# 16: Enzyme Kinetics, Inhibitor Kinetics

- Page ID
- 6106

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**Reading & Problems**: LNC p. 207-212; p. 239 prob. 9a,b, 10; Segel p. 319 prob. 6,7, p. 321, prob. 15,16,19 (except "Z")

### I. Determining [**P**] at a given time "t".

- Solve only for [
**S**]>>K_{m}, and for [**S**]<<K_{m}.

For [**S**]>>K_{m}, V = V_{max} (zero order for [**S**]), and [**P**]_{t} = V_{max}•t,

[**S**]_{t} =[**S**]_{0} - [**P**]_{t}

For [**S**]<<K_{m}, V = V_{max}/K_{m}•[**S**] (first order for [**S**]) and

### A.Amount of enzyme present - determined by the relationship between:

- Rate of synthesis, and
- Rate of degredation

### B. Inhibitors

- Irreversible inhibitors - irreversibly bind to and inhibit the enzyme. Examples include DIFP and TPCK as inhibitors of chymotrypsin. They are covalently bound and do not dissociate from the enzyme.
- Reversible inhibitors - bind and release, the amount of inhibitor bound is determined by the concentration of inhibitor and its binding constant (K
_{i}). Reversible inhibitors are important regulators of enzyme activity in cells.

### B. Noncompetitive inhibitor - can bind whether or not substrate bound, prevents reaction when bound.

### C. Uncompetitive inhibitor - binds only to ES complex, prevents release of S and production of P.

**Some take home information**:

### Information on reversible inhibitors:

Inhibitor | Binds to | Constant changed |
---|---|---|

Competitive | E | K_{m} higher |

Noncompetitive | ES, E | V_{max} lower |

Uncompetitive | ES | V_{max} lower, K_{m} lower |

**If constant is Higher** -> multiple by "the inhibitor factor" = 1+([**I**]/K_{I})

**If constant is Lower** -> divide by "the inhibitor factor" = 1+([**I**]/K_{I})

Formulas:

### Contributors

Charles S. Gasser (Department of Molecular & Cellular Biology; UC Davis)