Generalized thermodynamic description of complex biological systems

This thesis is divided into four chapters.
In the opening chapter the model construction process will be discussed. After presenting the fundamental aspects of the modeling process, the analysis will be focused on the issue of models classification. Lastly, a systematic approach for the model construction process will be proposed, in order to face the following problems through a rational procedure.
In the second chapter a theoretical preface will be done; it deals with the issues which will be afterwards practically treated. Particularly, there are three main disciplines which will be touched during the essay: Physics, Mathematics and Biology.
Physics is the theoretical base of the quasi-equilibrium models. Concepts as thermodynamic approach, slow invariant manifold and quasi equilibrium manifold will be widely discussed, for a complete understanding of the dynamic models based on quasi equilibrium approximation. Quasi equilibrium dynamic models are based on the knowledge of the steady states of the analyzed system; therefore a detailed analysis of the characteristics of the equilibrium states, according to the conserved quantities of the system, will be done. Moreover, it will be explained the principal component analysis, which will help to calculate the amount of conserved quantities in a system, and the direct or Montecarlo-like analysis, which will be used for the exact identification of the conservation laws.
Mathematics provides the tools in order to optimize and “tune” models. In detail, the mathematical tools explained will be: two optimization algorithms (genetic algorithm and constrained nonlinear optimization), which will be used for fitting the models to the studied system, and the constrained Jacobian matrix, which will have a fundamental role for the network construction process.
Finally, a close examination concerning the Biology of the studied systems will make it possible to identify the utility and the potential field of application of the introduced models. In the third chapter, the quasi-equilibrium model will be tested through several well-known biological systems (already modeled thanks to a detailed kinetic approach), following an increasing order of complexity.
In particular, the model will be used for predicting dynamics of a Michaelis-Menten enzymatic network, a simplified gene regulation system, the MAPK cascades process and the Calvin cycle. The best algorithms and Matlab functions will be identified for our tasks, in order to obtain an optimized QE model before its application on an experimental case. Moreover, a comparison between one-dimensional manifold models and two-dimensional ones will be attempted. Lastly, constrained Jacobian matrices will be utilized for the reaction network construction, and the space of equilibrium states of the above systems (and additionally IкB metabolism and Purine metabolism) will be explored, in order to obtain the number of conserved quantities for the analyzed systems.
In the last chapter the QE model will be applied to some experimental data obtained thanks to a collaboration with the MBC (Molecular Biotechnology Center) located in Turin: the transcriptional regulatory networks in embryonic stem cells will be studied. More precisely, thanks to the principal components analysis of a cloud of equilibrium states, it will be possible to deduce the amount of conservation laws; while, thanks to a direct or a Montecarlo-like analysis, the conservation laws will be precisely identified. Then, species dynamics will be fitted using QE models, and the Jacobian way of network construction process will be attempted.
Finally, a comparison between the results obtained by the QE models and a model proposed in literature [Schmidt, Lipson, Distilling Free-Form Natural Laws from Experimental Data, Science, Vol.324, 2009] will be conducted in appendix C.