Department of Biology, Wesleyan College, Macon, GA 31210.

1
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
RC FILTERS AND MEMBRANES
MEMBRANE CABLE PROPERTIES
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.
Current Spread and Rise Time to Threshold in
Small, Large, and Myelinated Axon Models
RC Cable Property Model (RCCPM)
Resistor-Capacitor Model (RCM)
Equivalent Resistances. Measure individual and
combined resistances for each of these two
circuits. Confirm the formulae for resistors in
series RTRARC and in parallel RT RA RC /(RA
RC).
TGase1 Positive
TGase1 Negative
TGase1 Positive
Small, Non-myelinated Axon
Node 0
Node 1
Rise time to threshold (node 5 ) 2.0 msec
Node 2
Series Voltage Drop. Measure individual and
combined voltage drops across A and C. Confirm
both Ohms Law VAIA RA, VCIC RC and
Kirchoffs First Current Law IA IC.
Node 3
RCM components and board. Individual resistors
and capacitors are connected by jumper cables to
form simple electronic circuits.
?
Node 4
Node 5
RCCPM circuit diagram and circuit board. Three
separate axons are modeled. Each axon consists
of six RC compartments with membrane resistance
Rm 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.
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 Ohms
Law for resistive circuits. 2) Calculating and
measuring equivalent resistances for resistors in
parallel and in series. 3) Calculating and
measuring series voltage drops. 4) Constructing
and testing a resistive voltage-divider
circuit. 5) Constructing a single compartment RC
membrane equivalent circuit and testing
capacitive rounding of a square-wave current
input. 6) Constructing and testing high-pass and
low-pass RC filters, and understanding
these circuits as frequency-dependent
voltage-dividers. Sample problems and results
are presented in the next panel.
Voltage Divider. Confirm that Vout Vin Rout /
(Rout Rin). What happens to Vout as the ratio
RinRout increases? Understand the utility of
this circuit for stepping down both Vout and Iout.
Large, Non-myelinated Axon
Node 0
Node 1
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 1) Capacitive
rounding of a square-wave input and
time-constants in a space-clamped axon. 2)
The space-constant for passive spread of the
trans-membrane voltage change accompanying
current injection. 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.
Node 2
Node 3
Node 4
Node 5
Rise time to threshold (node 5 ) 0.25 msec
High-Pass Filter. Working from the
voltage-divider 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?
?
COMMON PROBLEMS
Node 0
Node 1
Small, Myelinated Axon
Node 2
increasing resistance
increasing capacitance
Node 3
10?F
100K?
Node 4
1) Ohms Law, the Nernst Equation, the Goldman
Expression, Kirchoffs 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. 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.
Node 5
Rise time to threshold (node 5 ) 0.25 msec
1?F
10K?
?
1K?
0.1?F
Passive membrane voltage change at nodes 0-5
along each of three axon models, accompanying a
square-wave current pulse across compartment 0.
ACTION POTENTIAL GATING KINETICS
ELECTRICAL SYNAPSES
Rectification in Electrical Synapses
Timing of Events in Action Potentials
Single-Compartment RC Model (SCRCM)
Gated Equivalent Circuit Model (GECM)
ADVANTAGES OF HARDWARE MODELS
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 40MW resistance at
lower left steps down the output voltage to the
millivolt range.
1) Electronic hardware models are durable,
reusable, and cheap (lt75). 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. 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.
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.
Action Potential Exercise 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 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). 3)
Oversimplifications in the model - especially
holding threshold constant and representing
the higher-order voltage- and time-
dependence of a population of gates with a single
switch. 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.
Action potential template (in blue) and stimulus
pulse (in red). Horizontal lines show equilibrium
(EK, ENa, ECl), resting (VR), and threshold (V?)
potentials.
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) 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
Ohms Law (VIR) as applied to cells. 2) The
relationship between synapse size (inversely
related to resistance), presynaptic
attenuation, and synaptic gain. 3) Rectification
between cells of differing sizes (illustrated in
next panel). This latter property serves as
an introduction to command neurons.
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.
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
CONTACT
ACKNOWLEDGEMENTS
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.
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.
Barry K. Rhoades, Department of Biology.
Wesleyan College 4760 Forsyth Rd. Macon,
Georgia 31204. brhoades_at_wesleyancollege.edu.
[phone].