amplitude by the mean EPSP/IPSP value over the first 100 ms (Fig. S3).

Derivation of Arithmetic Rule for E–I Integration by Modeling.

To further investigate the shunting inhibition, we performed computer simulation with a realistic neuron model, using the morphology of a reconstructed CA1 pyramidal cell (15) (Fig. 2A) and the kinetics and distributions of ion channels reported previously (SI Appendix). The model parameters were adjusted to yield EPSPs and IPSPs (Fig. 2A) with kinetics similar to the experimentally observed iontophoretic EPSPs and IPSPs (Fig. 1A). We then simulated the EPSP, IPSP, and the summed response at the soma (Fig. 2A), and defined SC in the same manner as that for experimental measurements. The dependence of SC on the amplitudes of EPSP (0.2–8 mV) and IPSP (0.1–3.5 mV) was plotted for E at 151 μm and for I at 94 μm from the soma. Consistent with our experimental observations (Fig. 1 E and F), the SC amplitude depended linearly on both the EPSP and IPSP amplitudes (Fig. 2B and Fig. S3B).

Simulation of E–I integration in a realistic neuronal model and derivation of the arithmetic rule. (A) (Left) Reconstructed hippocampal CA1 pyramidal neuron used for simulation. Arrows indicate I and E were at 94 and 151 μm from the soma. (Scale: 100 μm.) (Right) Simulated EPSP, IPSP, their linear sum, simulated response (sum) of concurrently activated E and I, and the SC. (B) (Upper) SC vs. IPSP amplitude, with fixed EPSP amplitude (at 5.5 mV). Line indicates linear fit (R = 0.999). (Lower) SC vs. EPSP amplitude, with fixed IPSP amplitude (at 3.5 mV). Line indicates linear fit (R = 0.998). (C) Ratio between measured SC and EPSP (SC/EPSP) plotted against IPSP (red circle) and SC/IPSP plotted against EPSP (blue square) for the same cell in the slice recording. The amplitudes of the paired EPSP and IPSP were randomly set in the range of 1–10 and 0.2–4 mV, respectively. E and I locations were fixed at 110 and 45 μm. Lines indicate linear fit (red: R = 0.96, slope k = 0.142, n = 11 blue: R = 0.92, slope k = 0.145, n = 10). (D) Simulated SC/EPSP vs. IPSP (red circle, n = 20) and SC/IPSP vs. EPSP (blue square, n = 20). Lines indicate linear fit (red: R = 0.999, slope k = 0.086 blue: R = 0.999, slope k = 0.087). The EPSP amplitudes were randomly chosen from a 0.2- to 8-mV pool and the IPSP amplitude was from a 0.1- to 3.5-mV pool. I and E are at 94 and 151 μm. (E) Simulated SC as a function of both EPSP (0.2–8 mV) and IPSP (0.1–3.5 mV) amplitudes, with E and I at 202 and 123 μm, respectively. (F) k*EPSP*IPSP, with k adjusted to best fit the data in E k = 0.093, rms error: 4.9%.

Besides the above studies using fixed EPSP or IPSP amplitude, we further characterized the dependence of SC on IPSP and EPSP amplitudes by randomly varying both the EPSP (in a range of 0.2 to 10 mV) and the IPSP (0.1–4 mV) in experiments and simulations. When the amplitude ratio SC/EPSP was plotted against the IPSP amplitude or when SC/IPSP was plotted against the EPSP amplitude, we found that these two plots could be well fitted by straight lines through the origin, with nearly identical slopes (Fig. 2 C and D). This finding suggests that SC is directly proportional to EPSP*IPSP. We also plotted the simulated SC amplitude against both EPSP and IPSP amplitudes (Fig. 2E) and fitted the results by the function SC = k*EPSP*IPSP, with k as the free parameter (Fig. 2F). This multiplicative function provided a good approximation (rms error: 4.9%) for simulated SC over a range of EPSP and IPSP amplitudes. Thus, the summed response to coincident E and I can be approximated by a simple arithmetic rule: where k (in the unit of mV −1 ) reflects the strength of shunting inhibition (k > 0 for hyperpolarizing IPSPs). This arithmetic rule quantitatively describes two aspects of inhibition: hyperpolarization and shunting inhibition.

Dependence of k on E and I Locations Along the Apical Dendritic Trunk.

We further examined the dependence of k on E and I locations along the apical dendrite trunk in the CA1 pyramidal neuron model. For each combination of E and I locations, we computed the k value from 20 sets of arbitrarily chosen E and I amplitudes and plotted the results in Fig. 3A. As shown by the various cross-sections of the 3D graph, for each I location the dependence of k on the E location showed a clear asymmetry for proximal vs. distal Es (Fig. 3B): For a given I, the k value decayed rapidly with the I–E distance for proximal Es (space constant ≈83 μm), but remained relatively constant for distal Es. The maximal k value was higher for more distal Is.

Dependence of k on E/I locations. (A and B) Stimulation results showing coefficient k as a function of E and I distances from the soma. For each E/I location, k was computed from 20 sets of EPSP and IPSP amplitudes using the least-square fit. The value of k is color-coded (see bar) in a 3D map in A. In B, k is plotted as a function of E location, corresponding to the cross-section of the 3D map. Data points connected by each line depict k for a given I location (marked by the dashed line of the same color). (C–E) Experimental results on the location dependence of k. In C, changes of k with more distal E locations. Data grouped by the range of I locations. Line indicates best linear fit of each group. In D, changes of k with E/I locations of paired E and I from experiments in which E was more proximal to I, for different ranges of I location. Each point was averaged from more than three cells. In E, changes of k with E location, for three fixed I locations (marked by dashed lines).

