Cooperativity

Cooperativity is a phenomenon displayed by systems involving identical or near-identical elements, which act non-independently of each other, relative to a hypothetical standard non-interacting system in which the individual elements are acting independently. One manifestation of this is enzymes or receptors that have multiple binding sites where the affinity of the binding sites for a ligand is apparently increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to a binding site. For example, when an oxygen atom binds to one of hemoglobin's four binding sites, the affinity to oxygen of the three remaining available binding sites increases; i.e. oxygen is more likely to bind to a hemoglobin bound to one oxygen than to an unbound hemoglobin. This is referred to as cooperative binding. We also see cooperativity in large chain molecules made of many identical (or nearly identical) subunits (such as DNA, proteins, and phospholipids), when such molecules undergo phase transitions such as melting, unfolding or unwinding. This is referred to as subunit cooperativity. However, the definition of cooperativity based on apparent increase or decrease in affinity to successive ligand binding steps is problematic, as the concept of "energy" must always be defined relative to a standard state. When we say that the affinity is increased upon binding of one ligand, it is empirically unclear what we mean since a non-cooperative binding curve is required to rigorously define binding energy and hence also affinity. A much more general and useful definition of positive cooperativity is: A process involving multiple identical incremental steps, in which intermediate states are statistically underrepresented relative to a hypothetical standard system (null hypothesis) where the steps occur independently of each other. Likewise, a definition of negative cooperativity would be a process involving multiple identical incremental steps, in which the intermediate states are overrepresented relative to a hypothetical standard state in which individual steps occur independently. These latter definitions for positive and negative cooperativity easily encompass all processes which we humans call "cooperative", including conformational transitions in large molecules (such as proteins) and even psychological phenomena of large numbers of people (which can act independently of each other, or in a co-operative fashion).