Michaelis–Menten Kinetics¶

An initial-rate enzyme-kinetics regime in which a variable substrate drives a rectangular-hyperbolic rate toward a limiting value V, with Km marking the substrate concentration at half that limit.

Version: v2 · 2026-09-06 · History
Domain-specific #: 2272
Origin domain: biochemistry
Subdomain: enzyme kinetics
Aliases: Michaelis Menten Rate Law, Michaelis Menten Equation

Core Idea¶

Michaelis–Menten kinetics is the initial-rate enzyme-kinetics regime in which the rate varies with one substrate concentration as a rectangular hyperbola:

\[ v_0=\frac{V[S]_0}{K_m+[S]_0}. \]

Here $v_0$ is the initial rate measured for an assay begun with substrate concentration $[S]_0$; $V$, often written $V_{\max}$, is the limiting rate approached as substrate becomes saturating at a fixed temperature and fixed total enzyme concentration; and $K_m$ is the Michaelis constant, a concentration equal to the substrate level at which $v_0=V/2$.^[1]^[2] “Limiting” matters: the hyperbola approaches $V$ asymptotically and ordinarily has no finite substrate concentration at which a mathematical maximum is attained. The conventional $V_{\max}$ name remains useful, but it must not be confused with a true finite-concentration peak such as the one produced by substrate inhibition.^[2]

The empirical rate law is the retained identity. IUPAC defines the equation through the observed dependence of initial rate on initial substrate concentration, and IUBMB explicitly notes that indefinitely many mechanisms can generate Michaelis–Menten behavior.^[1]^[2] A successful hyperbolic fit therefore licenses parameterized rate prediction inside the tested regime; it does not by itself prove a unique molecular mechanism.

The familiar one-intermediate mechanism is

\[ E+S\;\mathop{\rightleftharpoons}^{k_1}_{k_{-1}}\;ES \;\xrightarrow{k_{\mathrm{cat}}}\;E+P. \]

Two historically important approximations reach the same algebraic form but attach different mechanistic readings to $K_m$. The rapid-equilibrium treatment associated with the Henri–Michaelis–Menten tradition treats $E+S\rightleftharpoons ES$ as equilibrated before the slower catalytic step; when $k_{-1}\gg k_{\mathrm{cat}}$, $K_m$ approaches the substrate dissociation constant $K_d=k_{-1}/k_1$. Briggs and Haldane instead imposed a quasi-steady state on the complex after the initial transient, $d[ES]/dt\approx0$, giving

\[ K_m=\frac{k_{-1}+k_{\mathrm{cat}}}{k_1}, \qquad V=k_{\mathrm{cat}}[E]_T. \]

The latter does not require rapid binding equilibrium.^[3]^[4] Consequently, $K_m$ is always the operational half-rate concentration when the hyperbola applies, but it is not generally an equilibrium binding affinity.

The canonical node is deliberately narrow: initial-rate, one-variable-substrate, saturating enzyme catalysis under conditions where substrate depletion, reverse flux, product inhibition, cooperative response, substrate inhibition, enzyme instability, and enzyme–substrate stoichiometric depletion do not invalidate the two-parameter law. Multi-substrate reactions can show an apparent Michaelis–Menten curve in one variable when the other substrates are fixed, but those apparent parameters depend on the fixed conditions and do not turn the underlying reaction into the elementary one-substrate mechanism.^[2]

This is an autonomous domain-specific abstraction beneath the broader live domain_specific:kinetics. Kinetics supplies the genus—rates, paths, rate laws, and control by conditions. Michaelis–Menten Kinetics adds a distinctive enzyme/substrate role system, saturation geometry, parameter semantics, assay protocol, derivation family, and diagnostic failure envelope not entailed by generic chemical kinetics.

