Model silicon cell

The Silicon Cell version of this model is available at http //www.jjj.bio.vu.nl/database/ hynne. 

Silicon Cell Models Construction, Analysis, and 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. 

Model reduction aims at simplifying without losing the essence of the dynamic behavior of a model. Reduction of silicon cells should thereby facilitate the understanding of real cells. Strategies for model reduction, pinpointing molecular organizational properties that are essential for network behavior, are essential to make silicon cell models understandable. 

This chapter addresses how silicon cell models can be used in biosimulation for systems biology. We first describe the process of model building, as well as its purpose and how it fits in systems biology. Then we compare the use of silicon cell models with the use of the less-detailed core models. We briefly discuss various simulation methods used to model phenomena involving diffusion and/or stochas-ticity as well as methods for model analysis. Finally we discuss balanced truncation as a method for model reduction. This method is illustrated by applying it to a silicon cell model of yeast glycolysis. 

The second method relies on the experimental determination of the kinetic parameters using techniques from biophysics or enzymology. Also in this case problems exist (1) the kinetic parameters are often determined under conditions different from the conditions in the cytoplasm (2) an enormous number of experiments need to be done, even for a network of moderate size, to determine all kinetic parameters experimentally. When the second method is used to parameterize a kinetic model then the resulting model is considered a silicon cell model. A number of silicon cell models exist [25-27, 29, 75-77]. 

Many methods have been developed for model analysis for instance, bifurcation and stability analysis [88, 89], parameter sensitivity analysis [90], metabolic control analysis [16, 17, 91] and biochemical systems analysis [18]. One highly important method for model analysis and especially for large models, such as many silicon cell models, is model reduction. Model reduction has a long history in the analysis of biochemical reaction networks and in the analysis of nonlinear dynamics (slow and fast manifolds) [92-104]. In all cases, the aim of model reduction is to derive a simplified model from a larger ancestral model that satisfies a number of criteria. In the following sections we describe a relatively new form of model reduction for biochemical reaction networks, such as metabolic, signaling, or genetic networks. 

The aim of the project reported here is to develop system reduction methods for large biochemical systems, including silicon cell models. Here we present our first approach using balanced truncation. The plan is to develop reduction methods custom-made for biochemical systems. To use balanced truncation is a natural first step towards the development of finer methods, since it is a basic method in system theory, and many other methods are variants of this. 

Here the procedures of linearization, balancing, and truncation are described such that the reader is enabled to use it. To start with, one has a nonlinear biochemical system, for example a silicon cell model, in the form of differential equations. 

Balanced Truncation in Action Reduction of a Silicon Cell Model of Glycolysis in Yeast... 

Fig. 1. Schematic drawing of proposed amorphous silicon cell model showing junctions at p+-i and n -i interfaces with intervening photoconductive / layer.

FIG. 72. Schematic cross-section of (a) a single junction p-i-n o-Si H superstrata solar cell and (b) a tandem solar cell structure. (From R. E. I, Schropp and M. Zeman. "Amorphous and Microcrystalline Silicon Solar Cells—Modeling, Materials and Device Technology," Kluwer Academic Publishers, Boston, 1998, with permission.)... 

R. E. I. Schropp and M. Zeman, Amorphous and Microcrystalline Silicon Solar Cells—Modeling, Materials and Device Technology. Kluwer Academic Publishers, Boston, 1998. 

Jiang, C.-W. Green, M. A. 2006. Silicon quantum dot superlattices Modeling of energy bands, densities of states, and mobilities for silicon tandem solar cell applications. J. Appl. Phys. 99 114902-114909. 

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