The Do-It-Yourself Neuron: Hardware Models and Exercises for
Exploring Electrical Properties of Neurons and Neuronal Recording
Barry K. Rhoades, PhD.
Department of Biology, Wesleyan College, Macon, GA 31210.
ABSTRACT
COMMON PROBLEMS
1) Ohm’s Law, the Nernst Equation, the Goldman Expression, Kirchoff’s
Current Laws, and “equivalent circuit models” are central theoretical
constructs of neurophysiology,
however,
for introductory students these “explanations” often make less intuitive
sense than do the phenomena they describe.
Current Spread and Rise Time to Threshold
in Small, Large, and Myelinated Axon Models
RC Cable Property Model (RCCPM)
Equivalent Resistances.
Measure
individual and
TGase1
Negative
combined resistances for each of these two circuits.
Confirm the formulae for resistors in series
RT=RA+RC and in parallel RT = RA RC /(RA + RC).
0
TGase1
Outside
1
2
3
PositiveAxon A
4
5
(small)
Rm=10K
Cm=0.1F
Ri=2.2K 
Node 0
Cm
Rm
Cm
Rm
Cm
Rm
Cm
Rm
Cm
Axon B
Rm
TGase1 Positive
Cm
Resistor-Capacitor Model (RCM)
(large)
Rm=1K 
Cm=1F
Ri=22
Node 1
RCM components and board. Individual resistors and capacitors are connected by
jumper cables to form simple electronic circuits.
RC Circuit Exercise
In this introductory exercise students connect resistors and capacitors to
form and test simple electronic circuits. In the process, they become
familiar with differentiating between electronic terms and components,
translating a circuit diagram to a physical circuit, tracing and
troubleshooting simple circuits, manipulating standard jumper and cable
types, operating stimulating devices from a simple battery to an electronic
stimulator, and operating recording devices from a multimeter to a
computer-based data-acquisition system. Among the specific topics are:
1) Measuring voltage, amperage, and resistance and confirming Ohm’s
Law for resistive circuits.
2) Calculating and measuring equivalent resistances for resistors in parallel
and in series.
Series Voltage Drop. Measure individual and
combined voltage drops across A and C. Confirm
both Ohm’s Law VA=IA RA, VC=IC RC and
Kirchoff’s First Current Law IA = IC.
Ri
0
High-Pass Filter. Working from the voltagedivider circuit, replace Rin with a capacitor.
What is the effect of this circuit on a square
wave input? How does this reflect the selective
removal of low-frequency components of the
signal? How is this effect modified by
increasing R? By increasing C?
4) Constructing and testing a resistive voltage-divider circuit.
100K
10K
5) Constructing a single compartment RC membrane equivalent circuit and
testing capacitive rounding of a square-wave current input.
1K
1
Ri
2
Ri
3
Ri
4
5
Inside
Voltage Divider. Confirm that Vout = Vin Rout /
(Rout + Rin). What happens to Vout as the ratio
Rin:Rout increases? Understand the utility of this
circuit for stepping down both Vout and Iout.
3) Calculating and measuring series voltage drops.
Ri
(small,
myelinated)
Rm(0,5)=10K 
Cm(0,5)=0.1F
Rm(1-4)=1M 
Cm(1-4)=0.001F
Ri=2.2K 
2) Recording from electronic hardware models uses much of the same
data-collection equipment (e.g. cables, amplifiers, computers,
stimulators) as recording from live preparations. This familiarizes
the student with this equipment, prior to applying it to time-critical
in vivo or in vitro preparations.

RCCPM circuit diagram and circuit board. Three separate axons are modeled. Each
axon consists of six RC compartments with membrane resistance R m and capacitance
Cm in parallel, coupled by internal resistances Ri. “Outside” terminals are permanently
shorted together. “Inside” nodes may be shorted together to space-clamp the axon.
Cable Properties Exercise
A represents a small (1X), non-myelinated axon. B represents a larger (10X)
diameter, non-myelinated axon. C represents a small (1X) diameter axon
with the central four nodes myelinated (Rm increased 100-fold, Cm decreased
100-fold). The student investigates the following:
increasing
resistance
increasing
capacitance
10F
1F
0.1F
3) The effects of increasing axon size and myelination on passive spread specifically the decreased rise time to a threshold voltage of 10mV
above rest at the node most distal to the site of current injection. This is
later related to the resulting effects on AP propagation velocity.