Structural Signature¶

A well-formed Michaelis–Menten claim declares the following roles and conditions:

The catalytic enzyme $E$ and its total active-site concentration $[E]_T$. The assay holds active enzyme concentration fixed across the substrate series. In the simple mechanism, $V$ scales with $[E]_T$.
The variable substrate $S$. The initial free substrate concentration $[S]_0$ is varied. “Single-substrate” here means the canonical one-variable law; for a multi-substrate enzyme, other reactants must be fixed and the fitted parameters labeled apparent.
The initial rate $v_0$. Rate is taken after the short complex-forming transient but early enough that substrate depletion and product accumulation are negligible. It is not an arbitrary late-course instantaneous rate.
The limiting rate $V$ or conventional $V_{\max}$. This is the horizontal asymptote for fixed enzyme, temperature, pH, medium, and other controlled conditions.
The Michaelis constant $K_m$. It has concentration units and is operationally the $[S]_0$ at which $v_0=V/2$. It is not automatically $K_d$.
The hyperbolic invariant. Across the valid range, one pair $(V,K_m)$ describes the initial-rate series by $v_0=V[S]_0/(K_m+[S]_0)$.
The low-substrate regime. If $[S]_0\ll K_m$, then $v_0\approx(V/K_m)[S]_0$; the reaction is first order in substrate and $V/K_m$ is the low-concentration slope.
The saturating regime. If $[S]_0\gg K_m$, then $v_0\approx V$; rate becomes approximately independent of further substrate addition.
The validity envelope. Enzyme amount and activity, temperature, pH, ionic conditions, cosubstrates, modifiers, and measurement protocol remain controlled, and the approximation used to interpret the rate law is justified.

The recognition sequence is

\[ \text{fixed active enzyme + varied substrate} \longrightarrow \text{initial-rate series} \longrightarrow \text{single hyperbolic fit} \longrightarrow (V,K_m)\text{ within a declared regime}. \]

For the Briggs–Haldane mechanism, enzyme conservation gives $[E]_T=[E]+[ES]$ and the quasi-steady-state condition gives

\[ [ES]\approx\frac{[E]_T[S]}{K_m+[S]}. \]

Since $v_0=k_{\mathrm{cat}}[ES]$, substitution yields the rate law. This derivation is one mechanistic realization, not part of the empirical definition of every Michaelis–Menten-shaped dataset.

What It Is Not¶

Not enzyme kinetics in general. Enzyme kinetics includes multi-substrate mechanisms, inhibition, activation, cooperativity, pre-steady-state transients, reversibility, processive catalysis, and nonhyperbolic regimes. Michaelis–Menten Kinetics is one named rate-law class inside it.
Not a unique mechanism certificate. A rectangular hyperbola does not prove the elementary $E+S\rightleftharpoons ES\rightarrow E+P$ mechanism. Different mechanisms can collapse to the same two-parameter initial-rate law.^[2]
Not identical to the rapid-equilibrium approximation. Rapid equilibrium is one sufficient derivation with $K_m\approx K_d$ when dissociation is much faster than catalysis. Briggs–Haldane steady state gives the same form without requiring that equilibrium.
Not a universal affinity measurement. In the simple steady-state scheme $K_m=(k_{-1}+k_{\mathrm{cat}})/k_1$, whereas $K_d=k_{-1}/k_1$. They coincide approximately only under an additional rate hierarchy. The safest definition of $K_m$ is operational: half the limiting rate.^[2]
Not an integrated progress curve. The standard equation relates initial rate to starting substrate across assays. Modeling the entire decline of substrate and rise of product over time requires an integrated or reversible model and additional assumptions.
Not substrate inhibition. If high substrate reduces rate, the curve peaks and falls rather than approaching one horizontal asymptote; an inhibition term and parameter such as $K_i$ are required.^[2]
Not cooperative kinetics. Positive or negative cooperativity commonly changes the curve from the simple hyperbola, often producing sigmoidal behavior and a Hill slope different from one. A half-response concentration in that model should not automatically be called $K_m$.^[2]
Not a guarantee of in-vivo flux. Cellular substrate, product, cosubstrate, enzyme, compartment, crowding, and regulatory states can violate the controlled initial-rate conditions. An in-vitro $V$ and $K_m$ do not by themselves determine pathway flux.
Not receptor occupancy merely because the formula is hyperbolic. A one-site equilibrium binding curve can share the algebra, but it reports bound fraction rather than enzyme-catalyzed product-formation rate and lacks $k_{\mathrm{cat}}[E]_T$ semantics.

