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(write your name on every sheet) Exam I, Sept 28, 2005
There are 17 questions. Point values for each are given; 100 points total. Equations given on the last pages.
- (6 points) Attribute the following properties or characteristics to axons (A), dendrites (D), both (B), or neither (N).
Multiple in number ___ D Usually myelinated ___ A Originates from the cell body ___ B Has protein synthetic machinery ___ B
Acute angle branching ___ D Uniform diameter ___ A Microtubule cytoskeleton ___ B Action potential propagation ___ B
(6 points) Name three functions of neuroglia
(a) Mechanical support (b) Guidance for migration and axonal growth (c) Growth factor secretion (d) Segregate receptive surfaces/synapses (e) Removal of ions (K+) from extracellular space (e) Removal of neurotransmitters (f) Regulation of blood vessel diameter (f) Antigen presentation to T-cells (g) Regulate metabolite exchanges with neurons and perivascular space (h) Proliferate in response to injury
- (6 points) Name three differences in the electron microscopic appearance between GABAergic and Glutamatergic synapses in the CNS:
GABAergic Glutamatergic
Vesicles tend to be round and clear (Glu) while they can be flattened (GABA). Width of the postsynaptic density (GABA is thin, Glu is thick). Cleft is large (Glu) or small (GABA) Glu preferentially occur on spines; GABA preferentially occur on shaft of dendrite
(write your name on every sheet) Exam I, Sept 28, 2005
+30 mV +10 mV -10 mV -30 mV
-50 mV
-70 mV
I (pA)
0
-
2
- (8 points) You are recording from a newly-discovered type of neuron to determine its physiological properties. You first record from a patch of membrane that has one or a few of a particular type of ion channel. The individual records at different membrane potentials look like this:
a. Does this channel appear to be voltage- gated? If so, in what way? No.:
b. The experimental solutions were these:
extracellular: 150 mM KGluconate, 10 mM NaCl, (Gluconate is a large impermeant anion) intracellular: 150 mM KCl, 1 mM MgCl (^2)
Which ion(s) do you think carries this current? Why? K+ (since Erev K+ = 0mV), and Na+ is only present in the pipette (Erev extremely low). Ca+ will be chelated.
c. Draw the I-V relationship for this channel, adding scale numbers Reverses at zero. Line with slope corresponding to conductance of 60 nS (below). -3pA at -50mV, -1.8pA at -30mV, etc.
d. What is the single-channel conductance of this channel type? G =60pS
(write your name on every sheet) Exam I, Sept 28, 2005
b. After blocking all the other channel types in the cell, you record in WHOLE-CELL mode, holding at -100 mV and stepping to -20 mV for 100 ms. Assuming your cell has ~1000 T-type calcium channels, draw the expected current using an appropriate scale.
Like the single channel recording, at -100mV will start out at 0pA. No current since the activation gates are almost all shut at -100mV (activation gates 0%, though inactivation gates are 90% open – per upper graph).
Then, after pulsing to -20mV, activation gates rapidly open (activation gates 100%). Peak current at -20mV (if all channels open) is -0.2pA per channel x1000 = -200pA. In order to calculate a peak, I arbitrarily picked 2ms after the pulse (four time constants for activation, but hardly any inactivation) and computed: Activation gates: 1.00 x (1-e^-2/0.5) = 1.00 x (1-e^-4) = 1.00 x (0.98) = 0. Inactivation gates: 0.9 x (e^-2/30) = 0. Thus, about 0.80 of the channels are open (0.85 x 0.98), giving a peak current of -160pA at 2ms. (Other short times may yield different answers).
However, over 100ms of the pulse, inactivation gates close: Activation gates: 1.00 x (1-e^-100/0.5) = 1. Inactivation gates: 0.9 x (e^-100/30) = 0. So, only 0.036 of the channels are open (about 36 channels), with a current of -7.2pA.
After we return to -100mV, peak current is -1.2pA per channel x1000 = -1200pA. Since we determined that at 100ms, all activation gates were open (100%), but most inactivation gates were closed (about 3.6%), this is an instantaneous increase in the driving force, and we see a tail of current reflecting this: 0.036 x -1200pA = -43.2pA. The tail rapidly decays, as now at -100mV, steady state activation gates are not open (0.00) and they approach this with a timecourse of 0.5 ms (so almost all closed at 2ms.
(write your name on every sheet) Exam I, Sept 28, 2005
- (5 points). Increasing the resting potassium conductance of an excitable neuron would: (circle true statements) a. decrease the peak voltage of the action potential b. speed the repolarization phase of the action potential c. decrease the refractory period duration d. decrease the threshold potential for eliciting an action potential e. increase the membrane time constant
- (7 points) For each of the following physiologic differences, (1) indicate whether the change would SPEED, SLOW or NOT AFFECT the velocity of action potential propagation down an axon and, (2) give a physiologic mechanism by which such a change or difference could arise.
A. Increased membrane resistance at rest
SPEED. Elimination of K+ leak channels.
B. Increased membrane capacitance
SLOW. Decreased myelination, perhaps secondary to a demyelinating disease.
C. Increased peak voltage-gated sodium channel conductance
SPEED. More sodium channels, or different type of sodium channel with greater single channel conductance.
D. Increased axial resistance
SLOW. Shrink the axon in diameter. Could also say changing the resistivity of cytoplasm.
