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Advan. Physiol. Edu. 25: 1-12, 2001;
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ADV PHYSIOL EDUC 25:1-12, 2001
© 2001 American Physiological Society

Innovations and Ideas

BASIC PRINCIPLES OF SYNAPTIC PHYSIOLOGY ILLUSTRATED BY A COMPUTER MODEL

Michael J. Davis

Department of Medical Physiology, Texas A&M University System Health Science Center, College Station, Texas 77843


   Abstract
TOP
 Abstract
Introduction
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A computer model is described that simulates many basic aspects of chemical synapse physiology. The model consists of two displays, the first being a pictorial diagram of the anatomical connections between two presynaptic neurons and one postsynaptic neuron. Either or both of the presynaptic cells can be stimulated from a control panel with variable control of the number of pulses and firing rate; the resulting presynaptic action potentials are animated. The second display plots the membrane potential of the postsynaptic cell versus time following presynaptic stimulation. The model accurately simulates temporal and spatial summation when the presynaptic cells are arranged and stimulated in parallel and simulates presynaptic inhibition when they are arranged and stimulated in series. Excitatory and inhibitory postsynaptic potentials can be demonstrated by altering the nature of the ionic conductance change occurring on the postsynaptic cell. The effects on summation of changing length constant or time constant of the postsynaptic cell can also be illustrated. The model is useful for teaching these concepts to medical, graduate, or undergraduate students and can also be used as a self-directed computer laboratory exercise. It is available for free download from the internet.

Key words: excitatory postsynaptic potential; inhibitory postsynaptic potential; time constant; length constant; accommodation; temporal summation; spatial summation


   Introduction
TOP
 Abstract
 Introduction
METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The transmission of information across a chemical synapse is a basic concept taught in most physiology courses (2, 3). The usual method of teaching this topic involves a sequential description of pre- and postsynaptic events using static illustrations to indicate how several factors interact to determine the summation of postsynaptic potentials. Laboratory demonstrations of these processes are difficult and expensive as they require live neurons impaled with glass microelectrodes. My objective was to develop a computer model to simulate many basic properties of the chemical synapse. The model needed to be appropriate for a laboratory exercise for first-year medical and graduate students. Additionally, it needed to demonstrate realistic responses of neuron-to-neuron synapses, including temporal and spatial summation, excitatory and inhibitory potentials, and the influences of the membrane time constant and length (space) constant on the degree of summation.

This article descibes a computer model that fulfills these criteria. Surprisingly, it is also effective as a dynamic classroom teaching aid. Although several other computer models on synaptic physiology are commercially available, this model is available in Macintosh and Windows versions for free distribution over the internet to interested faculty and students. Also available is a detailed worksheet that can be used as a self-directed laboratory exercise.


   METHODS
TOP
 Abstract
 Introduction
 METHODS
RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

Software.
All components of the model were developed using LabView (version 4.0, National Instruments, Austin, TX). The source code was subsequently complied as run-time (stand-alone) code capable of executing on computers without the LabView Development System. The program consists of a single "virtual instrument." Testing and development were performed on a 300 MHz Macintosh PowerPC computer and a 233 MHz Dell computer. The model will also run on slower hardware supporting either platform. A control has been added to enable adjustment of the drawing time (1 = fast, 100 = slow) so that the animation speed can be matched to the power of the computer being used.

The layout of controls and graphs is optimized for display on a color monitor supporting 832 x 624 or 800 x 600 resolution. The source code occupies ~450 kb of disk space, whereas the compiled code with embedded libraries occupies ~2.5 Mb of disk space and requires 6 Mb of system memory to execute. Macintosh and Windows versions, along with the worksheet found in the APPENDIX, can be downloaded from the following internet address: (http//mphywww.tamu.edu/davis/models/synapse.html.)

Displays.
After the model has loaded, a menu bar at the top of the screen controls program execution. The model initially loads, runs once, then stops. The "run" button, an arrow-shaped button in the upper left corner, is used to run the model again. In typical use, the stimulus controls are adjusted with the model off, then the run button is pressed and the displays are updated. The model can also be started with the button adjacent to the run button. This "continuous run" mode repeatedly executes the program, allowing changes to be made to any of the parameters "on-the-fly." The rate at which the displays are updated in this mode can be adjusted using the "display speed" control in the lower right corner. The model can be halted at any time using the "stop" button in the menu.