Scope of Application¶

The native use is a controlled enzyme assay: hold total active enzyme and environmental conditions fixed, vary one substrate, measure early product formation or substrate loss, and fit the initial rates nonlinearly to the hyperbola. The output supports comparison of the limiting catalytic capacity and half-rate substrate scale under those specified conditions.

The framework also supports mechanistic enzyme studies when independent evidence justifies the simple scheme or a broader mechanism that reduces to the same law. Under the Briggs–Haldane realization, $k_{\mathrm{cat}}=V/[E]_T$ and $k_{\mathrm{cat}}/K_m$ is the low-substrate specificity constant. Those normalized quantities allow comparisons that raw $V$ cannot, because $V$ changes with the amount of active enzyme in the assay.

Many biological enzymes use two or more substrates. IUBMB shows that varying one substrate while holding another constant can produce a Michaelis–Menten-shaped curve with apparent $V$ and $K_m$ values.^[2] This is legitimate scoped use, not proof that the reaction is single-substrate. The fixed cosubstrate concentration, product state, and modifiers must accompany the parameters.

The equation can also serve as a reduced component in biochemical-network models, pharmacokinetic clearance models, or transport-catalysis approximations. Such transfer is literal only when an enzyme-like saturable catalytic step and its timescale separation are established. When enzyme concentration is not negligible relative to substrate or complex sequestration materially changes free substrate, standard quasi-steady-state reduction can fail; total quasi-steady-state or full mass-action models may be needed.^[5]

It is outside scope when the data are sigmoidal, bell-shaped, multiphasic, hysteretic, time-dependent because the enzyme is changing, or materially driven by accumulated product. It is also outside scope when a cellular model imports in-vitro constants without checking the local substrate, product, pH, compartment, binding partners, and active-enzyme pool.

Clarity¶

The abstraction clarifies three questions that are often collapsed.

First, what is observed? A fixed-condition initial-rate series follows one rectangular hyperbola. This empirical criterion is primary. Second, what do the parameters mean operationally? $V$ is the limiting rate and $K_m$ is the half-rate substrate concentration. Third, what mechanism might produce it? Rapid equilibrium, Briggs–Haldane steady state, and more complex mechanisms can all do so. Keeping these levels distinct prevents a curve fit from masquerading as a molecular proof.

A compact diagnostic is: if doubling active enzyme doubles the fitted $V$ while leaving the fitted $K_m$ stable, and if increasing substrate moves the initial rate from a linear low-concentration regime toward a fixed asymptote, the data have the expected Michaelis–Menten organization. This is not sufficient by itself; residual structure, high-substrate downturn, sigmoidality, time-dependent activity, or parameter drift across assay windows signals a violated envelope.

The distinction from Kinetics is equally direct. Kinetics asks how rates depend on state and conditions across chemical systems. Michaelis–Menten asks whether a particular enzyme assay's one-variable initial rates obey this saturation law, and if so what $V$ and $K_m$ summarize that regime.

Manages Complexity¶

An enzyme mechanism can contain binding, conformational change, chemistry, product release, reverse reactions, modifiers, and coupled cosubstrates. Michaelis–Menten Kinetics compresses that possible machinery into two experimentally identifiable parameters when the rate law applies. Instead of tracking every microscopic state, the practitioner can distinguish three regimes from the ratios $[S]/K_m$: a low-substrate region controlled by $V/K_m$, a transition around $K_m$, and a saturating region controlled by $V$.

