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An active site is the region of an enzyme where a substrate binds and undergoes a chemical reaction. In a protein enzyme, it includes the amino acid residues that contact the substrate and those that directly assist catalysis. These roles can overlap: an amino acid side chain can both orient a substrate and participate in chemistry. The active site occupies only part of the folded protein; the remaining amino acid residues help establish its protein structure, stability and movement. An active site need not be a consecutive stretch of protein primary structure: protein folding can bring distant amino acid residues together. A ribozyme instead supplies an RNA active site. See Alberts et al., Molecular Biology of the Cell, Protein Function: binding sites and catalytic sites.

Binding and catalysis answer different questions. A protein binding site recognizes shape and chemistry through such interactions as hydrogen bonds, electrostatics and the hydrophobic effect. At an active site, appropriate positioning also helps a substrate reach the transition state of a chemical reaction. Some amino acid side chains transfer a proton; others participate transiently in a covalent bond. The enzyme-substrate complex is the associated enzyme and substrate, before conversion to a reaction product. Merely accumulating this complex does not establish rapid catalysis: stabilizing the bound substrate without sufficiently stabilizing the transition state can leave a large barrier. The important complementarity is chemical as well as geometric. See Geoffrey M. Cooper, The Cell, The Central Role of Enzymes as Biological Catalysts: substrate binding and transition-state stabilization.

The cartoon makes a useful experimental distinction. Changing a contacting amino acid residue might weaken substrate binding, change the reaction rate, or do both. Changing a distant amino acid residue can also disrupt the active site by changing protein folding. Therefore a loss of activity after a mutation alone does not locate a catalytic group: compare binding, protein structure and enzyme kinetics as well. This is an interpretation guide, not a report of a particular mutation experiment.

A concrete example is hexokinase: it transfers the terminal phosphate group of ATP to the $6$-position hydroxyl group of a sugar such as glucose. Specificity need not mean only one acceptable substrate: the hexokinase reaction class includes several possible acceptor sugars. Which are used, and at what reaction rates, depends on the particular enzyme and conditions. See Swiss Institute of Bioinformatics, ENZYME entry EC 2.7.1.1: hexokinase reaction and acceptor range.

Bennett and Steitz compared yeast hexokinase A crystallized with glucose against hexokinase B crystallized without glucose. X-rays scattered by the crystals supplied diffraction measurements from which the authors reconstructed protein structure; comparing coordinates located movement, rather than measuring a reaction rate. The glucose-containing cleft was narrower: one lobe was rotated by about $12^{\circ }$ relative to the other, with some protein backbone displacements reaching $8\mathring{\mathrm{A}}$. This makes the active site a moving arrangement of interacting groups, rather than a permanent hole. See William S. Bennett Jr. and Thomas A. Steitz, Glucose-induced conformational change in yeast hexokinase, PNAS 75 (1978), 4848–4852.

The structural comparison has two explicit limitations: different forms of hexokinase and different crystal environments were compared, and static coordinates do not record the order of binding and movement. Closure is consistent with induced fit, but those structures alone cannot exclude conformational selection. The solution experiment under induced fit addresses whether compaction also occurs outside a crystal.

An enzyme inhibitor lowers an enzyme's reaction rate. In reversible enzyme inhibition, reducing free inhibitor concentration can restore activity; slow release can make this difficult to distinguish experimentally from irreversible inactivation. Competitive inhibition and mixed inhibition describe different changes in enzyme kinetics; pure noncompetitive inhibition is a special case of mixed inhibition, not a name for every inhibitor that binds away from an active site.^[ref]

The useful question is how adding substrate changes the inhibition. The model below connects binding to a measurable reaction rate, predicts when more substrate can overcome inhibition, and supplies examples for comparison with an enzyme inhibition initial-rate assay. Its inhibition constants are explicitly defined; neither a binding cartoon nor one reduced reaction rate by itself determines a mechanism.

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 $E^{\ast }$ denote two structures of the same enzyme, and $S$ a substrate. The limiting routes areThe 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 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 $E^{\ast }S$. 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 Hammes, Chang and Oas, 2009: coupled pathways, their concentrations and the limitations of endpoint structures.

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 isWith the stated invented rate constants, $s=0.1,1,10\mu \mathrm{M}$ 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 $E^{\ast }$ 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 $0.95\pm 0.24\mathring{\mathrm{A}}$; binding the phosphorylated glucose product reduced it by $1.25\pm 0.28\mathring{\mathrm{A}}$, as reported by the authors. The glucose change agreed with the reduction calculated from the crystal coordinates. See 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.

