BIOPHYSICS OF NERVE CELLS & NETWORKS

Transcription

1 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: to 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 / 2 / 80 Turn over for questions

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

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 i m that flows per unit area across the membrane is given by i m = a 2ρ i θ 2 ( 2 ) V m t 2 where ρ i is the resistivity of the axoplasm, a is the axon radius, θ is the velocity of the action potential and V m is the membrane potential. [8 marks] 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. 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? What is myelin and how does it affect the propagation of nerve action potentials? Please turn over

4 2. (i) Explain the principle behind the voltage-clamp method for studying the electrical properties of nerve membranes. 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 depolarisation? Hodgkin and Huxley described the sodium current across the axonal membrane in terms of the following equation I Na = m 3 hḡ Na (V m V Na ). 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: ( ) t h = h (h h 0 ) exp. τ h [6 marks] 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 100 mv and is then stepped to 0mV. (b) The axon has been held under voltage clamp for a prolonged period at 0mV and is then stepped to 100 mv. (v) Explain clearly the difference between inactivation of the sodium channel and deactivation of the sodium channel

5 3. (i) Explain what is meant by the terms equilibrium potential and reversal potential, and discuss which factors determine their values. [3 marks] Consider an ohmic channel that is permeable to both sodium and potassium ions. Show that the reversal potential is given by V rev = g KV K + g Na V Na g K + g Na where V K and V Na are the equilibrium potentials for potassium and sodium respectively, and g K and g Na are the respective membrane conductances. Also show that the slope conductance of the channel is simply the sum of the individual ionic conductances. [3 marks] 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 30nScm 2 and were open at the same time as an ohmic chloride channel with a membrane conductance of 70nS cm 2, at what potential would the membrane potential rest? Please turn over

6 4. Are the following statements true or false? Explain your reasoning. ( N.B. no reasoning, no marks!) (i) (v) (vi) (vii) (viii) (ix) (x) Increasing the external potassium concentration will hyperpolarise a nerve cell which is resting at 65mV. The internal chloride ion concentration determines whether the action of the neurotransmitter GABA on GABA A receptors is excitatory or inhibitory. Inactivation of voltage-gated sodium channels does not influence the action potential duration. Energy is required when an ion flows through an open voltage-gated potassium channel. The probability of neurotransmitter release occurring at a central synapse is linearly related to external calcium ion concentration. The ability to sustain high frequency action potential firing requires energy. The voltage-clamp method measures the current required to maintain a specific voltage across a membrane. The subunit composition of a ligand-gated ion channel can influence the duration a postsynaptic conductance change. The potent neurotoxin TTX will reduce both the initial inward current and the sustained outward current recorded from the squid giant axon. The increased input conductance associated with opening of a potassium conductance will decrease the membrane time constant

7 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] What factors determine the concentration and duration of the neurotransmitter transient in the synaptic cleft. [5 marks] 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 0mV. 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] Please turn over

8 6. Records of membrane voltage responses to synaptic conductance changes are shown below. The arrows on the top trace indicate the timing of two identical synaptic conductance changes delivered 2ms apart. Each synaptic conductance change rises linearly to a peak of 1μS in 0.5ms and then decays exponentially with a half-time of 1ms. 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

9 (i) Sketch the synaptic conductance changes that are described above. Why does the passive membrane voltage response have a longer duration than the synaptic conductance changes? Calculate the passive membrane resistance. Estimate the membrane time constant. (v) (vi) (vii) (viii) (ix) (x) Why is the voltage response to the second synaptic conductance smaller than the first in the passive membrane example? What does this data tell you about the relative location of these two synaptic conductance changes within a neuron? Why is the peak amplitude of the second action potential smaller than the first? How would the resulting action potentials be altered if the second synaptic conductance occurred 10ms after the first? Sketch the sodium conductance change that occurs during the two action potentials. Sketch the potassium conductance change that occurs during the two action potentials. End 40820