This compression supports experimental design. Measurements only at $[S]\ll K_m$ identify mainly the ratio $V/K_m$ and cannot separately anchor both parameters. Measurements only at $[S]\gg K_m$ constrain $V$ but weakly constrain $K_m$. Spanning both sides of the half-rate scale exposes the curve's slope and plateau. Nonlinear fitting to the original rate law preserves the experimental error structure better than relying automatically on reciprocal linearizations, which magnify errors at low substrate.^[6]

The abstraction also localizes failure. A high-substrate downturn points toward substrate inhibition rather than a larger $K_m$; a sigmoid points toward cooperative or allosteric structure; systematic time-window drift points toward depletion, product effects, or enzyme instability; enzyme-comparable substrate concentrations point toward sequestration and a different quasi-steady-state reduction. The two-parameter model is useful partly because its residuals tell the practitioner when more mechanism is needed.

Abstract Reasoning¶

The equation licenses exact comparative inferences inside its validity envelope.

At $[S]=K_m$,

\[ v_0=\frac{VK_m}{K_m+K_m}=\frac{V}{2}. \]

At $[S]=9K_m$, $v_0=0.9V$; at $[S]=99K_m$, $v_0=0.99V$. Saturation is therefore graded and asymptotic, not a switch at $K_m$. Conversely, at $[S]=K_m/9$, the rate is $0.1V$. These ratios provide dimensionless assay planning without requiring a particular enzyme or unit system.

The local substrate sensitivity is

\[ \frac{dv_0}{d[S]}=\frac{VK_m}{(K_m+[S])^2}, \]

which decreases monotonically with substrate. The result explains diminishing marginal rate gain as active sites become increasingly occupied in the simple mechanistic picture. It does not establish that a real enzyme has one physical site or no conformational states; it describes the fitted law's sensitivity.

Under the simple Briggs–Haldane mechanism, doubling $[E]_T$ at unchanged microscopic constants doubles $V=k_{\mathrm{cat}}[E]_T$ but does not change $K_m$. If both fitted parameters change, the assay may have altered more than enzyme amount—for example aggregation, tight binding, modifier balance, or a changed model regime. Again, this is a diagnostic, not proof of a specific defect.

At low substrate,

\[ v_0\approx\frac{V}{K_m}[S] =\frac{k_{\mathrm{cat}}}{K_m}[E]_T[S], \]

so $k_{\mathrm{cat}}/K_m$ captures catalytic efficiency in that limit. At high substrate, the dependence on $[S]$ disappears to first order and $k_{\mathrm{cat}}$ controls rate per active site. The two limits answer different experimental questions and should not be ranked by $K_m$ alone.

Knowledge Transfer¶

Within enzymology, the full role system transfers across hydrolases, oxidoreductases, transferases, and engineered catalysts whenever one variable-substrate initial-rate series follows the law. The identities of enzyme and substrate change, but the assay, hyperbola, limiting rate, half-rate concentration, and boundary diagnostics remain intact.

Within multi-substrate enzymology, the form transfers conditionally. Varying substrate $A$ at a fixed concentration of $B$ can yield apparent $V_A^{\mathrm{app}}$ and $K_{m,A}^{\mathrm{app}}$; changing $[B]$ can change both. The transfer therefore carries an explicit “other reactants fixed” qualifier. Treating apparent parameters as intrinsic constants without that qualifier loses information.

In pharmacology and systems biology, a saturable metabolic or transport step may use a Michaelis–Menten term. The transfer is legitimate when the rate-generating step has a justified enzymatic or carrier mechanism and the reduction is validated. It becomes analogy when any saturating response is called Michaelis–Menten merely because it resembles a hyperbola. Receptor occupancy, resource-limited growth, and ecological functional responses may share mathematics while having distinct causal roles and parameter meanings.

The portable residue is a saturating input–rate relation and a low-input/high-input regime split. Those generic structures belong with asymptotic behavior, saturation, and diminishing sensitivity. The named Michaelis–Menten abstraction stays with catalytic rate, enzyme concentration, substrate concentration, and initial-rate parameter semantics.

