Neurons in the mammalian central nervous system typically receive synaptic inputs from many other neurons. For example, each individual human cerebellar Purkinje neuron is estimated to receive more than 100,000 excitatory synaptic contacts from granule cells, and additional contacts from local circuit inhibitory interneurons and the powerfully excitatory climbing fiber ( Ito 1984 ). Although Purkinje neurons are an extreme example of synaptic convergence, individual neurons that receive thousands of synaptic inputs are not unusual in the mammalian CNS. As pointed out by Pare and colleagues (1998) , the average cortical pyramidal neuron receives about 10,000 synaptic inputs, and most of them are from other cortical neurons, which typically fire about 10 spikes per second in awake animals. Thus, the average cortical pyramidal neuron can be expected to receive roughly 100,000 synaptic events every second. Even for globus pallidus neurons, which have significantly less membrane surface area and receive most of their synaptic contacts from striatal medium sized spiny neurons (which have low average spike rates in vivo), the total number of synaptic events received per second is expected to number in the thousands.

The potential significance of this ongoing synaptic activity for a neuron can be illustrated with a hypothetical example. Imagine a neuron that receives 5,000 excitatory and 500 inhibitory synaptic contacts, each active at an average rate of 10 impulses per second. If each excitatory input had a unitary peak conductance of 500 pS, each inhibitory input a peak conductance of 2 nS, and physiologically realistic time constants, the average total synaptic conductance applied to the neuron could surpass 300 nS. If a conductance of this size were present in a single physical location (a ‘point conductance’), every 10 millivolts of difference between the neuron’s membrane potential and the net reversal potential of the combined synaptic conductance would generate 3 nA of synaptic current—which is a lot of current. Although this example exaggerates the actual effect of in vivo synaptic conductances by ignoring their spatial distribution, it illustrates the point that for most types of neurons, the total membrane conductance level in vivo (1) is quite high, and (2) fluctuates independently of the membrane potential because it is dominated by synaptic rather than intrinsic (i.e. voltage or ion gated) conductance mechanisms. The existence of high levels of ongoing, fluctuating synaptic input to neurons in vivo has now been clearly demonstrated using intracellular electrophysiological recordings from laboratory animals.

There are many good reasons to include realistic patterns of synaptic input in computer simulations of neurons and neural circuits, but two of the reasons are particularly relevant to our work. The first is that we want to better understand how the morphological and biophysical properties of neurons contribute to their computational capabilities, and to address this issue we perform many electrophysiological experiments using the acute brain slice preparation, where we can manipulate biophysical properties of neurons in a controlled way. For example, we may examine the input-output properties of a neuron under ‘normal’ conditions, and then apply an agent that blocks a specific ion channel and assess how the loss of that channel type affects the cell’s function. This is a standard experimental method, but it suffers from the problem that unlike neurons in vivo, most of which are under the influence of substantial, fluctuating net synaptic conductances at all times, neurons in acute brain slices and most other in vitro preparations receive comparatively little synaptic input. Furthermore, what synaptic input does exist is often blocked during experiments in order to focus on the intrinsic biophysical properties of the neurons.

As an example, consider some experiments I did as a graduate student working with Dr. Peter H. Reinhart. The experiments involved blocking small conductance calcium-activated potassium channels (SK channels) in cerebellar Purkinje neurons in acute slices of rat brain. To avoid potential presynaptic effects of the SK channel blocker, fast synaptic transmission was blocked during the experiments. We observed that when SK channels were blocked, Purkinje neuron firing behavior changed dramatically ( Edgerton and Reinhart 2003 ), and we concluded that in Purkinje neurons, SK channels are critical determinants of both the rate and regularity of spiking (Fig. 1). Our conclusions were well supported for Purkinje neurons in vitro; however, whether or not a blocker of SK channels would have similar effects in vivo, where the conductance due to SK channels would be only a small fraction of the net synaptic conductance, is a question that remains to be answered.

Figure 1: Small conductance K (Ca2+) channels (Sk channels) regulate the firing rate of Purkinje neurons in vitro – but is this also true in vivo? Figure adapted from ( Edgerton and Reinhart 2003 )

Many similar experiments have been carried out in slice preparations or cultured neurons, and in most cases the extent to which the in vitro results would translate to the in vivo condition remains uncertain. However, dynamic clamp experiments investigating the role of SK channels in deep cerebellar nucleus neurons (Volker Gauck and Dieter Jaeger, unpublished data), and modeling studies on the influence of ion channels in the presence and absence of background synaptic input ( Destexhe and Pare 1999 ), suggest that only some of the pharmacological effects observed in vitro will hold true in the presence of in vivo synaptic input, meaning that the in vitro data should be interpreted with some caution.

