Lineweaver-Burke Plots

• The Michaelis-Menten equation describes the rate of an enzymatic reaction as a function of substrate concentration.
• It is written in the form :

$$V_0=\frac{V_{max}\ast [S]}{[K_m]+[S]}$$

• where :

  • $[S]$$[S]$ = substrate concentration

  • $V_0$$V_0$ = observed reaction rate at a given $[S]$$[S]$

  • $V_{max}$$V_{max}$ = maximum possible reaction rate

  • $[K_m]$$[K_m]$ :

    • Michaelis constant

    • substrate concentration at which $\frac{V_{max}}{2}$$\frac{V_{max}}{2}$ is achieved

    • also a "measure" of the affinity of Enzyme for Substrate

    • $\propto$$\propto$ Binding Tightness of ES complex

      • smaller values of $K_m$$K_m$ mean the Enzyme is more tightly bound to the Substrate

$$E+S\stackrel{k_f}{\underset{k_r}{\stackrel{-\rightharpoonup }{\leftharpoondown -}}}ES\stackrel{k_{cat}}{⟶}E+P$$

• Lineweaver-Burke plots are used to determine Michaelis-Menton kinetic parameters.

• These linear plots relate the inverse of reaction velocity $\frac{1}{V}$$\frac{1}{V}$ on the y-axis to the inverse of the substrate concentration $\frac{1}{[S]}$$\frac{1}{[S]}$ on the x-axis.

• This linear relationship is based on rearrangements of the Michaelis-Menton equation.

• On a Lineweaver-Burke plot :

  • the x-intercept corresponds to the negative inverse of the Michaelis constant

    • ( x-intercept = $-\frac{1}{K_m}$$-\frac{1}{K_m}$ )

  • And the y-intercept corresponds to the inverse of the maximum velocity

    • ( y-intercept = $\frac{1}{V_{max}}$$\frac{1}{V_{max}}$ )

• Because the y-intercept in a Lineweaver-Burke plot is $\frac{1}{V_{max}}$$\frac{1}{V_{max}}$ , an increase in $V_{max}$$V_{max}$ would lower the y-intercept.

$$V_{max}\frac{1}{\propto }\text{y-intercept}$$

• The enzyme affinity for substrate ( $K_m$$K_m$ ) is independent of enzyme concentration

  • so the x-intercept ( $-\frac{1}{K_m}$$-\frac{1}{K_m}$ ) would remain unchanged with varying enzyme concentration

• In this example , interleukin-$1\beta$$1\beta$ upregulates the synthesis of PGE1 , which results in increased enzyme concentration.
• The maximum velocity ( $V_{max}$$V_{max}$ ) of the enzyme-catalyzed reaction , which occurs when the enzyme is saturated with substrate , is equal to the product of the catalytic rate constant ( $k_{cat}$$k_{cat}$ ) and the concentration of enzyme in solution :

$$V_{max}=k_{cat}\ast [E_{total}]$$

• Therefore , increasing enzyme concentration would result in an increase in the maximum velocity o fhte reaction and a decrease in the y-intercept.

• An in crease in the amount of enzyme available in a particular system will cause an increase in $V_{max}$$V_{max}$ but no change in $K_m$$K_m$ in Michaelis-Menten kinetics.
• Lineweaver-Burke graphs are linear plots that relate inverse reaction velocity ( $\frac{1}{V}$$\frac{1}{V}$ ) to inverse substrate concentration ( $\frac{1}{[S]}$$\frac{1}{[S]}$ )
• An increase in enzyme concentration would cause a decrease in the y-intercept ( $\frac{1}{V_{max}}$$\frac{1}{V_{max}}$ ) and no change in the x-intercept ( $-\frac{1}{K_m}$$-\frac{1}{K_m}$ ) in a Lineweaver-Burke plot.

#concept , #graph , #enzyme , #kinetics