Examples¶

Numerical assay example. Suppose nonlinear fitting gives $V=120\ \mu\mathrm{M}\,\mathrm{min}^{-1}$ and $K_m=3.0\ \mathrm{mM}$ at a fixed enzyme concentration. At $[S]=3.0\ \mathrm{mM}$, $v_0=60\ \mu\mathrm{M}\,\mathrm{min}^{-1}$. At $0.30\ \mathrm{mM}$, $v_0=120(0.30)/(3.30)\approx10.9\ \mu\mathrm{M}\,\mathrm{min}^{-1}$, close to the low-substrate linear prediction of $12$. At $30\ \mathrm{mM}$, $v_0=120(30)/(33)\approx109.1\ \mu\mathrm{M}\,\mathrm{min}^{-1}$: a tenfold increase beyond $K_m$ reaches about 91% of the limit, not an exact maximum.

Original rapid-equilibrium boundary. Michaelis and Menten's invertase work belongs to the historical rapid-equilibrium lineage. In that special regime, fast substrate association and dissociation relative to catalytic conversion make $K_m$ approximate the $ES$ dissociation constant.^[4] The example illustrates one mechanism supporting the hyperbola; it does not redefine every modern $K_m$ as affinity.

Briggs–Haldane steady-state realization. For $E+S\rightleftharpoons ES\rightarrow E+P$, suppose $k_1=2\ \mu\mathrm{M}^{-1}\mathrm{s}^{-1}$, $k_{-1}=6\ \mathrm{s}^{-1}$, $k_{\mathrm{cat}}=4\ \mathrm{s}^{-1}$, and $[E]_T=0.50\ \mu\mathrm{M}$. Then $K_m=(6+4)/2=5\ \mu\mathrm{M}$ and $V=4(0.50)=2\ \mu\mathrm{M}\,\mathrm{s}^{-1}$. The dissociation constant is only $K_d=6/2=3\ \mu\mathrm{M}$, demonstrating why $K_m$ cannot generally be read as affinity.

Multi-substrate apparent kinetics. An enzyme that consumes $A$ and $B$ may show a hyperbola when $A$ varies and $B$ is held fixed. The fitted $K_{m,A}^{\mathrm{app}}$ belongs to that fixed-$B$ condition. Repeating the series at another $[B]$ can shift the curve. The observation is Michaelis–Menten-shaped in $A$ without converting the reaction into a one-substrate mechanism.^[2]

Substrate-inhibition failure. If rate rises, peaks, and then falls as $[S]$ becomes very high, no choice of positive $V$ and $K_m$ can reproduce the downturn because the canonical hyperbola is monotone increasing. The data require a substrate-inhibition or other non-Michaelis model; the true finite peak must not be mislabeled $V_{\max}$.^[2]

Product-buildup failure. A late progress curve may slow because substrate has been consumed, product drives reverse flux, product inhibits the enzyme, or the enzyme loses activity. Applying the initial-rate equation point-by-point to that course misattributes time-dependent conditions to substrate saturation. The repair is an integrated or reversible model, or a shorter validated initial-rate window.

Structural Tensions¶

Empirical economy versus mechanistic ambiguity. Two parameters can predict a rate series well, but the same hyperbola can arise from many mechanisms. The better the compression works, the easier it is to overread it. Diagnostic: does the claim stop at empirical rate behavior, or is a microscopic mechanism supported by independent transient, binding, structural, or perturbation evidence?

Operational $K_m$ versus affinity language. The half-rate concentration is always available when the law fits; the dissociation interpretation needs rapid equilibrium or other specific rate constraints. Diagnostic: has $k_{\mathrm{cat}}$ been shown negligible relative to $k_{-1}$, or is “affinity” merely being inferred from a fitted $K_m$?

Initial-rate control versus biological realism. Early assays suppress depletion, product, and regulation to isolate the forward catalytic response. Cells retain all of those complications. Diagnostic: are the fitted parameters answering a controlled catalytic question, or being asked to predict a steady cellular flux without a surrounding network model?

