Problem 1 [5 points] The resting membrane potential is dependent on the separation of charges created by the Sodium-Potassium ATPase, an active transporter which moves 3 Na+ ions out of the cell and 2 K+ ions into the cell with each pumping cycle, which gets its energy from the hydrolysis of 1 ATP -> ADP. This process sets up a concentration gradient across the cell, leading both K+ and Na+ to go back across the cell membrane by diffusion. Diffusion is described by Fick's Law (jid=- Diam) dc. Meanwhile though, as soon as the ions cross the membrane, being charged species, they set up a voltage difference, and thus a flow from electricity, described by Ohm's Law (iv=oE). These two fluxes describe the flow of ions across the membrane: jm=jid +jiv = At equilibrium, these two fluxes are equal. Find an expression for the membrane voltage as a function of concentration differences across the membrane at equilibrium. (Hint, when done, you should have the Nernst Equation). Problem 2 [3 points) Find typical values for the concentrations of Na+ and K+ inside and outside of the cell, and separately for Na+ and K+, calculate the membrane voltage when the flux from that ion is at equilibrium. Problem 3 [2 points). Calculate the field strength across the membrane at each of the equilibrium potential for each of those species. Problem 1 [5 points] The resting membrane potential is dependent on the separation of charges created by the Sodium-Potassium ATPase, an active transporter which moves 3 Na+ ions out of the cell and 2 K+ ions into the cell with each pumping cycle, which gets its energy from the hydrolysis of 1 ATP -> ADP. This process sets up a concentration gradient across the cell, leading both K+ and Na+ to go back across the cell membrane by diffusion. Diffusion is described by Fick's Law (jid=- Diam) dc. Meanwhile though, as soon as the ions cross the membrane, being charged species, they set up a voltage difference, and thus a flow from electricity, described by Ohm's Law (iv=oE). These two fluxes describe the flow of ions across the membrane: jm=jid +jiv = At equilibrium, these two fluxes are equal. Find an expression for the membrane voltage as a function of concentration differences across the membrane at equilibrium. (Hint, when done, you should have the Nernst Equation). Problem 2 [3 points) Find typical values for the concentrations of Na+ and K+ inside and outside of the cell, and separately for Na+ and K+, calculate the membrane voltage when the flux from that ion is at equilibrium. Problem 3 [2 points). Calculate the field strength across the membrane at each of the equilibrium potential for each of those species