Two display windows appear on the screen (Fig. 1) below the menu bar. On the left is a pictorial diagram of the anatomical connections between two presynaptic neurons (cells A and B) and one postsynaptic neuron (cell C). A diagram of a recording electrode placed near the axon hillock of cell C indicates the site of membrane potential (Em) measurements. Below this display are located various controls to alter the stimulus parameters, the anatomical arrangement between the cells, and membrane properties of the postsynaptic cell. The display on the right shows the change in Em ({Delta}Em) of cell C as a function of time.



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  		FIG. 1 The main display window of the model is shown. An animated view of pre- and postsynaptic cell firing is at the top left. Bottom left: controls for stimulation of the presynaptic cells and for changing the properties of the postsynaptic cell membrane. The graph to the right shows the change in membrane potential (Em) at the axon hillock of cell C. In this example, a single action potential in cell A is indicated by the darker appearance of axon A, and the resulting EPSP on cell C is indicated by the 2-mV depolarization shown on the Em-vs.-time graph.

 
The default settings for the model are set to stimulate one presynaptic cell (cell A) with one pulse at the lowest (firing) rate. Cell A briefly flashes red when the model starts up, or when the run button is pressed, and the Em display shows the associated excitatory postsynaptic potential (EPSP) on cell C, which has an amplitude of 2 mV and duration of 2 ms. The timing of the presynaptic stimulus pulses is also marked on the Em versus time graph by gray pulses just below the Em trace.

Calculation of postsynaptic Em.
In the absence of presynaptic stimulation, the resting potential of the postsynaptic cell is stable at -70 mV. Subthreshold synaptic potentials, i.e., EPSPs, inhibitory postsynaptic potentials (IPSPs), or any combination of the two, are seen as time-dependent deviations from the resting potential. Depolarizing stimuli that summate to exceed the postsynaptic cell threshold of -60 mV result in an action potential on the postsynaptic cell.

The program logic flow is illustrated by the diagram in Fig. 2. After presynaptic stimulation, the time course of the {Delta}Em is approximated using the equation: {Delta}Em = a x t x exp(-a x t), where a is the time constant and t is time. This parameter is calculated for both presynaptic inputs. Their sum is computed at each point in time for each of 50 time intervals and added to the value of the resting Em. The degree of summation of the two individual postsynaptic events is determined by, and proportional to, the value of the length constant for cell C, where 1 = complete summation and 0 = no summation. If the postsynaptic cell Em reaches its threshold value of -60 mV, the explosive voltage change that follows is computed by adding to Em a stored array of values generated from Hodgkin-Huxley-style equations (1) used in a separate model of the neuronal action potential (unpublished observations).



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  		FIG. 2 Flow diagram of the program logic. For details, see text. EPSP, excitatory postsynaptic potential; AP, action potential.

 
Animation.
To animate the sequence of pre- and postsynaptic cell firing, a simple LabView trick is employed. Separate layers of drawings, colored or clear, are made for each of the neuronal objects using Photoshop (Adobe Systems) and exported to LabView as PICT objects. These are imported into LabView and aligned on the front panel display as elements of individual cluster controls for which attribute nodes are created. Each of the nodes is then controlled programmatically by switching on or off its visibility attribute.


   RESULTS
TOP
 Abstract
 Introduction
 METHODS
 RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
The model is capable of simulating many aspects of chemical synaptic physiology, including temporal and spatial summation, presynaptic inhibition, the influence of different postsynaptic receptor ionic conductances, and the effect of changing postsynaptic membrane time constant or length constant.


