Complex biological systems are increasingly subject to investigation by mathematical modeling in general and stochastic simulation in particular. Advanced mathematical methods will be used to generate next-generation computational methods and algorithms for (1) formulating these models, (2) simulating or sampling their stochastic dynamics, (3) reducing them to simpler approximating models for use in multiscale simulation, and (4) optimizing their unknown or partly known parameters to fit observed behaviors and/or measurements. The proposed methods are based on advances in applied statistical and stochastic mathematics, including advances arising from operator algebra, quantum field theory, stochastic processes, statistical physics, machine learning, and related mathematically grounded fields. A central technique in this work will be the use of the operator algebra formulation of the chemical master equation. The biological systems to be studied include and are representative of high-value biomedical target systems whose complexity and spatiotemporal scale requires improved mathematical and computational methods, to obtain the scientific understanding underlying future medical intervention. Cancer research is broadly engaged in signal transduction systems and complexes with feedback, for which the yeast Ste5 MARK pathway is a model system. DNA damage sensing (through ATM) and repair control (though p53 and Mdm2) are at least equally important to cancer research owing to the central role that failure of these systems play in many cancers. The dendritic spine synapse system is central to neuroplasticity and therefore human learning and memory. It is critical to understand this neurobiological system well enough to protect it against neurodegenerative diseases and environmental insults. The project seeks fundamental mathematical breakthroughs in stochastic and multiscale modeling that will enable the scientific understanding of these complex systems necessary to create effective medical interventions of the future.

National Institute of Health (NIH)
National Institute of General Medical Sciences (NIGMS)
Research Project (R01)
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Special Emphasis Panel (ZGM1-CBCB-5 (BM))
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Hagan, Ann A
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University of California Irvine
Other Domestic Higher Education
United States
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Shapiro, Bruce E; Mjolsness, Eric (2016) Pycellerator: an arrow-based reaction-like modelling language for biological simulations. Bioinformatics 32:629-31
Shapiro, Bruce E; Tobin, Cory; Mjolsness, Eric et al. (2015) Analysis of cell division patterns in the Arabidopsis shoot apical meristem. Proc Natl Acad Sci U S A 112:4815-20
Johnson, Todd; Bartol, Tom; Sejnowski, Terrence et al. (2015) Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics. Phys Biol 12:045005
Stefan, Melanie I; Bartol, Thomas M; Sejnowski, Terrence J et al. (2014) Multi-state modeling of biomolecules. PLoS Comput Biol 10:e1003844
Mjolsness, Eric (2013) Time-ordered product expansions for computational stochastic system biology. Phys Biol 10:035009
Regner, Benjamin M; Vucinic, Dejan; Domnisoru, Cristina et al. (2013) Anomalous diffusion of single particles in cytoplasm. Biophys J 104:1652-60
Gordon, Elizabeth A; Whisenant, Thomas C; Zeller, Michael et al. (2013) Combining docking site and phosphosite predictions to find new substrates: identification of smoothelin-like-2 (SMTNL2) as a c-Jun N-terminal kinase (JNK) substrate. Cell Signal 25:2518-29
Mjolsness, Eric; Prasad, Upendra (2013) Mathematics of small stochastic reaction networks: a boundary layer theory for eigenstate analysis. J Chem Phys 138:104111
Cunha, Alexandre; Tarr, Paul T; Roeder, Adrienne H K et al. (2012) Computational analysis of live cell images of the Arabidopsis thaliana plant. Methods Cell Biol 110:285-323
Chan, Carlo; Liu, Xinfeng; Wang, Liming et al. (2012) Protein scaffolds can enhance the bistability of multisite phosphorylation systems. PLoS Comput Biol 8:e1002551

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