Molecular-level modeling reduction

Biosimulation has a dominant role to play in systems biology. In this chapter, we briefly outline two approaches to systems biology and the role that mathematical models has to play in them. Our focus is on kinetic models, and silicon cell models in particular. Silicon cell models are kinetic models that are firmly based on experiment. They allow for a test of our knowledge and identify gaps and the discovery of unanticipated behavior of molecular mechanisms. These models are very complicated to analyze because of the high level of molecular-mechanistic detail included in them. To facilitate their analysis and understanding of their behavior, model reduction is an important tool for the analysis of silicon cell models. We present balanced truncation as one method to perform model reduction and apply it to a silicon cell model of glycolysis in Saccharomyces cerevisiae. 

Although numerous experiments and spectroscopic characterizations have been conducted on the Phillips catalyst, the precise structure of the active site on the silica surface, reduction of the surface chromate species during the induction period, the formation of the first chromium-carbon bond, and the mechanism for ethylene polymerization still need to be further clarified [11]. In order to achieve more specific information, molecular modeling approaches could provide a useful complement to the experiments and enable us to study these obscure mechanistic problems directly at the atomic and molecular level. In the last decade, very precise mechanistic pictures of the Cr-based polymerization catalysts have been obtained using different theoretical methods, especially through a combination of the experimental findings with theoretical calculations. 

For better understanding the diverse relaxation behavior of confined polymers, researchers have utilized models or simulation tools to capture the kinetic features of the material at the molecular level, aiming to represent the results observed in experiments. The FVHD model, which has been widely employed in characterizing physical aging in bulk polymers, is reformulated to describe the relaxation behavior of polymers under nanoconfinement. A dual mechanism combines the effect of vacancy diffusion and lattice contraction, and was recently applied with time-dependent internal length scales to characterize the free volume reduction in the aging process [169]. The dual mechanism model (DMM) fits the data of thin film permeability fairly well. The potential predictive capability of the DMM model depends on the accuracy of the relationship between the internal length and time scale on the description of complex material dynamics [161]. 

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