1Physiology 472/572 - 2009 - Quantitative modeling of biological systems Lecture 1: Introduction to mathematical models in biology What is a theoretical model? • a representation of a system in abstract form that can be used to simulate some aspects of the system's behavior Why model biological systems? • to integrate different types of information, such as information at different scales • to identify key elements in a system • to test hypotheses about system function • to gain better understanding of a system Why is use of theoretical modeling in biological sciences increasing? • recognition that biological systems are too complex to be understood in qualitative and/or intuitive terms • recognition that many important biological problems cannot be solved by purely reductionist (bottom-up) approaches • vast amounts of data generated by molecular and genomic techniques • increases in readily available computational power ModelsPatient, symptomsSystems, organsCellsProteins, genesIdeal Reality2How should a theoretical model be developed? • start with biological questions • identify key underlying processes, express them in mathematical or computational form • estimate parameters a priori where possible • "Make everything as simple as possible, but not simpler." • carry out the required analysis or computations • treat the results with skepticism, test however possible, compare with independent experimental data • look for the biological significance of the results What types of theoretical model can be distinguished? Type Mechanisms/ Equations Parameters System properties I Phenomenological models Fitted Fitted Described II Qualitative conceptual models Deduced Free Used for testing III Quantitative conceptual models Assumed Optimized Used for validation IV Predictive (application) models Known Known Predicted Reference: Secomb, T.W., Beard, D.A., Frisbee, J.C., Smith, N.P., and Pries, A.R., 2008. The role of theoretical modeling in microcirculation research. Microcirculation, 15, 693-698. Basic propertiesof the systemPredictions that agreewith experimentMathematicalmodelNew insightsand
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