An entropic mechanism to generate highly cooperative and specific binding from protein phosphorylations

Cooperative interactions are essential to the operation of many biochemical networks. Such networks then respond ultrasensitively in a nonlinear manner to linear changes in network input, and network output, for example, levels of a phosphorylated protein or of gene expression, becomes a sigmoidal function of concentrations of input molecules. We present a novel, entropic ultrasensitivity mechanism that generates highly cooperative and specific binding between two proteins. We consider a disordered protein with multiple phosphorylation sites that binds to a single binding site on an interacting protein. We assume that each phosphorylation locally orders the protein. Such local order affects protein conformational entropy nonlinearly and generates binding that is a highly cooperative function of the number of protein phosphorylations (with Hill coefficients well above 10). Substantial binding may only occur once the disordered protein is phosphorylated a critical number of times or more. Cooperativity is determined by the size of the disordered region of the protein, the binding affinity, and unusually the concentration of the interacting protein. Given the widespread occurrence of disordered, multiply phosphorylated proteins, its highly ultrasensitive character, and the ease of its control, entropic, phosphorylation-driven cooperativity may be extensively exploited intracellularly.