The dependence of k on E and I locations observed in the above simulations was also tested experimentally by iontophoresis of glutamate and GABA at various locations along the main dendritic trunk of the CA1 pyramidal cell. For E at more distal sites than I (at three sets of I locations), k was largely independent of the E location and E–I distance, but markedly dependent on the I location (Fig. 3C). For Es located proximally to I (at three sets of I locations), k decreased with the E–I distance (Fig. 3D), consistent with that found by simulation. Finally, when k was plotted as a function of the E location for various fixed I locations, the k profile also showed a clear distal-proximal asymmetry (Fig. 3E), similar to that found by simulation. These results support and extend the notion of on-the-path shunting (10, 11).

Shunting Inhibition Involving Oblique Branches.

Because most synaptic inputs to pyramidal neurons are located on dendritic branches, we examined the shunting of Es distributed throughout the dendritic tree exerted by I located at either the dendritic trunk or an oblique branch. For each I location of the realistic neuronal model, we computed k as a function of the E location over the entire apical dendrite except at the distal stratum lacunosum moleculare layer, where local subthreshold EPSPs and IPSPs cause little change of the somatic membrane potential (16). For I located at the apical trunk (Fig. 4A), there was a prominent asymmetry k values were uniformly large for distal Es at both the trunk and branches but decreased rapidly with the E–I distance for proximal Es. For I located at an oblique branch (Fig. 4B), shunting was largely confined to the same branch. This finding is in line with the idea that each dendritic branch is an independent functional compartment (4–5, 11, 17–22). Notably, the asymmetry in the k profile observed at the apical trunk (Fig. 3) was also observed at the oblique branch when E and I were located at the same branch k was uniformly high for distal Es and decreased with the E–I distance for proximal Es (Fig. 4B).

Shunting inhibition for I located at dendritic trunk and oblique branches. (A and B) Simulation results of k values (color-coded) for I (black dot) located at apical trunk (A) and oblique branch (B), with E scattered on dendritic arbor in stratum radiatum. (C–H) Experimental results. (C) I at oblique branch: k was not significantly different between two distal Es (E1 and E2) within the same branch (P = 0.89, paired t test). E1 to E2 distances were >70 μm in all experiments. Lines connect data from the same cell. (D) As in C except that Es were more proximal to I (P = 0.001). (E) I at the trunk: k was not significantly different between Es at the trunk (E1) and at the first-order oblique branch (E2, P = 0.92). I to E distances were kept constant. (F) I at oblique branch: k was significantly different between Es at the same and different branch (P < 0.001). (G) E at the trunk: k was significantly different between Is at the trunk (I1) and at oblique branch (I2, P = 0.031). The trajectory distance of I to the soma was kept constant. (H) The decay of k value as a function of distance between I2 and the branch point for the configuration in G. Line indicates exponential fit (R = 0.97, length constant 44 μm).

The above modeling results were then tested experimentally in hippocampal slices. For the same location of GABA iontophoresis at an oblique branch, we measured the SC and calculated k for EPSPs induced at two locations along the same oblique branch. No significant difference was found in the k value (P = 0.89, paired t test) when the two E locations were both distal (spaced by ≈70 μm Fig. 4C). In contrast, for two Es at more proximal locations, k was significantly smaller (P = 0.001) for the E closer to the branch point (Fig. 4D). Furthermore, for I located at the apical trunk, the k values were not significantly different for distal Es located at either the trunk or branch (Fig. 4E P = 0.92, paired t test), consistent with the simulation results (Fig. 4A). When the I-soma distance was kept within 100–200 μm, k values for I and E located at the same branch were significantly higher than those for I and E located at different branches (Fig. 4F P < 0.001). Finally, for a fixed E location at the apical trunk, the k values for more proximal Is at the branch were lower than those at the trunk (Fig. 4G P = 0.03), with k decreasing rapidly with the distance to the branch point (Fig. 4H). Together, these experimental results are consistent with those found by simulation, indicating that shunting inhibition is largely compartmentalized to the same branch, with the distal–proximal asymmetry similar to that at the trunk.

Effects of Active Conductances and Transmitter Receptors.

Previous studies of E–I integration mostly addressed the role of passive cable properties (1, 10, 11). We have examined systematically how different ion channels and transmitter receptors affect the extent of shunting inhibition. For the CA1 pyramidal cell model, we calculated the k values for 15 sets of randomly chosen E and I locations before and after blocking 90% of each of the following conductances: voltage-dependent Na + channel, delayed rectifier K + channel (Kd), A-type K + channel (KA), hyperpolarization-activated cationic current (Ih), NMDA receptor (NMDAR), and GABABR (see SI Appendix). As shown in Fig. 5A, 90% blockade of Ih, KA, NMDAR, and Na + channels resulted in significant changes in the k value, whereas blockade of Kd and GABABR had no effect. These simulation results were tested by iontophoretic experiments in hippocampal slices using I and E located at the apical trunk within 100–200 and 100–300 μm from the soma, respectively. Specific blockers of Na + channel (tetrodotoxin, 3 μM), Kd (tetraethylammonium, 3 mM), KA (4-AP, 1 mM), Ih (ZD7288, 20 μM), NMDAR (D-AP5, 50 μM), and GABABR (CGP35348, 60 μM) were used separately to block each of these channels or receptors. We found that KA channel blockade increased the k value (≈12%, P < 0.01), an effect that may diminish the EPSP amplitude increase caused by the blockade of KA channels (23). In contrast, blocking Ih and NMDARs decreased the k value by 9% and 7%, respectively (P < 0.01), indicating contributions of these channels to the shunting effect. However, blockade of Kd, Na + channels, and GABABRs had no effect (P > 0.4 Fig. 5A). With the exception of the Na + channel, these experimental findings largely agreed with the simulation results. The discrepancy on Na + channel blockade may be attributed to a lower voltage threshold for the activation of Na + channels in the model cell.

