Question

Why is a V vs S plot often inadequate for determining enzyme kinetic constants, and how do various alternate plotting methods allow these values to be determined more adequately? Give examples of alternate methods of kinetic analysis and their utility.

The V vs S plot is inadequate because it makes the assumption that it’s only for a single subunit and substrate. The line on the graph usually represents a line that best fits the data and are not completely accurate. This only measures free enzymes or unstable enzyme substrate complex. An alternate method

Answer 1

Enzyme kinetics is the study of chemical reactions acrried out by enzymes and information about enzyme kinetics reveal the favourability of an enzyme at specific conditions, regulation of the activity of the enzyme, its role in metabolic processes and the how a drug or agonist can modify or inhibit the functioning of the enzyme. Enzyme kinetics can be studied by plotting the amount of substrate present ([S]) on the X-axis, since it is the independent variable, and the reaction rate (V)on the Y-axis, which would depend on the amount of substrate available. Such single substrate reactions can be represented by the Michaelis-Menten kinetic model of single-substrate reaction, wherein the increase in substrate concentration intitally causes an increase in reaction rate. The reaction rate eventually reaches a maxima, known as V_max ,after which there is no effect of increase in substrate concentratio on the reaction rate. The graphical representation of the Michaelis-Menten model for single-substrate reaction has been below :

However, this method of illustrating enzyme kinetics has its shortcomings. They are :

1.The simplistic nature of these V/[S] plots are effective for single-substrate enzymatic reactions, but cannot be used to study the kinetics of complicated enzymatic reactions.

2. This plot doesn't provide any information about the affinity (K_m) between the substrate and the enzyme and how V_max is affected by changing substrate concentrations.

3. The non-linearity of the graph made it difficult to calculate K_m and V_max accurately.

These factors have led to the formulation of double-reciprocal plots like the Lineweaver-Burke Plot, or the Eadie-Hofstee Plot and Woolf-Hanes Plot, all of which provide information about enzyme kinetics not restricted to single-substrate enzymatic reactions. These plots have been discussed below along with graphical representations of each of them :

LINEWEAVER-BURKE PLOT

The Lineweaver-Burke plot is a double-reciprocal plot, wherein the graph is plotted between the reciprocal values of both sides of the Michaelis-Menten equation. Therefore, instead of using V and [S], the Lineweaver-Burke plot uses a 1/V vs. 1/[S] plot, to illustrate enzyme kinetics data.

In order to circumvent the non-linearity problem, the Lineweaver-Burke plot has been designed into a linear representation of enzyme kinetics, by representing it in the form of the straight-line equation y=mx + c, such that :

1/v = K_m/(V_max[S]) + 1/V_max

V_max[S] being the slope,

and 1/V_max being the intercept on the y-axis.

Such linear representation of enzyme kinetics is helpful in obtaining accurate values of parameters like K_m and V_max.

EADIE-HOFSTEE PLOT

The Eadie-Hofstee Plot is another linear representation of enzyme kinetics data, wherein the velocity is plotted against a ratio of velocity and substrate concentration. This plot also helps in rapidly identifying and calculating the important kinetic parameters like K_m and V_max , while also being less error-prone than the Lineweaver-Burke plot. This is because the Lineweaver-Burke plot can give inaccurate results at low substrate concentrations, but the Eadie-Hofstee plot circumvents this problem by giving equal weightage to every data point even at low reaction rates and substrate concentrations.

WOOLF-HANES PLOT

The Woolf-hanes plot is yet another linear representation of enzyme kinetics wherein substrate concentration is plotted against a ratio of substrate concentration to velocity, and is used for obtaining rapid and accurate values of important kinetic values like K_m and V_max.