Imagine the
Possibilities
Mathematical Biology
University of Utah
A Brief Introduction to Mathematical Biology
Challenges and Opportunities
J. P. Keener
Mathematics Department
University of Utah
Math Biology: Challenges and Opportunities – p.1/7
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Introduction
Mathematical Biology
University of Utah
The Dilemma of Modern Biology
• The amount of data being collected is staggering. Knowing
what to do with the data is in its infancy.
• The parts list is nearly complete. How the parts work
together to determine function is essentially unknown.
What can a Mathematician tell a Biologist she doesn’t already know? – p.2/7
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Possibilities
Introduction
Mathematical Biology
University of Utah
The Dilemma of Modern Biology
• The amount of data being collected is staggering. Knowing
what to do with the data is in its infancy.
• The parts list is nearly complete. How the parts work
together to determine function is essentially unknown.
How can mathematicians help?
• The search for general principles; organizing and describing
the data in more comprehensible ways.
• The search for emergent properties; identifying features of a
collection of components that is not a feature of the
individual components that make up the collection.
What can a Mathematician tell a Biologist she doesn’t already know? – p.2/7
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Possibilities
Mathematical Biology
University of Utah
Quick Overview of Biology
• The study of biological processes is over many space and
time scales (roughly 1016 ):
Lots! I hope! – p.3/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Quick Overview of Biology
• The study of biological processes is over many space and
time scales (roughly 1016 ):
• Space scales: Genes → proteins → networks→ cells→
tissues and organs → organism → communities →
ecosystems
Lots! I hope! – p.3/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Quick Overview of Biology
• The study of biological processes is over many space and
time scales (roughly 1016 ):
• Space scales: Genes → proteins → networks→ cells→
tissues and organs → organism → communities →
ecosystems
• Time scales: protein conformational changes → protein
folding → action potentials → hormone secretion → protein
translation → cell cycle → circadian rhythms → human
disease processes → population changes → evolutionary
scale adaptation
Lots! I hope! – p.3/7
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Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
• Probability and stochastic processes
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
• Probability and stochastic processes
• ODE’s, PDE’s, Delay DE’s, Integro-Differential Equations, ...
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
• Probability and stochastic processes
• ODE’s, PDE’s, Delay DE’s, Integro-Differential Equations, ...
• Numerical Analysis
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
• Probability and stochastic processes
• ODE’s, PDE’s, Delay DE’s, Integro-Differential Equations, ...
• Numerical Analysis
• Topology - knots and scrolls, topological invariants
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
• Probability and stochastic processes
• ODE’s, PDE’s, Delay DE’s, Integro-Differential Equations, ...
• Numerical Analysis
• Topology - knots and scrolls, topological invariants
• Algebraic Geometry, Projective geometry
What about Galois Theory? – p.4/7
Imagine the
Possibilities
Kinds of Math I have Used
Mathematical Biology
University of Utah
• Discrete Math - graph theory, finite state automata,
combinatorics
• Linear algebra
• Probability and stochastic processes
• ODE’s, PDE’s, Delay DE’s, Integro-Differential Equations, ...
• Numerical Analysis
• Topology - knots and scrolls, topological invariants
• Algebraic Geometry, Projective geometry
Editorial Comment: Let the biology dictate the math, not the other
way around.
What about Galois Theory? – p.4/7
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Possibilities
Mathematical Biology
University of Utah
Some Biological Challenges
• DNA -information content and information processing;
Math Biology: Challenges and Opportunities – p.5/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Some Biological Challenges
• DNA -information content and information processing;
• Proteins - folding, enzyme function;
Math Biology: Challenges and Opportunities – p.5/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Some Biological Challenges
• DNA -information content and information processing;
• Proteins - folding, enzyme function;
• Cell - How do cells move, contract, excrete, reproduce,
signal, make decisions, regulate energy consumption,
differentiate, etc.?
Math Biology: Challenges and Opportunities – p.5/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Some Biological Challenges
• DNA -information content and information processing;
• Proteins - folding, enzyme function;
• Cell - How do cells move, contract, excrete, reproduce,
signal, make decisions, regulate energy consumption,
differentiate, etc.?