Effects of ion channels and transmitter receptors on shunting inhibition. (A) Simulation (green) and experimental (orange) results on the changes in k after blockade of each of the ion channels and transmitter receptors. (B) 3D plot of k as a function of E and I locations after simultaneous blockade of voltage-dependent sodium conductance, delayed rectifier potassium conductance (Kd), A-type potassium conductance (KA), Ih channel conductance, NMDARs, and GABABRs.

We also examined the role of these ion channels and receptors in the dendrite-location dependence of k in the model. By comparing the k profile before and after 90% blockade of each of Kd, Na + , KA, Ih, NMDAR, and GABABR channels, we found that although the overall k values were altered to different extents, the asymmetric spatial profile remained the same (Fig. S4). Furthermore, this asymmetry was found even after all of the above conductances and receptors were blocked (Fig. 5B). Thus, the asymmetry in the k profile results primarily from passive cable properties of the dendrite.

Theoretical Interpretation of the Arithmetic Rule.

The theoretical basis of the arithmetic rule was next examined, using two-port analysis of the passive dendritic tree (ref. 11 and see SI Appendix and Fig. S5 for details). The analysis yielded a simple analytic expression for E–I summation: where Vs is the somatic voltage response to concurrent E and I, and Vse and Vsi are the somatic response to the individual excitatory input at location e and to the individual inhibitory input at location i, respectively. Kei is the transfer resistance between location e and i, Kes is between e and soma, and Kis is between i and soma. Ere and Eri are the driving forces (the difference between the reversal potential and resting membrane potential) for E and I, respectively. By defining we obtain VsVse + Vsi + kVseVsi.

This equation has the same form as the empirically derived arithmetic rule, for which Vs, Vse, and Vsi correspond to sum, EPSP, and IPSP, respectively. Considering that EriEre, and Kes and Kis are of the same order of magnitude, k is reduced to Note that in the above equation, k is inversely proportional to Eri, a relation confirmed in our simulation (Fig. S6). When Eri approaches zero, k approaches infinity, but the product (k*IPSP) remains finite because IPSP also approaches zero. When Eri becomes positive, as the case of early developing synapse (24), k should be negative, so that the shunting component (k*EPSP*IPSP) remains negative (Fig. S7).

Integration of Multiple Es and Is.

Each CA1 pyramidal neuron receives a large number of inputs at its dendrite. Is the rule obtained from a pair of E and I applicable to multiple Es and Is? To address this question, we selected 20 Es and 5 Is randomly distributed in the dendritic tree of the model CA1 pyramidal cell (Fig. 6A), with a range of synaptic conductances (Es: 0.048–0.48 nS Is: 0.32–6.4 nS). We first compared the simulated response to coincident activation of these Es and Is with that predicted by a simple arithmetic rule, in which the response was given by the linear sum of individual EPSPs and IPSPs together with all of the pairwise E–I interactions, using the following equation where EPSPi and IPSPj are somatic responses evoked by Ei and Ij, respectively, and kij is a coefficient for the paired Ei and Ij (which depends on the dendritic locations of E and I but not on the amplitude or the number of other coactivated inputs). As shown in Fig. 6B (green circles), for 20 different sets of EPSP and IPSP amplitudes, the predicted responses deviated from the simulated responses (rms error was 8.5%) at both small and large sum amplitudes. This deviation could originate from nonlinear E–E and I–I interactions (2, 25), as indeed suggested by the systematic deviation of the simulated responses to 20 coincident Es (Fig. 6C) and 5 coincident Is (Fig. 6D) from the linear sum. We thus adjusted Eq. 4 by incorporating the nonlinear E–E and I–I interactions: where EPSP S and IPSP S represent simulated somatic responses to coincident Es and Is alone, respectively. Eq. 5 yielded predicted responses in excellent agreement with simulated responses (Fig. 6B, magenta circles rms error was 2.7%). Thus, the arithmetic rule for the pairwise E–I interaction can also be used for quantitative estimate of E–I integration with multiple coincident Es and Is. Of course, a complete arithmetic rule for multiple inputs can be obtained only if the rules for the summation of multiple EPSPs and multiple IPSPs are both available. Our finding on the E–I interaction represents an important step toward the goal of obtaining a complete rule for integration of multiple Es and Is.

Integration of multiple Es and Is. (A) Distribution of 20 Es (red dots) and 5 Is (blue dots) at the dendritic arbor of the model neuron. (B) Comparison between the simulated response and the responses predicted by Eqs. 4 (green) and 5 (magenta). (C) Summation of the 20 coactivated Es with individual conductances ranging from 0.05 to 0.48 nS. (D) Summation of the five Is with individual conductances ranging from 0.32 to 6.40 nS.

