# Structural Biochemistry/Enzyme/Double-Reciprocal plot: Lineweaver Burk plote

## Double Reciprocal Plot[edit]

The double-reciprocal equation is obtained by taking the reciprocal of both sides of the Michaelis-Menten equation. The double-reciprocal (also known as the Lineweaver-Burk) plot is created by plotting the inverse initial velocity (1/V_{0}) as a function of the inverse of the substrate concentration (1/[S]). The V_{max} can be accurately determined and thus K_{M} can also be determined with accuracy because a straight line is formed. The slope of the resulting line is K_{M}/V_{max}, the y-intercept is 1/V_{max}, and the x-intercept is -1/K_{M}. Using the Michaelis-Menten equation, the V_{max} is an asymptote and can thus only be approximated and as a result, the K_{M}, which is V_{max}/2, can't be determined accurately. This plot is a useful way to determined different inhibitors such as competitive, uncompetitive, and noncompetitive.

For competitive inhibitors, the inhibitor competes with the substrate molecule to bind to the binding site. Consequently, the K_{M} will increase without changing the V_{max} value. This means that the two graphs will have the same y-intercept as shown below. However the new x-intercept may be quite elusive. For this type of inhibitors, a higher concentration of the substrate is needed to get half of the active sites occupied. Therefore K_{M2} will be larger than K_{M1}. This translates to a higher reciprocal value of K_{M1} than that of K_{M2}. However the x-intercept has the negative sign in front of it, thus on the graph it has to move to the right relative to the previous intercept. To show this on the double reciprocal plot, the slope will increase to show the strength of the binding competitive inhibitor. While the slope increases with the presence of the inhibitor, the y-intercept remains the same in presence and absence of the inhibitor.

For uncompetitive inhibitors, the inhibitor will only bind to an enzyme-substrate complex; therefore, it does not compete with the substrate for the binding site. Consequently, both K_{M} and V_{max} values decrease. Consequentially, the reciprocal value of the new V_{max} should be at a higher position on the axis, as a fraction becomes larger when the denominator gets smaller. The new reciprocal value of K_{M} will move to the left and the explanation should be similar to that of competitive inhibitor. To show this on a double reciprocal plot, the slope will remain the same as if the enzyme was not bound to the inhibitor, but the x-axis intercept will decrease. The double reciprocal plot for enzyme with and without uncompetitive inhibitor will be two parallel lines.

For noncompetitive inhibitors, the inhibitor can bind to the enzyme before the substrate can bind to the binding site. It does not have to wait for the enzyme to become an enzyme-substrate complex in order to bind to the enzyme. The inhibition will cause a decrease in V_{max} value while the K_{M} is unaffected. This means the value of -1/K_{M} remains the same for the two lines, while the new value of 1/V_{max} is higher relative to the previous one. To show this on a double reciprocal plot, the decrease in V_{max} will increase the y-intercept with a larger slope.

The black lines represent the reciprocal of velocity when no inhibitor is present and the blue lines correspond to the presence of inhibitors.