Temporal summation.
Repeated stimulation of cell A (with cell B silent) at the lowest firing rate (1) results in multiple, successive, 2-mV EPSPs on cell C that decay before any summation occurs. An example using four pulses is shown in Fig. 3A. Because cell C repolarizes completely before the next presynaptic action potential arrives, it never reaches a value that is more positive than -68 mV. Under the same conditions, an increase in firing rate (to an arbitrary value of 7 in Fig. 3B) results in partial temporal summation of the individual EPSPs on cell C, causing the Em of cell C to depolarize to about -66 mV. Further increases in the firing rate or the number of pulses will produce even more summation. If the model is placed in continuous run mode, it will continuously redraw and recalculate these changes as the firing rate for cell A is varied.



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  		FIG. 3 Demonstration of temporal summation when cell A is stimulated at a high firing rate (B) but not a low firing rate (A). Cell B is silent. In each panel, the top halves of the controls have been repositioned near the Em-vs.-time displays to conserve space.

 
Spatial summation.
To demonstrate spatial summation, it is first advisable to reset the controls, either by manually returning the "# pulses" back to 1 or by selecting the "reinitialize all to default" from the control menu at the top of the screen. If cell B is now set to be stimulated simultaneously with cell A (using 1 pulse at the lowest firing rate), the two associated EPSPs (2 mV each) summate completely to produce a 4-mV depolarization of cell C (Fig. 4A). It may not be immediately obvious to students that spatial summation has occurred in this case as opposed an increase in the amplitude of a single EPSP by some other undefined mechanism. However, spatial summation can be more clearly detected by adding a slight delay to the pulse in cell B (to 1.6) in Fig. 4B; this shift is indicated by a shift in the timing marks of the two pulses below the Em trace. Now it becomes clear that two individual postsynaptic events are summating. Putting the model in continuous run mode allows the degree of spatial summation to be controlled on-the-fly by alterations in the value of "pulse delay."



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  		FIG. 4 Demonstration of spatial summation when cells A and B are stimulated at exactly the same point in time (A) or when cell B is stimulated 0.6 ms after cell A (B). Spatial summation occurs in both instances but is more easily visible in B.

 
By controlling the number of pulses and the respective firing rates of cells A and B, virtually any combination of temporal and spatial summation can be demonstrated. This is an effect that is very difficult to demonstrate or appreciate using a static figure.

Changes in postsynaptic receptor conductance.
Whether presynaptic stimulation results in an EPSP or IPSP on the postsynaptic cell depends on the nature of the postsynaptic receptor. So-called "excitatory transmitters" (a term that is actually a misnomer) typically interact with postsynaptic receptors, ligand-gated ion channels, that result in equal increases in postsynaptic cell Na+ and K+ conductance (3). The nicotinic ACh receptor is one example. This is the default setting of the model and produces the EPSP shown in Fig. 1. If the conductance of the postsynaptic membrane at the termination of cell A is set to "K," the Em of cell C will move toward the K+ equilibrium potential (EK) when cell A is stimulated. Because EK is normally more negative than the resting Em of cell C, the result is an IPSP, as illustrated by the -2-mV IPSP in Fig. 5A. If the receptor conductance is set to "K + Cl," simulating the action of a transmitter that produces an equal increase in postsynaptic K+ and Cl- conductance, the amplitude of the resulting IPSP is reduced from -2 mV to approximately -1 mV (arrow in Fig. 5A). To allow comparisons between these two parameter sets, the button "remember previous trace" needs to be set to "on" before the K + Cl conductance parameter set is executed, as illustrated in Fig. 5A. A lower amplitude EPSP will be produced if the equilibrium potential for Cl- is equal to the resting Em (-70 mV), as Cl- movement will act to anchor Em at its resting value and partially offset the hyperpolarizing effect of K+ movement through the same channel. Postsynaptic conductance can be switched between a number of different settings: "Na," "Na + K," K, K + Cl, or "Cl," each of which produces an appropriate change in the relative magnitude and sign of the resulting postsynaptic potential.



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  		FIG. 5 Effect of changing the nature of the postsynaptic receptor conductance change (i.e., receptor type). Same conditions as in Fig. 1 except that the postsynaptic receptor conducts K+ ions in this example, producing an inhibitory postsynaptic potential (IPSP) rather than an EPSP (Fig. 1). This is shown by the darker trace in A. Setting the conductance change to "K + Cl" (updated controller is not shown) results in a reduced IPSP amplitude (lighter trace marked by arrow in A). B: when both cell A and cell B are stimulated with a 1-ms delay between them, cell A causes an EPSP, whereas cell B causes an IPSP. The algebraic sum of these events produces the biphasic waveform shown. Note: in A, the "remember previous trace" feature was turned on to overlay the 2 traces.

