Physical Biology: From Gene Regulation to Living Matter

# How does a physicist think about a living cell? Watch the video first. Use this companion to revisit the reasoning and its evidence limits. A physicist reaches for a rule of thumb: the time to diffuse a distance L is roughly L squared over D, the diffusion coefficient. In the crowded cytoplasm, a typical protein has a D of about ten square microns per second. One micron squared over ten gives about a tenth of a second, and the factors we dropped could shrink that a few-fold. A fraction of a second. Not an hour. That habit is biological numeracy: knowing the rough sizes of things. It rules explanations out. A signal that must cross the cell in a microsecond can't rely on a diffusing protein, and an hour-long response isn't being slowed by diffusion across the cell. Strikingly few: about ten. In 2011, Hernan Garcia and Rob Phillips inferred about nine LacI tetramers per cell at wild-type levels, by passing gene-expression data through a physical model. With so few molecules, whether a repressor is bound at any moment is random. Physical biology treats that stochasticity as part of the problem. A real cell holds thousands of kinds of molecules, and no useful model keeps them all. The remedy is coarse-graining, which means zooming out: keep only the variables that matter, such as a few species, their copy numbers, binding energies and rates, and discard the rest. Whether that choice was good isn't a matter of taste. The predictions decide. This is the strategy the Phillips Lab describes on its website: develop quantitative, theoretical models, use them to guide experiments, and perform precision measurements to explore whether the predictions hold. Theory isn't decoration added afterward. It makes the prediction before the measurement. Why does the order matter? Give a curve enough adjustable knobs and it can fit almost any data afterward, which proves little. In a parameter-free prediction, every number in the formula was measured beforehand, in separate experiments. Nothing is left to tune, so the new data can genuinely prove the model wrong. So here is the loop for this course: a biological question, an estimate, a minimal physical model, a quantitative prediction, a precision measurement, and the verdict. The model survives, or it fails and points to the assumption that broke. Either way, a model is a deliberate approximation, never the cell itself. ## Evidence guide PHYSICAL-BIOLOGY BACKGROUND: Counting and coarse-graining support predictive minimal models, not exact descriptions of every molecule. MODEL PREDICTION and EXPERIMENTAL MEASUREMENT are distinct. A fitted curve is not a parameter-free prospective test. TEACHING ANALOGY: the cell as a city helps identify scales; it is not a cellular mechanism. Sources: [milo2015], [bintu2005a], [garcia2011]. See the course bibliography and claim audit.