Hybrid Circuits of Interacting Computer Model 
and Biological Neurons 
Syivie Renaud-LeMasson' 
Department of Physics 
Brandeis University 
Waltham, MA 02254 
Eve Marder 
Department of Biology 
Brandeis University 
Waltham, MA 02254 
Gwendal LeMasson  
Department of Biology 
Brandeis University 
Waltham, MA 02254 
L.F. Abbott 
Department of Physics 
Brandeis University 
Waltham, MA 02254 
Abstract 
We demonstrate the use of a digital signal processing board to construct 
hybrid networks consisting of computer model neurons connected to a 
biological neural network. This system operates in real time, and the 
synaptic connections are realistic effective conductances. Therefore, 
the synapses made from the computer model neuron are integrated 
correctly by the postsynaptic biological neuron. This method provides 
us with the ability to add additional, completely known elements to a 
biological network and study their effect on network activity. 
Moreover, by changing the parameters of the model neuron, it is 
possible to assess the role of individual conductances in the activity of 
the neuron, and in the network in which it participates. 
'Present address, 1XL, Universit6 de Bordeaux 1-Enserb, 
CNRSURA 846, 351 crs de la Liberation, 33405 Talence Cedex, 
France. 
Present address, LNPC, CNRS, Universit6 de Bordeaux 1, Place 
de Dr. Peyneau, 33120 Arcachon, France 
813 
814 Renaud-LeMasson, LeMasson, Marder, and Abbott 
1 INTRODUCTION 
A primary goal in neuroscience is to understand how the electrical properties of 
individual neurons contribute to the complex behavior of the networks in which they 
are found. However, the experimentalist wishing to assess the contribution of a given 
neuron or synapse in network function is hampered by lack of adequate tools. For 
example, although pharmacological agents are often used to block synaptic 
connections within a network (Eisen and Marder, 1982), or individual currents within 
a neuron (Tierney and Harris-Warrick, 1992), it is rarely possible to do precise 
pharmacological dissections of network function. Computational models of neurons 
and networks (Koch and Segev, 1989) allow the investigator the control over 
parameters not possible with pharmacology. However, beca realistic computer 
models are always based on inadequate biophysical data, the investigator must always 
be concerned that the simulated system may differ from biological reality in a critical 
way. We have developed a system that allows us to construct hybrid networks 
consisting of a model neuron interacting with a biological neural network. This 
allows us to work with a real biological system while retaining complete control over 
the parameters of the model neuron. 
2 THE MODEL NEURON 
Biophysical data describing the ionic currents of the Lateral Pyloric (LP) neuron of 
the crab stomatogastric ganglion (STG) (Golowasch and Marder, 1992) were used to 
construct an isopotential model LP neuron using MAXIM. MAXIM is a software 
package that runs on Macintosh systems and provides a graphical modeling tool for 
neurons and small neural networks (LeMasson, 1993). The model LP neuron used 
uses Hodgkin-Huxley type equations and contains a fast Na + conductance, a Ca + 
conductance, a delayed rectifier K + conductance, a transient outward current (ia) and 
a hyperpolarization-activated current (i0, as well as a leak conductance. This model 
is similar to that reported in Buchholtz et al. (1992) but because the raw data were 
refit using MAXIM, details are slightly different. 
3 ARTIFICIAL SYNAPSES 
Artificial chemical synapses are produced by the same method used in Sharp et al. 
(1993). An axoclamp in discontinuous current clamp (DCC) mode is used to record 
the membrane potential and inject current into the biological neurons (Fig. 1). The 
presynaptic membrane potential is used to control current injection into the 
postsynaptic neuron simulating a conductance change (rather than an injected current 
as in Yarom et al.). The synaptic current injected into the postsynaptic neuron 
depends on the programmed synaptic conductance and an investigator-determined 
reversal potential. The investigator also specifies the threshold and the function 
relating "ransmitter release"to presynaptic membrane potential, as well as the time 
course of the synaptic conductance. 
Hybrid Circuits of Interacting Computer Model and Biological Neurons 
[Mac Ilfx DSP 
data 
Vm & 
Ym Axoclamp a 
D.C. C. 
Is 
STG 
Figure 1: Schematic diagram of the system used to establish hybrid circuits. 
4 HARDWARE 
Our system uses a Digital Signal Processor (DSP) board with built-in A/D and D/A 
16 bit-precision converters (Spectral Innovations MacDSP256KNI), with DSP32C 
(AT&T) mounted in a Macintosh II fx (MAC) computer. A block diagram of the 
system is shown Fig. 1. The parameters describing the membrane and synaptic 
conductances of the model neuron are stored in the MAC and are transferred to the 
DSP board RAM (256x32K) through the standard NuBus interface. The DSP 
translates the parameter files into look-up tables via a polynomial fitting procedure. 
The differential equations of the LP model and the artificial synapses are integrated by 
the DSP board, taking advantage of its optimized arithmetic functions and data access. 
In this system, the computational model runs on the DSP board, and the Mac IIfx 
functions to store and display data on the screen. 
The computational speed of this system depends on the integration time step and the 
complexity of the model (the number of differential equations implemented in the 
model). For the results shown here, the integration time step was 0.7 msec, and 
under the conditions described below, 10-15 differential equations were used. The 
current system is limited to two real neurons and one model neuron because the DSP 
board has only two input and two output channels. A later generation system with 
more input and output channels and additional speed will increase the number of 
neurons and connections that can be created. During any one time step, the membrane 
potential of the model neuron is computed, the synaptic currents are determined, and a 
voltage command is exported to the Axoclamp instructing it to inject the appropriate 
current into the biological neuron (typically a few nA). During each time step the 
Axoclamp is used to measure the membrane potential of the biological neurons 
(typically between -80mV and 0mV) used to compute the value of the synaptic inputs 
to the model neuron. The computed and measured membrane potentials are 
periodically (every 500 time steps) sent to the computer main memory to be displayed 
and recorded. 
