Cellular Neuroscience (207)Ian Parker

Lecture # 2 - Passive electrical properties of membranes

(What does all this electronics stuff mean for a neuron?)

http://parkerlab.bio.uci.edu

Membrane structure

Fatty acid tail polar head

Permeation across the lipid bilayer increases with increasing lipid solubility.Ions and water are almost completely impermeant – protein channels and carriers.

Provide pathways for selective movement of ions and molecules across the membrane.

The cell membrane (lipid bilayer) acts as a very good insulator, but has high capacitance.(WHY?)

Specific membrane resistance

1 cmResistance of 1 cm2 of membrane (Rm)

Rm of a lipid bilayer >106 cm2

But membrane channels can greatly increase the membrane conductance

Specific membrane capacitance

membrane

extracellular fluid

intracellular fluid

The insulating cell membrane (dielectric) separates two good conductors (the fluids outside and inside the cell), thus forming a capacitor.

Because the membrane is so thin (ca. 7.5 nm), the membrane acts as a very good capacitor.

Specific capacitance (capacitance of 1 cm2 of membrane : Cm)

Cm ~ 1 F cm-2 for cell membranes

Input resistance of a cellInject current (I) Record voltage (V)

cellInput resistance Rin = V/I

Rin decreases with increasing size of cell (increasing membrane area)

Rin increases with increasing specific membrane resistance

[If I = 10 nA and V = 5 mV, what is Rm ???]

A neuron as an RC circuitInject current (I) Record voltage (V)

cell

RmCm

inside

outside

V

E

time

I

Voltage changes exponentially

with time constant m

m = Rm * Cm

So m will be longer if Rm is high “ “ “ “ “ and if Cm is high

We can directly measure Rm and m

so we can calculate Cm = m / Rm

Given that Cm ~ 1 F cm2, we can then calculate the membrane area of the cell

EXERCISE

From example trace given in class;

Measure time constantMeasure change in membrane potential resulting from a given injection of current

Calculate input resistanceCalculate total capacitance of cell membrane

Estimate diameter of the cell

But, neurons are not usually spheres!What about axons and dendrites?

For a spherical cell, all regions on the cell membrane are at the same potential as each other (isopotential). This is not the case for long, thin processes such as axons and dendrites.

The voltage change induced by a ‘square’ pulse of injected current gets smaller and more rounded with increasing distance along an axon

Space constant

Space constant () is the distance at which the change in membrane potential ( Vm) falls to 1/e of some initial value.

(What is the space constant in the example above?)

Equivalent circuit of an axon

The math for this gets complicated …So, we will just consider a simple case where the duration of current injection is long enough for the membrane capacitance to fully charge. Then;

(Qualitatively, how would the space constant be affected if the current pulse was brief?)

What determines the space constant (

For long current pulses we can ignore membrane capacitance, so the circuit simplifies to;

More current will flow along the inside of the axon (i.e. the voltage change will travel further) if;Ri (resistance of the axoplasm ) is lowerRm (‘leakage’ resistance across the membrane) is greater

An analogy: a leaky hosepipeMore water will flow out of the end of the pipe if its diameter is greater (fire hose vs garden hose), and if the number of leaks is smaller

How does vary with the diameter of an axon?

Membrane resistance Rm is proportional to the area of membrane per unit length . So, Rm is proportional to the circumference of the axon (2 r)

Longitudinal axoplasmic resistance (Ri) per unit length is proportional to cross sectional area ( r2)

As the diameter of an axon increases Rm decreases linearly, whereas Ri decreases as the square root of the diameter.

Because = Sqrt(Rm/Ri)increases proportional to the square root of the axon diameter.

Thus, a signal will passively propagate a longer distance in a fat axon than in a skinny axon.