September 12, 2017
Feature

Reconsidered: Non-Steady State Mass Action Dynamics

A new statistical formulation could mark a major advance for predictive modeling in systems biology

trajectory

Comparisons between non-steady state stochastic kinetic simulations (red) and simulations using the coupled reaction theorem (blue). 

The law of mass action was first described 150 years ago. Today, it is still a staple concept in every first-year chemistry text. The law states that the rate of a chemical reaction is proportional to the concentration of the reactants. For solutions in dynamic equilibrium, the law predicts how those solutions will behave.

But it is a challenge to apply the law of mass action to complex systems, such as biological metabolism. For one, most rate constants are not available, and measuring the missing ones is very labor-intensive.

In biological research, measuring rate constants requires isolating and purifying individual enzymes, then determining the rate constants with spectrophotometry - that is, by how much light a chemical absorbs. This slows down throughput speeds, making it hard to characterize each new genome. After all, to do this requires thousands of rate parameters.

Because of these issues, a large number of enzyme rate parameters have been determined for just a few well described systems, such as Escherichia coli. For most biological systems, scientists have not yet obtained rate constants.

Meanwhile, the method of choice for modeling large-scale biological processes (such as metabolism) involves constraint-based flux models. But these models suffer from a lack of physics regarding the law of mass action, limiting the ability of constraint-based approaches even when they are extended to include thermodynamics and other factors.

In answer, some researchers have proposed studying elementary reactions using the law of mass reaction through reaction affinities instead of rate constants.

A new paper in the journal Physical Biology by William R. Cannon and Scott E. Baker at the Pacific Northwest National Laboratory reviews the relationship between reaction affinity and free energy for isolated reactions by using concepts from statistical thermodynamic integration. Cannon and Baker set out to explicitly demonstrate the relationship between kinetic formulations of rates that use rate constants and a statistical thermodynamics formulation that uses chemical potentials.

Subsequently they present a theorem for coupled reactions based on chemical potentials, which can provide relative rates for all sequentially coupled reactions under all conditions, steady state or not. This obviates the need for rate constants in many applications.

Using chemical potentials instead of rate constants represents a methodological leap that the authors say could signal a major advance for predictive modeling in systems biology.

The new method will enable complex, large-scale biological systems such as metabolism to be modeled with kinetics and thermodynamics. This will result in more accurate predictions for the design of microorganisms to behave in desired ways, such as those that could be harnessed to produce biofuels.

Moreover, the authors say, the new method will shed fundamental insight into the thermodynamic coupling between living organisms and their environment.

Acknowledgements

Sponsors: The U.S. Department of Energy's Office of Biological and Environmental Research and the Environmental Molecular Sciences Laboratory (EMSL). Additional support came from the Microbiomes in Transition initiative at PNNL.

Reference: Cannon, WR and Baker SE. 2017. "Non-Steady State Mass Action Dynamics Without Rate Constants: Dynamics of Coupled Reactions using Chemical Potentials." Physical Biology.Phys. Biol. 2017 Aug. 16; 14(5):055003. DOI: 10.1088/1478-3975/aa7d80. 

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Pacific Northwest National Laboratory draws on its distinguishing strengths in chemistry, Earth sciences, biology and data science to advance scientific knowledge and address challenges in energy resiliency and national security. Founded in 1965, PNNL is operated by Battelle and supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit the DOE Office of Science website. For more information on PNNL, visit PNNL's News Center. Follow us on Twitter, Facebook, LinkedIn and Instagram.

Published: September 12, 2017

PNNL Research Team

William R. Cannon and Scott E. Baker