Tutorial for ICSB 2006:
Departments of Computer Science and Mathematics, and
Institute for Genomics and Bioinformatics
University of California, Irvine
Running time: 3 hours
Expectations and ambitions for the future of computational systems biology are ever growing, but several significant problems of applied mathematics and modeling stand in the way. These problems include the relations between stochastic and deterministic models and simulation algorithms, adequate models of molecular complexes, the role of spatial inhomogeneity at subcellular and multicellular scales, modeling biological graph structure and dynamics, inference from heterogeneous data sets, and the reuse and integration of modeling techniques across spatial scales from molecular to developmental and ecological.
Fortunately, there are relevant branches of applied mathematics that have been underexploited in attacking these problems, and it’s not too hard to understand their foundations. I suggest that the basic mathematical toolkit for systems biology will come to include not only such staples as differential equation and graphical probabilistic models, but also operator algebras, context-sensitive grammars, stochastic field theory of both particle-like and extended objects , partition functions, aspects of algebraic geometry, and dynamical systems defined on static and dynamic graphs. I will explain why, what, and how, and give examples from many spatial and temporal scales: bacterial metabolism [2, 3], eukaryotic transcriptional regulation  and signal transduction , developmental biology of plants  including phyllotaxis , and population biology.
 “Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview”, Eric Mjolsness. Proceedings of the Ninth International Symposium on Artificial Intelligence and Mathematics, January 2006.
 “A Mathematical Model for the Branched Chain Amino Acid Biosynthetic Pathways of Escherichia coli K12”, Chin-Ran Yang, Bruce E. Shapiro, She-pin Hung, Eric D. Mjolsness, and G. Wesley Hatfield, Journal of Biological Chemistry, 2005 Mar 25; 280(12):11224-32 .
 “Application of a Generalized MWC Model for the Mathematical Simulation of Metabolic Pathways Regulated by Allosteric Enzymes”, Tarek S. Najdi, Chin-Ran Yang, Bruce E. Shapiro, G. Wesley Hatfield, and Eric D. Mjolsness, Journal of Bioinformatics and Computational Biology, to appear 2006.
 “Gene Regulation Networks for Modeling Drosophila Development”, Eric Mjolsness, in Computational Methods in Molecular Biology, eds. J. M. Bower and H. Bolouri, MIT Press 2001.
 “Sigmoid: Towards an Intelligent, Scalable, Software Infrastructure for Pathway Bioinformatics and Systems Biology”, Jianlin Cheng, Lucas Scharenbroich, Pierre Baldi, Eric Mjolsness, IEEE Intelligent Systems, May/June 2005.
 “Modeling the Organization of the WUSCHEL Expression Domain in the Shoot Apical Meristem”, Henrik Jönsson, Marcus Heisler, G. Venugopala Reddy, Vikas Agrawal, Victoria Gor, Bruce E. Shapiro, Eric Mjolsness, Elliot M. Meyerowitz. Bioinformatics 21(Suppl. 1):i232-i240 June 2005.
 “An auxin-driven polarized transport model for phyllotaxis”, Henrik Jönsson, Marcus Heisler, Bruce E. Shapiro, Elliot M. Meyerowitz, Eric Mjolsness. Proceedings of the National Academy of Sciences, 13 January 2006.