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AMS 333, Mathematical Biology

Catalog Description: This course introduces the use of mathematics and computer simulation to study a wide range of problems in biology. Topics include the modeling of populations, the dynamics of signal transduction and gene-regulatory networks, and simulation of protein structure and dynamics. A computer laboratory component allows students to apply their knowledge to real-world problems.

Prerequisite: (i)  AMS 161 or MAT 127 or 132 or 142; (ii) BIO 150 or 201; and  AMS 210 or MAT 211 or BIO 202; OR permission of instructor

3 credits

Textbook (recommended): "Essential Mathematical Biology", by Nicholas Britton, Third, Edition; Springer; ISBN: 9781852335366


THIS COURSE IS OFFERED IN THE FALL SEMESTER ONLY

The course satisfies the WRTD requirement of the Stony Brook Curriculum.  It has three lab reports that require extensive writing.

Inst: Thomas MacCarthy  AMS 333 Webpage 

Week 1.

Grand challenges in biology; history of mathematical biology.

Week  2.

Introduction to non-linear systems; stationary points and simulation of dynamics.

Week  3.

Modeling of population dynamics; the Lotka-Volterra model; inter-species competition; oscillatory systems.

Week  4.

Mathematics epidemiology; modeling viral epidemics.

Week  5.

Biochemical kinetics; introduction to signal transduction.

Week  6.

Modeling of signal transduction networks; introduction to gene regulation in prokaryotes and eukaryotes.

Week  7.

Bi-stable networks; phage-l lysis/lysogeny; the “repressilator”

Week  8.

Spatial effects in biology; compartment models; PDEs in space and time; diffusion.

Week  9.

Whole cell modeling; the “e-Cell”; modeling Calcium flux.

Week  10.

Introduction to protein structure; molecular energetics.

Week  11.

Molecular dynamics; theory and implementation; applications.

Week  12.

Molecular interactions: the docking problem; affinity prediction.

Week  13.

Future directions in mathematical biology.

 

Learning Outcomes for AMS 333, Mathematical Biology:


1.) Familiarity with the major challenges in the field of Biology and the place of Mathematical Biology in making Biology a more quantitative science.

2.) Demonstrate a basic understanding of the use of dynamical systems theory in Biology
    
* understand the difference between models of continuously versus discretely reproducing species
     * state the difference between differential equations and difference equations and how they are used
     * understand the concepts of stationary point, stability and nullcline in linear dynamical systems
     * understand the difference between positive and negative feedback
     * develop programs in MatLab for numerical integration of one-dimensional systems.

3.) Demonstrate an understanding of models of population dynamics
     * understand the difference between linear and nonlinear dynamical systems
     * show an ability to use graphical approaches to analyze two-variable dynamical systems
     * model interactions between species using the Lotka-Volterra (predator-prey) model
     * understand elements of stability analysis and use of the Jacobian matrix
     * model interactions between species as competition for a common resource.

4.) Demonstrate an understanding of basic models in Mathematical epidemiology
      * understand basic biology and concepts necessary for modeling epidemics
      * model an epidemic of disease with recovery using the SIS model
      * model a disease epidemic with acquired immunity using the SIR model
      * understand the effect of vaccination strategies using the SIR model

5.) Demonstrate an understanding of Modeling in Cellular and Molecular Biology
     * develop models of biochemical kinetics including the Michaelis-Menten and Hill Equations
     * understand the fundamental mechanisms of signal transduction and associated models
     * model simple gene regulatory systems such as the bistable phage-λ lysis/lysogeny system.

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