neural network and biological circuits

Class 4: January 1 2015 (Th); How to study the Neural Network & Biological Circuits

Continuing from ‘Electrical Activity in Animals’ (Class 3)

Reference Book: Ion Channels of Excitable Membrane by Bertill Hille

Thursday 1 January 15

1900 2015

Journey of bioelectrical research from 1900-2015


Ion Intracellular Range (mM)

Extracellular Range (mM)

Na+ 5-‐20 130-‐160

K+ 130-‐160 4-‐8

Ca2+ 50-‐1000 nM 1.2-‐4

Mg2+ 10-‐20 1-‐5

Cl-‐ 1-‐60 100-‐140

HCO3-‐ 1-‐3 20-‐30


1900

-70 to -90 mV

V


Membrane as a Capacitor

+ + + + + + + + + + + + +

- - - - - - - - - - - - - - - - -

-80mV


The Membrane as a Capacitor

• C=Q/E

• Capacitance C is measure of how much charge (Q) needs to be transferred from one conductor to another to set up a given potential (E). The unit of capacitance is farad (F). A 1-F capacitor will be charged to 1V when +1.0 C of charge is on one conductor and -1.0 C charge on the other. In an ideal capacitor the passage of current simply removes charge from one conductor and stores it on another in a fully reversible manner and without evolving heat

• The rate of change of potential under current Ic is obtained by differentiating C=Q/E

• dE/dt=Ic/C

• Electric current is the rate of change of the charge with respect to the time (dQ/dt=Ic)


Membrane Capacitor &nits actual Capacitance

• The capacity to store charge arises from their mutual attraction across the gap and by the polarization they develop in the insulating medium. The capacitance depends on the dielectric constant of that medium and on the geometry of the conductors. In a simple capacitor formed by two parallel plates of area ‘A’ and separated by an insulator of dielectric constant epsilon and thickness ‘d’, the capacitance is

• C=epsilon*epsilon’0’*A/d

• epsilon’0’= Polarizability of free space 8.85*10-12 CV-1m-1

• Cell membranes are parallel plate capacitors with specific capacitance (1cm2 of membrane) near 1 µF/cm2,

slightly higher than that of a pure lipid bilayer, 0.8µF/cm2

• Thickness of the membrane d=23 angstorm or 2.3 nanometer, assuming dielectric constant of hydrocarbon chain is 2.1


Membrane Capacitor continued (Charge movement & Capacitance)

• The high capacitance gives a lower limit to how many ions/charges must move and how rapidly they must move to make a given electrical signal.

• In general, capacitance slows down the voltage response to any current by a characteristic time (tao)that depends on the product RCof the capacitance and any effective parallel resistance.


Membrane and the Discharge of an RC Circuit

R C+ +

- -

E

I = E/R


dE/dt= Ic/C= -E/RC

The solution to this first-order differential equation has an exponentially decaying time course

E= E0 exp (- tao/RC) = E0 exp (-t/tao)

E0 is the starting voltage, t is time in seconds, and exp is the exponential function (power of e, the base of natural logarithms)

For biological membranes the product, RmCm of membrane resistance and membrane capacitance is often called membrane time constant (Tao m)

Membrane Time Constant ‘Tao’


1900 2015

Journey of bioelectrical research from 1900-2015


Walther Nernst


IonIntracellular Range (mM) Extracellular

Range (mM)

Ion (outside)/Ion (Inside)

Equilibrium Potential (mV)

Na+ 5-‐20 130-‐160 145/12 +67 mV

K+ 130-‐160 4-‐8 4/155 -‐98 mV

Ca2+ 50-‐1000 nM 1.2-‐4

Mg2+ 10-‐20 1-‐5

Cl-‐ 1-‐60 100-‐140

HCO3-‐ 1-‐3 20-‐30


Physical Meaning of Nernst Equation

• Chemical gradient drives sodium into the cell (more sodium outside).

• Electrical gradient drives sodium into the cell (cell is more negative inside)

• As sodium enters the cell, it changes the electrical gradient

• When the electrical gradient reaches 0mV, we will still have the chemical gradient so there will still be net influx

• Chemical + electrical= Net sodium influx (+61mV)• +61mV is the voltage required to stop sodium influx across the membrane if sodium is allowed to pass freely

• So it is both gradients creating the net sodium influx. Electrical gradient is more effected.


Schwiening C J J Physiol 2012;590:2571-2575

©2012 by The Physiological Society

J. Z. Young, squid and the Marine Biological Association (MBA) A, John Zachary Young (1907–1997). His discovery of the squid giant axon in the 1930s was pivotal since it provided an electrically excitable membrane of suf]icient area for Hodgkin and Huxley's experiments. B, Loligo forbesi, the long-‐]inned squid (∼60 cm long). The giant axon allows the rapid conduction of action potentials driving the escape response.


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