 
Summation of EPSPs and IPSPs can also be demonstrated using the model, as shown in Fig. 5B. In this example, the transmitter released by cell A produces an EPSP on cell C, whereas the transmitter released by cell B produces an IPSP. If these events occur simultaneously (not shown), they will cancel exactly. If they occur slightly out of phase (by increasing pulse delay for cell B), this interaction becomes more obvious (Fig. 5B).

Effect of postsynaptic membrane time constant on temporal summation.
The value of the membrane time constant for cell C will determine the shape and duration of the EPSP resulting from presynaptic stimulation. This time constant is determined by a capacitance term, such that an increase in time constant decreases both the rate of depolarization and repolarization during the EPSP. Figure 6A illustrates this effect by comparing the shape of an EPSP resulting from identical single pulses in cell A before and after the time constant of cell C has been doubled from its arbitrary initial value of 0.4 (arrow in Fig. 6A).



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  		FIG. 6 Effect of increasing membrane time constant on the shape (time course) of an EPSP triggered by cell A (A). Dark line shows how both the time to maximum depolarization and the time to repolarization are lengthened by increasing the membrane time constant of cell C from 0.4 (lighter trace) to 0.8 (darker trace). B: the higher value for time constant results in temporal summation (dark trace) even at the lowest firing rate. For comparison, the lack of summation during the identical pulse protocol is shown by the lighter trace. Note: in both panels, the remember previous trace feature was turned on to overlay the 2 traces.

 
Postsynaptic neurons with high membrane time constants are known to exhibit enhanced temporal summation. This can be illustrated by using two pulses to stimulate cell A. With lower values for the time constant, the individual EPSPs do not summate, but they progressively do as the time constant is increased (arrow in Fig. 6B).

Presynaptic inhibition.
At least two types of presynaptic inhibition can occur physiologically (3). In both cases, a specific anatomical arrangement of the presynaptic cells is required. This can be demonstrated (see Fig. 7) if the "wiring" control is switched from "A-C" to "A-B," meaning that cell A now physically synapses on the terminal bouton of cell B. In presynaptic inhibition, an action potential traveling down the axon of cell A depolarizes the terminal bouton of cell B (another "presynaptic" cell with respect to cell C) just before an action potential travels down the axon of B. The action potential in cell A has no direct effect on cell C due to the lack of a direct anatomical connection (not shown here, but easily demonstrated using the model). When the two presynaptic action potentials are timed appropriately, accommodation (a form of voltage inactivation) may occur on cell B. The result is that the amplitude of the action potential at the terminal bouton in cell B is diminished slightly compared with normal, resulting in the opening of fewer voltage-gated calcium channels and less transmitter release from cell B. The resulting EPSP on cell C is thereby reduced in magnitude relative to its normal value (arrow in Fig. 7). Presynaptic inhibition can result either from the opening of an excitatory receptor-gated channel on cell B (as in Fig. 7) or from release of a transmitter such as GABA that increases Cl- conductance on the terminal bouton of cell B and thereby anchors the Em of cell B. These, again, are difficult concepts for many students to appreciate from static diagrams, and the model makes it easier to illustrate them.



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  		FIG. 7 Demonstration of presynaptic inhibition. When "wiring" is changed to "A->B," the anatomical arrangement between the cells changes so that cell A synapses directly onto the terminal bouton of cell B. Thus, when cell A fires alone, it does not produce an EPSP on cell C. When cell B fires alone, it produces a normal 2-mV EPSP on cell C. If cells A and B fire simultaneously (with A actually preceding B slightly), then the amplitude of the EPSP produced by cell B is reduced (arrow). Note: the remember previous trace feature was turned on to overlay the 2 traces.

