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UNIVERSITY OF LONDON MSci EXAMINATION May 2007

for Internal Students of Imperial College of Science, Technology and Medicine This paper is also taken for the relevant Examination for the Associateship

BIOPHYSICS OF NERVE CELLS & NETWORKS

For Third - & Fourth -Year Physics Students Monday 14th May 2007: 14.00 to 16.00

Answer THREE questions.

All questions carry equal marks.

General Instructions

Write your CANDIDATE NUMBER clearly on each of the THREE answer books provided.

If an electronic calculator is used, write its serial number in the box at the top right hand corner of the front cover of each answer book.

USE ONE ANSWER BOOK FOR EACH QUESTION.

Enter the number of each question attempted in the horizontal box on the front cover of its corresponding answer book.

Hand in THREE answer books even if they have not all been used.

You are reminded that the Examiners attach great importance to legibility, accuracy and clarity of expression.

© University of London 2007

40820 / 2 / 80

Turn over for questions

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R = 8.314JK−1mol−1 and F = 96, 500C mol−1

The distributions of sodium, potassium and chloride ions across the membrane of a nerve cell can be taken to be:

Ion Inside Outside

Sodium 14 mM 125 mM

Potassium 124 mM 5 mM

Chloride 6 mM 77 mM

40820 2

(3)

1. (i) Starting from the relationship between the membrane current per unit length and the variation of membrane potential along an unmyelinated nerve axon, show that the current imthat flows per unit area across the membrane is given by

im= a iθ2

2Vm

∂t2



where ρi is the resistivity of the axoplasm, a is the axon radius, θ is the velocity of the action potential and Vmis the membrane potential. [8 marks]

(ii) What can be inferred from the equation in part (i) about how the velocity of the action potential in an unmyelinated nerve varies with axon diameter? Explain your

logic clearly. [4 marks]

(iii) What is meant by the ‘absolute refractory period’ and how does it differ from the

‘relative refractory period’? What effect does a short refractory period have on the

properties of a nerve axon? [4 marks]

(iv) What is myelin and how does it affect the propagation of nerve action potentials?

[4 marks]

[ TOTAL 20 marks]

40820 3 Please turn over

(4)

2. (i) Explain the principle behind the voltage-clamp method for studying the electrical

properties of nerve membranes. [4 marks]

(ii) How was this method employed to describe the time-course of the changes in sodium ion conductance in the membrane of the squid giant axon following a sudden depolar-

isation? [4 marks]

(iii) Hodgkin and Huxley described the sodium current across the axonal membrane in terms of the following equation

INa = m3h ¯gNa(Vm− VNa) .

What do the various parameters in this equation represent and what are the main assumptions made in its derivation?

Show that the time course of h is given by an equation of the form:

h = h− (h− h0) exp

−t τh

 .

[6 marks]

(iv) Sketch the time-course of the parameter h under the following conditions.

(a) The axon has been held under voltage clamp for a prolonged period at

−100mV and is then stepped to 0mV. [2 marks]

(b) The axon has been held under voltage clamp for a prolonged period at 0 mV and is then stepped to−100mV.

[2 marks]

(v) Explain clearly the difference between inactivation of the sodium channel and de- activation of the sodium channel.

[2 marks]

[ TOTAL 20 marks]

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3. (i) Explain what is meant by the terms equilibrium potential and reversal potential, and discuss which factors determine their values. [3 marks]

(ii) Consider an ohmic channel that is permeable to both sodium and potassium ions.

Show that the reversal potential is given by

Vrev = gKVK+ gNaVNa gK + gNa

where VK and VNa are the equilibrium potentials for potassium and sodium respec- tively, and gK and gNa are the respective membrane conductances. [4 marks]

(iii) Also show that the slope conductance of the channel is simply the sum of the indi-

vidual ionic conductances. [3 marks]

(iv) If the channel is three times more permeable to sodium than potassium, calculate a value for the reversal potential.

