# Simulating Passive Properties of Neurons Using Matlab

#### Summary

This lab activity simulates a fundamental concept in cellular neuroscience; namely that all neurons can be modeled as circuits (i.e., the equivalent circuit) composed of resistors and capacitors in parallel. The students interact with a Matlab script that simulates a simple neuron and shows how changes in resistance and/or capacitance produce quantitative and qualitative changes in the response of the model. Students then use Matlab to test their quantitative predictions of the model cells responses by fitting the response to an exponential function. In this way, students get a practical experience with this fundamental concept prior to using the same protocols on biological neurons.

keywords: neuron, equivalent circuit, neuron model

keywords: neuron, equivalent circuit, neuron model

## Learning Goals

A major challenge in cellular neuroscience is having biology students understand the equivalent circuit model of a neuron. Specifically, this activity is designed to reinforce the idea that neurons can generally be modeled as parallel resistor-capacitor circuits. This physical manifestation, known as the equivalent circuit model of a neuron, is the basis for nearly all aspects of a neurons ability to generate electrical signals. Furthermore, the equivalent circuit model allows for a quantitative and qualitative explanation for how biological neurons respond to inputs. This exercise also serves as a student's first introduction to Matlab, and as such, the exercise is designed to have students become familiar with interacting with Matlab via the script editor.

This exercise has two specific learning outcomes:

1. students will learn how resistance and capacitance shape a neuron's response to injected currents

2. explore the similarities between their model and their physical equivalent circuit representations

In addition to these outcomes, students perform dimensional analysis to check that units for different components are appropriate (e.g., Why are the units of the time constant for a neuron in seconds?). Students are also allowed to answer the questions posed throughout the lab to develop their critical thinking and communication skills.)

This exercise has two specific learning outcomes:

1. students will learn how resistance and capacitance shape a neuron's response to injected currents

2. explore the similarities between their model and their physical equivalent circuit representations

In addition to these outcomes, students perform dimensional analysis to check that units for different components are appropriate (e.g., Why are the units of the time constant for a neuron in seconds?). Students are also allowed to answer the questions posed throughout the lab to develop their critical thinking and communication skills.)

## Context for Use

I use this activity in my BIO 199 Introduction to Undergraduate Research course for students doing research in my lab; typically one or two upper-division biology and/or kinesiology students per semester. I also use this as an introductory lab exercise for graduate students participating in the Neural Systems & Behavior Course (NS&B) offered every summer in Woods Hole MA, a course in which I have been a faculty member for 10 years. Whether for an undergrad in my research lab or a student in NS&B, this exercise is done on the first day, following a general introductory lecture on the equivalent circuit model of a neuron and the basic properties of these circuits. It also serves as a general introduction to the Matlab program and engages both the beginning Matlab student (i.e., no technical skills) as well as those (in the NS&B course) who have extensive knowledge of the program.

## Description and Teaching Materials

This simulation is run using the file "passive.m." The handout guides the students through some introductory material to familiarize them with the necessary background information. They then modify the script, according to the handout, to measure how a "passive neuron" responds to current injections when both the Resistance and Capacitance of the neuron are varied. The script runs the simulation and produces a figure of the model cell's response. From there, students calculate a key property of a neuron, the time constant, defined as the product of the membrane resistance and capacitance. They verify their calculation of the time constant (a function of Resistance and Capacitance) using Matlab to fit an exponential function to the model's voltage response (using the file "physiofit.m", which is called by passive.m.)

Student Handout for Passive Properties Exercise (Acrobat (PDF) 360kB Jun19 19)

Passive Model Script (Matlab File 4kB Aug16 18)

Passive Model Curve Fitting Script (Matlab File 11kB Aug16 18)

Student Handout for Passive Properties Exercise (Acrobat (PDF) 360kB Jun19 19)

Passive Model Script (Matlab File 4kB Aug16 18)

Passive Model Curve Fitting Script (Matlab File 11kB Aug16 18)

## Teaching Notes and Tips

This tutorial is designed to be run as-is; most of the background material is covered in lecture prior to this exercise. Students need only follow the instructions in the handout. As long as they do not modify the file beyond what the script says, it should not produce any areas.

## Assessment

Students collect data just as they would if they were doing an experiment, and record their answers in their handouts. As they progress, students must answer questions about the data they are collecting; students write their answers in the handout. I can then assess their thinking and understanding. For example, I have the students orally describe how changing the parameters of the cell changes the response both quantitatively (in terms of changes in voltage) and qualitatively (time to reach steady state.) This way, I can assess their ability to discern the differences in responses when resistances are changed rather than capacitance (e.g., "How are they the same? How are they different?) I also have them perform dimensional analysis so they can verify that the units of the parameters they calculate make sense. Taken as a whole, the exercise serves as a launching point for students to explore the same concept in biological neurons.