Factors affecting enzyme activity

Substrate concentration
Research into the enzyme kinetics of single-substrate reactions was carried out by Leonor Michaelis and Maud Leonora Mentenová. In this chapter, the laws of general kinetics are applied.

See the Kinetics page for more detailed information .

For catalyzed single-substrate reactions, we assume that they proceed in two steps:
 * $$\mbox{E} + \mbox{S} \; \overset{k_1}{\rightleftharpoons} \; \mbox{ES} \; \overset{k_{cat}}{\rightleftharpoons} \; \mbox{E} + \mbox{P}$$

where k cat is the rate constant of the catalyzed reaction. It is also called the turnover number and indicates the number of substrate molecules converted by one enzyme molecule per unit of time (most often in one second). Its values ​​range from 4.10^7 (for catalase) to 0.5 (for lysozyme).
 * The maximum rate of a catalyzed reaction It can be expressed as:


 * $$v_{max} = k_{cat} \cdot [\mbox{E}]_t$$


 * where [E] t is the total enzyme concentration.

The equation describes how the initial velocity at 0 depends on the rate constant k cat as well as where the equilibrium ES is located:
 * Michaelis and Menten equations
 * $$v_0 = \frac{\Delta [\mbox{P}]}{\Delta t} = \frac{k_{cat} \cdot [\mbox{E}]_t \cdot [\mbox{S}]}{K_M + [\mbox{S}]}$$

We assume that the amount of the enzyme does not change (and its concentration is significantly lower than the concentration of the substrate) and also the presence of a certain pseudo-steady state in which the concentration of the ES complex changes much more slowly than the concentrations of S and P.

By substituting equation (2), we can rewrite equation (3) into the form:
 * $$v_0 = \frac{v_{max} \cdot [\mbox{S}]}{K_M + [\mbox{S}]}$$

K M ( Michael's constant ) is experimentally defined as the substrate concentration at which the rate of the enzyme-catalyzed reaction is equal to half of the maximum rate (it therefore expresses the affinity of the substrate and the enzyme). The lower the K M value, the higher the affinity (a lower [S] is enough to saturate the enzyme by half).


 * $$\underline{K_M = [\mbox{S}]:}$$


 * $$v = \frac{v_{max}}{2}$$

The graph shows that the dependence of the rate of the enzyme-catalyzed reaction on the concentration of the substrate has the shape of a hyperbola. If the substrate concentration is small, the rate change curve approximately corresponds to 1st order kinetics (linear increase). But this almost linear increase cannot continue indefinitely due to the limited number of binding sites on the enzyme molecules. At a sufficiently high concentration of the substrate, after saturation of the binding sites of all available enzyme molecules, the maximum speed ( v max ) is thus achieved. The speed does not increase further and remains approximately constant. This part of the curve corresponds to 0th order kinetics (independent of concentration).

K M can then be determined graphically from the hyperbola, but in practice this determination is not used very often. More accurate is the determination using the inverted values ​​of 1/ v and 1/[S] – the so-called double reciprocal plotting according to Lineweaver and Burke. From equation (4) we then get:




 * $$\frac{1}{v} = \frac{K_M + [\mbox{S}]}{v_{max} \cdot [\mbox{S}]} $$

We can also write the equation in the form corresponding to the equation of the line y = a · x + b :
 * $$\frac{1}{v} = \frac{K_M}{v_{max} \cdot [\mbox{S}]} + \frac{1}{v_{max}}$$

Temperature
Due to their protein nature, enzymes can be denatured due to high temperature (conformational changes occur, with subsequent destruction of the active site). This usually occurs at temperatures around 55-60°C. The rate gradually decreases until the course of the respective reaction stops completely.

Low temperatures also reduce the activity of enzymes and thus the speed of reactions catalyzed by them. The enzyme has maximum activity at a temperature known as the temperature optimum (for most human enzymes, this is a temperature of around 37 °C).

pH (H + concentration )
Similar to changes in temperature, enzymes are also sensitive to fluctuations in pH. Extreme values ​​(both low and high) can again induce denaturation of the enzyme molecule. The concentration of H + also has a significant effect on the ionization of acidic and basic groups not only of the enzyme molecule, but also of the substrate molecule. Analogously to temperature, the pH optimum is considered to be the pH value at which the enzyme has maximum activity.