A mathematical way to think about biology
Why "is" biology log-normal? Why do some circuits oscillate? See biology from a physical sciences perspective.
Created by David Liao
Apply physical sciences perspectives to biological research
Be able to teach yourself quantitative biology
Be able to communicate with mathematical and physical scientists
Requirements
- Algebra
- Exposure to calculus (there is an appendix for students interested in review)
Description
A mathematical way to think about biology comes to life in this lavishly illustrated video book. After completing these videos, students will be better prepared to collaborate in physical sciences-biology research. These lessons demonstrate a physical sciences perspective: training intuition by deriving equations from graphical illustrations.
"Excellent site for both basic and advanced lessons on applying mathematics to biology."
-Tweeted by the U.S. National Cancer Institute's Office of Physical Sciences Oncology
Who this course is for:
- Undergraduate students
- Graduate students
- Postdoctoral scholars
- Lab managers
- Funding agency program staff
- Principal investigators and grant writers
- Citizen scientists
- Patient advocates
- Lifelong learners
- Integrative Cancer Biology Program members
- Physical Sciences Oncology Network members
- National Centers for Systems Biology members
Course content
14 sections • 134 lectures • 15h 24m total length
- Welcome to mathematics for insightful biology01:48
- Stochasticity a: Incommensurate periods05:15
- Stochasticity b: Practically unpredictable deterministic dynamics04:29
- Stochasticity c: Fundamentally indeterministic processes05:03
- Stochasticity d: Memory-free (Markov) processes and their visual representations04:46
- Canonical protein dynamics a: Translation and degradation events occur over time08:57
- Canonical protein dynamics b: Differential equation and flowchart09:50
- Canonical protein dynamics c: Qualitative graphical solution04:12
- Canonical protein dynamics d: Analytic solution and rise time11:02
- Mass action 1a: Law of mass action13:02
- Mass action 1b: Cooperativity and Hill functions11:58
- Mass action 1c: Bistability06:32
- Evolutionary game theory Ia: Population dynamics15:35
- Evolutionary game theory 1b: Preview comparison with tabular game theory12:32
- Evolutionary game theory IIa: Cells repeatedly playing games19:20
- Evolutionary game theory IIb: Relationship between time and sophisticated comput10:58
- Statistics a: Probability distributions and averages05:54
- Statistics b: Identities involving averages03:43
- Statistics c: Dispersion and variance05:33
- Statistics d: Statistical independence06:26
- Statistics e: Identities following from statistical independence07:20
- Probability a: Bernoulli trial03:49
- Probability b: Binomial distribution07:18
- Probability c: Poisson distribution08:13
- Preparation for central limit theorem: Stirling's approximation11:22
- Central limit theorem a: Statement of theorem06:37
- Central limit theorem b: Optional derivation (special case)09:01
- Central limit theorem c: Properties of Gaussian distributions03:50
- Prevalence of Gaussians a: Noise in physics labs is allegedly often Gaussian08:25
- Prevalence of Gaussians b: Noise in biology is allegedly often log-normal10:35
- Uncertainty propagation a: Quadrature07:45
- Uncertainty propagation b: Sample estimates09:38
- Uncertainty propagation c: Square-root of sample size (sqrt(n)) factor05:57
- Uncertainty propagation d: Comparing error bars visually03:18
- Uncertainty propagation e: Illusory sample size06:55
- Sample variance curve fitting a: Chi-squared08:18
- Sample variance curve fitting b: Minimizing chi-squared13:37
- Sample variance curve fitting c: Checklist for undergraduate curve fitting03:44
- Sample variance curve fitting exercise for MatLab5 pages
- Master equation07:49
- Stochastic simulation algorithm a: Specifying reaction types and stoichiometries03:13
- Stochastic simulation algorithm b: Time until next event10:45
- Stochastic simulation algorithm c: Determining type of next event03:18
- Poissonian copy numbers a: Stochastic transcription and deterministic degradation08:11
- Poissonian copy numbers b: Stochastic transcription and stochastic degradation14:11
- Linear algebra Ia: Teaser05:19
- Linear algebra Ib: Vectors09:56
- Linear algebra Ic: Operators13:44
- Linear algebra Id: Solution of teaser (part 1)09:35
- Linear algebra Id: Solution of teaser (continued)17:50
- Intro quasispecies a: Population dynamics from single-cell mechanisms06:37
- Intro quasispecies b: Eigenvalue-eigenvector analysis06:42
- Euler II: Complex exponentials04:29
- Linear algebra II: Rotation a: Rotation matrix04:51
- Linear algebra II: Rotation b: Complex eigenvalues08:43
- Numerical integration of differential equations11:03
- Linear stability analysis a: Transcription-translation model03:52
- Linear stability analysis b: Nullclines and critical point07:17
- Linear stability analysis c: Eigenvalue-eigenvector analysis16:30
- Linear stability analysis d: Cribsheet11:49
- Almost linear stability analysis a: Incoherent feed-forward loop07:49
- Almost linear stability analysis b: Adaptation06:13
- Almost linear stability analysis c: Eigenvalue-eigenvector analysis11:06
- Almost linear stability analysis d: Cribsheet05:48
- Oscillations a: Romeo and Juliet07:46
- Oscillations b: Twisting nullclines03:42
- Oscillations c: Time delays02:31
- Oscillations d: Stochastic excitation03:48
- Introduction to physical oncology01:54
- Dynamic heterogeneity a: Stochastic biochemistry06:23
- Dynamic heterogeneity b: Phenotypic interconversion04:54
- Dynamic heterogeneity c: Metronomogram08:10
- Cellular automata a: Deterministic cellular automata05:46
- Statistical physics 101a: Fundamental postulate of statistical mechanics06:47
- Statistical physics 101b: Cartesian product02:42
- Statistical physics 101c: Distribution of energy between a small system and a large bath12:05
- Statistical physics 101d: Expressions for calculating average properties of systems connected to baths05:15
- Ideal chain a: Introduction to model04:09
- Ideal chain b: Hamiltonian and partition function08:46
- Ideal chain c: Expectation of energy and elongation17:00
- Macroscopic irreversibility a: Microstates of universe are explored over time10:17
- Macroscopic irreversibility b: Microscopic reversibility05:06
- Macroscopic irreversibility c: Ratio of volumes in phase space11:08
- Macroscopic irreversibility d: Kinetically accessible volumes of phase space11:44
Instructor
Physicist (PhD, Princeton 2010)
![David Liao](data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 64 64"%3E%3C/svg%3E){kind=avatar}
- 4.1 Instructor Rating
- 509 Reviews
- 24,208 Students
- 1 Course
David's illustrations have been published in Science, Physical Review Letters, Molecular Pharmaceutics, Biosensors and Bioelectronics, and the Proceedings of the National Academy of Sciences.
University of California, San Francisco
Associate Professional Researcher 2015-Current
Analyst, 2012-2014
Postdoc, 2010-2012 Tlsty Lab
Princeton University (PhD, Physics, 2010 MA, Physics, 2007)Advisor: Robert H. Austin
2006-2009 National Defense Science and Engineering Graduate Research Fellowship
2009-2010 National Science Foundation Graduate Research Fellowship
Harvey Mudd College BS, Physics, 2005
Advisor: Robert J. Cave