[3 marks]

(v) Would the channel be inhibitory or excitatory? Give your reasons.

[3 marks]

(vi) If these channels had a membrane conductance of 30 nS cm−2 and were open at the same time as an ohmic chloride channel with a membrane conductance of 70 nS cm−2, at what potential would the membrane potential rest?

[4 marks]

[ TOTAL 20 marks]

40820 5 Please turn over

(6)

4. Are the following statements true or false? Explain your reasoning.

(N.B.no reasoning, no marks!)

(i) Increasing the external potassium concentration will hyperpolarise a nerve cell which

is resting at−65mV. [2 marks]

(ii) The internal chloride ion concentration determines whether the action of the neuro- transmitter GABA on GABAAreceptors is excitatory or inhibitory.

[2 marks]

(iii) Inactivation of voltage-gated sodium channels does not influence the action potential

duration. [2 marks]

(iv) Energy is required when an ion flows through an open voltage-gated potassium

channel. [2 marks]

(v) The probability of neurotransmitter release occurring at a central synapse is linearly related to external calcium ion concentration. [2 marks]

(vi) The ability to sustain high frequency action potential firing requires energy.

[2 marks]

(vii) The voltage-clamp method measures the current required to maintain a specific

voltage across a membrane. [2 marks]

(viii) The subunit composition of a ligand-gated ion channel can influence the duration a

postsynaptic conductance change. [2 marks]

(ix) The potent neurotoxin TTX will reduce both the initial inward current and the sus- tained outward current recorded from the squid giant axon.

[2 marks]

(x) The increased input conductance associated with opening of a potassium conduct- ance will decrease the membrane time constant.

[2 marks]

[ TOTAL 20 marks]

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5. (i) One popular theory to explain memory formation in the brain involves changes in the contribution of individual synapses to the total excitatory drive onto a neuron.

Describe what parameters could be altered at central synapses to induce such a

change in synaptic strength. [10 marks]

(ii) What factors determine the concentration and duration of the neurotransmitter tran-

sient in the synaptic cleft. [5 marks]

(iii) The single-channel conductance of a synaptic NMDA-type glutamate receptor is 50 pS. The NMDA receptor is predominantly permeable to sodium ions with a reversal potential of 0 mV. At a resting potential of−65mV the postsynaptic response to glutamate release is an inward current of 500 pA peak amplitude. Calculate how many NMDA channels are open at the peak of this response.

[5 marks]

[ TOTAL 20 marks]

40820 7 Please turn over

(8)

6. Records of membrane voltage responses to synaptic conductance changes are shown be- low. The arrows on the top trace indicate the timing of two identical synaptic conductance changes delivered 2 ms apart. Each synaptic conductance change rises linearly to a peak of 1 μS in 0.5 ms and then decays exponentially with a half-time of 1 ms. The reversal potential for the synaptic conductance is 0 mV. The traces compare the voltage responses that occur in a passive membrane with those that take place when Hodgkin/Huxley type sodium and potassium channels are active in the membrane.

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(i) Sketch the synaptic conductance changes that are described above. [2 marks]

(ii) Why does the passive membrane voltage response have a longer duration than the synaptic conductance changes?

[2 marks]

(iii) Calculate the passive membrane resistance. [2 marks]

(iv) Estimate the membrane time constant.

[2 marks]

(v) Why is the voltage response to the second synaptic conductance smaller than the

first in the passive membrane example? [2 marks]

(vi) What does this data tell you about the relative location of these two synaptic con-

ductance changes within a neuron? [2 marks]

(vii) Why is the peak amplitude of the second action potential smaller than the first?

[2 marks]

(viii) How would the resulting action potentials be altered if the second synaptic conduc-

tance occurred 10 ms after the first? [2 marks]

(ix) Sketch the sodium conductance change that occurs during the two action potentials.

[2 marks]

(x) Sketch the potassium conductance change that occurs during the two action poten- tials.

[2 marks]

[ TOTAL 20 marks]

End

40820

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