  Signal transduction, the information processing mechanism in biological
cells, is carried out by a network of biochemical reactions. The dynamics of
driven biochemical reactions can be studied in terms of nonequilibrium
statistical physics. Such systems may also be studied in terms of Shannon's
information theory. We combine these two perspectives in this study of the
basic units (modules) of cellular signaling: the phosphorylation
dephosphorylation cycle (PdPC) and the guanosine triphosphatase (GTPase). We
show that the channel capacity is zero if and only if the free energy
expenditure of biochemical system is zero. In fact, a positive correlation
between the channel capacity and free energy expenditure is observed. In terms
of the information theory, a linear signaling cascade consisting of multiple
steps of PdPC can function as a distributed "multistage code". With increasing
number of steps in the cascade, the system trades channel capacity with the
code complexity. Our analysis shows that while a static code can be molecular
structural based; a biochemical communication channel has to have energy
expenditure.
