  We propose to model the dynamics of metabolic networks from a systems biology
point of view by four dynamical structure elements: potential function,
transverse matrix, degradation matrix, and stochastic force. These four
elements are balanced to determine the network dynamics, which gives arise to a
special stochastic differential equation supplemented by a relationship between
the stochastic force and the degradation matrix. Important network behaviors
can be obtained from the potential function without explicitly solving for the
time-dependent solution. The existence of such a potential function suggests a
global optimization principle, and the existence stochastic force corresponds
natural to the hierarchical structure in metabolic networks. We provide
theoretical evidences to justify our proposal by discussing its connections to
others large-scale biochemical systems approaches, such as the network
thermodynamics theory, biochemical systems theory, metabolic control analysis,
and flux balance analysis. Experimental data displaying stochasticity are also
pointed out.
