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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


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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