parameter estimation and synthesis for systems biology: new algorithms for nonlinear and stochastic...

e8 SCAI Meeting Abstracts

Parameter estimation and synthesis for systems biology: Newalgorithms for nonlinear and stochastic modelsSumit Jha a, Alexandre Donze b, Rupinder Khandpur a,

Joyeeta Dutta-Moscato c, Qi Mi c, Yoram Vodovotz c,

Gilles Clermont c, Christopher Langmead a

aCarnegie Mellon UniversitybVerimag Laboratory, FrancecUniversity of Pittsburgh, Pittsburgh, PA, USA

Objectives: The study aim to develop efficient, scalable algorithmsfor identifying parameters in nonlinear and stochastic models, suchas those encountered in systems biology.Methods: We have developed 2 algorithms for performingsynthesis using reachability analysis. Our first algorithm can beapplied to systems of nonlinear, ordinary differential equations. Thesecond algorithm can be applied to stochastic models, includingagent- and rule-based models. Parameter synthesis is the task ofidentifying ensembles of models, differing only in their choice ofparameters, that exhibit qualitatively similar behaviors. In partic-ular, our algorithms partition the space of parameters into disjointdomains of dynamic behavior corresponding to user-definedconstraints (eg, “a mild infection triggers an inflammatory responsethat resolves within 24-48 hours”). These algorithms can also solvethe parameter estimation problem (ie, fitting to data) as a specialcase. Our methods provide more flexibility than related methods,such as bifurcation analysis, in the kinds of dynamical behaviorsthat can be considered.Results: Temporal changes, similar to those observed forendotoxemic mice (Chow et al, Shock.2005;24[1]:74-84) and rats(Daun et al, J Theor Biol.2008;253[4]:843-53), were observed in allinflammatory analytes. Although TNF was produced to a highdegree in all animals, PCA suggested that IL-1β rather than TNFmay be a main driver of systemic inflammation in this experimentalpreparation. The mathematical model was capable of describing thedynamics of inflammatory analytes in swine and predictedqualitative dynamics of MMP-2 and MMP-9.Conclusions: A mathematical model of inflammation in swine hasbeen defined that will aid us in elucidating the pathogenesis of acuteinflammation in this clinically relevant preclinical model.

doi:10.1016/j.jcrc.2010.12.031

Spatial effects of pro- and anti-inflammatory cytokines on chronicinflammation: A mathematical modelIan Price a, David Swigon a, G Bard Ermentrout a, Gilles Clermont a,b

aDepartment of Mathematics, University of Pittsburgh, Pittsburgh,

PA, USAbMedical Center, University of Pittsburgh, Pittsburgh, PA, USA

Objectives: Dysregulated pro- and anti-inflammatory cytokineproduction can lead to incomplete healing in tissue with acute traumaor to regions of inflammation in healthy tissue. We propose amathematical model including pro- and anti-inflammatory cytokines,chemokines, macrophages, neutrophils, NOS, and tissue that we firstuse to replicate dysregulated states and then to simulate treatment.Methods: A nonlinear mathematical model was constructed in asetting of ordinary differential equations. Parameters were fitted toviral response data and mathematical and heuristic biologiccriteria. Bifurcation analyses were performed. The model was then

altered into a spatial setting using partial differential equations.Conditions for pattern formation were established. Differentregimes of endogenous anti-inflammatory cytokine productionwere compared. Various treatment regimes using anti-inflamma-tory cytokines were implemented on acutely and chronicallydamaged systems.Results: In the ODE version of the model, conditions forbifurcations leading to a stable long-term state and loss of stabilityof the baseline state and, in the PDE version, on flux and diffusionfor pattern-forming instabilities were found. Self-perpetuatingregions of chronic inflammation were reproduced by the model.For various scenarios, a minimal treatment regimen was establishedthat would re-establish baseline health of the tissue, if a minimumexisted. For scenarios where baseline health did not re-establish, wecompare the difference between tissue given long-term care anduntreated long-term cases.Conclusions: Spatially oriented models permit some insight into thespread of inflammation throughout the tissue. The mathematicalmodel can explain observations such as rheumatoid arthritisbecoming localized in an otherwise homogeneous system. There-fore, any proposed treatment regimen must account for the localizedrather than systemic nature of a self-perpetuating region of chronicinflammation. The model provides insight into treatment optionsthat may disrupt the localization and speed up healing.

doi:10.1016/j.jcrc.2010.12.032

Characterization of fundamental aspects of biology with abstractmathematics: Category theory as a pathway for dynamic computationalmodeling of biologic systemsGary An

University of Chicago, Department of Surgery

Objectives: The complexity of biologic systems is well recognized,as well as the need and utility of mathematical modeling andcomputer simulation as means of addressing that complexity.Although multiple methods of mathematical and computationalmodeling have been applied in a tailored fashion to various aspectsof biologic systems, there is potential significant benefit toidentifying and mathematically representing a fundamental de-scription of biology. Category theory (1) is a branch of abstractmathematics that has been used to bridge and bind various otherbranches of mathematics, providing a means of allowing tools andmethods from one arena to be applied to others. Category theorymay be well suited as a means of describing the fundamentalproperties of biology from a computational perspective.Methods: Category theory is centered on the concept of a categorydefined as a collection of objects, functions between the objects, andthe effects of those behaviors on the overall structure of objectrelationships. Furthermore, category theory deals with the transfor-mations of one category into another that preserve the properties thatdefine the category; these transformations are termed morphismsand are described by “functors.” “Fundamental properties” ofbiology were identified, specifically targeted at distinguishingbiology from physics and chemistry. These classes of propertieswere then mapped onto a category theoretical framework.Results: A category theory–based description of biologic systemswas developed as described above. It was determined that biologicsystems cannot be represented without accounting for their