- (7 points) Attribute the following properties to an electrical synapse (E), a chemical synapse (C), both (B), or neither (N):
Allows for communication between neurons ___ B No synaptic delay ___ E Requires connexins ___ E Calcium-triggered neurotransmitter release ___ C Unidirectional ___ C/N (retrograde messages) Metabolically expensive ___ C Can amplify signal ___ C
(write your name on every sheet) Exam I, Sept 28, 2005
- (6 points) Tetanus toxin is a bacterial exotoxin discussed in class produced by Clostridium tetani. Please describe
a. its target in the synapse and the location of that target synaptobrevin, associated with vesicles
b. its effect on the target cleaves it (specific protease)
c. its effect on the synapse prevents vesicle release
d. Intoxication with botulinum and tetanus toxins cause very different clinical pictures. Briefly describe the symptoms of each and the basis for differences:
Botulinum: Flaccid paralysis with loss of muscle tone, etc. (tropism for motoneurons thus no firing)
Tetanus toxins: Tetanic paralysis, with arched back, muscle contraction, grimace, etc. Tropism for inhibitory interneurons in the spinal cord (thus increased excitation of motoneurons)
- (4 points) Name the ions to which each of the following receptors is normally permeable, and whether activation of the receptor is usually excitatory or inhibitory
a. AMPA receptor (Na, K, sometimes Ca; excitatory)
b. GABAA receptor (Cl-; inhibitory)
c. nACh receptor (Na, K; excitatory)
d. NMDA receptor (Na, K, Ca; excitatory)
(write your name on every sheet) Exam I, Sept 28, 2005
- (5 points) The following are symptoms or signs consistent with demyelinating peripheral neuropathy (circle all that apply):
a. Hyporeflexia on physical exam b. Stocking glove distribution of sensory loss in extremities c. Muscular appearance with accentuated muscle definition d. Burning sensation or pain in extremities e. Gait abnormalities
- (6 points) In the inherited disease hyperkalemic periodic paralysis, elevated serum potassium produces (by a mechanism that is not completely understood) failure of inactivation in the voltage-activated sodium channels of skeletal muscle. Three characteristics are surprising:
- only a few percent of the muscle sodium channels have failed inactivation at any given time
- the disease is dominantly inherited
- the same mutation can cause myotonia (sustained muscle contraction) and paralysis (no muscle contraction), sometimes as different phases of the same attack.
Explain how characteristic 1 is compatible with and explains the other two characteristics.
If only a few percent need to function abnormally to produce the disease, then half the sodium channels could be normal in a heterozygote and a small fraction of the mutant channels could produce enough abnormal inactivation. The symptoms are produced by the steady sodium influx through the non-inactivating channels causing depolarization of the muscle membrane. A moderate amount of depolarization causes sustained firing and constraction. A larger degree of depolarization (paradoxically) inactivates all the normal sodium channels, to prevent action potentials and to cause paralysis.
(write your name on every sheet) Exam I, Sept 28, 2005
- (5 points) Assume that the following infinitely long dendrite has no active conductances.
Assuming a membrane resistance per unit length of fiber of 1000 ohm-mm, and an axial resistance per unit length of fiber of 40 ohm/mm, what is the length constant of the fiber?
mm r
r i
m (^) 5 40
Given the length constant calculated above, if we apply 10 mV at V 1 , what voltage will we record at V 2?
V2 = 10 * exp(-2/5) = 6.7 mV
Next, instead of introducing the 10 mV depolarization via our electrode, we stimulate the nerve fiber input depicted with a single shock. At V 1 we record a peak depolarization (EPSP) of 10 mV in the fiber, but at V 2 the depolarization is less than we calculated above. What’s the source of this discrepancy?
For signals that occur in real (not infinte) time, you have to take into account the membrane capacitance. The depolarization will be spread out in time and consequently smaller in amplitude.
Neuronal Input
200 μm 2 mm
V (^1) V 2
(write your name on every sheet) Exam I, Sept 28, 2005
Some Constants and Equations
electron charge e = 1.6 x 10-^19 coul
gas constant R = 8.31 J/mol-Ko Faraday F = 96485 coul/mol
therefore RT/zF = 25.4 mV if z=1 and T=22oC
permittivity of free space εo = 8.85 x 10-^12 coul^2 /J-m or Farad/m
Avogadro's number NA = 6.02 x 10 23 mol -
Resistance R = V/I ohms=volts / amperes Conductance G = 1/R = I/V Siemens=amperes / volts Resistance in series R (^) T = R 1 + R 2 + R 3 + ...
Resistance in parallel 1/R (^) T = 1/R 1 + 1/R 2 + 1/R 3 + ...
Capacitance of parallel plates in vacuum
C = εo A/d Farads = permittivity * area / separation
for lipid: ε ~ 2.1 εo; d ~ 2 nm
so C ~ 1 μF/ cm^2 Charge Q = C V coulombs = Farads * volts Capacitance in series 1/C (^) T = 1/C 1 + 1/C 2 + 1/C 3 + ...
Capacitance in parallel C (^) T = C 1 + C 2 + C 3 + ...
Membrane capacitance Cm ~ 1 μF/cm^2 = 0.01 pF/μm^2
Nernst potential for an ion X E
RT
zF
X
X X
o i
= ln
[ ]
[ ]
Goldman equation for reversal potential with several permeabilities
V
RT
F
P K P Na P Cl rev P K P Na P Cl
K o Na o Cl i K i Na i Cl o
ln (^) ⎥
[ ] [ ] [ ]
[ ] [ ] [ ]
Time constant of a membrane τ = R Cm m