This exercise is paired in a single laboratory session with the hardware
resistor ladder model from Crawdad, which illustrates space-constants and
differences between intra-and extracellular recording. The same properties
are further explored in Neurons in Action computer simulations.
ACTION POTENTIAL
GATING KINETICS
3) Experience with simple circuits provides insight into properties of
both neurons (e.g. membrane capacitance) and recording
instrumentation (e.g. signal filtering, impedance matching).
4) Hardware models provide consistent, reproducible results and a
respite from the demands and frustrations of live preparations.
5) Exercises with hardware models can be used for all levels of students,
from middle-school science campers to college English professors.
Timing of Events in Action Potentials
Action potential template (in blue) and stimulus pulse (in red).
Horizontal lines show equilibrium (EK, ENa, ECl), resting (VR), and
threshold (V) potentials.
Large, Non-myelinated
Axon
Rise time to threshold (node 5 )
= 0.25 msec

Node 0
Node 1
Node 2
Node 3
Node 4
Node 5

Small, Myelinated Axon
Rise time to threshold (node 5 )
= 0.25 msec
Passive membrane voltage change at nodes 0-5 along each of three axon
models, accompanying a square-wave current pulse across compartment 0.
Rectification in Electrical Synapses
Single-Compartment RC Model (SCRCM)
SCRCM circuit diagram and circuit board. Each cell is modeled as a single
compartment with fixed resistance and capacitance in parallel across the membrane. A1
and A2 model identical small cells. B models a medium-sized cell in which resistance is
decreased by a factor of 10 and capacitance is increased by a factor of 10, relative to
cells A1 and A2. C models a large cell in which resistance is decreased by a factor of
100 and capacitance is increased by a factor of 100, relative to cells A1 and A2.
Electrical Synapse Exercise
One cell is directly stimulated via a square-wave current pulse. An
electrical synapse is simulated by connecting this “presynaptic” cell to a
“postsynaptic” cell via a resistor across the “inside” leads (“outside” leads
are shorted). The student investigates the following:
1) The relative timing of conductance changes underlying the AP.
2) The effects of changing selected components of the model (see lower
trace in next panel).
1) Cell size and I/V relationships - specifically how a larger cell requires a
greater input current to produce a constant-sized passive membrane
voltage response. This verifies Ohm’s Law (V=IR) as applied to cells.
3) Oversimplifications in the model - especially holding threshold
constant and representing the higher-order voltage- and timedependence of a population of gates with a single switch.
2) The relationship between synapse size (inversely related to resistance),
presynaptic attenuation, and synaptic gain.
This exercise is paired with Neurons in Action computer simulations of
action potentials in successive laboratory sessions, which allow the student
to explore a much broader range of parameters.
Rise time to threshold (node 5 )
= 2.0 msec
ELECTRICAL
SYNAPSES
GECM circuit diagram and circuit board. Na+, K+, Cl-, membrane capacitance, and
stimulus paths are wired in parallel. Three DC power adapters provide Na + , K+ ,
and Cl- equilibrium potentials. Toggle switches at the bottom represent H-H Na+
and K+ gates. A depolarizing (shorting) stimulus pulse may be produced by a
manual pushbutton or computer-triggered via the relay box at the right. The 40M
resistance at lower left steps down the output voltage to the millivolt range.
In this discovery-based exercise the student starts with an open-ended
problem: making the model output match an AP template. The student
proceeds by trial-and-error to a solution: a sequence of manipulations of the
“gating” switches. The student then refines the original solution to the
“correct” one on the basis of voltage- and time-dependence rules for gate
transitions in the H-H model. In the process the student investigates:
Node 0
Node 1
Node 2
Node
Node 3
4
Node 5
2) The space-constant for passive spread of the trans-membrane voltage
change accompanying current injection.
Sample problems and results are presented in the next panel.
Action Potential Exercise
Node 3
Node 4
Node 5
1) Capacitive “rounding” of a square-wave input and time-constants in a
space-clamped axon.
