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An in-depth analysis of a newly-discovered neuron's physiological properties, focusing on the identification and characterization of a specific type of ion channel. The document also discusses the properties of t-type calcium channels and their role in rebound firing in thalamic relay neurons.
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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.
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
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
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
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.
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
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)
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
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
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
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
zF
o i
= ln
Goldman equation for reversal potential with several permeabilities
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 (^) ⎥