Math 285J - Mechanics in Biology


Instructor: Marcus Roper

Meetings: MWF 11am in 5233 Math. Sci.

Office hours: W. 2.30-4, F. 4-5.30. Math Sci. 7619B. I’m currently in a temporary office, but I will put a notice up on the door of 7619B so you can find me.

Organisms are adapted for the challenges of life in physically difficult environments. Since the 1950s, when Lighthill and Taylor first analyzed the swimming of microbes and of fish, mathematical models have been used to predict and substantiate these adaptations. However, it is also clear that there are trade offs between ecophysiological optima – e.g. under limitations of biomass, a tree that grows tall to increase sunlight capture may be more susceptible to failure under wind or its own weight. Here our models can be used to quantify the stiffness of slackness of different physical constraints: providing organizing principles for understanding the tremendous diversity of the natural world. New methods in quantitative biology, that allow e.g. phenotypic shifts between species individuals or developmental stages to be traced to underlying genetic mechanisms, provide exciting new possibilities for modeling at the interface of math, mechanics and biology, and this course will devote time both to classic papers and new analyses that exploit these rich new sources of information.

There is no core textbook for the course, I will cover the following topics, as time allows:

Dispersal and transport: Spore dispersal and the challenge of crossing the boundary layer. Microbial swimming. Coordinated behaviors; swarming and pattern formation.

Feeding: Fluid dynamics of feeding. Dealing with uncertain or heterogeneous environments: strategies for chemo- and info-taxis.

Growth: Physical perspectives on tissue growth and repair. Embryo segmentation and morphogen gradients.

Requirements: I recommend that students have taken an introductory class in fluid mechanics, and have experience of mathematical modeling. No previous classes in biology will be assumed. In the first two weeks of the course, we will review both some of mechanics and modeling principles, including dominant balances and scaling arguments.

Assessment: There will be no homeworks in this class, but you should attempt all of the pre-readings (see below), and spend time after each class making sure that you understand the assigned papers. Grades will be assigned based on a final report, to be submitted during exam week, and a short (20 min) in-class presentation. I will post some potential projects during Week 2 (you can also work on your own ideas!) and I will schedule meetings with everyone individually in Week 3 to help you get started.

(Provisional) key references:

Dispersal and transport: S. Vogel “Living in a physical world II. The bio-ballistics of small projectiles”, J. Biosci. 30:167—75, 2005.

M. Roper et al. “Dispersal of fungal spores on a cooperatively-generated wind”, Proc. Nat. Acad. Sci. USA 107:17474—9, 2010

M.A. Reidenbach, J R. Koseff, and M. A. R. Koehl “Hydrodynamic forces on larvae affect their settlement on coral reefs in turbulent, wave-driven flow.” Limnol. Oceanogr. 54: 318-330, 2008.

M.E. Cates et al. “Arrested phase separation in reproducing bacteria creates a generic route to pattern formation”, Proc. Nat. Acad. Sci. USA, 107:11715-20.

Feeding: M. J. Lighthill “Flagellar hydrodynamics”, SIAM Rev. 18:161-230, 1976

I. Tuval et al. “Bacterial swimming and oxygen transport near contact lines”, Proc. Nat. Acad. Sci. USA 102:2277—82 2005

M.B. Short et al. “Flows driven by flagella of multicellular organisms enhance long-range molecular transport:, Proc. Nat. Acad. Sci. USA 103:8315-9, 2006

Clark, D.A. and Grant L.C. “The bacterial chemotactic response reflects a compromise between transient and steady-state behavior”, Proc. Nat. Acad. Sci. USA 102:9150—55, 2005.

M. Vergassola, E. Villermaux and B.I. Shraiman “‘Infotaxis’ as a strategy for search without gradients”, Nature 445:406-9 2007

Growth and morphogenesis: TA McMahon and RE Kronauer. "Tree structures: deducing the principle of mechanical design," J. Theor. Biol. 59: 443-466, 1976.

KJ Niklas and V Kerchner “Mechanical and photosynthetic constraints on the evolution of plant shape,” Paleobiology 10:79-101, 1984.

D. Ambrosi et al. “Perspectives on biological growth and remodeling”, J. Mech. Phys. Solids 59:863-83, 2011.

H. Jonsson et al. “An auxin-driven polarized transport model for phyllotaxis”, Proc. Nat. Acad. Sci. USA, 103:1633-8 (2008).

P Friedl and K Wolf “Plasticity of cell migration: a multiscale tuning model”, J. Cell Biol. 188:11-19, 2009.

O. Pourquie “The segmentation clock: Converting embryonic time into spatial pattern”, Science 301:328—330, 2008.