  A comparison is made between conventional Michaelis-Menten kinetics and two
models that take into account the duration of the conformational changes that
take place at the molecular level during the catalytic cycle of a monomer. The
models consider the time that elapses from the moment an enzyme-substrate
complex forms until the moment a product molecule is released, as well as the
recovery time needed to reset the conformational change that took place. In the
first model the dynamics is described by a set of delayed differential
equations, instead of the ordinary differential equations associated to
Michaelis-Menten kinetics. In the second model the delay, the discretization
inherent to enzyme reactions and the stochastic binding of substrates to
enzimes at the molecular level is considered. All three models agree at
equilibrium, as expected; however, out-of-equilibrium dynamics can differ
substantially. In particular, both delayed models show oscillations at low
values of the Michaelis constant which are not reproduced by the
Michaelis-Menten model. Additionally, in certain cases, the dynamics shown by
the continuous delayed model differs from the dynamics of the discrete delayed
model when some reactant become scarce.
