*Tutorial for ICSB 2006:*

To register: https://mailman.ics.uci.edu/mailman/listinfo/icsb-mjolsness-tutorial

Eric Mjolsness

*Departments of Computer
Science and Mathematics, and*

*Institute for Genomics and
Bioinformatics*

*University of California,
Irvine*

*www.ics.uci.edu/~emj*

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 itÕs 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 [1], 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 [4] and signal transduction [5], developmental biology of plants [6] including phyllotaxis [7], and population biology.

[1]
ÒStochastic Process Semantics for Dynamical Grammar Syntax: An OverviewÓ, Eric
Mjolsness. *Proceedings of the
Ninth International Symposium on Artificial Intelligence and Mathematics*, January 2006.

[2] ÒA Mathematical Model for the
Branched Chain Amino Acid Biosynthetic Pathways of *Escherichia coli K12*Ó, 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 .

[3] ÒApplication of a
Generalized MWC Model for the Mathematical Simulation of Metabolic Pathways
Regulated by Allosteric EnzymesÓ, 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.

[4] ÒGene Regulation
Networks for Modeling *Drosophila* DevelopmentÓ, Eric Mjolsness, in *Computational Methods in
Molecular Biology*, eds.
J. M. Bower and H. Bolouri, MIT Press 2001.

[5] ÒSigmoid: Towards an Intelligent,
Scalable, Software Infrastructure for Pathway Bioinformatics and Systems
BiologyÓ, Jianlin Cheng, Lucas Scharenbroich, Pierre Baldi, Eric Mjolsness, *IEEE
Intelligent Systems*, May/June 2005.

[6] ÒModeling the
Organization of the WUSCHEL Expression Domain in the Shoot Apical MeristemÓ, Henrik Jšnsson, 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.

[7] ÒAn auxin-driven
polarized transport model for phyllotaxisÓ, Henrik
Jšnsson, Marcus Heisler, Bruce E. Shapiro, Elliot M. Meyerowitz, Eric
Mjolsness. *Proceedings of the National Academy of Sciences*, 13 January 2006.