M1) The Nernst equation. M1.1-1.6) Match the following equations (2 pts each):1.1)Md = ______a) MK + zF1.2) Me = ______b) - RT zF 1 C dC dx1.3) I = ______c) = -D dC dx1.4) \mu = ______d) 58 z log xéë ùûoutside xéë ùûinside1.5) d y dx = ______e) - \mu C d y dx1.6)Vm = ______f ) zDF RT M1.7) For there to be a Nernst potential the following condition must be true (2 pts): a) A non-zero divergence scalar of the concentration change (vector) must exist b) A non-zero gradient vector of the concentration change (scalar) must exist c) A non-zero curl vector of the concentration change (vector) must exist d) A zero divergence scalar of the concentration change (vector) must exist M1.8) In addition, the following condition must also be true (2 pts): a) The membrane must be semi-permeable to potassium b) The membrane must have voltage-gate ion channels c) The membrane must contain active transporters d) The membrane must be semi-permeable to whichever ion the answer for 1.7 above is true. M1.9) Finally, the following third condition must also be true (2 pts): a) A voltage gradient must exist across the cell membrane b) Active transporters must have established a difference in concentration across the membrane. c) The membrane must be hydrophobic d) The first two conditions are sufficient M1.10) Understanding the mechanism underlying the Nernst potential helps (2 pts): a) Understand batteries b) Understand the electrode-tissue interface c) Understand how action potentials are generated d) All of the above e) a and c only M1.11) Which of the following was not described intuitively in class (2 pts): a) Einstein’s relationship b) Molar flux c) Conversion of flux to current d) Logarithms
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Match the equations to their applications. used to calculate equilibrium potential based on the ion concentrations inside and out used to calculate membrane potential given a particular change in current used to calculate current given a change in conductance Used to relate current to driving force, in the format: I = g(Vm-Ex) A. Nernst Equation B. Ohm's law
Dave K.
1. [3] The following table lists the concentrations, permeabilities and conductance of the permeant ions of a neuronal cell at the steady state equilibrium potential. Ion | Extracellular Concentration (mOsm) | Intracellular Concentration (mOsm) | Relative Permeability at Resting Membrane Potential | Conductance at Resting Membrane Potential (µS) (micro Siemens) --- | --- | --- | --- | --- K+ | 4 | 132 | PK | 0.07 Na+ | 140 | 10 | 0.02 PK | 0.007 Cl- | 110 | 3.5 | 0.15 PK | 0.0035 a. [0.5] What is the Nernst potential for each permeant ion of this neuronal cell? b. [0.5] Use the Goldman-Hodgkin-Katz equation to calculate the resting membrane potential of the cell considering all the permeant ions. Calculate the resting membrane potential of the cell neglecting the contribution of the permeability of the chloride ions to the membrane potential. What is the percent error of neglecting the chloride permeability? c. [0.5] Use the chord conductance equation to calculate the resting membrane potential of the cell. d. [0.5] Using the resting membrane potential found in part c, determine the driving force and current of each of the permeant ions of the cell at the resting membrane equilibrium (steady-state). Assume that a positive current corresponds to a positive ion leaving the cell. Determine the direction (in or out of cell) of each ion. e. [0.5] If at some point, the permeability of the cell membrane to Sodium ions is increased by 3 orders of magnitude, use the full GHK equation to determine the new membrane potential. Assume the movement of sodium across the membrane is not large enough to significantly change the concentrations of sodium in or out of the cell. f. [0.5] Repeat part e for an increase the permeability of potassium. (Note: do not scale the permeabilities of sodium and chloride.)
Adi S.
For this problem set, please show all work. Provide neat, clear answers, with the work on a SEPARATE SHEET from this one. Feel free to make liberal use of the Nernst equation. A Nernst reminder follows: Ex = RT / zF { ln [X+]out / [X+]in } Chloride (Cl-), a negatively-charged ion, is in equilibrium with regards to its flux across a membrane at a potential of -75 mV (inside of membrane negative relative to outside). (Elsewise stated, ECl = -75 mV.) a. Describe the gradient and electrostatic forces (in terms of both direction and magnitude) acting on chloride across a membrane resting at -75 mV. If the normally low permeability to chloride is suddenly increased, what will happen in terms of chloride flow across the membrane and why? (1 pt) b. An experimenter alters the voltage across the membrane by passing current to make the inside -40 mV relative to the outside, and then treats the membrane in a way that briefly makes it very permeable to Cl-. What are the direction (in, out, net zero) and relative magnitude (zero, small, moderate, large) of the electrostatic and diffusional gradient forces acting on chloride? Will chloride flow cause the voltage to change (from -40 mV), and if so, in which direction? Explain. (5 pts) c. In an experiment similar to part c, current is passed which hyperpolarizes the membrane to -100 mV before it is made permeable to chloride. Answer the same questions as in c for this new experiment. (2 pts)
Sri K.
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