 
Events at threshold.
When the controls of the model are set appropriately so that sufficient summation of postsynaptic potentials occurs, the Em of cell C may reach the threshold for firing an action potential. This is illustrated by the model as shown in Fig. 8. With "# pulses" set to 20, both presynaptic cells firing, and the firing rate of one of the cells set to a value of at least 9, an action potential is triggered on cell C. This minimal combination of temporal and spatial summation brings the Em of cell C to threshold. The animation shows this by briefly turning cell C dark at the point in time at which the action potential is initiated (the flash actually occurs at 2.6 ms under the conditions shown in Fig. 8). The corresponding graph shows the explosive change in Em for cell C during the action potential. The entire action potential cannot be shown on the same voltage scale required to resolve 1- to 2-mV EPSPs and IPSPs, but its presence is readily noted on both displays and is usually effective at regaining students’ attention during a lecture.



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  		FIG. 8 Behavior of model when summation of presynaptic input brings the Em of cell C to threshold for firing an AP. The animation shows that cell C has fired an AP, and this is also reflected in the Em trace of cell C. The lighter trace shows the result of settings that produced a subthreshold summation, using the remember previous trace feature to overlay the 2 traces.

 

   DISCUSSION
TOP
 Abstract
 Introduction
 METHODS
 RESULTS
 DISCUSSION
APPENDIX
 REFERENCES
 
This computer model simulates many basic physiological properties of the neuronal chemical synapse. A number of possible uses for it are envisioned: as a method to teach this subject to medical, undergraduate, or graduate students in a didactic setting, as an alternative to a supervised animal laboratory, or as a completely self-directed computer laboratory exercise.

The model has been used in at least four courses at Texas A&M University by faculty, medical students, graduate students, and undergraduate students. In each case, the student response has been positive, and their understanding of this topic has increased. To facilitate distribution and use of the model at other educational institutions, it is compiled in Macintosh and Windows versions and available for free download by faculty and students at the following internet address: http://mphywww.tamu.edu/davis/models/synapse.html. A comprehensive worksheet is provided in the APPENDIX and is also available for download as a Microsoft Word file.


   APPENDIX
TOP
 Abstract
 Introduction
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
REFERENCES
 
Computer Laboratory Worksheet (Synaptic Function)
I. Objective:
To help students better visualize basic principles of chemical synapse function.

II. Student Preparation for this Laboratory Exercise:
It is assumed that students have attended lectures on the appropriate subjects or done preliminary readings before doing this exercise. Students should at least know the definitions of the terms presynaptic, postsynaptic, temporal summation, and spatial summation before doing the laboratory exercise.

III. General Information:
The simulation program name is "Synapse.rt" and is located on PowerMac and Pentium-based computers in the College of Medicine, Learning Resource Center (LRC). The program may also be downloaded from the World Wide Web for use at home. The program may be run on computers with a processor speed of 40 MHz or greater.

IV. Start/Stop/Reset Directions:
Double-click on the "Synapse.rt" icon to load the program. After it loads, the program runs once to redraw the two displays. Run the program either by clicking on the "Run" button (->) in the upper left-hand corner of the program window or by selecting "Run" from the "Operate" menu at the top of the program page. The program can be stopped at any time by clicking on the stop button (stop-sign symbol) in the upper left-hand corner of the program window. If necessary, the model parameters can be reset to their initial conditions at any time by selecting "Reinitialize All to Default" from the "Operate" menu at the top of the screen.

Selecting "About" from the "Help" menu will pause the model and bring up a series of informational screens about the model and the experimental setup that would be used to make actual recordings in live neurons.

V. Orientation and Brief Description of the Model:
Load and start the program as described above. While the program is running, but before beginning the laboratory exercise, look at the computer screen and note that there are three general areas displayed on the screen. These areas include:

A. Animated Display of Neuronal Firing (top left side of screen):
On the left side of the screen is shown a pictorial diagram of the anatomical connections between two presynaptic neurons (cells A and B) and one postsynaptic neuron (cell C). A diagram of a recording electrode placed near the axon hillock of cell C indicates the site of membrane potential (Em) measurements.

The default settings for the model are such that when the program is first initiated, one presynaptic cell (cell A) will be stimulated with one pulse at the lowest stimulation (firing) rate. Cells A and B each synapse on the cell body of C. At any time, the user may pull down the "Operate" menu at the top of the program page and select "Reinitialize All to Default" to reset the program to the initial conditions.

