ProbSet10_solutions

ProbSet10_solutions - *1 2*3 4 5*6*7 A protein called a...

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Unformatted text preview: **1. 2. **3. 4. 5. **6. **7. A protein called a sodium pump couples ATP hydrolysis to the pumping of sodium ions out of the cell. Consider a cell at 25°C in which the intra-cellular concentration of sodium ions is 100 mM and the extracellular sodium ion concentration is 150 mM. The total membrane potential, including contributions from all species of ions, is -70 mV. How many moles of ATP would need to be hydrolyzed under standard conditions to move 0.5 moles of sodium ions out of the cell (take G° = -30 kJ/mol for ATP hydrolysis, assume the membrane potential is not altered by the transported ions) Work done against the potential = FV where F is the Faraday constant to move delta G / n = 96500x(0.070) = 6755 J/mol Since delta G° = -30 kJ/mol for ATP hydrolysis at 300K, it would take 0.112 moles of ATP to move 0.5 moles of Na+ out of the cell. 8. The diagram below shows the propagation of an action potential along an axon. The voltagedependent ion channels can take on three states in equilibrium, as shown. a) Explain the roles of the three different states of ion channels in propagating the action potential in a forward direction along an axon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b) Indicate schematically the states of sodium channels in the vicinity of the first electrosde at various time points of the action potential marked V1. c) If a nerve cell has a mutant form of the sodium channel, which cannot adopt the inactivated state, diagram what the action potentials would look like at the three positions above. 9. In living biological cells, the concentration of sodium ions inside the cell is kept at a lower concentration (0.05 M) than outside (0.20 M) but actively transporting sodium out. a) Consider the following process at 37°C: 1 mol NaCl (inside) 1 mol NaCl (outside)Write an expression for the free energy change for this process, define any symbols used G = NaCl_OUT – NaCl_IN NaCl = °NaCl + RTln(aNaCl) where °NaCl = chemical potential at standard conditions and aNaCl = activity of NaCl G = RTln(aNaCl_OUT / aNaCl_IN) = Free energy to transport 1 mole of NaCl For dilute solutions, a can be replaced with [conc.] b) Calculate G for moving 3 moles of NaCl from inside to outside under these conditions. = RTln([NaCl]OUT/[NaCl]IN) = RT ln (0.20/0.05) = 3.57kJ/mol G = n* G = 3.57kJ/mol * 3 moles = 10.71kJ **10. A cell membrane at 37°C is found to be permeable to Ca+2 but not to anions, and measurements show the inside concentration of Ca+2 to be 0.10 M with the outside 0.001 M. a) What potential difference in volts would have to exist across the membrane for Ca+2 to be in equilibrium at the stated concentrations? Specify the sign of the potential inside relative to outside [Ca2+]IN = 0.1M [Ca2+]OUT = 0.001M G = RTln([Ca2+]IN/[Ca2+]OUT) + zF V where V = VOUT - VIN, z = charge on the ion = +2, F = Faraday constant of 96500 C/mole, R = 8.314 J/mol*K, T = 310K At equilibrium G=0 G = RTln([Ca2+]IN/[Ca2+]OUT) + zF V = 0 8.314*310*ln(0.1/0.001) = -(+2)(96500)( V) V = 0.06V so the potential inside relative to outside is -0.06V b) If the measured inside potential is +100 mM relative to outside, what is the minimum work required to transfer 1 mole of Ca+2 from outside to inside under these conditions? Given that V = VOUT - VIN = 100mV = 0.1V G = {RTln([Ca2+]IN/[Ca2+]OUT) + zF V} = reversible work to transfer 1 mole of Ca2+ from outside to inside. G = {11869.0 + 19300} J/mol = 31.2kJ/mole ...
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