The heat-shock response is an essential mechanism present in all cells 
for the
purpose of combating the effects of an increase in ambient cellular 
temperature
among other stressors. Cells respond to this stress by producing an 
array of
protective proteins referred to as heat shock proteins (HSPs). Such 
proteins are
regulated directly by alterations in the level, activity, and stability
of regulatory proteins called sigma-factors. The logic of the heat shock 
response
is implemented through an intricate hierarchy of feedback and feedforward
controls that regulate both the amount of the sigma-factor and its 
function-
ality. We present a dynamic model that captures known aspects of the heat
shock system. With the aid of this model, we discuss the logic of the re-
sponse from a control theory perspective, drawing comparisons to synthetic
engineering control systems. Questions related to robustness analysis, and
model validation will also be discussed and related mathematical challenges
will be outlined.
<br><br>
While mathematical modeling of genetic networks like that of the heat
shock system often represents gene expression and regulation as determin-
istic processes, there is now considerable experimental evidence indicating
that significant stochastic fluctuations are present in these processes. 
The
investigation of stochastic properties in genetic systems involves the 
formu-
lation of a correct representation of molecular noise and devising 
efficient
computational algorithms for computing the relevant statistics of the mod-
eled processes. We present some of these techniques and use them to provide
compelling examples that illustrate the richness of phenomena that can 
result
from the interaction of dynamics and noise in genetic networks.