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# Calculations Involving Enzymes (Essay Sample)

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1a) The rate at which (v) is formed may be
V=k-cat(E)(S). In this case (E) exhibits the enzyme concentration while (S) depicts the substrate concentration. In addition, k-cat shows maximum reaction rate of the enzyme or the rate of turnover. In such condition, the enzyme is at super saturation level with the substrate in this case.
The rate at which the concentration of the substrate changes in respect to time can be shown as;
* Change in S with respect to change in t
=k1x(E)x(S)+K2(ES)+k-1x ES+K3(p)x(ES);
The symbols represented above can be shown as; k= the constant at which the complex is formed i.e. (ES). The rate at which the enzyme complex is dissociated whereas k2 shows the rate at which the complex enzyme is converted to products and subsequent free enzyme represented by (E)+(P). k3 however shows the constant rate of conversion of products to raw materials.
* d(ES-1)/dt
The equation can expressed; change in (ES-1/ with respect to change in time=k1 times (E) times (S) times -(K2+k1+K4)(ES-1)+k3 times eS-2. In such a case the symbols above represent; k4 shows the conversion of the ES-1 to the next complex, i.e., enzyme substrate.
K1(E)(S) shows ES-1 formation from the enzyme free product formed above (E and S substrate). In addition, k2+k-1+k4 and ES-1 shows dissociation of the product and the subsequent formation of the product. Furthermore, P and E product and free enzyme are represented. K3(ES-2 shows the rate at which the latter is converted to (ES-1)
* d(EP)/dt can be shown as; k2(ES)+KE(P)+(ES)-(K-2+K-3)(EP)

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