Question

1. What does it mean to have positive cooperatively in protein-ligand binding?

2. The protein “Mariota” binds to the ligand “football” with an association rate of 8.0 x 10 10³M^-1s^-1 and an overall dissociation constant, Kd of 10 nM. Calculate the dissociation rate, kd, including appropriate units.

3. An antibody binds to an antigen with a Kd of 8 X 10^-6M. At what concentration of antigen will the fractional saturation (Υ_antigen) be (a) 0.2, (b) 0.5, (c) 0.6, and (d) 0.8?

Answer 1

1. Cooperative binding occurs in binding systems that are constituted by more than one type (species) of molecule (say molecules A and B) and in which one of the partners is not mono-valent; i.e., it binds more than one molecule of the other molecular species. For example, one molecule of type A can bind 6 molecules of type B (in such cases, B is usually referred to as the "ligand"). Binding in this type of system can be considered "cooperative" if the binding of B to one site on A is affected by the binding of B to other site(s) on A. In other words, the binding of B molecules to the different sites on A do not constitute mutually independent events. This can be due, for instance, to an affinity for the ligand that depends on the amount of ligand bound. Cooperativity can be positive or negative. Cooperative binding is observed in many biopolymers, including proteins and nucleic acids. Cooperative binding has been shown to be the mechanism underlying a large range of biochemical and physiological processes.

Cooperativity can be positive if binding of a ligand molecule increases the receptor's apparent affinity, and hence increases the chance of another ligand molecule binding) or negative (if binding of a ligand molecule decreases affinity and hence makes binding of other ligand molecules less likely.

2. Kd , the dissociation constant, is the ratio of kd (the rate constant for the dissociation reaction) to ka , the rate constant for the association reaction:

Kd = kd/ka

Solving for kd: kd = Kdxka

kd = 8x10³ x 10x10^-9 = 8x10⁵ s^-1

I have a doubt with question 3, so, Post this in a new question so I can answer properly once I figure out the formula to do it.