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# Using mathematical methods to study complex biological networks

(Nanowerk News) Complex biological processes, such as the metabolism, often involve thousands of different compounds coupled by chemical reactions. These process chains are described by researchers as chemical reaction networks. Researchers from the University of Luxembourg have developed new mathematical methods to study the energetic properties of these networks. The scientists published their findings in the scientific journal Physical Review X ("Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics").
The paper was prepared by the research group led by Prof Massimiliano Esposito that investigates how very small biological systems work at the molecular level. These systems are subject to large fluctuations in mass which make their behavior difficult to predict.
In order to be able to describe them nonetheless, the researchers use a probalistic approach that calculates the dynamics of these systems based on the statistical likeliness that changes occur.
Pictorial representation of the transformation between two nonequilibrium concentration distributions. The nonequilibrium transformation (blue line) is compared with the equilibrium one (green line). The equilibrium transformation depends on the equilibrium states corresponding to the initial and final concentration distributions.
Using these probabilistic descriptions, the group studies how these systems exchange energy and matter with their environment and how much energy they dissipate during these processes – a discipline known as stochastic thermodynamics.
However, in the realm of complex chemical reaction networks, probabilistic descriptions become unfeasible since thousands of molecules are involved. The authors showed how the mathematical methods developed for small system can be used to investigate these networks.
“Currently, rigorous thermodynamic models for this kind of networks are lacking. Our work paves the way for thermodynamic characterizations of real chemical networks, such as metabolism,” explains Riccardo Rao, the main author of the paper. “We think of these networks as machines transforming some compounds into others. Some compounds are consumed as they ‘fuel’ the processes. Our description allows to answer questions such as: Is this process efficient? How much energy does it dissipate? If we slightly tweak the system, how will it react?”
At the moment, their research focuses on models of metabolic networks, for which some simplifying approximations are required. “We are now using this framework to investigate specific classes of chemical reaction networks, such as metabolic networks” Riccardo Rao said. Also, the research team will work with biologists and chemists to test and apply the results to concrete biological systems. Research in this direction with groups from the Luxembourg Center for Systems Biomedicine is already ongoing.
 Source: Université du Luxembourg
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