“Electrical Properties of Neuron”

Learning Objectives

At the end of the lecture,

  • Student should be able to understand the morphology of neuron and its basic physical and electrical properties.
  • Students should also be able to appreciate the mechanics of action potential initiation and measurements of action potentials.
  • The basics of patch-clamp technique should also be introduced.

Lecture Outline

Morphology of Nerve cells (The Neuron):

•Dendrites -- Input

• Cell body (soma) -- Integration

• Axon – Output.

Structure of neurons – Dendrites:

•At dendrites, the neurons recieve input via axons of other neurons at synapses.

Structure of neurons – Soma:

In the soma of the cells, the cell nucleus is located (containing the DNA, i.e. genetic code); the synthesis of the proteins (within ribosomes and endoplasmatic reticulum) as well as energy production (mitochondria) are performed.

Structure of neurons – Axon:

The axon transmits the information electrically from the soma to the synapses –

It is surrounded by myelin that insulates the axon, provided by oligodendrocytes (glial cells).

Electrical properties of neurons:

Neurons are enclosed by a membrane separating interior from extra cellular space

The concentration of ions inside is different (more –ve) to that in the surrounding liquid.

-ve ions therefore build up on the inside surface of the membrane and an equal amount of +ve ions build up on the outside

The difference in concentration generates an electrical potential (membrane potential) which plays an important role in neuronal dynamics.

Cell membrane: 2-3 nm thick and is impermeable to most charged molecules and so acts as a capacitor by separating the charges lying on either side of the membrane.

NB Capacitors, store charge across an insulating medium. Don’t allow current to flow across, but charge can be redistributed on each side leading to current flow.

The ion channels are proteins in the membrane, which lower the effective membrane resistance by a factor of 10,000 (depending on density, type etc)

Excitation and Conduction:

Most biological neurons communicate by short electrical pulses called action potentials or spikes or nerve impulses

These action potentials are generated by means of influx and out flux of ions through the ion channels embedded in membrane

Suitable electrical probe (electrode) and measurement instrumentation (amplifier and read-out) can measure these tiny potentials on the order of few milli-volts

Nerve cells have a low threshold for excitation – may easily be excited by electrical, chemical or mechanical stimuli

Two types of physiochemical disturbances are produced as a result

Local or Non-Propagated Potentials such as Synaptic, Generator or Electrotonic Potentials.

Propagated Disturbancessuch as Action Potentials or Nerve Impulses

The Patch-Clamp Technique:

This is a novel technique (developed by Neher and Sakmann et al. for which they were awarded with a Nobel prize) in which physiological currents flowing through the cells can be detected without disrupting the cell or its contents

A micropipette (diameter in microns) filled with a buffer solution and carrying a metal electrode is gently touched to the cell membrane and the membrane contents are sucked in, forming a giga-seal. This is called a patch-clamp. Because of high resistance, very small currents (pico-Ampere, 10E-12A) corresponding to ion channel movements can be measured, with the help of Ohm’s law.

Advanced Topics:

Membrane Capacitance, Membrane Current and Membrane Resistance

Biophysical Models of the Neuron

The Integrate-and-Fire Model

The Hodgkin-Huxley Model

Membrane Capacitance and Resistance:

Most channels are highly selective for a particular type of ion

Capacity of channels to conduct ions can be modified by eg membrane potential (voltage dependent), internal concentration of intracellular messengers (Ca-dependent) or external conc. Of neurotransmitters/neuromodulators

k Also have ion pumps which expend energy to maintain the differences in concentrations inside and outside

Exterior potential defined to be 0 (by convention). Because of excess –ve ions inside, resting membrane potential V (when neuron is inactive) is –ve

G Resting potential is the equilibrium point when ion flow into the cell is matched by ion flow out of cell

V will vary at different places within the neuron (eg soma and dendrite) due to the different morphological properties (mainly the radius)

Neurons without many long narrow cable segments have relatively uniform membrane potentials: they are electrotonically compact

Start by modelling these neurons with assumption that membrane potential is constant: single compartment model

Denoting membrane capacitance by Cm and the excess charge on the membrane as Q we have:

Q = CmV and dQ/dt = CmdV/dt

Shows how much current needed to change membrane potential at a given rate

Membrane also has a resistance: Rm Determines size of potential difference caused by input of current: IeRm

Both Rm and Cm are dependent on surface area of membrane A.

Therefore define size-independent versions, specific membrane conductance Cm and specific membrane resistance Rm

Membrane time constant tm = RmCm sets the basic time-scale for changes in the membrane potential (typically between 10 and 100ms)

The Nernst Equation and Equilibrium Potential

Potential difference between outside and inside attracts +ve ions in and repels –ve ions out

Difference in concentration between inside and outside mean ions diffuse through channels (Na+ and Ca2+ come in while K+ goes out)

Define equilibrium potential E for a channel as membrane potential at which current flow due to electric forces cancels diffusive flow

Eg Consider +ve ion and –ve membrane potential V: V opposes ion flow out, so only those with enough thermal energy can cross the barrier so at equilibrium get:

 [outside] = [inside] exp(zE/VT)

Z - is no. of extra protons of ion

VT - is a constant (from thermal energy of ions)

E - is equilibrium potential

Solve to get the Nernst Equation:

From Nernst equation get equilibrium potentials of channels:EK is typically between –70 and –90 mV, ENa is 50mV or higher, Eca is around 150mV while Ecl is about 65mV (near resting potential of many neurons)

A conductance with an equilibrium potential E tends to move membrane potential V towards E eg if V > EK K ions will flow out of neuron and so hyper polarise it

Conversely, as Na and Ca have +ve E’s normally V < E and so ions flow in and depolarise neuron

Membrane current:

The membrane current is total current flowing through all the ion channels

We represent it by I m which is current/unit area of membrane

Jj Amount of current flowing through each channel is equal to driving force (the difference between equilibrium potential Ei and membrane potential) multiplied by channel conductance gi

Therefore:

im = gi(V - Ei)

Conductance change over time leading to complex neuronal dynamics.

However have some constant factors (eg current from pumps) which are grouped together as a leakage current.

Over line on g shows that it is constant. Thus it is often called a passive conductance while others termed active conductances

Equilibrium current is not based on any specific ion but used as a free parameter to make resting potential of the model neuron match the one being studied

Similarly, conductance is adjusted to match the membrane conductance at rest

This leads to the prediction that the firing rate is a linear function of current (fig A above).

However, while the model fits data from the inter-spike intervals from the first 2 spikes well, it cannot match the spike rate adaptation which occurs in real neurons

For this to occur, we need to add an active conductance (fig C)

Biophysical Models:

Although many crucial properties of real neuron remain unknown, biophysical model incorporate some known properties of neural tissue

Like real, spiking neurons these models produce spikes rather than continuous valued outputs

Integrate – and – Fire Model

The Hodgkin – Huxley Model

Integrate and Fire Model:

Divides membrane behavior conceptually into two regimes.

A prolonged period of linear “integration”

A sudden “firing”

Relaxes the requirements that a single set of continuous differential equations describe the cell’s two very different regimes.

Easily implement using simple electronic circuits.

The Hodgkin – Huxley Model:

Biophysically much more accurate single cell models that can account for the very complex, non stationary behavior of real neurons

The dynamics are modeled by numerous coupled ,nonlinear differential equations that describe the behavior of continuous currents that depend in a nonlinear manner on the membrane potential

Although this model is powerful, if suffers from the drawback that it requires detail knowledge of a myriad of parameters. It is frequently difficult to properly constrain all these degrees of freedom.