= Induced fit
In <induced fit>, a <substrate> binds to an <enzyme> and the resulting <enzyme-substrate complex> subsequently changes its <protein structure>. This adjustment can position interacting groups at the <active site> for <catalysis>. The mechanistic claim concerns order: binding precedes the relevant change. In <conformational selection>, the unbound <enzyme> already visits an alternative <protein structure>, which the <substrate> preferentially binds. Both processes can occur in one system. Let $E$ and $E^*$ denote two structures of the same <enzyme>, and $S$ a <substrate>. The limiting routes are
$$
\begin{aligned}
\text{induced fit:}\quad &E+S\rightleftharpoons ES\rightleftharpoons E^*S,\\
\text{conformational selection:}\quad &E\rightleftharpoons E^*,\qquad E^*+S\rightleftharpoons E^*S.
\end{aligned}
$$
The star labels a structure, not a different <protein primary structure>, and does not by itself mean catalytic activity. Each reversible arrow abbreviates a step, not the whole catalytic cycle. See https://pmc.ncbi.nlm.nih.gov/articles/PMC2728963/[Gordon G. Hammes, Yu-Chu Chang and Terrence G. Oas, Conformational selection or induced fit: a flux description of reaction mechanism, PNAS 106 (2009), 13737–13741].
A rigid lock-and-key cartoon usefully suggests selective <substrate> recognition, but it suppresses movement of the <protein> and chemical changes at the <active site>. Replacing it with two static drawings, “open” and “closed”, still does not establish <induced fit>: both routes above can end at $E^*S$. Also, if complete closure prevents a <substrate> entering, the pre-existing structure selected in <conformational selection> might be partly open and undergo further <induced fit> after binding. The usefulness of the distinction is that it turns an attractive shape story into questions about <enzyme kinetics>. Relative traffic through the routes depends on populations, <rate constants> and free <substrate> <concentration>, rather than affinity alone. See https://pmc.ncbi.nlm.nih.gov/articles/PMC2728963/[Hammes, Chang and Oas, 2009: coupled pathways, their concentrations and the limitations of endpoint structures].
\Image[/active-sites-induced-fit-binding-orders.png]
{title=<Induced fit> and <conformational selection>: two orders, one bound endpoint}
{description=Original reaction-order schematic and an analytical first-event model, not a <hexokinase> structure or measured data. In the upper square, horizontal steps bind or release a <substrate>; vertical steps change <protein structure>. In the lower plot, an initially unbound $E$ can bind with rate $a=k_{\mathrm{on}}s$ or change structure with rate $b$, for chosen $k_{\mathrm{on}}=1\,\mathrm{\mu M^{-1}s^{-1}}$ and $b=1\,\mathrm{s^{-1}}$. The plotted <probability> $a/(a+b)$ concerns only the first event from $E$, not the fraction completing either full route. Subsequent binding, reversals and <catalysis> are not modelled by that curve.}
For this analytical illustration, hold the free <substrate> <concentration> $s$ constant and assume independent waiting times with <exponential distributions> of constant rates. The <law of mass action> gives the binding rate $a=k_{\mathrm{on}}s$; the competing change has rate $b$. The <probability density function> for binding to happen first at time $t$ is $a e^{-(a+b)t}$, because neither event has happened earlier. Its integral is
$$
P(\text{binding first})=\int_0^\infty a e^{-(a+b)t}\,dt=\frac{a}{a+b}.
$$
With the stated invented <rate constants>, $s=0.1,1,10\,\mathrm{\mu M}$ gives $1/11,1/2,10/11$, respectively. Raising free <substrate> <concentration> makes binding more likely to win this initial competition. This <probability> is deliberately narrower than a full-route fraction: returns to $E$, later changes and the binding properties of $E^*$ would all matter for the latter. The illustration explains why timing and <concentration> must accompany structural evidence, without assigning a binding mechanism to a real <enzyme>.
A motivating experiment tested the crystal interpretation in solution. McDonald, Steitz and Engelman prepared solutions of monomeric <yeast> <hexokinase> B and compared the unbound preparation with sugar-bound preparations. Their apparatus measured small-angle scattering of <X-rays>; the spatial extent inferred from that readout was the <radius of gyration>, rather than a catalytic <reaction rate>. Binding <glucose> reduced the <radius of gyration> by $0.95\pm0.24\,\mathrm{\mathring A}$; binding the phosphorylated <glucose> product reduced it by $1.25\pm0.28\,\mathrm{\mathring A}$, as reported by the authors. The <glucose> change agreed with the reduction calculated from the crystal coordinates. See https://pubmed.ncbi.nlm.nih.gov/369601/[Robert C. McDonald, Thomas A. Steitz and Donald M. Engelman, Yeast hexokinase in solution exhibits a large conformational change upon binding glucose or glucose 6-phosphate, Biochemistry 18 (1979), 338–342: primary abstract].
The comparison without added <substrate> supplies a baseline within the same form of <hexokinase>; the second bound preparation tests another binding condition. Together with the crystal comparison, solution compaction supports closure beyond crystal packing. It still gives an average spatial readout, not a movie of individual binding events, and product-associated compaction does not demonstrate ongoing <catalysis>. Neither experiment alone proves that binding precedes movement. To distinguish <induced fit> from <conformational selection>, structural comparisons must be combined with measurements sensitive to timing and with a model of the relevant populations and <enzyme kinetics>.
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