Part of the problem is that there is no simple way to generate large amounts of asynchronous, spatially distributed, ongoing synaptic input to a neuron in vitro without directly affecting the intrinsic properties of the neuron. For example, electrical stimulation of presynaptic axons could be used to drive synaptic inputs, but would typically result in synchronous activation of a restricted subset of inputs. Certain pharmacological manipulations, such as elevating the external potassium concentration or bath application of low concentrations of the potassium channel blocker 4-aminopyridine (4-AP) have been shown to induce high levels of spontaneous synaptic input in brain slice preparations ( Avoli et al. 2002 ). But in most cases these manipulations will directly alter the neuron being studied, such that the ‘control’ condition no longer captures the normal electrophysiological properties of the cell.

This brings up an important point about modeling: in a multicompartmental model of a neuron, all of the synaptic inputs and intrinsic conductances can be controlled explicitly, allowing any pattern of synaptic input to be tested. The influence of a particular ion channel can then be assessed in simulations of both in vitro and in vivo conditions. Although the model will never be more than an approximation of the real neuron, a model that replicates the in vitro data accurately can make strong predictions about the in vivo condition because the only change is the addition of background synaptic input, which can be simulated with a reasonably high degree of precision.

The second reason why in vivo-like synaptic input patterns are particularly relevant to our work is that we want to understand what types of computations single neurons carry out. Since single neuron computations involve transforming complex, spatially distributed synaptic input trains into single output trains, it is obviously necessary to include such patterns of synaptic input in the models. Because every input can be controlled explicitly, modeling may offer the best way of beginning to address this difficult question.

There are multiple ways to do just about anything in GENESIS, and synaptic input is no exception. But we find the method presented here to be convenient and effective. We use a combination of three standard GENESIS objects for our synapses, each of which is described in detail in the online GENESIS manual at the following link: http://www.genesis-sim.org/GENESIS/Hyperdoc/Manual.html

Steps involved in setting up the simulations:

First, the characteristics of the individual synaptic conductances—peak size, kinetic properties, and reversal potential—are defined using the synchan object. Example code showing the creation of a synchan element called AMPA is shown below. The synchan object also allows the user to set a frequency of activation, but we don’t use this mechanism, so the frequency field of all of our synchan elements is set to 0. We begin by making a single, template synchan element and placing it into a neutral element called library. Individual, independent synchan elements can then be copied from this template to different compartments of the model cell using the copy command, creating a population of synaptic inputs like a real neuron would receive. Since the different instances of the synchan are independent of one another, their properties can be set individually so that the population of synapses is heterogeneous. Synchan elements are conductances that must be taken into account by the simulation solver, so they are placed within compartments in the cell path just like tabchannels and other conductances.

GENESIS script defining AMPA-type conductances

//GENESIS script to define AMPA-type conductance
function make_AMPA_syn
	// make AMPA-type synapse
	if (!({exists AMPA}))
		create synchan AMPA
	end
	// assign specific synapse properties
	setfield AMPA Ek {E_AMPA} 
	setfield AMPA tau1 {tauRise_AMPA} 
	setfield AMPA tau2 {tauFall_AMPA} 		
	setfield AMPA gmax {G_AMPA} 
	setfield AMPA frequency 0 
end

//GENESIS script to create library template objects

         
//First, include my synapse and channel function files
include Syns.g
include Chans.g

         
//Check if library already exists
if (!{exists /library})
        	create neutral /library
        	disable /library
end

         
//Push library element, make conductance elements, pop library
pushe /library
	make_AMPA_syn
	make_G_Na
	make_G_K
pope

Second, the activation times of each synapse are determined using timetable objects. A separate timetable is needed for every synapse that is to be independent; if two synchan objects share the same timetable, they will be active in perfect synchrony. Each timetable is simply a list of times at which any connected synapses will be activated. The list of times can be a pseudorandom distribution with a specified mean and shape (exponential or gamma distribution), or it can be read from an ascii text file. Timetables are maintained in a separate location outside the cellpath, because they don’t need to be handled by the solver. We create a separate neutral element called ‘inputs’ to hold these objects.

Figure 2: Element tree for a simulation of a 2-compartment model (with ‘soma’ and ‘dendrite’ compartments). Each colored box represents a GENESIS element. Yellow boxes represent the essentials of the model—its morphological and physiological features. Green boxes represent elements that control synaptic input timing. Pink boxes represent template objects that can be copied from the library and inserted into the model (at which point they would become yellow boxes).

Last, each timetable needs to be connected to the synapse(s) it will control, and to do this we use the spikegen object. A separate spikegen element is created for each timetable and placed in the same location. Whenever the simulation run time matches a time in the timetable’s list, the timetable sends a message to the spikegen and the spikegen activates the synchan.

