MA565
Course Syllabus
Mathematical
Models in the Life Sciences
T/TH
11AM12:15PM, MCS B33
Instructor Information:
Samuel
Isaacson
Associate
Professor
Department
of Mathematics and Statistics
111
Cummington Mall, Room 231 (MCS)
Course Webpage (all homeworks will be posted here):
http://math.bu.edu/people/isaacson/ma565spring2018/ma565.html
Office Hours:
Tuesday
from 12:151:15pm and 4:305:30pm in MCS 231.
Textbooks: (We will use
material and assign problems from each of the following):
[EK1]:
LA Segel and L EdelsteinKeshet,
A Primer on Mathematical Models in Biology. (Main textbook)

Ebook available through the BU library: here.
[EK2]:
L EdelsteinKeshet, Mathematical Models in Biology

Ebook available through the BU library: here.
[SO]: E. Sontag, Lecture Notes on
Mathematical Systems Biology.

PDF available online: here.
Description and Goals:
This
course introduces methods for analytically investigating mathematical models of
biological systems. An emphasis will be placed on ODE, PDE and stochastic
models, along with related mathematical tools for analyzing the models. Mathematical
topics will include dimensional analysis, qualitative analysis of ODE models,
asymptotic methods, quasisteady state approximations, multistability,
oscillatory systems, excitable systems, stochastic differential equations and
driftdiffusion models. Biological topics will include chemotherapy, viral and
disease dynamics, cellular signaling and receptor dynamics, gene regulation,
neural excitation, polymer dynamics and transport within cells.
Prerequisites:
MA
226 or 231 or the equivalent. It is
assumed that students are comfortable with solution methods for linear first
and second order ODEs, phaseplane methods for systems of ODEs in 2D, and fully
recall multivariable calculus (GreenÕs theorem, divergence theorem, partial
derivatives, surface integrals, and area/volume integrals). This material will
be used throughout the course without review.
Grading:
10%
 Homework assignments (graded only on completeness)
30%
 Midterm I (2/22 in class)
30%
 Midterm II (4/5 in class)
30%
 Final (Tuesday May 8^{th}, 12:302:30pm)
Exam Policy:
You
are expected to be able to attend class, and as such, makeup exams will not be given
for scheduling conflicts. Similarly, it is your responsibility to make sure you
both know the official registrarÕs final exam date and can attend the exam.
(For example, booking a plane flight before the exam date is not an excusable reason
to be unable to take the exam.) If you feel you have an extraordinary reason
you will not be able to attend an exam, the instructor must be notified the
first week of class (otherwise no consideration will be given to providing a
makeup exam). If you miss an exam, a makeup will be provided only if you have
missed the exam for medical reasons and notify the instructor within 24 hours
of the reason. Makeup exams will generally be oral exams with you answering
questions on the blackboard.
Homework Policy:
Homework
will be due in class, and will not be accepted late. Homework must be neatly
written up, stapled, and have all problems and related work solved in order as
listed on the assignment. Homework that does not satisfy this policy will be
returned with a grade of zero.
Grading Policy:
If
you feel an exam problem has been incorrectly graded, the professor must be
notified the day the assignment/exam is returned to you. After 24 hours all grades are final.
Tentative Course Outline
(Subject to change):
1.
Continuous Growth Models
a.
Logistic models in population dynamics.
b.
Chemostats, effect of chemotherapeutic agents on cells.
c.
Nondimensionalization.
d.
Epidemiology, SIRS models (viral and disease dynamics).
2.
Chemical Kinetics and Cellular Signaling
a.
Types of chemical reactions, simple models.
b.
Enzymatic reactions and quasisteady state approximations.
c.
MichaelisMenton approximation and asymptotic analysis.
d.
Allosteric inhibition, cooperativity and multistability.
e.
Hill models and GoldbeterKoshland
approximations.
f.
Applications to signaling networks, receptor systems and gene
regulation.
g.
Oscillations and excitable systems. Genetic oscillators,
HodgkinHuxley, and FitzhughNagumo models.
3.
Stochastic and PDE Models
a.
From NewtonÕs equations to stochastic differential equations.
b.
Brownian motion and diffusion equation.
c.
Exit time problems and cellular signaling.
d.
Driftdiffusion processes and the FokkerPlanck equation.
e.
Polymer dynamics and microtubule transport.