6) Constructing and testing high-pass and low-pass RC filters, and
understanding these circuits as “frequency-dependent voltage-dividers”.
Gated Equivalent Circuit Model (GECM)
Node 2
ADVANTAGES OF
HARDWARE MODELS
1) Electronic hardware models are durable, reusable, and cheap (<$75).
Small, Non-myelinated
Axon
Axon C
2) Laboratory exercises with living preparations provide practical
applications of classroom concepts,
however,
students must simultaneously master surgical techniques, unfamiliar
instrumentation, and theoretical concepts in a time-critical setting.
3) Computer simulations provide rapid, convenient, reproducible results,
however,
it is too easy for students to simply “twiddle” parameters without ever
mastering the underlying concepts.
MEMBRANE CABLE
PROPERTIES
Rm
Ohm's Law, Kirchoff's Current Laws, and the "equivalent circuit model”
are standard tools for explaining the central physiological properties of
neurons and neuronal membranes in terms of simple electronic components
and circuits. However, most introductory neuroscience students who are
presented with these tools have had no prior exposure to electronics.
Electronic formulas and circuit diagrams presented as theoretical constructs
are of little practical use to them in understanding and predicting neuronal
behavior.
I describe here a set of electronic hardware boards and accompanying
exercises which are physical realizations of equivalent circuit models.
Hardware simulations combine concrete, "hands-on" experience with
simple recording preparation and completely reproducible results. As such,
they can effectively complement parametric computer simulations and
standard "wet" laboratory exercises involving in vivo or in vitro recording.
I have implemented the following hardware exercises in upper-level
undergraduate neurobiology and animal physiology classes: basic RC
circuits and filters, the single-compartment membrane equivalent circuit,
cable properties in a resistor ladder and coupled RC compartments,
mechanically-gated action potentials, and electrical synapses with
rectification.
RC FILTERS AND
MEMBRANES
An experiment on the effects of changing the sodium equilibrium
potential on the the action potential. The resting potential is in green ,
while traces produced with three ENa values are in blue.
3) Rectification between cells of differing sizes (illustrated in next panel).
This latter property serves as an introduction to command neurons.
Small
Presynaptic
Cell
Small
Postsynaptic
Cell
Small
Postsynaptic
Cell
Small
Presynaptic
Cell
Small
Presynaptic
Cell
Small
Postsynaptic
Cell
Medium
Postsynaptic
Cell
Medium
Presynaptic
Cell
Small
Presynaptic
Cell
Small
Postsynaptic
Cell
Large
Postsynaptic
Cell
Large
Presynaptic
Cell
Responses to a square-wave current pulse in the stimulated (presynaptic)
and unstimulated (postsynaptic) RC cell models, with no connection (red)
or a 1K resistor (green) between the cells. This illustrates the ability of
large command neurons to drive smaller cells via electrical synapses.
COURSE DESIGN
BIO 325 Neurobiology is a laboratory-based, cellular-to-systems
level core course in neurophysiology for the Wesleyan Neuroscience
Minor.
In this course three types of laboratory exercises are interwoven:
a) Software simulations from Neurons in Action allow students to
explore theoretical aspects of neurophysiology;
b) Electronic hardware simulations of the Do-It-Yourself Neuron
provide practice with computer-based data recording and analysis
with stable solid-state “subjects”;
c) Recording from the crayfish nervous system, primarily with
exercises from Crawdad, develops skills such as microsurgery,
pulling and positioning microelectrodes, manipulating amplifiers,
controlling electronic noise, etc.
REFERENCES
Moore, J.W. & Stuart, A.E. (2000) Neurons in Action. Sinauer.
Wyttenbach, R.A., Johnson, B.R., Hoy, R.R. (1999). Crawdad:
A CD-ROM Lab Manual for Neurophysiology (Student
Version). Sinauer.
ACKNOWLEDGEMENTS
All traces in this poster were captured from the
screen output of the ADInstruments PowerLab
Scope system.
This project was supported, in part, with funds from
NSF/CCLI grant #DUE9950546.
CONTACT
Barry K. Rhoades, Department of Biology. Wesleyan College 4760
Forsyth Rd. Macon, Georgia 31204. brhoades@wesleyancollege.edu.
(478) 757-5238.