CHM-05

Michaelis–Menten rate

v = Vmax [S] / (Km + [S]). Enzyme kinetics.

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KineticsMichaelis–Menten 1913

Governing equation

v=\dfrac{V_{\max}[S]}{K_m+[S]}

$[S] \in \left[0.5, 800\right]$

where

V_{max}: Vmax (µM/s)
K_m: Km (µM)
[S]: Substrate (µM)
v: Rate (µM/s)

The figure, part by part

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①

Governing law — red

v=\dfrac{V_{\max}[S]}{K_m+[S]}

$[S] \in \left[0.5, 800\right]$

$[S] = 0.5$ $v = 0.119$

Along the curve

②

Domain of the variable — blue

[S]_{\min} = 0.5,\quad [S]_{\max} = 800

$[S] \in \left[0.5, 800\right]$

$[S] = 0.5$ $[S] = 0.5$

Along the curve

③

Response curve — green

v=\dfrac{V_{\max}[S]}{K_m+[S]}

$[S] \in \left[0.5, 800\right]$

$[S] = 0.5$ $v = 0.119$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}[S]}

$[S] \in \left[0.5, 800\right]$

$[S] = 5.528$ $v^{\prime} = 0.196$

Along the curve

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-05 — Michaelis–Menten rate) is the form associated with Michaelis–Menten 1913. Working symbols: $V_{max}$ , $K_m$ , $[S]$ $\rightarrow$ $v$ . Km is the substrate at half Vmax. Lineweaver–Burk linearises 1/v vs 1/[S].

Purpose

Purpose: compute

v

from

V_{max}

K_m

[S]

in Physical chemistry via

v=\dfrac{V_{\max}[S]}{K_m+[S]}

v = Vmax [S] / (Km + [S]). Enzyme kinetics. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V_{max} = 12.000\,\mathrm{\mu M/s}

K_m = 50.000\,\mathrm{\mu M}

[S] = 40.000\,\mathrm{\mu M}

, the governing relation

v=\dfrac{V_{\max}[S]}{K_m+[S]}

yields

v = 5.333\,\mathrm{\mu M/s}

. Single substrate, quasi-steady [ES], no inhibition. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Vmax V_{max}12 µM/sKm K_m50 µMSubstrate [S]40 µM

Outputs

Rate v5.333 µM/s

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Narration of this film

Single substrate, quasi-steady [ES], no inhibition.

Km is the substrate at half Vmax. Lineweaver–Burk linearises 1/v vs 1/[S].

Reading speed

Watch on YouTube