1. An enzyme acts to ligate two reactants, A and B, forming product C. The enzyme has an "A" site which can react reversibly with dissolved reactant A (kA+, _kA-) and an "B" site that can react reversibly with dissolved reactant B (kB+, kB-). There is no influence of whether one reactant is bound or not on the the binding of the other reactant. The enzyme can thus exist in four states, E, EA, EB, EAB. When both the A and B binding sites are occupied, the reaction A + B = C occurs at a rate vmax. Write the full set of equations necessary to describe the rate of formation of C from a spatially uniform solution in which there are concentrations a, b, e0 and no c. If you are given a similar problem on the mid-term, you will not be asked to solve these equations, but it would be good preparation for the examination to solve them for this practice problem.
2. A microporous membrane is t cm thick. One face of the membrane is covered with a sheet of impermeable polymer that contains a catalyst. This catalyst breaks a hexose into two trioses, e.g. H= 2 T. H and T diffuse from and to a solution on the other face of the membrane, thus to and from the polymer surface where the dissociation occurs. The rate-limiting step is diffusion. Assume the reaction to occur as written and to be irreversible. Write an expression for the steady-state flux, NH assuming the diffusivity to be DHT, the total of the molar concentrations of H and T to be c (uniform throughout the membrane) and the mole fractions to be represented as xH and xT. Assume the solution rinses the membrane well so that there is never any T on the solution side of the membrane.
Consider, also, the identical problem, still with diffusion as the rate limiting step, but with the reaction reversible: K = [T]2/[H]. Write but do not solve the equations for this case.
3. An "engineered" cell conducts the reaction sequence: AO <=> A <=> B <=> C <=> D <=> DO. The symbol <=> is meant to indicate reversible reaction involving forward and reverse reactions that need not be infinite. The first and last reactions are spatial translocations across the cell membrane. The middle three reactions are chemical transformations. The concentrations in units of micromoles/liter are:
| aO | a | b | c | d | dO |
| 3 | 2.67 | 0.25 | 2 | 0.1 | 0 |
(At equilibrium, as is known from other experiments, the concentrations of A and D within the cell are equal to the corresponding concentrations in the surrounding cytoplasm.) The chemical transformations inside the cell are, in fact, enzymatic but will be treated as reversible first-order reactions here. (This would be the case if all concentrations were below the relevant KM's and there were no co-reactants -- good teaching and test-simplifying assumptions but not very realistic). The standard-state free energy changes, in kcal/g-mole, for each of the reactions are:
| A <=> B | B <=> C | C <=> D |
| -3 | +1.25 | -1.8 |
Calculate the free energy change for each step of this process and state which step ( __ <=> __ ) is rate-limiting.
4. Blood is flowing over the membrane of an experimental blood gas exchanger in a layer that is 0.3 cm thick. The membrane lies in the x-y plane at z=0. Blood flows in the x direction at a velocity vx = 0.1 * z. Thus the velocity of the blood is zero at the membrane and 0.03 cm/sec at the other side of the layer. The oxygen concentration of the blood at the entrance, x=0, is uniform at a value of 5 (arbitrary concentration units). The oxygen concentration of the blood at the exit, x = L, varies linearly across the film from a value of 12.5 at the membrane (z=0) to a value of 5 at the other side of the layer (z = 0.3cm). If the blood at the exit is allowed to flow into a container and the oxygen content of the mixed blood in the container is measured, what value will be found? How much blood, in cm3 will enter the container in 1 min if the dimension of the membrane in the y direction (i.e. the width of the membrane) is 10 cm ?
5. A cylinder of tissue is consuming oxygen at the spatially uniform rate of 10-17 g-moles/cc-sec. (rO2 = 10-12) A cylinder of this tissue is inside a glass tube 0.1 cm in radius. The tissue is perfused with blood (its sole oxygen source) through a tube of 0.05 cm radius. This tube is concentric with the axis of the cylinder. What is the steady state oxygen flux in g-moles/cm2-sec at the blood-cylinder boundary? At a radius of 0.075 cm? At a radius of 0.1 cm?
6. Droplets of a fluorocarbon mixture are used as an emergency blood substitute. The droplets may be roughly modeled as having a uniform concentration of oxygen within them, covered with a membrane that has a permeability, P, equal to 10-4/R. If R is in cm, P is in cm/sec. The equilibrium concentration of oxygen in the fluorocarbon compound is 5 X that in the surrounding plasma. What is the largest droplet that is useful if a useful droplet must load to 85% of full capacity in 1 sec?