#### 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 MAT 132 or MAT 142; and
AMS 210 or MAT 211; OR permission of instructor

3 credits

SBC: EXP+, WRTD

*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.