Objectives

 

1. To understand how neuron is represented as simple RC (Resistor capacitor) circuit.
2. To study the effects of membrane capacitance and resistance in action potential propagation.

 

Theory

 

Structure of Neurons

 

Neurons are the elementary processing units in the central nervous system that are interconnected to each other in an intricate pattern. A typical neuron consists of cell body, cell membrane, axon, dendrites; presynaptic terminals (i.e. electrical synapses and chemical synapses etc). Axon is responsible for transforming signals between different points of the nervous system (Figure 1). Its function is similar to the wires that are connected to different points in an electric circuit. The transforming signal causes ionic fluctuations in the neuronal plasma membrane and creates an electrical flow in the neuron which develops a membrane potential. Ions are diffused across the membrane through specific ion channels. Each ionic channels in the membrane act as a resistor and its detailed study can be done by understanding each part of neurons and its functions. 

 

 

Figure 1 : Structure of a neuron

 

Image source : http://www.enfermedad-de.org/psiquiatrias/angus

 

Neuronal Cell body

 

It is the main factory of a neuronal cell. It consists of specialized organelles such as mitochondria, Golgi apparatus, secretory granules, ribosomes etc. Cell body is the main energy providing area of a cell. Nucleus in the cell body consists of DNA which contains all cell history, information for manufacturing proteins necessary to that cell etc. Mitochondrion is responsible for the supply of energy in the form of ATP. Golgi apparatus present in the cell body plays a role in packaging of peptides and proteins (neurotransmitter) into the vesicles. Also cell contains endoplasmic reticulum which is responsible for the transportation of materials within the cytoplasm.

 

 

Neuronal Membrane

 

Neuronal membrane serves as a barrier which contains cytoplasm inside the neuron and allows the diffusion of certain substance to exterior of the cell through specialized channels known as ion channels. The membrane is about 5nm thick and it contains glycerophospholipids, sphingolipids, cholesterol and proteins. The functions of the membrane are:

• Accumulating nutrients and rejecting harmful substances.
• Catalyzing enzymatic reactions.
• Developing electrical potential inside the cell and conducting specific impulses.
• Being sensitive to particular neurotransmitters and modulators.

 

The structure of the neuronal membrane is a lipid bilayer of phospholipids organized in such a way that charged region (polar) faces outward and the non polar region faces inward. The outer region of the membrane contains certain receptor specialized for the attachment of other specific external molecules. When these receptor is attached by specific molecules, some alterations of the membrane occurs which allows the permeability of certain ions through the ion channels.

 

Dendrities

 

Dendrites are the main part of the neuron that receiving signals from other nerve cells. These are the antennae of neurons and consist of thousands of synapses. The receptors in the dendrite membrane detect neurotransmitter in the synaptic cleft. The dendrites branches to a various number and is covered by denritic spines where the synaptic connections are made.

 

Axon

 

Axons are the main signal conducting unit of neuronal cell. It is capable of conveying electrical signals along the distance which ranges between 0.1mm to 2mm.Some of the neuronal cell that doesn’t has the axon and are called amacrine neuron where all the neuronal process are done by dentrities.Some of the neurons have very short axons also. The axons are covered by myelin sheath which is broken at various points by the Node of Ranvier.The cells that wrap around peripheral nerve fiber are called Schwann cells .The cells that cover the axons in the central nervous system are called oligodendrocytes.Also axon hillock is the point where axon is joined to the cell. It is area where the electrical firing known as action potential usually occurs.

 

Presynaptic Terminals/ Nerve Ending

 

Synapses are referred to the junction between two nerve cells. In this junction, the presynaptic terminal of one cell comes into contact with the postsynaptic membrane of another. At this junction the neurons are excited, inhibited and modulated. Mainly there are two synapses: electrical and chemical synapses. For more details about synapses refer, http://amrita.vlab.co.in/?sub=3&brch=257&sim=1488&cnt=1

 

How a neuron is represented as simple RC circuit ?

 

A neuron is the basic building block of the nervous system. A one-year old human has about 100 billion neurons. The brain is a vastly complicated signalling system, with neurons forming the basis of that system. Electrochemical signals flow in one direction only in neurons, originating at the dendrites or cell body (usually in response to stimulation from other neurons) and propagating along axon branches which terminate on the dendrites or cell bodies of perhaps thousands of other neurons. The basis of neuronal electrochemical signals lies in the neuron membrane. Like all cell membranes, the neuron membrane is a phospholipid bilayer. In other words, the membrane is a "fat sandwich", with fatty acids between two slices of polar (phosphate) "bread". The membrane is pierced with proteins that serve as channels for ions to "flow" though (like straws stuck in a sandwich).

 

In Neurophysiology lab experiments we explained the basic Physiology and Anatomy of neuron and action potential, for understanding mathemathical modeling of simple HH neuron one may go to Neuron Simulation lab. In this experiment we study the basic electric properties of an electricaly excitable neuron. The electrical properties of neurons can be described in terms of electrical circuits. To understand the behavior of this circuit, we need to know the behavior of the basic components of electrical circuit such as resistor and capacitor.

