# Structural Biochemistry/Enzyme/Rates and constants

## Enzyme Rates and Constants

Enzyme Thermodynamics

For enzyme thermodynamic, the most important constant is probably ∆G. ∆G is the free-energy difference between products and reactants, also known as the amount of energy required to convert reactants to products. More importantly, it can tell whether a reaction will occur spontaneously, which are what enzymes are concerned with.

If ∆G is negative then the reaction will occur spontaneously (exergonic). If ∆G is zero, the system is at equilibrium and no net change can take place. If ∆G is positive, energy is required for the reaction to occur (endergonic).

A thermodynamic explanation of this starts with the definition of Gibbs free energy, which says

∆G = ∆H - T∆S,

where ∆H is the change in enthalpy (joules) and ∆S is the change in entropy (joules/Kelvin). As we can see, if the energy due to entropy (disorder of a system) exceeds the enthalpy (thermodynamic potential of a system), the Gibbs free energy will be negative and thus no energy is needed for the reaction to occur.

Enzyme Kinetics

Enzyme Kinetics contain a few more constants and rates; starting with Vmax, this is the maximal rate when all the catalytic sites on the enzyme are saturated (bounded) with substrates. Another constant is Km, which is the substrate concentration when it is half the Vmax. Their relationship to each other can be seen through the Michaelis-Menten equation.

Enzyme Kinetics is measuring rate of enzyme reaction. One way to measure of rate of reation is by using spectroscopy change, absorb light at different wavelength. Another way to study enzyme kinetics is through the graph that has substrate concentration (x-axis) vs. reaction velocity (initial velocity). km(michaelis constant) is substrate concentration at which our enzyme reacts half of maximum velocity.

Vo = Vmax([S]/([S]+ KM))

where [S] is the substrate concentration and Vo is the initial rate of the reaction (t=0). Finally, there is the rate of kcat/KM which measures the catalytic efficiency. kcat is the turnover number of an enzyme, which is the number of substrate bounded to an enzyme in a unit of time when the enzyme is fully bounded. Given this, the higher the kcat/KM rate is, the more efficient it is at binding substrates.