Systems Biology (Methods in Molecular Biology)

dA½Š

dt

¼k 2 ½ŠA^2 ð 3 Þ

wherek 2 is the second-order rate constant. It has dimensions of

(mol/L)^1 s^1.

A chemical reaction can also be reversible, where speciesAcan

become speciesBand vice versa with different rate constants:

A$

k 1

k 1

B

dB½Š

dt

¼

dA½Š

dt

¼k 1 ½ŠA k 1 ½ŠðB 4 Þ

It follows that for any system in chemical equilibrium, the rate

of an elementary reaction is proportional to the product of the

concentrations of the reacting species. These types of reactions are

called the mass-action kinetics, and Cato Maximilian Guldberg and

Peter Waage first devised them in 1864 [7].

2.2 Enzyme Kinetics In certain types of biochemical reactions, such as in metabolic
reactions, other species can involve and aid a reaction without
themselves being affected through the process. These species are
usually catalytic proteins. To consider such situations, the hyper-
bolic rate equation, which we now popularly call the Michaelis-
Menten enzyme kinetics, was introduced. This is a more sophisti-
cated form of mass-action type reaction, which considers the role of
enzymes (proteins that act as catalyst). Unlike mass-action, the
kinetics of reactions saturates at higher substrate concentrations
instead of ever increasing profile for the former.
For reactions that require catalytic enzymes, the mechanism to
account for such reactions assumes that the speciesAcombines
with speciesE(catalyst or enzyme), in a reversible manner to give
complexEA, which then dissociate reversibly or react irreversibly to
produce speciesBwhile leavingEunchanged.

Substrate

Rate or Velocity

A –Mass-action

B –M-M kinetics

C –Hill-type kinetics

Fig. 2Schematic of velocity (rate) versus substrate (species) concentration for (A) mass-action, (B) Michaelis-
Menten kinetics, and (C) Hill-type allosteric reactions

Complex Biological Responses Using Simple Models 175