Course Announcement: Mathematics of Chemical Reaction Networks and Kinetic Systems by Prof. Eduardo Mendoza

MA 291 (Mathematics of Chemical Reaction Networks and Kinetic Systems)

  • Tue & Thur., 1:00 - 2:30pm, IMSP Bldg. UP Los Baños
  • Also accessible via the Web
  • Start date: 6 Aug. 2015

The mathematical theory of chemical reaction networks is unique in several ways: it has had good coverage in high impact science journals such as PNAS, Nature and Science, was pioneered and sustained by chemists and chemical engineers over decades until mathematicians started applying it to biological systems over a decade ago and is now emerging as a valuable contribution to Synthetic Biology. Most recently, the application of the "reaction kinetics" paradigm to ecology, epidemiology and the social sciences (via evolutionary game theory) has been progressed. The field as experienced tremendous growth in the last five years, with over 200 research papers in journals in mathematics, biology, chemistry and chemical engineering, physics and computer science.

The course intends to provide a comprehensive introduction to both the "classical" results (mainly developed by chemical engineers 1972 - 2000) and new developments in the field (since its application to biology in 2001). Important network properties such as multistationarity (existence and number of equilibria), persistence (non-extinction of species) and robustness have been successfully studies using combination of methods from linear algebra/matrix theory, graph theory, ordinary differential equations/dynamical systems and most recently, algebraic geometry. The course this semester covers the following topics:

  • Mathematics of Chemical Reaction Networks and Kinetic Systems: from Chemical Engineering and Chemistry to Systems Biology and beyond
  • Fundamentals of Chemical Reaction Networks (CRN)
  • A Structural View of Positive Vectors in Reaction Space
  • Fundamentals of Chemical Kinetic Systems (CKS)
  • Deficiency-oriented Theory for Generalized Mass Action Kinetic (GMAK) Systems
  • Injectivity and Concordance Theory
  • Topological Methods for Chemical Kinetic Systems (including graph theory and degree theory)
  • Stoichiometric Network Analysis

Mathematical prerequisites: lecturer's consent to be based on the student's knowledge of linear algebra/matrix theory, fundamentals of graph theory and ordinary differential equations. Topological concepts needed will be covered in short tutorials within the course.

A set of Lecture Notes (~300 pages), which have been developed from the original course at UP Diliman last year, will be available to course participants. 

The lectures will highlight opportunities for research with mathematical, computational or biological application focus, many of which are suited for MS and PhD thesis work.

Course Organization

Graduate students wishing to get units credited will need to register for at UP Los Baños for the MA 291 course (contact: Dr. Editha Carreon-Jose, ecjose1@up.edu.ph or editz16@yahoo.com). Participant evaluation will be based on submission of problem set solutions and a paper presentation at the end of the course.

The lectures will be open via the Web (on a non-credit basis) to students and researchers of other academic institutions in the Philippines. Persons interested in participating should email the lecturer at mendoza@lmu.de.

Lecturer Info

Ed Mendoza studied mathematics at Ateneo de Manila, Heidelberg University and Bonn University. He completed his PhD under G. Harder and F. Hirzebruch with a thesis on the "Cohomology of PGL2 over imaginary quadratic integers". While an Assistant Professor of Mathematics at Wuppertal University, his collaboration with communications engineers led to a strong interest in computer networks and a move to the IT industry in October 1980.

After spending 22 years in the software industry in various positions, his interest in the dynamics of complex systems and systems biology led to a move back to academe in October 2002. He has since co-authored over 30 publications, is a Co-Editor of a recent book on "Systems Biology and Psychiatric Research" (Wiley-Blackwell 2010) and a Section Editor of the "Encyclopedia of Systems Biology" (Springer 2013).

He is an adjunct professor in Mathematics and Computer Science at the University of the Philippines in Diliman, Los Baños and Manila. He is currently a Visiting Scientist at the Max Planck Institute of Biochemistry and at the Physics Department, Ludwig Maximilians University (both in Munich, Germany). He can be contacted at ermendoza@dcs.upd.edu.phmendoza@biochem.mpg.de or mendoza@lmu.de.