In accordance with the Michaelis-Menten equation, the initial reaction rate (V_{0}) increases at increased substrate concentrations [S]. The reaction rate increases more at lower substrate concentrations, and it eventually reaches a plateau, approaching the maximum velocity V_{max} (Fig. 1). The maximum initial velocity is reached when the enzyme is saturated, i.e., when enough substrate is present to ensure that practically all the enzyme is part of the enzyme-substrate complex. Because the enzyme can never be completely saturated, V_{max} is never fully reached. V_{max} is dependent on 2 things: the turnover number of the enzyme (k_{cat}), and the concentration of the enzyme [E] [1].

Vmax = [E] • kcat

Thus, a higher [E] leads to a higher V_{max}. The turnover number will be described in more detail on the following page.

**Figure 1:** An illustration of the Lineweaver-Burk equation fitted to a double-reciprocal transformation of an enzyme kinetic dataset.

## Determining V_{max}

Just like k_{m}, V_{max} can be determined using the
Lineweaver-Burk equation (Figure 1):

1/V_{0} = 1/V_{max} + K_{m}/V_{max} • 1/[S]

Based on this equation, a straight line fitted to a double reciprocal plot will have the y-intercept 1/V_{max}, and V_{max} can therefore be obtained by taking the reciprocal to this intercept [1].

## References

- Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008).
*Principles of Biochemistry* (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 978-0-7167-7108-1.

K_{m}

k_{cat}

Theory overview