Biology 290 and 290L: Introduction to Quantitative Biology
Syllabus
Credit Hours: 4. This will be a 4 hour credit course with 3 hours of lecture and 1 hour for a computational
lab each week.
Instructor:
Laura Miller
Associate Professor of Biology and Mathematics
Email: lam9@unc.edu
Website: http://www.unc.edu/~lam9
Phone: 919-943-2434
Office: Wilson G44A
Office Hours: Tuesday 11-12:30, Wednesday 9-10:30
Teaching Assistant:
Shannon Jones
Email: skjohnsn@email.unc.edu
Website: www.skjones.web.unc.edu
Office: Chapman 442
Target Audience: Biology majors who are interested in quantitative biology, mathematical modeling, and
computer simulation. Mathematics, physics, chemistry, and computer science majors who are interested
in biological applications of mathematics.
Course Prerequisites: MATH 231 and one of BIO 201/202/205
Course Goals and Key Learning Objectives:
 Write down mathematical models to describe molecular, cellular, and organismal processes.
 Solve the mathematical models numerically or analytically and evaluate them against
experimental data.
 Become proficient in the use of MATLAB for biological applications, both in terms of writing
programs and using software packages.
Course Requirements:
Students will be expected to review assigned readings from the textbook, lecture notes, and other
materials posted on sakai before each class. Comprehension of the material covered in lectures will be
evaluated from weekly homework assignments that will involve writing down mathematical models,
solving them numerically or analytically, and evaluating them against experimental data. Two midterms
and a final exam will also be used to evaluate comprehension and will be based upon material in the
homework assignments. Finally, students will be expected to attend the weekly computing lab and
complete associated weekly computational homeworks.
Dates:
Last Day of Late Registration………………………………………………….………Tuesday, Jan. 14
Midterm 1……………………………………………………………………Assigned: 2/14, Due: 2/21
Spring Break………………………………………………………………………….……..March 7-17
Midterm 2……………………………………………………………………Assigned: 2/14, Due: 2/21
Classes End……………………………………………………………………………...Friday, Apr. 25
Final Exam……………………………………………………………….….…Friday, May 2, 8-11 am
Grades: Graded work will consist of Matlab computing assignments (30%), weekly written homework
assignments (10%), two take home midterms (15% each), and a final exam (30%). Matlab computing
assignments will be applications relevant to medicine and the life sciences. Lectures and written
homework will also cover a range of applications relevant to the medicine and the life sciences.
Course Policies:
Honor Code Statement: “It is expected that each student will conduct him or herself within the guidelines
of the Honor System. All academic work should be done with the highest level of honesty and integrity
that this University demands.” In particular, all tests and quizzes should be taken without texts without
consultation with other student’s work. Students are encouraged to work together on all homework
assignments.
Calculators: Hand-held calculators may be used in all work including examinations, however cell phones
may not be used as calculators.
Exams: The course final exam is given in compliance with UNC final exam regulations and according to
the UNC Final Exam calendar.
Attendance: Sign-in sheets will be circulated during each class, but attendance will not be figured into
your grade directly. However, attending class is highly recommended.
Course Resources:
Required Text: F.C. Hoppensteadt and C.S. Peskin. Modeling and Simulation in Medicine and the Life
Sciences. Second Edition, New York: Springer-Verlag, 2002.
Sakai Resources: Supplemental reading, lecture notes, and problem sets will be posted to
www.unc.edu/sakai throughout the semester. Digital assignments will be turned in to and gradebook will
be maintained on www.unc.edu/sakai.
Webassign: Homework will be assigned and submitted through webassign. Please create an account using
your onyen as the username at http://www.webassign.net. You will need the following information to
enroll in the course:
Instructor
Section
Class Key
Laura Miller BIOL 290, section 1
unc 1584 7718
Time Table:
I. Weeks 1-3: Brownian Motion and Diffusive Processes (Hoppensteadt and Peskin, Chapter 10)
A. Random walks
i. Biased random walks of bacteria chemotaxis
ii. Movement of ions across cell membranes
B. The Process of Diffusion
i. Diffusion of a drop on a substrate
ii. Counter current exchange
Lab 1: Introduction to Matlab.
Lab 2: Random walks and programming in Matlab.
Lab 3: Developing a model of diffusion.
http://biomath.usu.edu/files/uploads/Documents/Reprints/Kohler_BMB72-2010.pdf
II. Weeks 4-5: Genetics (Hoppensteadt and Peskin, Chapter 8)
A. Natural Selection
1. Slow selection
2. Genotype Frequencies
B. Random genetic drift
C. Genetic algorithms
1. Mathematical representations of mutation and crossover
2. Fitness functions
Lab 4: Introduction to GA’s and Dawkin’s biomorphs.
Lab 5: Vector representations of genomes.
III. Weeks 6-7: Regulatory networks
(from Tyson et al. Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways
in the cell. Current Opinion in Cell Biology 2003, 15:221–231)
A. Models of protein synthesis and degradation
1. Linear signal-response curves
2. Hyperbolic signal-response curves
B. Feedback models
1. Positive feedback and irreversible switches
2. Negative feedback: homeostasis and oscillations
C. Complex networks
1. Cell control cycle
Lab 6: Simulating feedback loops using differential equations in Matlab (numerical methods and Matlab
tools).
IV. Weeks 8-9: Electrical Properties of Cell Membranes (Hoppensteadt and Peskin, Chapter 3)
A. Osmotic Pressure
1. Cell volume control
B. The movement of ions across membranes
C. Interaction of Electrical and Osmotic Effects
D. The Hodgkin Huxley equations
1. Computer simulations of action potentials
E. The Fitz-Hugh Nagumo equations
1. Phase plane analysis
Lab 7: Analyzing the FitzHugh Nagumo model with phase planes.
Lab 8: Simulating nerve dynamics in Matlab (code taken from Hoppensteadt and Peskin).
V. Weeks 10-11: Muscle Mechanics (Hoppensteadt and Peskin, Chapter 5)
A. The Force-Velocity Curve
B. A microscale model of crossbridge attachment
1. Computer simulation of attachment and detachment.
C. Neural Activation of Muscles
Lab 10: Simulating crossbridge attachments in Matlab.
Lab 10: Writing down a mathematical model for muscle dynamics.
VI. Weeks 12-13: Noisy Regulatory Networks (D. T. Gillespie. Exact Stochastic Simulation of Coupled
Chemical Reactions. The Journal of Physical Chemistry, Voi. 8 1, No. 25, 1977.
A. Stochastic Formulation of Biochemical Kinetics
B. Examples
1. Radioactive decay
2. Couple reactions
3. The Lotka Reactions
C. Computer simulations
Lab 11: Simulating coupled reactions deterministically and stochastically in Matlab
Lab 12: Comparing the deterministic and stochastic Lotka Reactions for small numbers of molecules.
VII. Weeks 14-15: Neural Systems (Hoppensteadt and Peskin, Chapter 6)
A. Biological Rhythms
1. Phase locking
2. Biological clocks
B. Neural Networks
1. Models for neural networks
2. A thalamocortical circuit
3. Hippocampus model
Lab 13: Simulating neural networks Part I.
Lab 14: Simulating neural networks Part II.
Syllabus Changes: The professor reserves to right to make changes to the syllabus, including project due
dates and test dates. These changes will be announced as early as possible.