Protein A binds to protein B to form a complex, AB. At...

Protein A binds to protein B to form a complex, AB. At equilibrium in a cell the concentrations of $A, B,$ and $A B$ are all at $1 \mu M$. A. Referring to Figure $3-19$, calculate the equilibrium constant for the reaction $A+B \rightleftharpoons A B$ B. What would the equilibrium constant be if $A, B,$ and AB were each present in equilibrium at the much lower concentrations of 1 nM each? C. How many extra hydrogen bonds would be needed to hold $A$ and $B$ together at this lower concentration so that a similar proportion of the molecules are found in the $\mathrm{AB}$ complex? (Remember that each hydrogen bond contributes about $1 \mathrm{kcal} / \mathrm{mole} .$

Protein A binds to protein B to form a complex, AB. At equilibrium in a cell the concentrations of $A, B,$ and $A B$ are all at $1 \mu M$.
A. Referring to Figure $3-19$, calculate the equilibrium constant for the reaction $A+B \rightleftharpoons A B$
B. What would the equilibrium constant be if $A, B,$ and AB were each present in equilibrium at the much lower concentrations of 1 nM each?
C. How many extra hydrogen bonds would be needed to hold $A$ and $B$ together at this lower concentration so that a similar proportion of the molecules are found in the $\mathrm{AB}$ complex? (Remember that each hydrogen bond contributes about $1 \mathrm{kcal} / \mathrm{mole} .$

Key Concepts

Equilibrium Constant

The equilibrium constant (K) is a measure of the ratio of the concentrations of products to reactants at equilibrium for a reversible chemical reaction. In the context of binding equilibria, it quantifies the affinity between two interacting partners by indicating how much of the bound complex is formed relative to the individual components, and is calculated by using the equilibrium concentrations of all species involved.

Reaction Equilibrium

Reaction equilibrium refers to the state in which the rates of the forward and reverse reactions are equal, resulting in constant concentrations of all reactants and products. Understanding this concept is crucial when analyzing systems where binding interactions occur, as it underpins the calculation of equilibrium constants and predictions of how changes in conditions, such as concentration, affect the system.

Gibbs Free Energy

Gibbs free energy is a thermodynamic quantity that links reaction spontaneity with equilibrium. For binding reactions, the change in Gibbs free energy (?G) is related to the equilibrium constant (K) through the equation ?G = -RT ln K. This relationship helps explain how variations in binding affinity, such as those brought on by the addition of extra interactions like hydrogen bonds, impact the stability and formation of complexes.

Hydrogen Bond Contribution

Hydrogen bonds, though individually weak, can cumulatively contribute significant stabilization energy to a molecular complex. In binding reactions, each hydrogen bond typically contributes around 1 kcal/mole, and altering the number of hydrogen bonds can effectively change the binding free energy and, consequently, the equilibrium distribution of the bound and unbound states, enabling control over the complex formation at different concentrations.

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