Substrate excess versus enzyme sequestration. The standard quasi-steady-state approximation is reliable in a common low-enzyme regime, but when enzyme is comparable to substrate, binding materially removes free substrate and the ordinary reduction can fail.^[5] Diagnostic: is total enzyme negligible on the relevant substrate-plus-$K_m$ scale, or should total-QSSA/full mass action replace the standard law?

Simple hyperbola versus regulated enzyme. Cooperativity, allostery, substrate inhibition, isoform mixtures, and slow conformational change can produce systematic deviations. Forcing the two-parameter model may yield precise but meaningless values. Diagnostic: are residuals random around one monotone hyperbola, or do they retain sigmoidality, downturn, phases, or time structure?

Limiting rate versus attainable maximum. $V$ is an asymptote, while a substrate-inhibited curve has a true finite maximum. Casual use of $V_{\max}$ hides the distinction. Diagnostic: does rate approach a plateau monotonically, or actually peak and decline?

Structural–Framed Character¶

Michaelis–Menten Kinetics is structural-leaning and strongly domain-bound. The rate law is mathematical, evaluatively neutral, observer-independent, and reproducible across enzyme systems. Its predictions follow from declared concentrations and parameters, not institutional rules or human judgment.

Yet the complete abstraction does not travel substrate-free. “Enzyme,” “substrate,” “active catalytic center,” “turnover,” “initial product-formation rate,” $K_m$, and $k_{\mathrm{cat}}$ bind the roles to biochemical catalysis. A generic saturating response may instantiate the same rational function without inheriting the enzyme-kinetic interpretation. That combination—formal structure plus biochemical role semantics—supports domain-specific rather than prime classification.

Structural Core vs. Domain Accent¶

The structural core is a monotone saturating input–rate map with two regimes. At low input, output is approximately proportional to input; at high input, a finite-capacity bottleneck fixes an asymptote; one scale parameter marks the midpoint. The core supports dimensionless comparison through $[S]/K_m$ and diminishing marginal sensitivity.

The domain accent fixes the input as substrate concentration, output as enzyme-catalyzed initial reaction rate, capacity as active-enzyme turnover, and midpoint as the Michaelis concentration. It also supplies enzyme conservation, the $ES$ intermediate, rapid-equilibrium and quasi-steady-state derivations, $V=k_{\mathrm{cat}}[E]_T$, assay-window requirements, and characteristic failure modes from products, modifiers, cooperativity, and depletion.

Removing the domain accent leaves a generic saturation curve, not Michaelis–Menten Kinetics. Conversely, generic Kinetics includes rate laws with arbitrary order, activation barriers, reversibility, and multi-step paths without requiring this hyperbola. The candidate therefore has a real residual beneath Kinetics rather than being an alias or a composite restatement of generic primes.

Kinetics is the minimal DAG parent and the exact genus. Michaelis–Menten Kinetics is chemical rate-and-path analysis specialized to an enzyme-catalyzed, one-variable initial-rate saturation law. The proposed relation is strict subsumption: every valid instance is kinetics, while most kinetics is not Michaelis–Menten.

Catalysis is constitutive to the canonical mechanism because the enzyme accelerates substrate conversion and is regenerated. It is strongly related but does not by itself supply the substrate-dependence equation or parameter semantics, so a second parent edge is unnecessary.

The live Asymptotic Behavior prime describes the approach to $V$, while generic saturation and model-validity reasoning describe declining sensitivity and the need to keep approximation conditions explicit. These are structural readings and audit aids rather than additional minimal parents.

One proposal-only edge is recommended: domain_specific:michaelis_menten_kinetics is a strict subtype of live domain_specific:kinetics. No live DAG or canonical artifact is changed here.

Relationships to Other Abstractions¶

Current abstraction Michaelis–Menten Kinetics Domain-specific

Parents (1) — more general patterns this builds on

Michaelis–Menten Kinetics is a kind of Kinetics Domain-specific

Kinetics is the minimal DAG parent and the exact genus.

