basic neurophysiology

7/29/2019 basic neurophysiology

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Computational Biology, Part H

Neuronal Modeling

Robert F. Murphy

Copyright 1996, 1999-2004.All rights reserved.


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Basic Neurophysiology

An imbalance of charge across a membrane

is called a membrane potential

The major contribution to membrane

potential in animal cells comes from

imbalances in small ions (e.g., Na, K)

The maintenance of this imbalance is anactive process carried out by ion pumps


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The cytoplasm of most cells (including

neurons) has an excess of negative ions over

positive ions (due to active pumping ofsodium ions out of the cell)

By convention this is referred to as a

negative membrane potential (insideminus outside)

Typical resting potential is -50 mV


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Ion pumps require energy (ATP) to carry

ions across a membrane up a concentration

gradient (theygenerate a potential)

Ion channels allow ions to flow across a

membrane down a concentration gradient

(they dissipate a potential)


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A cell is said to be electrically polarized

when it has a non-zero membrane potential

A dissipation (partial or total) of the

membrane potential is referred to as a

depolarization, while restoration of the

resting potential is termed repolarization


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Ion channels can switch between open and

closed states

If an ion channel can switch its state due to

changes in membrane potential, it is said to

be voltage-sensitive

A membrane containing voltage-sensitiveion channels and/or ion pumps is said to be

an excitable membrane


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An idealized neuron consists of

soma orcell body

contains nucleus and performs metabolic functions

dendrites

receive signals from other neurons through synapses

axonpropagates signal away from soma

terminal branches

form synapses with other neurons


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The junction between the soma and the axon

is called the axonhillock

The soma sums (integrates) currents

(inputs) from the dendrites

When the received currents result in a

sufficient change in the membrane potential,a rapid depolarization is initiated in the axon

hillock


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The depolarization is caused by opening of

voltage-sensitive sodium channels that

allow sodium ions to flow into the cell

The sodium channels only open in response

to a partial depolarization, such that a

threshold voltage is exceeded


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As sodium floods in, the membrane

potential reverses, such that the interior is

now positive relative to the outside

This positive potential causes voltage-

sensitive potassium channels to open,

allowing K+ ions to flow out The potential overshoots (becomes more

negative than) the resting potential


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The fall in potential triggers the sodium

channels to close, setting the stage for

restoration of the resting potential bysodium pumps

This sequential depolarization, polarity

reversal, potential overshoot andrepolarization is called an action potential


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Action Potential

-80

-60

-40

-20

0

20

40

60

Voltage(mV)

0

10

20

30

40

0 2 4 6 8 10Time (ms)

G(Na)

G(K)

0

50

100

150

Stimulus

(uA)


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The depolarization in the axon hillock

causes a depolarization in the region of the

axon immediately adjacent to the hillock

Depolarization (and repolarization)

proceeds down the axon until it reaches the

terminal branches, which releaseneurotransmitters to stimulate neurons

with which they form synapses


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These sequential depolarizations form a

traveling wave passing down the axon

Note that while a signal is passed down theaxon, it is not comparable to an electrical

signal traveling down a cable


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Current flows in an electrical cable

are in the direction that the signal is propagating

consist of electrons

Current flows in a neuron

are transverse to the signal propagation

consist of positively-charged ions


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The Hodgkin-Huxley Model

Based on electrophysiological

measurements of giant squid axon

Empirical model that predicts experimentaldata with very high degree of accuracy

Provides insight into mechanism of action

potential


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Define

v(t) voltage across the membrane at time t

q(t) net charge inside the neuron at t

I(t) current of positive ions into neuron at t

g(v) conductance of membrane at voltage v

Ccapacitance of the membrane

Subscripts Na, K and L used to denote specific

currents or conductances (L=other)


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Start with equation for capacitor

v(t) q( t)

C


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Consider each ion separately and sum

currents to get rate of change in charge and

hence voltagedq

dt INa IK IL

INa

gNa

(v vNa

)

IK gK(v vK )

IL gL (v vL )

dv

dt

1

CgNa

(v)(v vNa

) gK

(v)(v vK

) gL

(v vL

)


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Central concept of model: Define three state

variables that represent (or control) the

opening and closing of ion channelsm controls Na channel opening

h controls Na channel closing

n controls K channel opening


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Define relationship of state variables to

conductances of Na and K

gNa gNam3h

gK gKn4

0 m, n, h 1


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Can write differentials form,n,h with

respect to t

Gives set of four coupled, non-linear,ordinary differential equations

Must be integrated numerically


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Hodgkin-Huxley Gates

-80

-60

-40

-20

0

20

40

60

Voltage(mV)

0

50

100

150

Stimulus

(uA)

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10Time (ms)

m gate (Na)

h ga te (Na)

n gate (K)


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Interactive demonstration

(Integration of Hodgkin-Huxley equations

using Maple)


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Interactive demonstration

(Fitzhugh-Nagamo simplification)

basic neurophysiology

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