Pseudocode for all compartments receiving input:

//Using the same random seed means you get the same timetables next time too.
randseed 78923456 
//Loop: for each compartment that receives a synapse…
    1. copy the AMPA synapse from the library to the compartment 
    2. addmsg: connect the synaptic conductance to the compartment with 
	CHANNEL and VOLTAGE messages

         
    //set up the timetable
    1. create a unique timetable object for this compartment’s AMPA synapse	
    2. set timetable fields with setfield:			
	method: 	
1 = exponential distribution of intervals
		2 = gamma distribution of intervals
		3 = regular intervals
		4 = read times from ascii file
	meth_desc1: mean interval (= 1/rate) 
	meth_desc2: refractory period (we use 0.005) 
	meth_desc3: order of gamma distribution (we use 3)	
    3. call /inputs/Excit/soma/timetable TABFILL

         
//set up spikegen
      create a unique spikegen object for this compartment’s synapse
      set the spikegen fields with setfield
	output_amp: 1 
	thresh 0.5
      //the spikegen tells the synapse when to activate based on the timetable
      addmsg from timetable to spikegen: type = INPUT, message = activation
      addmsg from the spikegen to the compartment’s AMPA element, type = SPIKE
	        		
         
// Next loop iteration or END

Since separate timetables and spikegens are needed for each independent synapse, it is easiest to set these up in a for loop. Example code for such an operation can be found in the read_STN_syns file , listed below.

Example code to create a while loop in GENESIS:

/*
Script to add STN synaps es (AMPA synapses from subthalamic nucleus) to GP model. 
The compartments that re ceive the inputs must be listed in an ascii text file.
*/
str STNfilename = “stn_syns.asc”
randseed 78923456 
str stncompartment
//create input element t ree outside of the cell path
if (!{exists /inputs})
      create neutral /inputs
end
create neutral /inputs/STN
num_STN = 0
// Open the file with th e list of compartment names
// File MUST NOT have an y blank lines at the end, or function will fail.
openfile {STNfilename} r
stncompartment = {readfile {STNfilename}}
//cycle through STN inpu t compartments
while (! {eof {STNfilename}})
      num_STN = {num_STN} + 1
      //Add AMPA synapse from library
      copy /library/AMPA {cellpath}/{stncompartment}/AMPA
      addmsg  {cellpath}/{stncompartment}/AMPA \ 
             {cellpath}/{stncompartment} CHANNEL Gk Ek
      addmsg  {cellpath}/{stncompartment} \
             {cellpath}/{stncompartment}/AMPA VOLTAGE Vm
      //set up timetable
      create neutral /inputs/STN/{stncompartment}
      create timetable /inputs/STN/{stncompartment}/timetable
      if ({STN_rate} > 0)
             setfield /inputs/STN/{stncompartment}/timetable        \
                   maxtime {rundur} act_val 1.0 method 2            \
                   meth_desc1 {1/{STN_rate}} meth_desc2 0.005 meth_desc3 3     
             call /inputs/STN/{stncompartment}/timetable TABFILL
      end
      //set up spikegen
      create spikegen /inputs/STN/{stncompartment}/spikegen
         setfield /inputs/STN/{stncompartment}/spikegen                   \
             output_amp 1 thresh 0.5
      //connect timetables to AMPA synapses
      if ({STN_rate} > 0)
             addmsg /inputs/STN/{stncompartme nt}/timetable \
                   /inputs/STN/{s tncompartment}/spikegen INPUT activation
             addmsg /inputs/STN/{stncompartme nt}/spikegen \
                   {cellpath}/{st ncompartment}/AMPA SPIKE
      end
      
      // get next compartment name
      stncompartment = {readfile {STNfilename}}
end
closefile {STNfilename}

In summary, it is important to keep in mind that in the mammalian central nervous system, neurons typically receive large amounts of ongoing, fluctuating synaptic conductance input, and that this conductance can significantly alter the integrative properties of the neurons. As such, experiments done using in vitro preparations lacking synaptic input should be interpreted with some caution and supplemented with modeling where possible. Complex, in vivo-like patterns of synaptic input can easily be implemented in multicompartmental computer simulations with the GENESIS software package. The main points of this tutorial can be summarized as follows:

Avoli M, D'Antuono M, Louvel J, Kohling R, Biagini G, Pumain R, D'Arcangelo G, Tancredi V (2002). Network and pharmacological mechanisms leading to epileptiform synchronization in the limbic system in vitro. Prog Neurobiol 68: 167-207.

Destexhe A, Pare D (1999). Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J Neurophysiol 81: 1531-1547.

Edgerton JR, Reinhart PH (2003). Distinct contributions of small and large conductance Ca2+-activated K+ channels to rat Purkinje neuron function. J Physiol 548: 53-69.

Ito M (1984). The Cerebellum and Neural Control. Raven Press, New York.

Koch C (1999). Biophysics of Computation. Oxford University Press, New York.

Pare D, Shink E, Gaudreau H, Destexhe A, Lang EJ (1998). Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo. J Neurophysiol 79: 1460-70.

Salinas E, Thier P (2000). Gain modulation: a major computational principle of the central nervous system. Neuron 27: 15-21.