Systems Biology (Methods in Molecular Biology)

any set of positive real parameter values. Note that we do not use
negative or complex numbers for parameter values for biochemical
systems. Figure3b shows the concentrations of species with time.
To consider reversible reactions, from X 3 to X 2 with rate
constantk 3 :

X 1!

k 1

X 2 $

k 3

X 3

dX 2

dt

¼k 1 ½ŠX 1

Vmax½ŠX 2

KMþ½ŠX 2

þk 3 ½ŠðX 3 14 Þ

dX 3

dt

¼

Vmax½ŠX 2

KMþ½ŠX 2

k 3 ½ŠðX 3 15 Þ

Here, the reversible reaction is assumed to follow mass-action
kinetics to the previous situation. Figure3c shows the concentra-
tions of species with time.
In this manner, biochemical reactions can be connected to form
complicated biological pathways and networks, where each reaction
is represented based on the detailed information available. In the
case where sufficient data are unavailable, simple mass-action kinet-
ics can be used as a first approximation to compare simulation with
experimental dynamics.
The mass-action and enzyme kinetic equations have widely
been used to model reaction pathways that are known to display
deterministic responses consisting of formation and depletion
waves. That is, when the stimulation or perturbation of cells
in vitro (in a dish) with respective biochemicals resulted in the
dynamic activation profiles of intracellular molecular species that
followed gradual increase from their initial state to reach peak
activation levels and, subsequently, decay to their original state or
a new stable state. Figure4 gives examples observed in glycolysis,
epidermal growth factor (EGF) receptor, and toll-like receptors
(TLRs) signaling response. Although the kinetics can vary slightly
from sample to sample or dish to dish (due to technical or cellular
variability,seeSubheading6), the general average response profiles
are very well reproducible. In other words, even in complex reac-
tion networks, certain systems’ averaged properties display simple
deterministic waves.
A vast majority of cellular models today are based on mass-
action kinetics, Michaelis–Menten kinetics, or even Boolean logics.
In most circumstances, if not all, the investigations considered
“closed” system modular approach, where the models did not
include continuous exchange of materials between the internal
and external environments and, hence, chemical and thermal equi-
librium have been assumed. That is, the approaches often adopted
well-mixed, homogenous, and isothermal environment where each
reaction in the cellular network is connected through first-order,

Complex Biological Responses Using Simple Models 179