In the absence of enzymes, the rate of a reaction can be thought to increase linearly with substrate concentration. The reaction rate is given as dp/dt, or the change in product over time:
where S is the substrate concentration, and k is the frequency at which substrate is converted to product.
The rate of a reaction involving enzymes also increases as the substrate concentration increases. However, the number of enzyme active sites available is limited. At low enzyme concentrations or high substrate concentrations, all of the available enzyme active sites could be occupied with substrates. Therefore, increasing the substrate concentration further will not change the rate of diffusion. In other words, there is some maximum reaction rate (Vmax) when all enzyme active sites are occupied. The reaction rate will increase with increasing substrate concentration, but must asymptotically approach the saturation rate, Vmax. Vmax is directly proportional to the total enzyme concentration, E, and the cata lytic constant of the enzyme, k<span>cat, </span>which describes the frequency at which the enzyme-substrate complex is converted to product. How quickly enzyme active sites become saturated can be described by the variable K, the substrate concentration at which the reaction rate is Vmax. K is called the Michaelis-Menten constant after the scientists who originally derived it. The reaction rate can be described by the equation
where S is the substrate concentration.