Another potential consequence of simultaneous activation of a large number of inputs is the generation of somatic and/or dendritic spikes. We have tested whether the rule is valid in the presense of backpropagating action potentials (APs). In the simulation, an AP was evoked by injecting a depolarizing current (2 ms, 1.5 nA) into the soma, and the concurrent EPSP and IPSP were initiated 2, 5, or 10 ms after the AP. We then computed EPSP, IPSP, and the sum by subtracting the AP measured separately (Fig. S8A). We found that the arithmetic rule for subthreshold EPSP–IPSP summation still holds in the presence of a preceding AP (Fig. S8B). However, with the AP, there was an increase in the k value, which may be caused by the decrease of driving force for inhibitory input when the summation occurred at the after-hyperpolarization phase of AP (Fig. S8A). We also examined the interaction between an IPSP and a dendritic spike, which appeared as spikelet-EPSP at the soma (Fig. S9A Inset). In 46 of 79 dendrites tested, large excitatory inputs evoked somatic spikelets (the remaining 33 dendrites, in which dendritic spikes caused somatic APs, were excluded from the analysis). Among these 46 dendritic branches, the arithmatic rule holds for E (spikelet-EPSP) and I at different branches or for I at the trunk (Fig. S9 A and B), but it does not hold for E and I within the same branch (Fig. S9 C and D). This difference may be attributed to the mechanism for dendritic spike generation. When E and I are located at different dendritic branches, I had little impact on dendritic spike generation. However, the large shunting effect of I on the same branch can prevent or reduce dendritic spike generation induced by E, resulting in the violation of the simple arithmetic rule.


T. A. Vardapetyan, "Characteristics of reactions of neurons of auditory cortex of the cat," in: Mechanisms of Hearing [in Russian], Nauka (1967), pp. 74–90.

L. L. Voronin, "Postsynaptic potentials of neurons of the motor zone of the cortex of an unanesthetized rabbit," Fiziol. Zhurn. SSSR,53, 623–631 (1967).

D. S. Vorontsov, General Electrophysiology [in Russian], Medgiz (1961), p. 401.

G. Jasper, G. Ricci, and B. Doane, "Microelectrode analysis of the discharges of cortical cells in the development of conditioned defensive reactions in monkeys," in: Electroencephalographic Study of Higher Nervous Activity [Russian translation], Moscow (1962), pp. 129–146.

V. Mountcastle, "Some functional properties of the somatic afferent system," in: Theory of Communication in Sensory Systems [Russian translation], Moscow (1964), pp. 185–213.

F. N. Serkov, "The genesis and functional significance of evoked potentials of the cerebral cortex," Neirofiziologiya,2, 349–359 (1970).

F. N. Serkov and V. M. Storozhuk, "Reaction of neurons of the auditory cortex to sound stimuli," Neirofiziologiya,1, 147–156 (1969).

F. N. Serkov and E. Sh. Yanovskii, "Reactions of neurons of the auditory cortex to paired clicks," Neirofiziologiya,2, 227–235 (1970).

V. G. Skrebitskii and L. L. Voronin, "Intracellular study of the electrical activity of neurons of the visual cortex of an unanesthetized rabbit," Zhurn. Vyssh. Nervn. Deyat.,16, 864–873 (1966).

V. G. Skrebitskii and E. G. Shkol'nik-Yarros, "Questions of the functional and structural organization of the visual cortex," in: Visual and Auditory Analyzers [in Russian], Meditsina, Moscow (1969), pp. 179–186.

O. Feher, "Data on the location of the inhibitory system in the auditory cortex of the cat," in: Visual and Auditory Analyzers [Russian translation], Meditsina, Moscow (1969), pp. 202–209.

R. Jung, "Integration in neurons of the visual cortex," in: Theory of Communication in Sensory Systems [Russian translation], Mir, Moscow (1964), pp. 375–415.

M. Abeles and M. H. Goldstein, "Functional architecture in cat primary auditory cortex," J. Neurophysiol.,33, 172–186 (1970).

S. A. Andersson, "Intracellular postsynaptic potentials in the somatosensory cortex of the cat," Nature,205, 297–298 (1965).

S. D. Erulcar, I. E. Rose, and P. W. Davies, "Single unit activity in the auditory cortex of the cat," Johns Hopkins Hosp. Bull.,99, 55–86 (1956).

E. F. Evans and J. C. Whitfield, "Classification of unit responses in the auditory cortex," J. Physiol.,171, 476–493 (1964).

R. Galambos and D. F. Bogdanski, "Studies of the auditory system with implanted electrodes," in: Neuronal Mechanisms of the Auditory and Vestibular Systems, Springfield, Illinois, USA (1960), pp. 137–151.

G. L. Gerstein and N. Y. Kiang, "Responses of single units in the auditory cortex," Exper. Neurol.,10, 1–18 (1964).

J. E. Hind, "Unit activity in the auditory cortex," in: Neuronal Mechanisms of the Auditory and Vestibular Systems, Springfield, Illinois, USA (1960), pp. 201–210.

J. Katzuki, T. Watanabe, and N. Marujama, "Activity of auditory neurons in upper levels of brain of cat," J. Neurophysiol.,22, 343–359 (1959).

C. L. Li, "Cortical intracellular potentials and their response to strychnine," J. Neurophysiol.,22, 436–449 (1959).

C. L. Li and S. N. Chou, "Inhibitory interneurons in the neocortex," in: Inhibition in the Nervous System and γ-Aminobutyric Acid, London (1960), pp. 34–39.

C. L. Li, A. Ortiz-Galvin, S. N. Chou, and S. Y. Howard, "Cortical intracellular potentials in response to stimulation of laterale geniculate body," J. Neurophysiol.,23, 592–601 (1960).

A. C. Nacimienko, H. D. Lux, and O. D. Creutzfeldt, "Postsynaptische potentiale von nervenzellen motorischen cortex nach elektrischen reizung spezifischer und undspezifischer thalamuskerne," Pflug. Arch.,281, 152–168 (1964).

C. G. Phillips, "Intracellular records from Betz cells in cat," Quart. J. Exp. Physiol.,41, 58–69 (1956).

C. G. Phillips, "Actions of antidromic pyramidal volleys on single Betz cells in the cat," Quart. J. Exp. Physiol.,44, 1–25 (1959).

C. Stefanis and H. Jasper, "Intracellular microelectrode studies of antidromic response in cortical pyramidal tract neurons," J. Neurophysiol.,27, 828–854 (1964).

C. Stefanis and H. Jasper, "Recurrent collateral inhibition in pyramidal tract neurons," J. Neurophysiol.,27, 855–877 (1964).

J. Tasaki, E. H. Polley, and F. Orrego, "Action potentials from individual elements in cat geniculate and striate cortex," J. Neurophysiol.,17, 454–474 (1954).

S. Watanabe, M. Konishi, and O. D. Creutzfeldt, "Postsynaptic potentials in the cat's visual cortex following electrical stimulation of afferent pathways," Exp. Brain Res.,1, 272–283 (1966).


Abstract

Neural mass models offer a way of studying the development and behavior of large-scale brain networks through computer simulations. Such simulations are currently mainly research tools, but as they improve, they could soon play a role in understanding, predicting, and optimizing patient treatments, particularly in relation to effects and outcomes of brain injury. To bring us closer to this goal, we took an existing state-of-the-art neural mass model capable of simulating connection growth through simulated plasticity processes. We identified and addressed some of the model's limitations by implementing biologically plausible mechanisms. The main limitation of the original model was its instability, which we addressed by incorporating a representation of the mechanism of synaptic scaling and examining the effects of optimizing parameters in the model. We show that the updated model retains all the merits of the original model, while being more stable and capable of generating networks that are in several aspects similar to those found in real brains.


We simulate the inhibition of Ia-glutamatergic excitatory postsynaptic potential (EPSP) by preceding it with glycinergic recurrent (REN) and reciprocal (REC) inhibitory postsynaptic potentials (IPSPs). The inhibition is evaluated in the presence of voltage-dependent conductances of sodium, delayed rectifier potassium, and slow potassium in five -motoneurons (MNs). We distribute the channels along the neuronal dendrites using, alternatively, a density function of exponential rise (ER), exponential decay (ED), or a step function (ST). We examine the change in EPSP amplitude, the rate of rise (RR), and the time integral (TI) due to inhibition. The results yield six major conclusions. First, the EPSP peak and the kinetics depending on the time interval are either amplified or depressed by the REC and REN shunting inhibitions. Second, the mean EPSP peak, its TI, and RR inhibition of ST, ER, and ED distributions turn out to be similar for analogous ranges of G. Third, for identical G, the large variations in the parameters’ values can be attributed to the sodium conductance step ( ⁠⁠ ) and the active dendritic area. We find that small on a few dendrites maintains the EPSP peak, its TI, and RR inhibition similar to the passive state, but high on many dendrites decrease the inhibition and sometimes generates even an excitatory effect. Fourth, the MN's input resistance does not alter the efficacy of EPSP inhibition. Fifth, the REC and REN inhibitions slightly change the EPSP peak and its RR. However, EPSP TI is depressed by the REN inhibition more than the REC inhibition. Finally, only an inhibitory effect shows up during the EPSP TI inhibition, while there are both inhibitory and excitatory impacts on the EPSP peak and its RR.

In the past few years, the physiological and morphological properties of the cat and rat -motoneurons have been intensively studied (Bui, Grande, & Rose, 2008a, 2008b Heckman, Hyngstrom, & Johnson, 2008 Hyngstrom, Johnson, & Heckman, 2008 Jean-Xavier, Pflieger, Liabeuf, & Vinay, 2006 Larkum, Rioult, & Luscher, 1996). This revealed a large number of voltage-dependent conductances on motoneuron (MN) dendrites, uniquely located relative to other types of neurons (Heckmann, Gorassini, & Bennett, 2005 Kim, Major, & Jones, 2009 Kuo, Lee, Johnson, Heckman, & Heckman, 2003 Saint Mleux & Moore, 2000). In contrast to hippocampal and neocortical pyramidal cells, which show a variety of different channel distributions depending on the neuron and channel type (see Magee, 1998) in MNs some dendrites are active, while others remain passive (Luscher & Larkum, 1998). The voltage-dependent channels and the depolarizing shunting inhibition provide the excitatory potential not only for input amplification or attenuation but also for nonlinear interactions.

