= Conformational population
{title2=$p_i$}
A <conformational population> is the fraction of otherwise specified <molecules> occupying a particular <conformation>. It describes how a <conformational ensemble> is distributed, rather than a single mean structure. For two equilibrium conformations of the same molecular composition, let $G_A,G_B$ be their effective <molar Gibbs free energies> at fixed temperature and pressure. Their population ratio is
$$
\frac{p_B}{p_A}=\exp\left[-\frac{G_B-G_A}{RT}\right].
$$
The effective free energies include each state's internal degeneracy. A higher-free-energy state can remain appreciably populated even though it is not the most common structure.
Populations and exchange rates are different observables. A two-state kinetic model $A\rightleftarrows B$ with rates $k_{AB},k_{BA}$ has equilibrium balance $k_{AB}p_A=k_{BA}p_B$. Multiplying both rates by ten leaves the populations unchanged but speeds exchange tenfold.
In a primary <nuclear magnetic resonance> study of <cyclophilin A>, measurements detected coordinated conformational exchange in the free enzyme and related motions during turnover, illustrating why a static structure is insufficient to describe enzyme dynamics.<Intrinsic dynamics of an enzyme underlies catalysis by Elan Z. Eisenmesser and others>[Abstract: NMR measurements of free-enzyme motions and exchange during catalysis]{ref} Inferring a catalytic mechanism requires the relevant exchange and reaction rates as well as the <conformational populations>.
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