![Page 1: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/1.jpg)
University of UtahMathematical Biology
theImagine Possibilities
A Brief Introduction to Mathematical BiologyChallenges and Opportunities
J. P. Keener
Mathematics Department
University of Utah
Math Biology: Challenges and Opportunities – p.1/7
![Page 2: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/2.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Introduction
The Dilemma of Modern Biology
• The amount of data being collected is staggering. Knowingwhat to do with the data is in its infancy.
• The parts list is nearly complete. How the parts worktogether to determine function is essentially unknown.
How can mathematicians help?
• The search for general principles; organizing and describingthe data in more comprehensible ways.
• The search for emergent properties; identifying features of acollection of components that is not a feature of theindividual components that make up the collection.
What can a Mathematician tell a Biologist she doesn’t already know? – p.2/7
![Page 3: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/3.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Introduction
The Dilemma of Modern Biology
• The amount of data being collected is staggering. Knowingwhat to do with the data is in its infancy.
• The parts list is nearly complete. How the parts worktogether to determine function is essentially unknown.
How can mathematicians help?
• The search for general principles; organizing and describingthe data in more comprehensible ways.
• The search for emergent properties; identifying features of acollection of components that is not a feature of theindividual components that make up the collection.
What can a Mathematician tell a Biologist she doesn’t already know? – p.2/7
![Page 4: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/4.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Quick Overview of Biology
• The study of biological processes is over many space andtime scales (roughly 1016):
• Space scales: Genes → proteins → networks→ cells→tissues and organs → organism → communities →
ecosystems
• Time scales: protein conformational changes → proteinfolding → action potentials → hormone secretion → proteintranslation → cell cycle → circadian rhythms → humandisease processes → population changes → evolutionaryscale adaptation
Lots! I hope! – p.3/7
![Page 5: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/5.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Quick Overview of Biology
• The study of biological processes is over many space andtime scales (roughly 1016):
• Space scales: Genes → proteins → networks→ cells→tissues and organs → organism → communities →
ecosystems
• Time scales: protein conformational changes → proteinfolding → action potentials → hormone secretion → proteintranslation → cell cycle → circadian rhythms → humandisease processes → population changes → evolutionaryscale adaptation
Lots! I hope! – p.3/7
![Page 6: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/6.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Quick Overview of Biology
• The study of biological processes is over many space andtime scales (roughly 1016):
• Space scales: Genes → proteins → networks→ cells→tissues and organs → organism → communities →
ecosystems
• Time scales: protein conformational changes → proteinfolding → action potentials → hormone secretion → proteintranslation → cell cycle → circadian rhythms → humandisease processes → population changes → evolutionaryscale adaptation
Lots! I hope! – p.3/7
![Page 7: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/7.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 8: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/8.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 9: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/9.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 10: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/10.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 11: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/11.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 12: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/12.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 13: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/13.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 14: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/14.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Kinds of Math I have Used
• 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
![Page 15: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/15.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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, neuralsystems).
• Populations and ecosystems- biodiversity, extinction,invasion
Math Biology: Challenges and Opportunities – p.5/7
![Page 16: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/16.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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, neuralsystems).
• Populations and ecosystems- biodiversity, extinction,invasion
Math Biology: Challenges and Opportunities – p.5/7
![Page 17: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/17.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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, neuralsystems).
• Populations and ecosystems- biodiversity, extinction,invasion
Math Biology: Challenges and Opportunities – p.5/7
![Page 18: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/18.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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, neuralsystems).
• Populations and ecosystems- biodiversity, extinction,invasion
Math Biology: Challenges and Opportunities – p.5/7
![Page 19: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/19.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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, neuralsystems).
• Populations and ecosystems- biodiversity, extinction,invasion
Math Biology: Challenges and Opportunities – p.5/7
![Page 20: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/20.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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, neuralsystems).
• Populations and ecosystems- biodiversity, extinction,invasion
Math Biology: Challenges and Opportunities – p.5/7
![Page 21: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/21.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Places Math is Needed
• Moving across spatial and temporal scales - What details toinclude or ignore, understanding emergent behaviors (Thereis no such thing as a homogeneous environment ormedium).
• 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 ofrobustness).
• Data handling and data mining - Extracting information andfinding patterns when you don’t know what your are lookingfor.
• Imaging and Visualization (Medical imaging, proteinstructure, etc.)
Math Biology: Challenges and Opportunities – p.6/7
![Page 22: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/22.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Places Math is Needed
• Moving across spatial and temporal scales - What details toinclude or ignore, understanding emergent behaviors (Thereis no such thing as a homogeneous environment ormedium).
• 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 ofrobustness).
• Data handling and data mining - Extracting information andfinding patterns when you don’t know what your are lookingfor.
• Imaging and Visualization (Medical imaging, proteinstructure, etc.)
Math Biology: Challenges and Opportunities – p.6/7
![Page 23: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/23.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Places Math is Needed
• Moving across spatial and temporal scales - What details toinclude or ignore, understanding emergent behaviors (Thereis no such thing as a homogeneous environment ormedium).
• 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 ofrobustness).
• Data handling and data mining - Extracting information andfinding patterns when you don’t know what your are lookingfor.
• Imaging and Visualization (Medical imaging, proteinstructure, etc.)
Math Biology: Challenges and Opportunities – p.6/7
![Page 24: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/24.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Places Math is Needed
• Moving across spatial and temporal scales - What details toinclude or ignore, understanding emergent behaviors (Thereis no such thing as a homogeneous environment ormedium).
• 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 ofrobustness).
• Data handling and data mining - Extracting information andfinding patterns when you don’t know what your are lookingfor.
• Imaging and Visualization (Medical imaging, proteinstructure, etc.)
Math Biology: Challenges and Opportunities – p.6/7
![Page 25: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/25.jpg)
University of UtahMathematical Biology
theImagine Possibilities
Places Math is Needed
• Moving across spatial and temporal scales - What details toinclude or ignore, understanding emergent behaviors (Thereis no such thing as a homogeneous environment ormedium).
• 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 ofrobustness).
• Data handling and data mining - Extracting information andfinding patterns when you don’t know what your are lookingfor.
• Imaging and Visualization (Medical imaging, proteinstructure, etc.)
Math Biology: Challenges and Opportunities – p.6/7
![Page 26: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/26.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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
![Page 27: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/27.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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
![Page 28: A Brief Introduction to Mathematical Biology Challenges ...keener/lectures/PCMI/PCMI_1.pdf · Mathematical Biology Imagine the Possibilities A Brief Introduction to Mathematical Biology](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b96947e708231d4313fec/html5/thumbnails/28.jpg)
University of UtahMathematical Biology
theImagine Possibilities
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