815 
To make this system run in real time, it is necessary to maintain perfect timing among 
all the components. Therefore in every experiment we first determine the minimum 
time step needed to do the integration depending on the complexity of the model being 
implemented. For complex models we used the internal clock of the MaclI to drive 
the board. Under some conditions it was preferable to drive the board with an external 
clock. It is critical that the Axoclamp sampling rate be more than twice the board time 
step if the two are not synchronized. In our experiments, the Axoclamp switching 
816 Renaud-LeMasson, LeMasson, Marder, and Abbott 
A 
Model LP 
real synapses 
artificial synapses 
B 
LP 
Model 
C ' increase of lh 0.5 sec 
LP 
Model 
10mV 
J10mV 
50 mV 
Figure 2: Hybrid network consisting of a model LP neuron connected to a PD neuron of 
a biological stomatogastric ganglion. A: Simplified connectivity diagram of the pyloric 
circuit of the stomatogastric ganglion. The AB/PD group consists of one AB neuron 
electrically coupled to two PD neurons. All chemical synapses are inhibitory. B: 
Simultaneous intracellular recordings from two biological neurons (PD and LP) and a plot 
of the membrane potential of the model LP neuron connected to the circuit. The 
parameters of the synaptic connections and the model LP neuron were adjusted so that 
the model LP neuron fired in the same time in the pyloric cycle as the biological LP 
neuron. C: Same recording configuration as B, but maximal conductance of ih in the 
model neuron was increased. 
Hybrid Circuits of Interacting Computer Model and Biological Neurons 
A 
real synapses 
artificial synapses 
817 
J10mV 
J50 mV 
I10mV 
PY _ 
0.5 sec 
Figure 3: Hybrid network in which the model LP neuron is connected to two different 
biological neurons. A: Connectivity diagram showing the pattern of synaptic connections 
shown in part B. B: Simultaneous recordings from the biological AB neuron, the model 
LP neuron, and a biological PY neuron. 
circuit was nmning about three times faster than the board time step. However, if 
experimental conditions force a slower Axoclamp sampling rate, then it will be 
important to synchronize the Axoclamp clock with the board. 
5 RESULTS 
The STG of the lobster, Panulirus interruptus contains one LP neuron, two Pyloric 
Dilator (PD) neurons, one Anterior Burster (AB), and eight Pyloric (PY) neurons 
(Eisen and Marder, 1982; Harris-Warrick et al., 1992). The connectivity among 
these neurons is known, and is shown in Figure 2A. The PD and LP neurons fire in 
alternation, because of the reciprocal inhibitory connections between them. Figure 2B 
shows a model LP neuron connected with reciprocal inhibitory synapses to a 
biological PD neuron. The parameters controlling the threshold, activation curve, 
time course, and reversal potential of the model neuron were adjusted until the model 
neuron fired at the same time within the rhythmic pyloric cycle as the biological LP 
neuron (Fig. 2B). Once these parameters were set, it was then possible to ask what 
effect changing the membrane properties of the model neuron had on emergent 
network activity. Figure 2C shows the result of increasing the maximal conductance 
of one of the currents in the model LP neuron, i. Note that increasing this current 
818 Renaud-LeMasson, LeMasson, Marder, and Abbott 
increased the number of LP action potentials per burst. The increased activity in the 
LP neuron delayed the onset of the next burst in the PD neurons because of the 
inhibitory synapse between the model LP neuron and the biological PD neuron, and 
the cycle period therefore also increased. Another effect seen in this example, is that 
the increased conductance of i in the LP neuron delayed the onset of the model LP 
neuron's firing relative to that of the biological LP neuron. 
In the experiment shown in Figure 3 we created reciprocal inhibitory connections 
between the model LP neuron and two biological neurons, the AB and a PY (Fig. 
3A). (The action potentials in the AB neuron are highly attenuated by the cable 
properties of this neuron). This example shows clearly the unitary inhibitory 
postsynaptic potentials (IPSPs) in the biological neurons resulting from the model LP's 
action potentials. During each burst of LP action potentials the IPSPs in the AB 
neuron increase considerably in amplitude, although the AB neuron's membrane 
potential is moving towards the reversal potential of the IPSPs. This occurs 
presumably because the conductance of the AB neuron is higher right at the end of its 
burst, and decreases as it hyperpolarizes. The same burst of LP action potentials 
evokes IPSPs in the PY neuron that increase in amplitude, here presumably because 
the PY neuron is depolarizing and increasing the driving force on the artificial 
chemical synapse. These recordings demonstrate that although the same function is 
controlling the synaptic 'release' properties in the model LP neuron, the actual 
change in membrane potential evoked by action potentials in the LP neuron is affected 
by the total conductance of the biological neurons. 
6 CONCLUSIONS 
The ability to connect a realistic model neuron to a biological network offers a tmique 
opportunity to study the effects of individual currents on network activity. It also 
provides realistic, two-way interactions between biological and computer-based 
networks. As well as providing an-important new tool for nenroscience, this 
represents an exciting new direction in biologically-based computing. 
7 ACKNOWLEDGMENTS 
We thank Ms. Joan McCarthy for help with manuscript preparation. Research 
supported by MH 46742, the Human Science Frontier Program, and NSF DMS- 
9208206. 
8 REFERENCES 
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Hybrid Circuits of Interacting Computer Model and Biological Neurons 
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