In this applet we explore the Michaelis-Menten mechanism of enzyme catalysis and the analysis of data using a Lineweaver-Burke plot; we also investigate the effects of inhibition.

The Michaelis-Menten mechanism of enzyme catalysis is

where E is the enzyme, S the substrate, and P is the product. By applying the steady-state approximation to the rate of change of the concentration of the enzyme-substrate complex, ES, the rate of formation of the product can be expressed as the Michaelis equation in terms of:

• the initial concentration of substrate c_s
• the Michaelis constant K_M = (k₂ + k₃) / k₁
• the maximum velocity of the reaction v_max = k₃[E]_o, where [E]_o is the initial concentration of enzyme

The Michaelis equation is:

Where c_S is the initial concentration of the substrate (mol L^-1), K_M is the Michaelis constant (mol L^-1), and v_max is the maximum velocity (mol L^-1 s^-1). To plot this equation select the M-M Plot tab, enter the parameters and hit New Plot. Up to 5 plots can be displayed at one time. The Clear button will remove all plots. To see the parameters for each plot hit the Legend on/off button. The Redraw button will refresh the graph. This is useful when the function domain has been changed. To see the value of each plot at a given point, move your cursor to the desired location then click and hold. Note: A dotted v_max line is graphed for each plot.

It is convenient to express the Michaelis equation as

A plot of 1 / v against 1 / c_S is called a Lineweaver-Burke plot. The y-intercept is 1 / v_max, the slope is K_M / v_max and the x-intercept is -1 / K_M.

This equation is graphed on the L-B Plot tab.

As an example, consider the reaction

catalysed by 2.3 nmol L^-1 of the enzyme carbonic anhydrase at pH = 7.1, 273.5 K.

From the Lineweaver-Burke plot it follows that:

Where slope(1 / c_S,1 / v)) and y-intercept(1 / c_S,1 / v) are the slope and y-intercept, respectively, of a plot of 1 / v against 1 / c_S. The Data, Data Plot, and Data Analysis tabs analyse data from this reaction for v_max and K_M.

An inhibitor, I, decreases the rate of product formation from the substrate by binding to the enzyme, E, to the ES complex, or to the enzyme and ES complex simultaneously. The Michaelis equation then becomes

The EI/M-M Plot and EI/L-B Plot tabs graph the Michaelis equation and Lineweaver-Burke plot in the presence of an inhibitor. Note: