Learning Biology by Recreating and
Extending Mathematical Models
IBI* SERIES WINNER
Dynamics of Biological Systems, the IBI Prize–
winning module, brings mathematics into the
Hillel J. Chiel,1,2,3 Jeffrey P. Gill,1 Jeffrey M. McManus,1 Kendrick M. Shaw1
Biological systems are dynamic. Pro- teins fold into three-dimensional shapes to serve as catalysts, motors,
or regulators. A fertilized egg divides exponentially, and gradients and internal cell
states choreograph fetus formation. Neurons become active or are inhibited in shifting spatial and temporal patterns as an animal moves through its environment. Flocks
of birds migrate together, and schools of fish
form and disperse to avoid predators and
forage for food. The only constant in biological systems is change.
Although biological systems generate beautiful patterns that unfold in space
and time, most students are taught biology
as static lists of names. Names of species,
anatomical structures, cellular structures,
and molecules dominate, and sometimes
overwhelm, the curriculum and the student.
Cookbook labs may demonstrate advanced
techniques but have a foregone conclusion.
Not surprisingly, students often conclude
that biology is boring.
In contrast, students who participate in
research discover that biological systems
can be understood by developing a “
feeling for the organism,” a qualitative sense of
the system (1). Successful students learn the
skill of asking the right question with the
right technique to find the key elements that
make biological systems work.
Can biology be taught by focusing on
unfolding patterns in space and time? Can
one also reach students who are repelled by
details; are more comfortable with abstractions and clear principles; and who often
become mathematicians, physicists, or engineers? The divide between the cultures of
biology and the more quantitative sciences is
unfortunate because interdisciplinary opportunities are expanding. Engineers are fascinated by self-assembling, self-repairing, and
self-replicating nanomachines (2), exem-
CREDI T: JEFFRE Y P. GILL
1Department of Biology, Case Western Reserve University, Cleveland, OH 44106, USA. 2Department of Neurosciences, Case Western Reserve University, Cleveland, OH
44106, USA. 3Department of Biomedical Engineering, Case
Western Reserve University, Cleveland, OH 44106, USA.
*IBI, Science Prize for Inquiry-Based Instruction;
Author for correspondence. E-mail: email@example.com
Classroom setup. Each of the six hexagonal tables in the classroom has power outlets and connections to the
CWRU fiber optic network for students’ laptops.
plified by proteins. How can these nanomachines be combined into cell-like modular
reorganizing components? What is the basis
for multifunctional designs that allow biological organisms to use the same neural control and periphery to flexibly switch among
multiple behaviors (3)? How do many agents
use distributed computing and cooperation
to solve common goals (4)? Can we further
enhance evolutionary algorithms (5) to solve
otherwise intractable problems? Life is an
alien technology whose mastery would create
novel approaches to hard problems.
These considerations are the basis for
the inquiry-based module Dynamics of Biological Systems, developed at Case Western Reserve University (CWRU) (6, 7). The
module’s learning goals are as follows: construct and extend mathematical models of
biological phenomena, analyze these models using the concepts and tools of nonlinear
dynamical systems theory, and write clearly
about the modeling process and the results
obtained from the model.
During the module’s first half, students
work in teams (see the photo) to solve
increasingly complex problems by creating
mathematical models using a programming
language (Mathematica) and to analyze these
models using nonlinear dynamical systems
theory. After being shown how to find model-
ing papers, each team selects a peer-reviewed
paper that describes a mathematical model of
a biological system. They spend the second
half of the module using the skills gained in
the first half to reconstruct, analyze, and then
modify and extend the published model. At
the module’s end, each student submits a final
term paper (7).