Homework 2 Answerkey. 1. After a particular step depolarization in Hodgkin and Huxley s squid axon the parameter n follows the curve

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1 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae 1 of 7 Homework Answerkey 1. After a particular step depolarization in Hodkin and Huxley s squid axon the parameter n follows the curve n = e t /1.7( msec) t is in msec, and _ K is known to be 4.3mS/cm. Plot K as a function of time, usin 1 msec steps for msec. What is K? Use K = n 4 K K (ms/cm ) t (msec) K = 15.3mS / cm. After the same depolarization as above, the parameters m and h follow the curves t / 0.5( msec) ( e ) t /0.84( msec) m = and h = 0.605e. t is in msec and _ Na = 70.7 ms/cm. What is the larest value of Na reached? Use Na 3 = m h Na Na (ms/cm ) Na = 14 cm, max ms / t (msec)

2 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae of 7 3. When a healthy squid axon is voltae-clamped in artificial sea water, one obtains the followin membrane current in response to a step chane in membrane potential from V m = - 70 mv to V m = 0 mv. Draw similar plots of I m vs. t (when Vm is stepped from -65 mv to 0 mv) when the recordins are made under each of the followin experimental conditions. For each of your plots, explain in one or two sentences how and why your raph differs from that in the fiure above. (a) TTX is added to the bath surroundin the axon. TTX blocks I Na (b) TEA is added to the interior of the axon. TEA blocks I K (c) [Na + ] out is adjusted so that [Na + ] out = [Na + ] in. E Na = V clamp = 0 mv I Na = 0

3 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae 3 of 7 (d) [K + ] out is adjusted so that [K + ] out = [K + ] in. E K = V clamp = 0 mv I K = 0. (e) Ouabain, a specific inhibitor of the Na + -K + pump is added to the bath five minutes before the experiment. E Na = E K = V clamp = 0 mv I Na = I K = 0 4. The fiure below shows the atin current (I ) obtained (in the presence of aents that block all ion currents, and with linear capacitive transients subtracted) usin a voltae depolarization (from -80 to 0 mv). This atin current is known to be associated with openin Na + channels in a snail neuron, and atin particles (each carryin a chare of e = 1 electronic chare) are required to open one Na + channel. In the absence of Na + channel blocker, the activation curve of the Na + channel is shown below:

4 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae 4 of 7 (a) What is the density (channel/cm ) of Na + channels in the membrane of the snail neuron? 3 Q = I dt =.375µ A msec/ cm t= 0 = = A sec/ cm C / cm Gatin chare per channel, q = e = C Channel density = 8.5 channels / cm = 19 (b) What is the sinle channel conductance of the Na + channels in the snail neuron? 0.9S / cm Sinle channel conductance γ = / cm = 9 ps

5 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae 5 of 7 (c) Assumin that Na + channels do not inactivate, redraw fiure A on raph paper, and add the atin current trace you would expect upon repolarization. Q ON = Q OFF

6 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae 6 of 7 5. You are a researcher interested in discriminatin between two models (shown in the fiure) for the relative movement of the voltae-sensor (rectanles in the fiure) of a voltae-ated ion channel in response to chanes in membrane potential. You desin a novel small molecule nonfluorescent hydrophobic cation (XYZ) that can quickly redistribute in the inner and outer leaflets of the membrane in response to chanes in membrane potential. You enineer in a fluorophore to the voltae sensor at the position shown (blue square). The emission spectra of the fluorophore overlaps extensively with the absorbance spectra of XYZ, enablin you to use FRET to probe voltae sensor movements. The channel is normally closed at the restin membrane potential (-80 mv), and maximum conductance is achieved followin a step depolarization to + mv. (a) For each model, draw the profiles of donor emission fluorescence you would expect to see followin a step depolarization to + mv from a holdin potential of -80 mv. Briefly explain your answers. There is a monophasic decline of fluorescence with depolarization. At -80 mv, XYZ is in inner leaflet so fluorescence emission is hih. At + mv, XYZ distributes to the outer leaflet, quenchin the fluorophore. At -80 mv, both XYZ and fluorophore on the voltae sensor are in the inner leaflet, leadin to quenchin. Upon depolarization XYZ rapidly distributes to outer leaflet resultin in fluorescence dequenchin. Requenchin occurs as paddles slowly move to the outer leaflet. Same process happens with repolarization.

7 Homework, Calcium Sinals in Bioloical Systems (580.47/ ), Pae 7 of 7 (b) For each model, draw the profiles of donor emission fluorescence you would expect to see followin a hyperpolarization to -130 mv from a holdin potential of -80 mv. Briefly explain your answer. MODEL 1 MODEL Fluorescence remains hih. There is no chane in relative position of XYZ and fluorophore with hyperpolarization. Fluorescence remains relatively quenched. There is no chane in relative position of XYZ and fluorophore with hyperpolarization.