12/01/2012

# Finding a Steady-State Solution in Dynamical Biological Networks

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment.

## The Science

Cellular biochemical networks govern biological function and are strongly influenced by the exchange of molecules between the cell and its environment. Modeling this exchange process and its impact on cellular networks for whole microbial cells will be a key step in developing biology-based applications in bioenergy and other Department of Energy (DOE) mission areas. However, it has been a problem to represent nutrient exchange with the environment for genome-scale kinetic models, in a manner consistent with the existence of a steady state. New research has developed a mathematical model that establishes sufficient conditions for a non-equilibrium steady-state for cellular biochemical networks. The research proves the theorem that reactions conserving mass and kinetic rate laws are sufficient conditions for the existence of a non-equilibrium steady state. The new study demonstrates how to mathematically model the exchange of molecules between any cell and its environment. The results of this DOE Scientific Discovery through Advanced Computing (SciDAC) research by Fleming and Thiele of the University of Iceland are foundational for future efforts to computationally model non-equilibrium steady states as part of whole cell microbial models.

## References

Fleming, R. M. T., and I. Thiele. 2012. “Mass Conserved Elementary Kinetics Is Sufficient for the Existence of a Non-Equilibrium Steady State Concentration,” *Journal of Theoretical Biology* **314**, 173–81. DOI:10.1016/j.jtbi.2012.08.021.