The Mathematics of Systems Biology

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The Mathematics of Systems Biology
Raina Robeva Sweet Briar College Terrell
Hodge Western Michigan U
June 14, 2009 BERE Symposium, Izmir, Turkey
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Connections between biology and the other
scientific disciplines need to be developed and
reinforced so that interdisciplinary thinking and
work become second nature.
The New Frontier
Major Changes in Research Compel Major Changes
in Undergraduate Education
BIO 2010 Report
Executive Summary BIO 2010
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Terminology
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Terminology
Biology
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Significant problems
Similar behaviors, different mechanisms a major
challenge for mathematical modeling

• Models that capture the biological behavior
  are useless

• Different mechanisms apply at different
  scales.

• Need to study the actual biology

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Significant problems
Different Species different behavior
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Significant problems
Experimentation and Data
I also met Stan Ulam, a brilliant Polish
topologist with a charming French wife, who
immediately told me that he had sunk so low that
his latest paper actually contained numbers with
decimal points Otto Frisch describing his
arrival in Los Alamos in late 1943
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Systems Biology
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Mathematical Models are Essential in

• Providing an approximate description of the
  system that could serve as a microscope to
  examining the systems structure and properties

• Serving as virtual laboratories for
  examining the systems responses to internal and
  external stimuli, and, thus, generating more
  indebt knowledge regarding the system

• Generating specific new hypotheses regarding
  the system and suggesting ways for designing
  experiments to be carried out in through
  laboratory experiments, clinical trials, and so on

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A Good Mathematical Models Should Be Able To

• Capture the basic biological behaviors of the
  system

• Simulate the systems responses to stimuli and
  robustness to noise

• Reproduce systems key properties such as
  long-term behavior, equilibrium states, limit
  cycles, stability, robustness

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Types of Mathematical Models
What type of model would be best?
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Systems Biology
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Success Story Undergraduate Bio-Calculus
Courses

• The most popular choice in the undergraduate
  curricula linking mathematics and biology

• Material builds on a long and successful
  track record of the importance of those methods

• Calculus and ODE are the foundation of the
  kind of mathematics biologists know best

But

• Course material does not always capture the
  energy and excitement of the new
  interdiscip-linary landscapes.

• Other mathematical methods such as various
  algebraic approaches have also proved to be
  critically important

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Course Offered

• At SBC
• Spring 2002 as an honors course
• 2004, 2006, 2007, 2008 as BIOL/MATH
• At UVA
• Fall 2004-2006 as BIMS 341/541

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Course Participants and Structure

• Students
• Teams constructed by matching those with strength
  in biology with those with strength in mathematics

• Faculty team taught
• 1 biologist
• 1 mathematician

• Visiting Faculty

• 3 hours lecture/seminar and 3 hours lab per
  week

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Course Components
Biology content
Mathematics content
Model Development, Validation, and Refinement
Computer assisted
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Team of Authors
Raina Robeva (Math) Michael Johnson
(Biophysics) James Kirkwood (Math) Marty Straume
(Biochemistry) Boris Kovatchev (Statistics) Robin
Davies (Biology)
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Acknowledgements

• NSF CCLI Award 0126740
• NSF CCLI Award 0304930
• NIH Award R25 DK064122
• NIH Award R0I DK51562

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Course Outline

• Part I Modeling of Hormone Feedback Networks
  (statistical and ODE approaches control
  functions understanding endocrine oscillations)
  Raina Robeva
  
  

• Part II Modeling of Gene Regulation
  (emphasis on algebraic models, comparing Boolean
  networks models with ODE models)
  
  Raina Robeva

• Part III Linear Algebraic Approaches to
  Metabolic Systems Analysis (linear algebraic
  approaches pathway analysis) Terrell
  Hodge