Neighborhood in Abstraction Space¶

Michaelis–Menten Kinetics sits in a sparse region of the domain-specific corpus (98^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Pharmacodynamics & Reaction Kinetics (12 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08

Not to Be Confused With¶

The strongest catalog neighbor, Kinetics, is broader exact ancestry rather than collision. It covers how chemical rates depend on concentrations, temperature, catalysts, barriers, and paths. Michaelis–Menten Kinetics fixes enzyme and substrate roles, an initial-rate assay, a rectangular hyperbola, $V$ and $K_m$, and a narrow validity envelope.

Catalysis is the generic rate acceleration of a reaction by a regenerated catalyst. It does not imply saturable substrate dependence, an $ES$ complex, or Michaelis–Menten parameters. Enzyme Inhibition models modifier-induced rate changes and may alter apparent parameters or produce non-Michaelis behavior; inhibition is neither the uninhibited baseline law nor an alias for it.

Reaction Intermediate captures the general role played by $ES$, but many reactions have intermediates without the Michaelis–Menten rate law, and many empirical hyperbolas do not identify a unique intermediate mechanism. Receptor Saturation concerns occupancy or signaling limits in receptor systems; algebraic resemblance does not import catalytic turnover.

Hill kinetics or a Hill equation introduces a slope/cooperativity parameter and can be sigmoidal. Langmuir adsorption describes equilibrium surface coverage. Monod kinetics describes microbial growth as a function of limiting nutrient. These may share a hyperbolic form at special parameter values, but their measured outputs, mechanisms, and parameter meanings differ.

Vocabulary must keep Michaelis–Menten equation, Michaelis–Menten rate law, and controlled hyperbolic enzyme kinetics as candidate-local surfaces. Briggs–Haldane kinetics is a mechanistic derivation label; rapid-equilibrium kinetics is a special derivation regime; Michaelis constant and maximum velocity are components; substrate inhibition, cooperative kinetics, reversible Michaelis–Menten kinetics, and total QSSA are extensions or contrasts, not aliases.

References¶

[1] International Union of Pure and Applied Chemistry, “Michaelis–Menten equation” and “Michaelis–Menten kinetics,” Compendium of Chemical Terminology (Gold Book), 5^th ed. https://goldbook.iupac.org/terms/view/11546 and https://goldbook.iupac.org/terms/view/M03892 registry ↩a ↩b

[2] Nomenclature Committee of the International Union of Biochemistry, “Symbolism and Terminology in Enzyme Kinetics,” Recommendation 1981, published in Biochemical Journal 213 (1983): 561–571 and companion journals. https://iubmb.qmul.ac.uk/kinetics/ and https://iubmb.qmul.ac.uk/kinetics/ek4t6.html registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k

[3] George Edward Briggs and J. B. S. Haldane, “A Note on the Kinetics of Enzyme Action,” Biochemical Journal 19, no. 2 (1925): 338–339. https://doi.org/10.1042/bj0190338 registry ↩

[4] Kenneth A. Johnson and Roger S. Goody, “The Original Michaelis Constant: Translation of the 1913 Michaelis–Menten Paper,” Biochemistry 50, no. 39 (2011): 8264–8269. https://doi.org/10.1021/bi201284u registry ↩a ↩b

[5] Justin Eilertsen and Santiago Schnell, “The Quasi-Steady-State Approximations Revisited: Timescales, Small Parameters, Singularities, and Normal Forms in Enzyme Kinetics,” Mathematical Biosciences 325 (2020): 108339. https://doi.org/10.1016/j.mbs.2020.108339 registry ↩a ↩b

[6] Athel Cornish-Bowden, “One Hundred Years of Michaelis–Menten Kinetics,” Perspectives in Science 4 (2015): 3–9. https://doi.org/10.1016/j.pisc.2014.12.002 registry ↩