In our previous research, we analyzed the influence of active MN's dendritic properties on the EPSP (Gradwohl & Grossman, 2008) and IPSP (Gradwohl & Grossman, 2010). We concluded that voltage-dependent channels on the dendrites boost EPSP peak and diminish IPSP peak. However the mean EPSP and IPSP peaks of step function (ST), exponential rise (ER), and exponential decay (ED) distributions are similar when the range of G is equal. Our model is a continuation of our previous simulations. We analyze the effective modulation of the EPSP by the IPSPs in the presence of the same basic voltage-dependent channels and explore any relation between the type of voltage-dependent channel distribution in the dendrites and the EPSP inhibition.

Gain modulation is used for integrating data from different sensory, motor, and cognitive sources. At the neuronal level, gain modulation can be seen as a nonlinear summation of the synaptic response of excitatory synapses containing a voltage-dependent parameter (Mel, 1993 Volman, Levine, & Sejnowski, 2010).

There are two types of motor neuron inhibition: the orthodromic reciprocal inhibition (REC) and the antidromic Renshaw inhibition (REN). The latter is part of a feedback system of the -MN and operates within a polysynaptic interneuronal pathway (Schneider & Fyffe, 1992). The REC inhibitory inputs are distributed on the soma and proximal dendrites (Burke, Fedina, & Lundberg, 1971 Curtis & Eccles, 1959 Stuart & Redman, 1990) and the REN inhibitory inputs on the dendrites distally to the soma (Fyffe, 1991 Maltenfort, McCurdy, Phillips, Turkin, & Hamm, 2004), similar to the excitatory AMPA and NMDA inputs. Additionally, the time course of the REC IPSP compared to the REN IPSP is shorter. Thus, the presence of the REN and REC inhibitory inputs in the simulation serves as a basis for analyzing the effect of voltage-dependent channels on differently located synapses with distinct conductance time course. Glycine (not GABA) is the major neurotransmitter involved in the inhibitory pathway of the spinal cord (Capaday & van Vreeswijk, 2006) in REC inhibition. Although REN inhibition employs glycine and GABA neurotransmitters (Cullheim & Kellerth, 1981 Jonas, Bischofberger, & Sankuhler, 1998) we neglected the latter in order to compare REC and REN inhibition with the same glycinergic neurotransmition. The ionic current of the inhibitory synapses is carried by chloride, and, as a result, the reversal potential is close to the resting potential (Gao & Ziskind-Conhaim, 1995 Jean-Xavier, Mentis, O'Donovan, Cattaert, & Vinay, 2007 Jean-Xavier et al., 2006 Stuart & Redman, 1990 Yoshimura & Nishi, 1995). It is known that in mature motoneurons after spinal cord injury (Boulenguez et al., 2010 Edgerton & Roy, 2010) and in a newborn rat (Marchetti, Pagnotta, Donato, & Nistri, 2002), the inhibitions have depolarizing characteristics. Inhibition is mainly attained by a shunting effect. It is regularly mentioned as a mechanism by which gain modulation is controlled through changes in the input resistance, without affecting the membrane potential (Prescott & De Koninck, 2003). Shunting inhibition modulates synaptic excitatory depolarization, whereas hyperpolarizing inhibition has a subtractive effect on the depolarization. The inhibition in our model has both depolarizing and shunting properties that are similar to our previously published model (Gradwohl & Grossman, 2010). Consequently, it is of special interest to examine its interaction with the depolarizing excitatory synaptic potentials since the depolarizing inhibition occurs in mature motoneurons after spinal cord injury (Boulenguez et al., 2010 Edgerton & Roy, 2010) and also in newborn rats (Marchetti et al., 2002).

In this work, the inhibition of Ia-EPSP synaptic potentials is evaluated in the presence of the basic voltage-dependent components: sodium, delayed rectifier potassium, and slow potassium currents distributed at different locations on the dendrites. Although persistent inward currents (PIC) are a dominant conductance on the MN's dendrites (Heckman et al., 2008), we do not include them in our investigation, as we are interested in the basic active components in the absence of neuron firing (see Luscher & Larkum, 1998). REN and REC inhibitions were inserted into the model and mediated by the glycinergic neurotransmission. We then analyzed the interaction of excitatory and inhibitory inputs between themselves and the voltage-dependent channels. In addition, we incorporated the dendritic branching (Cullheim, Fleshman, Glenn, & Burke, 1987a, 1987b Segev, Fleshman, & Burke, 1990) and the MN's size. As a result, we were able to simulate realistic morphological MNs and compare their distinct physiological properties.

Which kind of inhibition depresses the Ia-EPSP components of peak, time integral, and rate of rise most efficiently?

How does an active dendrite contribute to the efficacy of inhibition? Alternatively, which kind of dendritic voltage-dependent channels distribution depresses Ia EPSP most effectively?

Is Ia-EPSP inhibition monotonically dependent to the input resistance of the MNs?


Synaptic Potential

The synaptic potentials are electrotonic potentials: they decay passively as a function of time and distance. The time course of the rising phase of the synaptic potential is determined by both active and passive properties of the membrane. As the synaptic channels spontaneously reclose, the PSP decays in an exponential fashion. The decay of the PSP is purely a passive process whose time course is a function of the membrane time constant, τ. The membrane time constant is the time required for an electrotonic potential to decay to 1/e or 37% of its peak value. The time constant of neurons is in the range of 1–20 ms. The amplitude of the synaptic potentials decreases exponentially from the maximum recorded focally at the synapse as a function of the membrane length constant, γ. The length constant is the distance at which electrotonic potentials decay to 1/e or 37% of their amplitude at the point of origin. The length constant of dendrites is typically in the range 0.1 to 1 mm.


