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

1. 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. Axon A Outside (small) 0 1 2 3 4 5 Rm=10K W Cm=0.1 m F Ri=2.2K W Axon B (large) Rm=1K W m m m m m m m m m m m m Cm=1 m F R C R C R C R C R C R C Ri=22 W Axon C (small, myelinated) R R R R R i i i i i Rm(0,5)=10K W Cm(0,5)=0.1 m F 0 1 2 3 4 5 Rm(1-4)=1M W Cm(1-4)=0.001 m F Inside Ri=2.2K W 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 RT=RA+RC and in parallel RT = RA RC /(RA + RC). TGase1 Negative TGase1 Positive 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 Ohm’s Law VA=IA RA, VC=IC RC and Kirchoff’s 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 Ohm’s 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 Rin:Rout 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 100K 10F Node 4 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. 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 (<$75). 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 Ohm’s Law (V=IR) 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@wesleyancollege.edu. (478) 757-5238.