# Syllabus

**Required text:** Physical Biology of the Cell (2nd ed) by Phillips, Kondev, Theriot and Garcia (ISBN: 0815344503)

The syllabus (PDF) is tentative and subject to change. Refer to the list below for the prerecorded video lectures.

Date |
Topic |
---|---|

Mon. Jan. 3 | ## 1. Perspective, Vision, and PreliminariesThis vignette introduces the goal of the course, nothing less than to develop a quantitative feeling for the nature of the living world. I wonder... (37:04) This vignette focuses on the importance of asking questions in science as much as in finding answers. One route to those questions is by tapping into our sense of wonder. Order of magnitude toolkit (11:39) This vignette provides some of the key tools used when doing order of magnitude thinking. Biological numeracy exam (13:00) This video is a "biological numeracy exam" with roughly 15 multiple choice questions that you will self grade in the following vignette. Biological numeracy exam (answers) (23:33) This vignette gives the answers to the biological numeracy exam and showcases the order-of-magnitude-thinking spirit that we consider a critical pillar of physical biology. |

Wed. Jan. 5 | ## 2. Scales and Scaling in Physical BiologyThis vignette describes two ways in which we will use the word scale. First, in the spirit of "what sets the scale of X?" and second, how some quantity of interest, such as the diffusion time, scales with some other quantity such as the length over which that scaling occurs. Scaling of diffusion time (16:47) This vignette develops one of the most important rules of thumb in all of science - how we estimate the time that diffusive processes will take. Nucleolar scaling (23:45) This vignette starts with an introduction to scaling relations between organelle size and cell size and then turns to the study of how the size of the nucleolus scales with nuclear size in the developing C. elegans embryo. Mitochondrial surface volume (18:58) This vignette explores the idea that when cells get too large, the plasma membrane is no longer large enough to contain enough ATP synthases to provide enouch ATP for the cellular interior. |

Mon. Jan. 10 Wed. Jan. 12 |
## 3. Physics of Animal Migration, Dispersal, and HerdingThis vignette talks about the physical challenges faced by bar tailed godwit birds in their 10,000 km nonstop migratory journey between Alaska and New Zealand. Frogs sao tome puzzle (18:50) This vignette introduces one of the fun challenges of island biogeography - how do amphibians end up on oceanic islands. Ocean currents dispersal (13:43) This vignette explores the hypothesis that amphibians landed on the islands in the Gulf of Guinea by being transported by ocean currents. Physics of frogs in saltwater (14:08) This vignette describes the physics of water transport that frogs suffer when placed in saltwater. Interlude on entropy (21:58) Here we make our first quantitative acquaintance with the all important concept of entropy and the corresponding variational statement of equilibrium. Osmotic pressure (14:11) When there is a concentration difference across a membrane such as a frog's skin, water will flow as a result of osmotic pressure. Here we use simple free energy arguments to explain osmotic pressure. Linear transport laws (20:35) This vignette discusses one of the most powerful tools in the physicochemical arsenal for working out the dynamics of how systems approach the maximum entropy (equilibrium) state. Here our focus is on the law of water transport due to osmotic pressure, a key player in the response of frogs to being in salt water. Frog osmotic shock (15:36) This vignette writes the differential equation for water flow out of an osmotically shocked frog and uses that to estimate the time for the frog to dry out. |

Mon. Jan. 17 Wed. Jan. 19 |
Collective animal motions (8:31) This vignette observes that animals of all kinds participate in organized collective motions, providing a "many-body" challenge to the theory of active matter. Origins of field theory (27:11) This vignette introduces the idea of field theory, with roots that date back to the early days of mechanics. After a historical introduction, we examine the nature of field theories of matter. Toner Tu theory intro (16:17) This brief vignette shows how Toner and Tu developed a field theoretic description of animal motions culminating in the famed Toner Tu partial differential equations. ## 4. Diffusive DynamicsThis vignette introduces diffusion as molecular and cell biology's dynamical null hypothesis. As we will see in subsequent vignettes, like many of the key ideas of physics, there are many different ways to view this subject. Diffusion - coin flips (19:15) One view of diffusion is as the dynamics that result when independent agents "choose" what they are going to do next by flipping coins. While this observation seems contrived and trivial, it is actually very deep. Diffusion - continuum theory (22:11) As with Toner Tu theory, we can write a field theory for diffusion that culminates in the famed partial differential equation known as the diffusion equation. This vignette describes that theory. Diffusion - master equation (17:46) Another very powerful paradigm we will use over and over is that of probabilistic reasoning. Dynamics of probability distributions can be written in the language of master equations and this vignette explains that approach. |

Mon. Jan. 24 Wed. Jan. 26 |
## 5. Shape, Space and Pattern in BiologyThis vignette introduces the idea of biological pattern as a prelude to the mathematical exploration of these phenomena using the twin concepts of positional information and the Turing instability. Continuum theory protocol (20:05) This vignette describes how continuum field theories can be used in a myriad of different settings including for pattern formation. Paradigms for patterning (11:55) This vignette describes two distinct classes of models for thinking about the emergence of patterns - the concept of positional information and the self-organization properties of Turing patterns. On positional information (12:22) This vignette gives a more detailed introduction to the Wolpert idea of positional information. Positional information - reaction-diffusion equation (19:50) This vignette shows how to use the continuum theory protocol to derive a beautiful generalization of the diffusion equation that accounts for protein degradation as well. Positional inforamtion - the French flag model (11:12) This vignette is a very concrete case study of reaction-diffusion equations as they pertain to anterior-posterior patterning in the fly. Note that part of the fun of taking this model seriously is that we see that it falls quantitatively short of accounting for the experimental data, raising the need to consider further refinements. |

Mon. Jan. 31 Wed. Feb. 2 |
Meeting Turing (19:07) This vignette gives an introduction to the Turing mindset that complements the positional information perspective from the previous few vignettes. In the steps of Turing (31:11) This vignette works through the technical details of the simplest example of Turing's ideas, a two-cell system. Turing ring of cells (25:02) This vignette shows how to generalize the results of the previous vignette to a large collection of cells with periodic boundary conditions. Turing - Closing the loop (18:40) This vignette describes some very recent biological examples of the Turing instability. ## 6. Life as defianceThis vignette introduces us to the direction of natural processes implied by the 2nd law of thermodynamics and the way that living organisms get around that stricture by consuming energy. Statistical mechanics protocol (18:49) This vignette gives a formal but superficial introduction to statistical mechanics. We need this introduction here because these tools will help us compute entropic forces when DNA is pulled on by optical tweezers. Stat mech ion channel (20:03) This vignette uses the statistical mechanical protocol to solve a real world problem of great biological interest, namely, what is the probability that an ion channel will be open as a function of some driving force such as voltage, ligand concentration or membrane tension. Entropic elasticity DNA (44:53) This vignette shows how we can use statistical mechanics to carefully understand our first concrete example of an entropic force, namely, the way that DNA resists being stretched. Interlude on Taylor series (17:51) This vignette provides a powerful and important mathematical tool that we will use repeatedly in a huge variety of different situations. In the current context it will serve us in understanding how Hooke's law emerges in DNA pulling experiments. |

Mon. Feb. 14 Wed. Feb. 16 |
Biological batteries (15:21) This vignette is a very important overview of the way that universal energy currencies are provided in living cells, similar to how the batteries and the electrical sockets we use in our daily lives are available for a myriad of different tasks. Cost of transport up a gradient (12:55) One of the most important classes of biological battery is concentration gradients. This vignette shows how to compute the entropic contribution to the total free energy of such gradient batteries. Proton motive force (9:51) A variety of molecular machines are run by a biological battery known as the proton motive force that has both an entropic contribution and a contribution due to the electrical potential differences across the cell membrane. This vignette gives an elementary description of that biological battery. The great Gibbs and the chemical potential (24:16) This vignette describes one of the most important ideas in statistical physics, the chemical potential. We will use this tool for thinking about out of equilibrium dynamics. Binding via chemical potential (14:12) This vignette gives an example of how to use the chemical potential in the context of the statistical mechanics protocol to describe ligand-receptor binding. Note the huge simplification of using Gibbs' brilliant approach compared to the explicit treatment of the solution. One of the single most powerful ideas in all of physics is that of formally and rigorously integrating degrees of freedom out of our treatment. The relaxation to equilibrium (21:31) This vignette describes the all important topic of how we compute the dynamics of systems as they relax towards equilibrium. We show how the classic linear transport laws are a small perturbation limit of the more general free energy relaxation. Allostery no physicists allowed (8:54) This vignette is a very brief introduction to the subject of allostery. A noted biologist said that they would not even talk to physicists thinking of working in biology if they could not define allostery. The famed Monod-Wyman-Changeux (MWC) model can be thought of as biology's version of the Ising model. Cashing in concentration gradients symporters (28:17) This super fun vignette is based upon a beautiful paper of Daniel Zukerman that shows how we can think about the out of equilibrium dynamics using simple ideas about free energy as a driving force. I think of this as a very deep example of how biological fuel can be demystified through careful statistical mechanical reasoning. Dynamics of symporter (23:35) This vignette continues with the exemplary problem of the symporter to describe the process from a chemical kinetics perspective that explicitly shows how the reaction rates violate detailed balance. ATP battery (07:01) This vignette describes yet another one of the motive forces that power the cellular economy. Nonequilibrium steady states are often maintained through coupling some reaction of interest to the hydrolysis of ATP. ATP biological battery - phosphorylation-dephosphorylation dynamic> This vignette uses the ubiquitous phosphorylation-dephosphorylation nonequilibrium steady state as a way to understand how the ATP biological battery drives molecular reactions of importance to biological phenomena. Phosphorylation energetics (50:37) This vignette now examines the free energy cost of running the phosphorylation-dephosphorylation cycle and gives an example of the much broader subject of how the ATP Biological Battery operates. Fidelity as defiance (20:00) This vignette asks the question of how accurate the processes of biological polymerization such as transcription and translation can be if their recognition mechanism is strictly based on equilibrium binding. Why equilibrium? (22:04) This vignette addresses the equilibrium elephant in the room. One of the most persistent comments that I have met in my time in biophysics is that living systems are not equilibrium and hence we have no right to use equilibrium thinking. This vignette takes a more nuanced view of that question. Kinetic proofreading (18:28) This vignette explores one of the great conceptual ideas of modern molecular biology, namely, kinetic proofreading. We consider a highly schematized view of the phenomenon that illustrates the tradeoffs between speed, energy consumption, and fidelity. |

Mon. Feb. 21 Wed. Feb. 23 Mon. Feb. 28 Wed. Mar. 2 Mon. Mar. 7 Wed. Mar. 9 |
7. Signaling, Regulation, Feedback, and Control This vignette describes one of the most important models in biology, the Monod-Wyman-Changeux model of allostery. We will only scratch the surface of this important topic. Introduction to gene networks (9:44) This vignette introduces the concepts of gene regulation as we did in class last week. Rate equations for mRNA dynamics (19:25) This vignette explains how we can use rate equations to compute the mean number of mRNA molecules per cell. Rate equations for auto-activation (15:35) This vignette gives a first taste of the fascinating topic of feedback and how the theory of dynamical systems allows us to qualitatively dissect such processes. Rate equations for mutual repression (20:11) Thsi vignette describes a classic genetic circuit in which the products of two genes repress each other. Interestingly, this gives rise to very rich behavior including the existence of a switch. Mutual repression switch - fixed points (13:08) This vignette describes how to find the fixed points (the steady state values) of the mutual repression switch. Stability analysis for mutual repression switch (25:01) This vignette uses one of the most powerful tools we can draw from dynamical systems theory, namely, linear stability analysis, to see if perturbations shrink or grow. We earlier saw this kind of thinking in the context of the Turing instability. Chemical master equation for the constitutive promoter (15:15) This vignette explores a more powerful tool for exploring dynamics of biological systems, namely, the chemical master equation. This approach allows us to solve for the entire probability distribution rather than just the means. Chemical master equation for the two-state model of transcription (18:24) The constitutive promoter null model is often not consistent with the data. The phenomenological model is often used to describe regulated transcription is the two-state promoter introduced in this vignette. Chemical master equation for the two-state model of transcription, part 2 (25:26) Here we finish up our description of the two-state promoter. |

## Overflow Vignettes

**Molecules as documents of evolutionary history (16:07)**. This vignette describes the use of DNA sequences as a tool for studying the history of life.

**Genomics without genomes - Hemoglobin (17:00)**. This vignette shows how early workers were able to compare "sequences" of hemoglobin even before sequences was a thing. As a result, the hemoglobin protein was used as a document of evolutionary history.

**Science is not a smorgasbord (24:44)**. This vignette argues that science is an approach to generating a self-consistent, actionable, and predictive body of knowledge about the world around us. We do not get to pick and choose which parts of science suit our moods or philosophies.

**Science is not a smorgasbord - Germ theory disease (14:28)**. This vignette briefly describes the science behind the modern germ theory of disease arose.

**Viruses as infectious agents (10:50)**. This vignette gives a very brief introduction to how we came to know of viruses and how the tobacco mosaic virus taught many important lessons.