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Introduction to Mathematical Biology

Introduction to Mathematical Biology. Mathematical Biology Lecture 1 James A. Glazier. P548/M548 Mathematical Biology. Instructor: James A. Glazier Classes: Tu. Thu. 8:00AM–9:30AM Office Hours: By appointment Texts: 1) Murray – Mathematical Biology volumes 1 & 2

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Introduction to Mathematical Biology

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  1. Introduction to Mathematical Biology Mathematical Biology Lecture 1 James A. Glazier

  2. P548/M548 Mathematical Biology Instructor: James A. Glazier Classes: Tu. Thu. 8:00AM–9:30AM Office Hours: By appointment Texts: 1) Murray – Mathematical Biology volumes 1 & 2 2) Fall, Marland, Wagner and Tyson – Computational Cell Biology 3) Keener and Sneyd – Mathematical Physiology Requirements: Weekly Homework (40% of Grade) Written Project Report (40% of Grade) Oral Presentation (20% of Grade) No Final Exam – Late Assignments Will Be Marked Down. Software: CompuCell 3D

  3. Course Topics • Population Dynamics and Mathematical Background • Stochastic Gating • Reaction Kinetics, Oscillating Reactions, and Reactor Networks • Molecular Motors • Collective Phenomena – Flocks and Neural Networks • Higher Dimensional Models: Mathematics • Excitable Media – Heart and Calcium Waves • Turing Patterns

  4. What is Mathematical Biology? • Can be abstruse and self focused when it concentrates on what is soluble analytically rather than what is important. • However, simplified models can teach about general classes of behavior and types of parameter dependence.

  5. Goals • Teach a set of generally useful methodologies. • Give a set of key examples • Build a computational models (hopefully leading you to publish something)

  6. Main Methods • Linear Stability Analysis • Bifurcation Analysis • Phase Plane Diagrams • Stochastic Methods • Fast/Slow Time-Scale Separation • Scaling Theory and Fractals

  7. What is Computational Biology? • Modeling, Not just Curve Fitting • Must have a mechanistic basis • Can address multiscale structures and feedback between elements. • Not Bioinformatics/Genomics (primarily statistics) • Not Cluster Analysis, Image Processing, Pattern Recognition

  8. Goals • To explain biological processes that result in an observed phenomena. • To predict previously unobserved phenomena. • To identify key generic reactions. • To guide experiments: • Suggest new experiments. • Eliminate unneeded experiments. • Help interpret experiments.

  9. Why Needed? • A huge gap between level of molecular data and observed patterns. • Most Modern Biology is descriptive rather than predictive. • Epistemology – Car parts metaphor. • Simplify impossible complexity by forcing a hierarchy of importance – identifying key mechanisms. • In a model know what all processes are. • Failure of models can identify missing components or concepts.

  10. Biological Scales

  11. Biological Scales—Continued

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