Biochem Problem Set #4: Equilibrium Constants & Binding in Hemoglobin, Assignments of Biochemistry

Download Biochem Problem Set #4: Equilibrium Constants & Binding in Hemoglobin and more Assignments Biochemistry in PDF only on Docsity! BIOCHEMISTRY 440 Problem Set #4 1 ANSWER (1a): E+I E·I ANSWER (1b): Ka = [EI] units are M-1 [E] [I] Kd = [E] [I] = 1/Ka units are M [EI] ANSWER (1c): ANSWER (1d): Since Kd = 1/Ka, Kd = 1 x 10-11 M ANSWER (1e): for 50% occupancy, [I] = Kd = 1 x 10-11 M 90% occupancy means: θ = 0.9 = 9/10 = [I]/([I] + Kd) So [I] = 9 x Kd = 9 x 10-11 M (i.e., an additional 40% of the sites (50% to 90%) are filled with just under a 10- fold increase in inhibitor concentration) 10% occupancy means: θ = 0.1 = 1/10; so [I] = Kd/9 = 1.1 10-12 M (i.e., to fill an additional 40% of the sites (i.e., from 10% to 50%) requires almost 10-fold higher ligand.) 99% occupancy means: θ = 0.99 = 99/100, so [I] = 99 x Kd = 9.9 x 10--10 M = ~1 x 10--9 M (i.e., only an additional 9% of the sites are filled (90% to 99%) by another 10-fold increase in inhibitor concentration. 99.9% occupancy means: θ = 0.999 = 999/1000 so [I] = 999 x Kd = ~1 x 10--8 M (i.e., only an additional 0.9% of the sites are filled (99% to 99.9%) by another 10-fold increase in inhibitor concentration. ANSWER (1f): For binding that follows a hyperbolic binding curve, occupancy of the binding site increases steeply over a narrow range of [ligand] around Kd, but due to the asymptotic nature, large increases in [ligand] are required to push the occupancy past 90%. ANSWER (2): As BPG binding lowers the affinity of the Hb for 02, crocodile Hb has higher affinity for 02. This will allow the crocodile to load up its Hb w/02 before it goes under water. As it stays under, metabolic processes will produce CO2 , which we already learned will form HCO3- when dissolved. Since the deoxy form of Hb binds HCO3- , ! = EI[ ] total sites = EI[ ] EI[ ] + E[ ] = E[ ] I[ ]/Kd E[ ] I[ ] K d + E[ ] ! = I[ ] K d I[ ] K d +1 " # $ % & ' = I[ ] I[ ] + K d BIOCHEMISTRY 440 Problem Set #4 2 this binding favors (or stabilizes) this form, thereby promoting dissociation of 02 into the crocodile’s tissues, allowing him to remain under water. We can think of the process as the following series of equilibria: CO2 + H2O → H+ + HCO3- HCO3- + crocHb· 02 → Hb· HCO3- +02 Want to learn more about how crocodile Hb may help human health in the future? go to: http://www.accessexcellence.org/WN/SUA04/crocodile_blood.html ANSWER (3): At sea level, the arterial blood’s Hb is almost fully saturated with 02, so hyperventilation will not help here. Instead, excessive removal of CO2 will alter the pH according to the reaction. H+ + HCO3- H2O + CO2 As CO2 is removed by hyperventilation, the reaction will be driven to the right, causing an increase in blood pH. Because of the Bohr effect (see Figure 7-15), this could actually result in lowering the amount of O2 released in the diver’s tissues… the opposite effect from what was desired. So, if you see a skin diver hyperventilating, you can be sure he/she hasn’t studied Biochemistry! N.B. For a more thorough discussion of this point, please see the end of this Answer key. ANSWER (4): (a) Doping the athletes with Hb that binds BPG tighter (i.e., higher affinity) would be equivalent to increasing their circulating levels of BPG, as occurs after conditioning at high altitudes. (b) BPG has 3 negatively-charged groups, so designing a mutant with some additional positive charge in the BPG binding site might be a reasonable strategy, Also, trying to maximize the vdW’s interactions along the uncharged edge of BPG might enhance binding. ANSWER (5): As we said in Question 3, Hb is almost saturated w/ O2 at sea level. But, while increasing the amount of Hb won’t alter the percent saturation, it will increase the actual amount of O2 bound in the arterial blood. Increasing the amount of Mb will increase the swimmers’ capacity to store O2 for later use in the absence of the breath. Remember that diving mammals (whales, seals, etc..) have very high levels of Mb in their tissues. Hence, it would seem that up-regulation of both globins could make for an unbeatable synchronized swimming team. ANSWER (6): Inhibition of carbonic anhydrase will result in increased concentrations of CO2 in respiring tissues. Recall that Hb can bind CO2, which lowers its affinity for O2, causing its release. Since the symptoms of high altitude sickness stem from a decrease in O2 delivery to tissues, binding of CO2 may ameliorate the symptoms. CO2 + HbO2 CO2·Hb + O2 Further discussion on hyperventilation and diving. A student in a previous year's class was particularly interested in this point, having been taught by his diving instructor to hyperventilate before a dive. Here is the additional information I provided him regarding this: