PHYS120: Physics of Biological Systems
Spring 2008 - Science Center 113 (physics seminar room) - Monday 7 - 10 PM
THOMASINA. Each week I plot your equations dot for dot, x's against y's in all manner of algebraical relation, and every week they draw themselves as commonplace geometry, as if the world of forms were nothing but arcs and angles. God's truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?
SEPTIMUS. We do.
THOMASINA. Then why do your equations only describe the shapes of manufacture?
SEPTIMUS. I do not know.
THOMASINA. Armed thus, God could only make a cabinet.
SEPTIMUS. He has mastery of equations which lead into infinities where we cannot follow.
-- Tom Stoppard, Arcadia, I.3
Student coordinator: Benjamin Blonder - firstname.lastname@example.org
Faculty sponsor: John Boccio - email@example.com
This student-run course focuses on the fundamental principles of living systems. We search for those laws that are common to broad classes of life-forms in order to understand the limits of life on Earth or anywhere else it might be discovered or created. The physics of biology will enable a new synthetic and predictive science.
The field is rapidly developing; we will find many open questions. We will not be comprehensive; there are more topics and depth than we can reasonably hope to cover. It also will not be a biophysics course; the new laws may be independent of the laws of physics or the specifics of Earth-based life. The course will be mathematical and rely on many techniques from physics; this cannot be helped. We cannot escape the unreasonable effectiveness of mathematics in the natural sciences.
The course is offered on a credit/no-credit basis.
The class will be run as a seminar. Each week we will discuss the assigned readings and resolve any difficulties you may have had. There will also be four presentations each week on relevant topics. These presentations should be under twenty minutes in length and may be in any format (blackboard, overhead projector, PowerPoint/Keynote). Sometimes the presentations will explore new material and sometimes they will provide background or a clearer explanation of the reading. We will often have introductory presentations on unfamiliar subjects. There may be guest lectures by biology and physics faculty some weeks.
There will also be a weekly seminar break with food and drink. A bag of pretzels from Tarble is unacceptable and shameful.
Each week you will be assigned a set of readings. These will be available either as PDFs from this website or will be on reserve in Cornell. The assignments for each week are listed in the order you should read them. We have no official textbook, but you may consider purchasing one or several of our references. Don't worry if you don't understand all of the reading. Some weeks I have assigned an excessive amount in the hopes that you will skim and find the interesting parts. Read first for theme, then focus on the mathematical details. You are expected to contribute to discussion every week, even if you were not able to complete or understand all the readings. Focus on what you do understand, and be able to articulate what you don't.
Each week, at least four hours before seminar, you will have to submit a short (one page at most) note to the discussion section of the website. This note should describe what you found difficult and what you found interesting this week. If you have any interesting ideas, describe them briefly too. This note will help set the direction and focus of the seminar and also provide valuable feedback on the course.
If you are giving a presentation, make it compelling: explain why the subject is interesting and relevant before getting into details. Make sure it takes less than twenty minutes to give - I will be timing presentations and cutting off ramblers. You will get to volunteer for presentation topics, but everyone should have given approximately the same number by the end of the semester.
There will be a final project or paper, on any topic of interest to you. There is no length requirement; do the topic justice. The final week of seminar we will have presentations from everyone on their subject. There will be no midterm or final exam.
You may find some of these resources useful during the semester and while choosing a topic for your final presentation.
- M. Gell-Mann, The quark and the jaguar: adventures in the simple and complex
- P. Bak, How nature works: the science of self organized criticality
- S. Kauffman, At home in the universe: the search for laws of self organization and complexity
- B. C. Goodwin, How the leopard changed its spots: the evolution of complexity
- J. Gleick, Chaos: making a new science
Week 1 - January 21: Concepts and single-species population models
This week looks at some of the background and motivation for this kind of science and this class. We also have a short introduction to population biology.
- Continuous models of single species populations. Discrete models of single species populations. What are different models for growth? What are their properties and how do we solve them? Are they realistic? Jen Trinh.
- Lotka-Volterra model. How can we model interacting species? Briefly, what are the possible outcomes of competition? Ethan Deyle.
- Bifurcations and chaos: techniques and applicability. Where do these appear in discrete and continuous models? Is there a role for chaos or period-doubling in biological systems? Eric Duchon.
Seminar break: Benjamin Blonder.
Faculty guest: John Boccio.
Week 2 - January 28: Population biology in depth
This week is a survey of a classic topic in mathematical biology, population dynamics. Differential equations and linear algebra are very useful.
- J. D. Murray, Mathematical Biology, chapters 1, 2, and 3. Focus most on chapter 3; read chapter 4 if you have time. Try problem 3.1.
- You may also want to (but don't have to) consult L. Edelstein-Keshet, Mathematical Models in Biology for more detail on mathematical techniques. Look at chapters 2, 3, 4, 5, or 6.
- If the Murray reading is confusing, a simpler introduction to the topic can be found in M. Kot, Elements of Mathematical Ecology, pages 1-109.
- L. Becks et al., Experimental demonstration of chaos in a microbial food web.
- This week has a lot of mathematics, which may be unfamiliar. Help us through some of the tricky parts of chapter 3; maybe a basic introduction to linear algebra? Stephan Hoyer.
- Can these models be extended to deal with spatially distributed populations? Give us a short introduction. Consider looking at A. Okubo and S. A. Levin, Diffusion and Ecological Problems, chapter 10. If this doesn't interest you, help us through some of the details of nullclines and phase planes. Ben Good.
- What is the biological evidence for these models? Are they at all realistic? Explore this for us. Kaz Uyehara.
- Present problem 2.7 (the interesting parts) and 3.4. Tom Emmons.
Seminar break: Caitlin O'Neil and Emily Hager.
Faculty guest: none.
Week 3 - February 4: Communities and food webs
This week focuses on a particular aspect of population dynamics, competition. Competition and interaction between species are well described by food webs. What kinds of food webs are stable? How strongly do species interact? Linear algebra may be useful.
Seminar break: Jen Trinh.
Faculty guest: Steve Wang.
Week 4 - February 11: Network biology
Many properties of food webs are best understood through the lens of graph theory. Many other biological networks can also be analyzed in this way. How relevant is network architecture to biology? Or is the network the fundamental object?
Seminar break: Seth Donoughe.
Faculty guest: none.
Week 5 - February 18: Size and scaling
This week shifts our focus to the issue of size in biology. Life exists on many different scales - are there any similarities across these scales? What is responsible for these fundamental similarities? We will encounter scaling exponents here, but this week is meant more as a biological survey than a mathematical adventure.
- K. Schmidt-Nielsen, Scaling: Why is animal size so important?. Read chapters 2, 7 (now out of date, but for background), 12, 13, 14, 15. This book is an easy read; you may also find other chapters interesting.
- T. A. McMahon, Size and Shape in Biology. Old, but interesting.
- P. A. Marquet et al., Scaling and power-laws in ecological systems.
- T. A. McMahon and J. T. Bonner, On Size and Life. This is also an easy read with lots of pictures. Please read as much of the book as captivates you. I hope we'll all find something interesting in this book to discuss in seminar.
- V. M. Savage et al., The predominance of quarter-power scaling in biology. This is a teaser for next week.
- A. A. Biewener, Biomechanical consequences of scaling. This may be a difficult read if you don't have familiarity with the field; skip it if you want.
- Dinosaurs are cool. What are the consequences of being big? Vogel's book may be useful, but you can take this topic wherever you want. Ari Strandburg-Peshkin.
- Tell us about scaling in ecology. What are some of the interesting issues and models? Body size and abundance, perhaps? You may want to start with R.H. Peters, The Ecological Implications of Body Size or J. A. Wiens, Spatial Scaling in Ecology. Kaz Uyehara.
- How do organisms fly? Seth Donoughe.
- Give an overview of important physical forces at different scales. What is important to cells, and what is important to organisms? Do small organisms care about different forces than big ones? You might find S. Vogel, Comparative Biomechanics useful. The library has a copy, and so do I (you can borrow it). You might want to instead choose a more specific example of a transition and highlight two organisms which are on opposite sides of it. Tom Emmons.
Seminar break: Stephan Hoyer.
Faculty guest: Rachel Merz.
Week 6 - February 25: Metabolic theory
This week looks at one particular aspect of scaling: metabolism. What is responsible for this relationship? Is resource flow a more fundamental issue? We will need a basic understanding of fractals and a lot of patience to understand these models, though the result is worth it.
- J. H. Brown et al., Toward a Metabolic Theory of Ecology.
- G. B. West, J. H. Brown, B. J. Enquist, A General Model for the Origin of Allometric Scaling Laws in Biology. This is nasty going, but very important. If it's too confusing, try the Etienne paper below.
- J. F. Gillooly et al., Effects of size and temperature on metabolic rate. You can skip this paper if you're pressed for time.
- G. B. West, J. H. Brown, B. J. Enquist, A general model for ontogenic growth.
- J. R. Banavar et al., Size and form in efficient transportation networks.
Seminar break: Tom Emmons.
Faculty guest: Aaron Clauset (Santa Fe Institute).
Week 7 - March 3: Fractals and automata
Fractals and cellular automata are closely related and may have biological application: many structures are self-similar, are governed by simple rules, or are cell-based. This week we look closely at these topics and focus in particular on plant form. The mathematics of fractals will be new but not difficult. To understand cellular automata we will need some discrete math.
- S. Wolfram, A New Kind of Science. Chapter 3, 6, 8.5, 8.6, 8.7. Wolfram is a jerk, but a smart jerk; read the preface if you want evidence of this.
- G. B. Ermentrout and L. Edelstein-Keshet, Cellular Automata Approaches to Biological Modeling. You can skim this; we'll look into a lot of her examples in later weeks.
- N. C. Kenkel and D. J. Walker, Fractals in the biological sciences. This is a good introduction to the basic mathematics and applicability of fractals. Skip section 4 and 6.
- B. Mandelbrot, The fractal geometry of nature. Read as much as interests you.
- P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants. Read as far as interests you; understanding how the pictures are generated is the most important part. Please don't try to print the whole book.
- Give us a solid introduction to the mathematics of fractals. Jen Trinh.
- Tell us more about modeling plant form - go into L-systems and other appraoches to fractal trees. Some demos might be nice. Prusinkiewicz has published a lot of interesting papers. Kaz Uyehara.
- Explain and demo some interesting and/or biologically relevant cellular automata. Ari Strandburg-Peshkin.
- Tell us about some of the statistical physics of cellular automata. You want to begin with S. Wolfram, Statistical mechanics of cellular automata. Ethan Deyle.
Seminar break: Ben Good.
Faculty guest: none.
Week 8 - March 17: Evolution
This week surveys some of the important open issues in evolution and genetics. Not much math is hiding anywhere.
- Tell us about some interesting (to you) aspects of quantitative genetics. You may want to start here. Maybe focus on one or two issues? Talking to Vince Formica may focus your search. Eric Duchon.
- Michael Lynch does some interesting work on genome complexity and recombination. Present one or more of his papers; make sure to explain the biological context. Make sure you take us through the paper everyone is reading. Seth Donoughe.
- What does fitness mean in an evolutionary context? Is it well defined? What are some of the definitions, and what are they good for? Tell us also about adaptive landscapes too, if you have time. Emily Hager.
- How optimal is the genetic code? Probe deeper into the issue for us; you'll need to do some literature research. Maybe (but not necessarily) look at S. Naumenko et al., On the optimality of the standard genetic code: the role of stop codons. There are many more traditional papers on the subject which you should definitely consider. Ben Good.
Seminar break: John Boccio.
Faculty guest: Vince Formica.
Week 9 - March 24: Evolutionary avalanches
This week we follow up our work on evolution by analyzing some well known models of macroevolution proposed by physicists. A hallmark of these models is criticality. Are these models relevant? Is criticality? We will need some statistical physics and an understand of self-organized criticality.
- G. P. Wagner and L. Altenberg, Complex Adaptations and the Evolution of Evolvability. This really should have been assigned last week and stands conceptually apart from the other readings.
- If you didn't have time over break, re-read the Solé and Bascompte paper from last week.
- J. M. Yeomans, Statistical Mechanics of Phase Transitions. Read chapter 1 and chapter 2; don't worry about the details of the math too much. If you don't like this book, you can try J. Binney, The Theory of Critical Phenomena, chapter 1; you'll have to get this book off the stacks.
- P. Bak and K. Sneppen, Punctuated Equilibrium and Criticality in a Simple Model of Evolution.
- S. A. Kauffman and S. Johnsen, Coevolution to the Edge of Chaos: Coupled Fitness Landscapes, Poised States, and Coevolutionary Avalanches. If you wish, skip some of the numerical results in the main body of the paper. Focus on understanding the model; look at one of Kauffman's earlier papers (1987, maybe) if the NK model confuses you.
- C.R. Shalizi and W. A. Turner, A Simple Model of the Evolution of Simple Models of Evolution.
Seminar break: Ari Strandburg-Peshkin.
Faculty guest: none.
Week 10 - March 31: Pattern and form
This week looks broadly at different types of biological patterns. We survey self-assembly and phyllotaxis, which relates the Fibonacci series to plant leaf placement. The math this week will not be very difficult.
- We didn't get to read nearly all of Thompson's book. Choose another section and present it to us. Kaz Uyehara.
- Give us a more in-depth look at phyllotaxis with a biological focus. You'll want to think about S. Douady and Y. Couder, Phyllotaxis as a Physical Self-Organized Growth Process, D. Reinhardt, Regulation of phyllotaxis by polar auxin transport and J. Jönsson et al., An auxin-driven polarized transport model for phyllotaxis. Also consider R.S. Smith et al., A plausible model of phyllotaxis. Seth Donoughe.
- Show us some bacterial colony patterns and explain some of the
models for their growth. Eshel Ben-Jacob's work will be useful.
- Give us an overview of swarming or collective behavior (in bacteria, fish, birds, etc.) and
the models that explain it. You may want to look at A. Okubo and S. A.
Levin, Diffusion and Ecological Problems, chapter 7. Or more
recently (and almost certainly, more excitingly), try the work of Iain Couzin. Ari Strandburg-Peshkin.
Seminar break: Eric Duchon.
Faculty guest: none.
Week 11 - April 7: Reaction-diffusion systems
This week we move into further issues of pattern formation. What are the mechanisms that generate patterns in nature? Why do we see the same kinds of patterns on vastly different scales? Reaction-diffusion systems are one possible mechanism. We will need an understanding of differential equations this week.
- J. D. Murray, Mathematical Biology, chapter 14. Skim chapter 15 to see some of the biological applications. All the methods are in ch. 14, but the cool stuff is in ch. 15; we will have a presentation on this material. If you need an introduction to the methods, look at the previous two chapters. Do problems 14.6 and 14.7; we'll discuss them in seminar.
- L. Edelstein-Keshet, Mathematical Models in Biology, chapter 11. Most of this is redundant, but presented in a different order. This book has a good background/introduction section, and a few nice tables. Don't focus on the mathematics.
- M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium. Entirely optional, but I recommend starting with sections IIIA, IIIB, IIIC, X, XI. Please don't print the whole article (273 pages, 58 MB).
- How realistic are Turing-type reaction diffusion systems in real biological systems? Take a look at the evidence; the references at the end of Edelstein-Keshet's chapter will be useful starting points. Kaz Uyehara.
- Choose a nifty problem from either book and present the solution to us. Maybe do a computer simulation too? Ben Good.
- Murray's chapter 15 is about animal coat patterns. Present it to us. Ethan Deyle.
Seminar break: Kaz Uyehara.
Faculty guest: none.
Week 12 - April 14: Development
This week very briefly addresses a very complicated question: how does a strand of DNA become an organism with trillions of cells whose activity is coordinated? More simply, how does a single cell establish polarity? We will look at the topic in the context of symmetry and oscillations. The mathematics of this week will be new but not difficult.
- S. A. Newman and W. D. Comper, Generic physical mechanisms of morphogenesis and pattern formation.
- A. R. Palmer et al., Symmetry breaking and the evolution of development.
- S. Kumar and P.J. Bentley, eds., On Growth, Form, and Computers, chapter 10: Broken symmetries and biological patterns.
- J. D. Murray, Mathematical Biology, chapter 6. Skip section 6.4.
- G. B. Müller and S. A. Newman, Origination of Organismal Form: beyond the gene in developmental and evolutionary biology. Read the introduction to the book for a good perspective. If you have time, read chapters 10, 11 and 13. This is optional. The book is also available online through Swarthmore.
- Tell us about natural biological oscillators, clocks, and rhythms. Digress on development briefly? You may want to use some of the videos at HHMI or the documents at Warwick. The Müller and Newman book also has a good chapter. Emily Hager.
- Choose an artificial biological oscillator and explain how it works - in detail. Let's see the theory, experimental realization, and possible engineering uses. Maybe the repressilator or brusselator? Also link in Biobricks or another similar synthetic biology project. Eric Duchon.
- Choose a model biological system and tell us about polarity in this system. How about FtsZ's role in mitosis? Take a look at the model of H. Meinhardt and P. A. J. de Boer and then survey the biological evidence. How about other polarity establishing events in prokaryotes or in the development of larger organisms? Frances Taschuk.
- Tell us about the work of Brian Goodwin, or choose your own topic. Take a look at Edelstein-Keshet on development models, or start with something in Origination of organismal form. Or how about homeobox genes, like Hox? You can take this presentation anywhere. Tom Emmons.
Seminar break: Frances Taschuk.
Faculty guest: none.
Week 13 - April 21: Thermodynamics and information theory
This week seeks to answer the most fundamental questions about biology: why should life exist at all? Does it have a point? Does evolution have a direction? We will address these issues with non-equilibrium thermodynamics. Those who have studied equilibrium thermodynamics before will have an advantage but almost all this material will be new. Calculus and lots of algebra are important here.
- E. D. Schneider and J. J. Kay, Order from disorder: the thermodynamics of complexity in biology.
- B. H. Weber, D. J. Depew, J. D. Smith, Entropy, information, and evolution: new perspectives on physical and biological evolution. Read chapters 5 and 6. If you're interested in the topic, consider chapter 2. If you have philosophical (or skeptical) leanings, try any of the chapters in part IV.
- S. E. Jørgenson and Y. M. Svirezhev, Towards a thermodynamic theory for ecological systems, chapters 2, 3, 4, 5, 12. This is a lot, and very mathematical too. If you're put off by this, don't feel bad about skimming over the math. Chapters 2 and 3 are an introduction to thermodynamics, which may be useful. The last section of each chapter is always a good summary. I think chapter 5 and its definition of exergy are worth looking at, as exergy is a concept not widely known. Please read also the summaries of chapters 10 and 11.
- There's a lot of very complicated thermodynamics in this week's work. Give us a clear introduction to entropy, exergy, energy gradients, and (if you have time) analyze a topic of your choice. You may wish to use the Svirizhev book. Alternatively, take us through some of the philosophy and implications of a thermodynamic, teleological biology.Seth Donoughe.
- Tell us about thermodynamics' application to ecological networks; begin with chapter 9 of Jørgenson. If you have time, extend to other networks. Ethan Deyle.
- Tell us about algorithmic information theory and Kolmogorov complexity. Is it useful for biology? Have a poke into other information theoretic aspects of life. Is there a connection to symmetry? Eric Duchon.
- There has been a lot of speculation about life on other planets, life with other biochemistry, the origin of life on earth, and on the nature of artificial life. Can you give us some guiding principles and thermodynamic realities which will shape our understanding of these putative life forms? You will want to use the Weber book, perhaps. Stephan Hoyer.
Seminar break: Benjamin Blonder.
Faculty guest: Carl Grossman.
Week 14 - April 28
There is no seminar meeting this week.
Week 15 - May 5: Student presentations
This is our last meeting. Everyone will choose an interesting topic for their final project or paper and present it to the group. Expect to have 10 to 15 minutes for a presentation. Please also prepare a handout which describes your work in more depth; this could take the form of a paper (or not).
- There is no assigned reading this week.
Seminar break: team effort.
Faculty guest: none.
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