B. Controls (lower left side of screen):
Below the animation are located various controls to alter the stimulus parameters, the anatomical arrangement between the cells, and the membrane properties of the postsynaptic cell. Each presynaptic stimulus will produce an action potential in the respective presynaptic cell that will travel down to that cell’s terminal bouton and release transmitter.

The controls are organized such that there are four for each presynaptic cell, two for the postsynaptic cell (C) and two general controls. The "Status" control for each presynaptic cell refers to whether that cell is being stimulated (by an external stimulator that is not shown) to fire an action potential. "Firing Rate" (rate) determines the interpulse interval if multiple stimuli are delivered to the presynaptic cell (1 = lowest rate, 10 = highest rate). "Pulse Delay" (delay) controls the timing between the stimulation of the two presynaptic cells. "Time Constant" and "Length Constant" control these properties for the membrane of cell C. "# Pulses" determines the number of stimuli delivered to the presynaptic cell(s) and can be used to fire a "train" of action potentials. "Wiring" controls the anatomical arrangement between the cells, i.e. whether cell A synapses on cell C or on cell B. It is only used to demonstrate presynaptic inhibition.

C. Em vs. Time Graph for Cell C (right side of screen)
The display on the right shows the change in Em of cell C as a function of time. This display provides quantitative information about the impact of presynaptic stimulation on the postsynaptic cell C. For this reason, it is more important than the animation display, but many students are less confused if they can see that the animation is synchronized with the change in the Em. The timing of the presynaptic stimulus pulses is marked on the Em-vs.-time graph by gray pulses just below the Em trace.

VI. Laboratory Exercise:
1. Temporal summation.
This exercise demonstrates how stimulation of a single presynaptic cell generates excitatory postsynaptic potentials (EPSPs) that summate over time.

RESET all variables and set cell A = fire. Click the "Run" button. Note the shape of the EPSP (a rapid rise in Em with exponential decay back to the resting potential). What accounts for this shape?      Why isn’t the Em change a square-shaped pulse like the stimulus pulse?     

Increase "# Pulses" = 4 and run the model. Note that a train of four action potentials (APs) travelling down cell A produces four individual EPSPs on cell C without any summation. Now sequentially increase the firing rate of A from 1 to 9 and RUN the model after each increase. Temporal summation should be observed; what is the maximum amplitude of the summed EPSP?      At the highest firing rate (=9), how many pulses are required to reach the threshold (-60 mV) for firing an AP on cell C?     (progressively increase the # pulses and RUN each time to find out; alternatively, run the model in "Continuous Run" mode while changing the number of pulses) What should happen to the Em tracing if the threshold is reached?     

2. Effect of Changing the Time Constant on Temporal Summation.
How does the time constant of the postsynaptic cell influence the degree to which EPSPs summate on the surface of the postsynaptic cell?

a. Keep all variables the same as they were at the end of exercise 1 (i.e. a rapid train of pulses firing on cell A that gives a large but NOT-QUITE-threshold EPSP on cell C (a 10- to 12-mV depolarization). Now change the time constant of cell C from 0.4 to 0.5. What is the effect?     

b. To observe the effect of changing time constant on a single EPSP, RESET all variables, set A = fire, # Pulses = 1. RUN. Change time constant and repeat. Describe how changing time constant alters the EPSP magnitude:     and EPSP shape:    .

3. Spatial summation.
This exercise demonstrates how stimulation of multiple presynaptic inputs can generate EPSPs that sum over distance.

RESET. Compare the amplitude of the EPSP on cell C when A fires one pulse vs. when A and B both fire one pulse in synchrony. A alone (set A = fire):     A + B (set A and B = fire):    

To more clearly observe that summation occurs, try increasing the delay of cell B to {approx} 1.4 ms: amplitude =    . At what value of Bdelay does no summation occur?     What is the maximum EPSP amplitude that can be achieved in this model with spatial summation alone (i.e. without increasing the # of pulses)?     Why?     