EPSP/IPSP amplitude values? - Psychology

FIGURE 21 Excitatory and inhibitory postsynaptic potentials in spinal motor neurons. (A) Intracellular recordings are made from a sensory neuron (SN), interneuron, and extensor (E) and flexor (F) motor neurons. (B) An action potential in the sensory neuron produces a depolarizing response in the motor neuron (MN). This response is called an excitatory postsynaptic potential (EPSP). (C) An action potential in the interneuron produces a hyperpolarizing response in the motor neuron. This response is called an inhibitory postsynaptic potential (IPSP).

Postsynaptic Mechanisms Produced by Ionotropic Receptors

Ionic Mechanisms of EPSPs

Mechanisms responsible for fast EPSPs mediated by ionotropic receptors in the CNS are fairly well known. Specifically, for the synapse between the sensory neuron and the spinal motor neuron, the ionic mechanisms for the EPSP are essentially identical to the ionic mechanisms at the skeletal neuromuscular junction. Transmitter substance released from the presynaptic terminal of the sensory neuron diffuses across the synaptic cleft, binds to specific receptor sites on the postsynaptic membrane, and leads to a simultaneous increase in permeability to Na+ and K+, which makes the membrane potential move toward a value of 0 mV.

Although this mechanism is superficially the same as that for the neuromuscular junction, two fundamental differences exist between the process of synaptic transmission at the sensory neuron-motor neuron synapse and the motor neuron-skeletal muscle synapse. First, these two different synapses use different transmitters. The transmitter substance at the neuromuscular junction is ACh, but the transmitter substance released by the sensory neurons is an amino acid, probably glutamate. (Although beyond the scope of this chapter, many different transmitters are used by the nervous system— up to 50 or more, and the list grows yearly. Thus, to understand fully the process of synaptic transmission and the function of synapses in the nervous system, it is necessary to know the mechanisms for the synthesis, storage, release, and degradation or uptake, as well as the different types of receptors for each of the transmitter substances. The clinical implications of deficiencies in each of these features for each of 50 transmitters cannot be ignored. Fortunately, most of the transmitter substances can be grouped into four basic categories: ACh, monoamines, amino acids, and the peptides.)

A second major difference between the sensory neuron-motor neuron synapse and the motor neuron-muscle synapse is the amplitude of the postsynaptic potential. Recall that the amplitude of the postsynaptic potential at the neuromuscular junction was approximately 50 mV and that a one-to-one relationship existed between an action potential in the spinal motor neuron and an action potential in the muscle cell. Indeed, because the EPP must only depolarize the muscle cell by approximately 30 mV to initiate an action potential, there is a safety factor of 20 mV. In contrast, the EPSP in a spinal motor neuron produced by an action potential in an afferent fiber has an amplitude of only 1 mV.

The small amplitude of the EPSP in spinal motor neurons (and other cells in the CNS) poses an interesting question. Specifically, how can an ESP with an amplitude of only 1 mV drive the membrane potential of the motor neuron (i.e., the postsynaptic neuron) to threshold and fire the spike in the motor neuron that is necessary to produce the contraction of the muscle? The answer to this question lies in the principles of temporal and spatial summation.

Temporal and Spatial Summation

When the ligament is stretched (see Fig. 20), many stretch receptors are activated. Indeed, the greater the stretch, the greater the probability of activating a larger number of the stretch receptors present this process is referred to as recruitment. Activation of multiple stretch receptors is not the complete story, however. Recall the principle of frequency coding in the nervous system (see Chapter 4). Specifically, the greater the intensity of a stimulus, the greater the number per unit time or frequency of action potentials elicited in a sensory receptor. This principle applies to stretch receptors as well. Thus, the greater the stretch, the greater the number of action potentials elicited in the stretch receptor in a given interval and, therefore, the greater the number of EPSPs produced in the motor neuron from that train of action potentials in the sensory cell. Consequently, the effects of activating multiple stretch receptors add together (spatial summation), as do the effects of multiple EPSPs elicited by activation of a single stretch receptor (temporal summation). Both these processes act in concert to depolarize the motor neuron sufficiently to elicit one or more action potentials, which then propagate to the periphery and produce the reflex.

Temporal Summation. Temporal summation can be illustrated by considering the case of firing action potentials in a presynaptic neuron and monitoring the resultant EPSPs. For example, in Fig. 22A and B, a single action potential in SN1 produces a 1-mV EPSP in the motor neuron. Two action potentials in quick succession produce two EPSPs, but note that the second EPSP occurs during the falling phase of the first, and the depolarization associated with the second EPSP adds to the depolarization produced by the first. Thus, two action potentials produce a summated potential that is 2 mV in amplitude. Three action potentials in quick succession would produce a summated potential of 3 mV. In principle, 30 action potentials in quick succession would produce a potential of 30 mV and easily drive the cell to threshold. This summation is strictly a passive property of the cell. No special ionic conductance mechanisms are necessary.

A thermal analog is helpful to understand temporal summation. Consider a metal rod that has thermal properties similar to the passive electrical properties of


Differences Between EPSP and Action Potential

Neuroscience has captivated the interest of many. It is a study on how the nervous system works and how the body is able to respond with different stimuli. The body itself contains chemicals which enable us to function and survive in this challenging environment. The brain is in command of the whole body and tells us what we need to do or how to react. It is the general of our body with its minions, the neurons. Neurons communicate with each other and send the messages to the general. With information at hand, the brain general can process new tactics on how to counter such feats. Most often, EPSP and action potential are involved in generating specific actions. The difference between EPSP and action potential will be elaborated upon in this article.