In the branching model, mixed inhibition retains inhibitor binding to both free enzyme and the enzyme-substrate complex. Unequal $K_i$ and $K_i^{\prime }$ shift both apparent parameters; their equality gives pure noncompetitive inhibition. For the chosen unequal case, $I=30\mu \mathrm{M}$ gives $\alpha =4$ and ${\alpha }^{\prime }=2$, hence $V_{\max ,\mathrm{app}}=50\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$ and $K_{M,\mathrm{app}}=40\mu \mathrm{M}$. Because $K_i<K_i^{\prime }$, binding favours free enzyme, and the apparent Michaelis constant increases. Reversing that inequality decreases it.

The limiting behaviour provides a useful diagnostic within this model:Low substrate concentration isolates $\alpha$ through the initial slope; high substrate concentration isolates ${\alpha }^{\prime }$ through the plateau. At $I=30\mu \mathrm{M}$, the chosen competitive inhibition and unequal mixed inhibition examples have the same low-$s$ slope, $1.25\mathrm{mi}{\mathrm{n}}^{-1}$, but different plateaus, $100$ and $50\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. Measuring only low substrate concentrations would miss that distinction.

For an experiment beginning by mixing unbound enzyme with substrate, take $\boxed{[E](0)=e_0>0,[S](0)=s_0>0,[X](0)=[Y](0)=[E_i](0)=[P](0)=0}$. The enzyme-substrate complexes, inactivated enzyme and product are initially absent. Nonzero pre-existing product could be allowed without changing the dynamics here, since it has no feedback reaction in the specified scheme.

Set $K_i=K_i^{\prime }$, so that $\alpha ={\alpha }^{\prime }$. The reversible enzyme inhibition equation reduces toAt the chosen $I=30\mu \mathrm{M}$, every reaction rate is one quarter of its uninhibited value. The plateau falls to $25\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$, but half that plateau still occurs at $s=20\mu \mathrm{M}$. Increasing substrate cannot restore the uninhibited plateau. An unchanged apparent Michaelis constant here expresses equality of the two binding effects, rather than an absence of inhibitor binding to the enzyme-substrate complex.

A quasi-steady-state approximation for enzyme-substrate complexes can remain useful when total enzyme and initial substrate concentrations are comparable. The relevant parameter can involve the sum $s_0+K_m$, rather than $s_0$ alone. In a mechanism-based inhibition model with $s_0/K_m=O(\epsilon )$, bounded intermediate decay rates and an inactivation rate of order $\epsilon$, the fast complexes adjust in a layer of scaled width $O(\epsilon )$. On bounded slow-time intervals the main complex follows the substrate, the later complex and accumulated inactivated enzyme remain $O(\epsilon )$, and the substrate has leading exponential depletion. An outer algebraic complex concentration does not satisfy the unbound initial condition inside that initial layer.

Construct a minimal model with one substrate and no appreciable accumulated reaction product. Only the enzyme-substrate complex $ES$ produces product, with catalytic rate constant $k_{\mathrm{cat}}$; $EI$ and $ESI$ are inactive. Write $s=[S]$ and $I=[\mathrm{I}]$ for free molar concentrations, and $E_T$ for total enzyme molar concentration. Assume a suitable quasi-steady-state approximation, rapid inhibitor binding and release relative to turnover, and negligible depletion of free inhibitor. In this construction the population relations areHere $K_M$ is the uninhibited Michaelis constant, and $K_i,K_i^{\prime }$ are the inhibition constants for the two indicated binding branches. The symbol $I$ denotes a free concentration, not an amount added to the tube. Define $V_{\max }=k_{\mathrm{cat}}{E}_T$. Conservation of enzyme gives an original short derivation:Thus fitting a Michaelis-Menten equation at a fixed $I$ would return the apparent parameters“Apparent” means conditional on that inhibitor concentration. The uninhibited Michaelis constant has not been redefined. Dimensional analysis checks the denominator: both $\alpha K_M$ and ${\alpha }^{\prime }s$ have units of molar concentration; the resulting $v$ has units of reaction rate.

The shared numerical choices make the mechanisms comparable. At $I=0$ and $s=20\mu \mathrm{M}$, all three models give $v=50\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. At $I=10\mu \mathrm{M}$, the respective reaction rates are $100/3$, $25$, and $30\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$; at $I=30\mu \mathrm{M}$ they are $20$, $12.5$, and $50/3\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. These are independently chosen teaching models, not measured inhibition constants for a named enzyme.

The complementary limit of the branching model permits inhibitor binding only to the enzyme-substrate complex: set $K_i\to \infty$, hence $\alpha =1$, with finite $K_i^{\prime }$. Then both $V_{\max ,\mathrm{app}}$ and $K_{M,\mathrm{app}}$ decrease by ${\alpha }^{\prime }$, while their ratio stays fixed. This limit helps distinguish preferential binding to $ES$ in mixed inhibition from exclusive binding to $ES$ in uncompetitive inhibition.