Structural Analysis of Biochemical Reaction Networks 2012

Description

Developing mechanistic mathematical models of biological systems often involves dealing with high levels of uncertainty. Hence the increasing interest in exploring the connections between the structure of potential underlying mechanisms and dynamic features. The course introduces mathematical methods and recent results connecting the structure of biochemical reaction networks with key steady-state.

Objective

The aim of the course is to provide the student with mathematical and computational methods for the structural analysis of biochemical reaction networks. The dynamics of biological networks is usually encoded in models of nonlinear ODEs which, due to the particular connectivity and thermodynamic/kinetic constraints inherent to the mechanisms involved, are endowed with a rich structure. In the recent years, this structure has been exploited in several ways to infer important properties of the dynamics and steady states of biochemical networks, in order to overcome the limited knowledge usually hampering model development in systems biology. This course provides a comprehensive overview of several such methodologies, including a more in depth analysis of some concepts and theories already introduced in Computational Systems Biology course, and introducing new elements and results from Chemical Reaction Network Theory, Monotone systems, Flux Balance Analysis and Bifurcation Theory.
This comprehensive approach includes (i) the understanding of the main results and their connections, (ii) the interplay with different branches of mathematics, and (iii) the applications in systems biology, contributing to the in-depth understanding of biochemical reaction network systems and, in addition, to demonstrate interesting applications and connections of results from nonlinear systems theory, linear algebra, algebraic geometry, graph theory, and linear optimization.

Lecture Material

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