Gene expression model parameters

Figure 1.1 A simple model of gene expression. The model has been implemented and simulated in the program Gepasi.41 42 Nonlinear saturable functions chosen for the kinetics of all 6 reactions and parameter values chosen to produce extreme behaviors (details available from authors).

Further extensions of the model are required to address the dynamical consequences of these additional regulatory loops and of the indirect nature of the negative feedback on gene expression. Such extended models have been proposed for Drosophila [112, 113] and mammals [113]. The model for the circadian clock mechanism in mammals is schematized in Fig. 3C. The presence of additional mRNA and protein species, as well as of multiple complexes formed between the various clock proteins, complicates the model, which is now governed by a system of 16 or 19 kinetic equations. Sustained or damped oscillations can occur in this model for parameter values corresponding to continuous darkness. As observed in the experiments on the mammalian clock. Email mRNA oscillates in opposite phase with respect to Per and Cry mRNAs [97]. The model displays the property of entrainment by the ED cycle... 

Brief details are given below of some numerical approximations used to compute the posterior distribution of the fold change 9k (3), for k = 1,..., g. We assume that, given the model parameters, the expression data ykj, are independent for different genes and samples. 

Pharmacometrics and PK/PD modeling can provide important insights into gene expression and proteomics data because these approaches can reduce the dimensionality of the problem time courses of expression are expressed in terms of a limited number of model parameters that are readily interpreted by the users. 

The variables, parameters, mathematical models, and the genetic algorithm (GA) approach to model the gene expression profiling are discussed in this section. The various variables are discussed first. 

Bioassays are frequently used as an alternative or in addition to immunoassay techniques. Bioassays, in contrast to immunoassays, quantify not the pharmacologically active substance, but its biological activity, for example, in cell culture models based on cell differentiation, cell proliferation, or cytotoxicity as well as gene expression assays or whole animal models. Frequent major problems with bioassays comprise a high variability in the measured parameters, lack of precision, and their time- and labor-intensive performance. Furthermore, bioassays oftentimes also lack specificity for the measured compound, as they may also detect the response to bioactive metabolites [16,17]. 

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