“EPSP” stands for “excitatory postsynaptic potential.” When there is a flow of positively charged ions towards the postsynaptic cell, a momentary depolarization of the postsynaptic membrane potential occurs. This phenomenon is known as EPSP. A postsynaptic potential becomes excitatory when the neuron is triggered to release an action potential. The EPSP is like the parent of the action potential since it is created when the neuron is triggered. There can be EPSP when there is a decrease in the outgoing positive ion charges. We call the trigger the excitatory postsynaptic current, or EPSC. EPSC is the flow of ions that causes EPSP.

In a single patch of postsynaptic membrane, multiple EPSPs can likely occur. EPSPs have an additive effect which means that the sum of all the individual EPSPs will result in a combined effect. Greater membrane depolarization takes effect when there are larger EPSPs created. The larger the EPSPs become, the more it reaches the limit of firing an action potential. The amino acid glutamate is the neurotransmitter associated with EPSPs. It is also the main neurotransmitter of the vertebrates’ central nervous system. Amino acid glutamate is then called the excitatory neurotransmitter.

Action potential is fired by EPSP. It is a momentary event wherein the cell’s electrical membrane potential instantly rises and falls. A consistent trajectory then follows. In neurons, action potentials are also called nerve impulses or spikes. A sequence of action potentials is called a spike train. Action potentials frequently occur in human cells since humans have neurons, endocrine cells, and muscle cells. When there is a signal, the neurons communicate with each other reaching EPSP until it needs to fire an action potential. Voltage-gated ion channels produce action potentials. These channels lie inside the plasma membrane of the cell. There is a phase called resting potential. When the membrane potential is nearing the resting phase, the voltage-gated ion channels are shut, but they immediately open when there is an increase in the membrane potential value. Sodium ions will flow when these channels open which further increases the membrane potential. As membrane potentials increase, more and more electric current flows. There are two basic types of action potentials in animal cells: voltage-gated sodium channels and voltage-gated calcium channels. Voltage-gated sodium channels last for about less than one millisecond while voltage-gated calcium channels last for about a hundred milliseconds or even longer.

“EPSP” stands for “excitatory postsynaptic potential.”

Excitatory postsynaptic potential occurs when there is a flow of positively charged ions towards the postsynaptic cell, a momentary depolarization of postsynaptic membrane potential is created.

Action potentials are also called nerve impulses or spikes.

A postsynaptic potential becomes excitatory when the neuron is triggered to release an action potential.

Action potential is a momentary event wherein the cell’s electrical membrane potential instantly rises and falls.


Www.neuron.yale.edu

(exp(-t/tau2) - exp(-t/tau1)). How do experienced modelers fit EPSP/IPSP data to synapse parameters, and which synaptic mechanism you use?
Thank you!

Re: Fitting time constants for EPSPs

Post by ted » Tue Apr 24, 2012 9:13 pm

The time constant parameters in ExpSyn and Exp2Syn govern the time course of the synaptic conductance. Your observations, however, are descriptions of membrane potential time course, not the same thing at all. I don't know what you mean by "rise time"--is it 10-90 rise time, 20-80, or what? And half-width is only a rough guide to the time course of the PSP waveform, because it doesn't say whether the entire PSP is well approximated by two time constants, or whether three or more are required.

If you know that your PSP is small enough that the electrical properties of the cell can be treated as approximately linear over that range of membrane potentials, then the time course of the PSP can be interpreted as the convolution of the actual synaptic current and an impedance. If the PSP was observed at the same point at which the synapse was located, the impedance is the input impedance of the cell at that point. If the synapse was located at point A, but the PSP was observed at some other point B, the impedance is the transfer impedance between A and B. For many mammalian central neurons, the local response to an injected current step applied by patch clamp is well described by a single exponent, so the input impedance (and perhaps the transfer impedance as well) is described by a single exponent. For such a cell, a synaptic current with a very fast rise (smaller than 0.5 ms, e.g. produced by an AMPAergic synapse) and a monoexponential decay will generate a PSP that is described by two time constants--but neither of them will be exactly the time constant of the synaptic conductance. Similarly, a biexponential synaptic current--e.g. produced by a GABAergic synapse--will generate a PSP that is described by three time constants, none of which will be the time constants of the synaptic conductance itself.

First, start with the cleanest experimental data you can get. Best would be voltage clamp recording of the current produced by a synapse very close to the location of the clamp electrode. This is your best indication of the actual time course of synaptic current. Then you need to know the driving force for synaptic current entry ("reversal potential") and the clamp's holding potential. From these you can determine the time course of synaptic conductance itself. That's the gold standard. There's not a lot of that kind of data floating around, and it's scattered here and there in the experimental literature.

If the clamp and synapse are at different locations in the cell, and you happen to have detailed morphometric data from the cell, and a good estimate of the cytoplasmic and membrane properties of the cell, you could construct a computational model of the cell (under current or voltage clamp, depending on what the original experimental conditions were), then tinker with the synaptic mechanism's parameters until the simulated PSP or PSC is a close match to the experimental observation. This is more work and produces a result that is a much more indirect indication of the dynamics of the synaptic conductance.


Watch the video: Excitatory Post Synaptic Potential EPSP. Easy Flowchart. Physiology (January 2022).