• Multicellularity - organs, tissues, organisms, morphogenesis
Math Biology: Challenges and Opportunities – p.5/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Some Biological Challenges
• DNA -information content and information processing;
• Proteins - folding, enzyme function;
• Cell - How do cells move, contract, excrete, reproduce,
signal, make decisions, regulate energy consumption,
differentiate, etc.?
• Multicellularity - organs, tissues, organisms, morphogenesis
• Human physiology - health and medicine, drugs,
physiological systems (circulation, immunology, neural
systems).
Math Biology: Challenges and Opportunities – p.5/7
Imagine the
Possibilities
Some Biological Challenges
Mathematical Biology
University of Utah
• DNA -information content and information processing;
• Proteins - folding, enzyme function;
• Cell - How do cells move, contract, excrete, reproduce,
signal, make decisions, regulate energy consumption,
differentiate, etc.?
• Multicellularity - organs, tissues, organisms, morphogenesis
• Human physiology - health and medicine, drugs,
physiological systems (circulation, immunology, neural
systems).
• Populations and ecosystems- biodiversity, extinction,
invasion
Math Biology: Challenges and Opportunities – p.5/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Places Math is Needed
• Moving across spatial and temporal scales - What details to
include or ignore, understanding emergent behaviors (There
is no such thing as a homogeneous environment or
medium).
Math Biology: Challenges and Opportunities – p.6/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Places Math is Needed
• Moving across spatial and temporal scales - What details to
include or ignore, understanding emergent behaviors (There
is no such thing as a homogeneous environment or
medium).
• Understanding stochasticity - Is it noise or is it real?
(Periodic behaviors do not exist in biology)
Math Biology: Challenges and Opportunities – p.6/7
Imagine the
Possibilities
Places Math is Needed
Mathematical Biology
University of Utah
• Moving across spatial and temporal scales - What details to
include or ignore, understanding emergent behaviors (There
is no such thing as a homogeneous environment or
medium).
• Understanding stochasticity - Is it noise or is it real?
(Periodic behaviors do not exist in biology)
• The challenge of complex systems (e.g., the nature of
robustness).
Math Biology: Challenges and Opportunities – p.6/7
Imagine the
Possibilities
Places Math is Needed
Mathematical Biology
University of Utah
• Moving across spatial and temporal scales - What details to
include or ignore, understanding emergent behaviors (There
is no such thing as a homogeneous environment or
medium).
• Understanding stochasticity - Is it noise or is it real?
(Periodic behaviors do not exist in biology)
• The challenge of complex systems (e.g., the nature of
robustness).
• Data handling and data mining - Extracting information and
finding patterns when you don’t know what your are looking
for.
Math Biology: Challenges and Opportunities – p.6/7
Imagine the
Possibilities
Places Math is Needed
Mathematical Biology
University of Utah
• Moving across spatial and temporal scales - What details to
include or ignore, understanding emergent behaviors (There
is no such thing as a homogeneous environment or
medium).
• Understanding stochasticity - Is it noise or is it real?
(Periodic behaviors do not exist in biology)
• The challenge of complex systems (e.g., the nature of
robustness).
• Data handling and data mining - Extracting information and
finding patterns when you don’t know what your are looking
for.
• Imaging and Visualization (Medical imaging,
Math Biology:
Challenges and Opportunities – p.6/7
protein
Imagine the
Possibilities
Mathematical Biology
University of Utah
Summary
• What you will learn here is barely the tip of the iceberg.
Math Biology: Challenges and Opportunities – p.7/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Summary
• What you will learn here is barely the tip of the iceberg.
• The challenges are enormous, but so are the opportunities.
Math Biology: Challenges and Opportunities – p.7/7
Imagine the
Possibilities
Mathematical Biology
University of Utah
Summary
• What you will learn here is barely the tip of the iceberg.
• The challenges are enormous, but so are the opportunities.
• Explore, Experiment, Create, Work Hard, Have Fun!
Math Biology: Challenges and Opportunities – p.7/7