4. Effect of Changing the Length Constant on Spatial Summation.
RESET; A = fire, # Pulses = 1. Compare the EPSP amplitude with the length constant set to 1.0 vs. 0.1:     . Set Pulses = 3 and Arate = 9, RUN. Compare the maximum EPSP amplitude with length constant set to 1.0 vs. 0.1:     

[note: changing the length constant of cell C would not affect EPSP amplitude directly under the terminal bouton of A, but remember that the Em tracings are being measured at the axon hillock; therefore, changing the length constant affects how the amplitude of the EPSP changes as it spreads from the bouton to the axon hillock].

5. Combinations of Spatial and Temporal Summation.
RESET, set A = fire, Pulses = 5, Arate = 8, RUN. What is the maximum EPSP amplitude?     What type of summation is involved?     Now add excitatory input from cell B (B = fire, Brate = 5). What is the maximum EPSP amplitude now?    . Progressively increase Brate to determine at what minimal rate an AP fires on cell C:    . Keep these settings and then increase Bdelay to 1.2 ms (this should change the degree of summation slightly but enough to prevent an AP from firing). What happens?    

For another example of the interaction between temporal and spatial summation, RESET, set A = fire, B = silent, Arate = 9, Pulses = 5, tau = 0.6 then RUN. Note that threshold is not quite reached, but if cell B fires even once (set B = fire to see this), an AP fires on cell C.

[This shows how cell B could act as an ON-OFF gate to control "information" transfer from cell A to cell C, i.e. if B is off, then repeated bursts of firing by cell A do not elicit APs from cell C, but if B fires a pulse during that time (Bdelay = 1.0–2.0 ms), an AP fires on C. Try to verify this].

6. Effects of Changing Postsynaptic Conductance (transmitter/receptor type).
[it may be useful to run the program in continuous loop mode for exercises 6 and 7].

a. RESET, set A = fire. Measure the amplitude of the EPSP:    and the default conductance (cond) setting:    

This could simulate the effects of ACh as the transmitter released from cell A, because ACh typically increases the membrane conductance of the postsynaptic cell to both K and Na ions. To illustrate how this can cause a depolarization (despite K efflux), compare the size of this EPSP with one resulting from a selective increase in gNa (i.e. change Acond = "Na"):    

b. Now set Acond = "Cl" and note the magnitude of the EPSP:     Explain the difference:     Compare this with the inhibitory postsynaptic potential (IPSP) amplitude when Acond = "K + Cl":     or when Acond = "K"     If changes in gCl have "no effect" on Em, why is the IPSP amplitude smaller when Acond = "K + Cl" than when Acond = "K" alone?    

7. Presynaptic inhibition.
Demonstration of this phenomenon requires an anatomical change in the configuration of the cells. RESET all variables, then set "Wiring" = A -> B and RUN once.

a. Set A = fire, B = silent. Now what effect does cell A firing have on the Em of cell C?      Why?      Now set A = silent, B = fire. You should see a "normal" EPSP on cell C. What happens when cell A fires also (set A = fire)?      What mechanism underlies this phenomenon?      Keep the settings the same. What happens if the Bdelay is progressively increased to 3.0?      Why?     


   Acknowledgments
 
The author thanks Dan Phillips at National Instruments for easing the licensing restrictions and thereby allowing free distribution of reasonable numbers of this program, along with complied LabView libraries, to faculty and students who contact this website. Judy Davidson provided assistance with proofreading and printing. Medical and graduate students at Texas A&M College of Medicine provided valuable assistance in testing early versions of the model.


   Footnotes
 
Address for reprint requests and other correspondence: M. J. Davis, Rm. 346 Reynolds Medical Building, Texas A&M University HSC, College Station, TX 77843.

Received for publication February 23, 2000. Accepted for publication December 7, 2000.


   REFERENCES
TOP
 Abstract
 Introduction
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

  1. Hogdkin AL and Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117: 500–544, 1952.
  2. Katz B. Nerve, Muscle and Synapse. New York: McGraw-Hill, 1966.
  3. Matthews GG. Cellular Physiology of Nerve and Muscle. Palo Alto, CA: Blackwell, 1986.




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