Turing patterns have also been generated using the Brusse-
lator equations for the reaction terms [38]. Thus, depending on
the form of the activator-repressor reaction-diffusion system
used, diverse 2-D pattern formations can be achieved. However,
the spontaneous pattern formations are due to the instability
brought in, mainly, by the diffusion terms rather than the reac-
tion terms. In other words, stable heterogeneous patterns or
states arise from a homogenous field due to the instability caused
when the diffusive terms are very different between the two
reacting species.6 Stochasticity and Heterogeneity
The population-wide averaging approaches, discussed so far, have
been instrumental in our basic understanding of myriad deter-
ministic biological processes such as growth, metabolism, cell
signaling, and diseases. For developmental biology, on the other
hand, the major challenge has been to understand how multi-
modal decisions are undertaken. For instance, how a single stem
or progenitor cell can producedistinct lineages, which can be
tilted even by small external perturbations? Also, it is intriguing
how genetically identical cellscan produce diverse phenotypes
during cell cycle, aging, and epigenetic regulation [39]. The
cooperative behavior of microorganisms, such asEscherichia coli
and yeast, to form biofilms that enhance their survival capacity to
environmental threat, is distinct from their individual activity.
These observations on phenotypic diversity or individual to
cooperative response cannot lend itself to population-based read-
out as multiple measurements of single cells across time are
required in order to unravel the multifaceted decision capability
of the living system.
It is now known that the single-cell heterogeneity within cell
populations, measured by transcription, phosphorylation, mor-
phology, and motility, arises from a combination of intrinsic and
extrinsic elements. Stochasticity in gene or protein expression is a
result of two sources of biological noise: (1) intrinsic or “uncorre-
lated” noise; the random nature of biochemical reactions, e.g., due
to low copy numbers of intracellular molecules in a Poisson process,
and (2) extrinsic or “correlated” noise; fluctuations in other cellular
components or states that indirectly affect the expression of a
specific gene or protein [40, 41]. However, stochasticity in
mRNA and variability in protein expression are not simply due to
the effect of low copy numbers on a Poisson gene regulatory
process, but can also be due to the quantal or bursting nature of
promoter activity (Fig.14)[42, 43]. Moreover, by varying the rates196 Kumar Selvarajoo