 

Resistors: A resistor is a component of a circuit that resists the flow of electrical current. It has two terminals across which current flows and drop the voltage of the current as it flows from one terminal to the other. Resistors are primarily used to create and maintain known currents within electrical components. Their purpose is to create specified values of current and voltage in a circuit (Figure 2).

 

                      

                                          Figure 2:  Symbolic representation of a Resistor                          Resistor

 

   image source : http://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Resistor.jpg/800px-Resistor.jpg

 

We model the neuronal cell membrane as a resistor in series with a capacitor as the diagram below illustrates (Figure 3). The amount of current, i that flows through these resistors, R is given by Ohm's Law:

I = V/R

 

V= Voltage drop across the resistance
 

In a neuronal membrane there are ion channels which allows the flow of charged ions across the membrane, which results in the action potential generation and propagation. When there are more open ion channels more currents can flow through these channels to the extracellular medium. With this property each ion channel is act as a small resistor and the number of opened ion channels increased can be represented by more number of resistors are in parallel. So that the net resistance of the circuit is smaller.

  

Capacitor: In a RC (resistor, capacitor) equivalent circuit model for passive neuron membrane, the capacitor represents the fact that cellular membranes are good electrical insulators (Figure 3).

 

                  

                                           Figure 3:    Symbolic representation of a Capacitor                           Capacitor

 

   image source :  http://en.wikipedia.org/wiki/File:Condensador_electrolitico_150_microF_400V.jpg

 

Capacitor is a device useful for storing electric charge. The capacitors only function is to store electric charge. A capacitor is simply two metallic plates separated by a gap, where the gap between the plates is usually filled with a a non-conductive material called a dielectric. A voltage across the plates of the capacitor charges up one plate, pushing charge off the nearby plate. But the plates can only hold so much charge, so current only flows for a short while. The capacitive property of phospholipid bilayer is shown in figure 4.

 

Figure 4. Schematic representation of capacitive property of Phospholipid bilayer.

 

In a cell, the conducting plates are the intracellular and extracellular solutions, separated by the non-conducting membrane. Just like the electrical element, applying a voltage step across the membrane induces a brief current.

 

I = C dV/dt

 

Current 'I' is proportional to the capacitance 'C' and the rate at which voltage changes with time.

 

RC Equivalent Circuit of Neuron

 

In a neuron membrane potential is controlled by the inflow and outflow of ions. In fact, the triggering of the action potential is caused when ions flow in or out of the neuron. This in turn changes the potential across the cell. This type of interaction can be modeled in an electrical equivalent circuit using a battery, resistor and a capacitor (Figure 5). The battery represents the stored potential that is maintained across the ion channels and the resistor represents the quantity of ions that are allowed to flow in or out of the cell. Capacitor represents the intracellular and extracellular solutions, separated by the non-conducting membrane. When more ion channels are opened, the more ions flow. In other words, the resistance to flow for the ions is decreased, conductance is increased, by having more ion channels open. So the passive transports or ion channels are basically just variable resistors.

 

Figure 5: Schematic representation of RC Equivalent Circuit of Neuron.

Image source : http://upload.wikimedia.org/wikipedia/en/thumb/1/13/NeuronResistanceCapacitanceRev.jpg/300px-NeuronResistanceCapacitanceRev.jpg

 

Another important contributor to the electrical behavior of the cell is the charge separation that is maintained across the cell membrane. This separation of charge by an insulating material causes a capacitive affect on the cell. Figure 6 shows a simple RC circuit. If a voltage is applied to this circuit then the capacitor begins storing the electricity. Eventually it will reach its maximum storage capacity and simply stay there. Once the external voltage is removed however the capacitor then begins to discharge its stored power across the resistor until it has been fully discharged. The important thing to see here is that the voltage across the capacitor resists change. For example, if this circuit had only a resistor in it then as soon as the power was applied the voltage would change to its steady state value, and when removed it would then go to zero immediately. But the capacitor resists the change because it takes time for it to charge and discharge. Neurons also display this type of electrical behavior.

 

Figure 6: RC Circuit and output voltage characteristics.

 

 Remotely studying the RC properties of a cell membrane

 

In our remote trigger experiment one can study the effects of R and C properties in the generation and propagation of action potential. Here we use different values of capacitor and resistor to understand RC properties. User can select prefixed membrane resistance and capacitance, and one can select the input signal (stimuli) to the RC circuit  with varying amplitude, frequency and duty cycle.

 

After selecting the RC values and input signal parameters user can set these values to the model by clicking the start button. This will set the parameters for the experiment and start the simulation. Immediately after the start button is clicked the capacitor starts charging it will reach maximum capacity and it discharge the charge through resistor. Detailed explanation to perform experiment on remote pannel is given in the procedure.