is inheritance, where an existing behavior is taken and augmented with a few
modifications. This encapsulates the
previous behavior and overrides or extends parts of it. One of the major challenges in biological modeling is to find
similar means to encapsulate biological
and biochemical complexity that will
allow us to use abstraction beneficially
to bridge and relate different scales in
order to manage the immense complexity observed in living systems. Once we
have such multiscale models we will
need to search for the right computational frameworks that will allow us to
zoom back and forth between lower-scale data and higher-scale behavior,
while experimenting in-silico. This, we
feel, is an ideal way to study emergence
computationally. A modest attempt in
this direction can be found in the
Biocharts approach of Kugler et al.
52
Noise and choice. Stochasticity has
received much attention in systems biology,
4, 55, 56 as numerous experimental
studies have reported the presence of
probabilistic mechanisms in cellular
processes.
26, 29, 61 The investigation of stochastic properties of biological systems
requires that computational models
take into consideration the inherent
randomness of biochemical reactions.
Stochastic kinetic approaches give rise
to dynamics that differ significantly
from those predicted by deterministic
models because a system may follow
very different scenarios with non-zero
but varying likelihoods.
The dogma for this kind of model-
ing assumes that a molecular mixture
is well stirred and has fixed volume and
temperature (though PDEs can be used
to model variations in these too). The
state of a network of biochemical reac-
tions at any point in time is then given
by the population vector of the involved
chemical species (such as, molecules).
The temporal evolution of the system
can be described by a continuous-
time Markov process,
37 which is usu-
ally represented as a system of ordinary
differential equations (ODEs) called
the chemical master equation (CME).
While individual system parameters,
such as the mean of the state distribu-
tion changing in time, can be studied
using deterministic differential equa-
tions, this is inadequate for uncovering
branching, switching, or oscillatory
behavior, such as cell fate determina-
tion (the mean between two alternative
cell fates is hardly meaningful). Such
phenomena require a fully stochastic
analysis.
