Design Principles of Life, Disease, and Aging

# How do you discover a design principle? *Evidence guide: Mathematical model results and experimental tests. Minimal equations leave molecular details out.* Start with a variable, x of t: the amount of something at time t, such as a protein, a hormone, or a number of cells. The question is how it changes. The simplest model says that the rate of change of x equals production minus removal. In symbols, d x over d t equals alpha minus beta x. Alpha is the production rate. Beta x is removal: the more x there is, the faster it is degraded or diluted. This equation ignores almost everything: binding sites, folding, cell shape. That is deliberate. A minimal model keeps the smallest mechanism needed to explain a phenomenon, so we can see which ingredients matter. It is not a complete description of the molecules. When production equals removal, d x over d t equals zero, and x stops changing. This is a steady state, or fixed point, here at x equals alpha over beta. Push x above it, and removal wins, so x falls back. Push it below, and production wins, so x rises. That makes it a stable fixed point. Now compare d x over d t equals r x, which describes cells that come from cells. Here x equals zero is also a fixed point, but it is unstable: if r is positive, any small population grows exponentially. Stability is not automatic. It depends on the circuit. Some equations have more than one stable fixed point, separated by an unstable one. That is bistability. And when a parameter changes, fixed points can appear, collide and vanish. That is a bifurcation. We will meet both in diabetes and in fibrosis. Physiology also mixes fast and slow processes, like hormone secretion over minutes, and tissue growth over weeks. Treating the fast variables as already settled, while the slow ones drift, is called timescale separation. It makes such models understandable. Real biological processes also saturate. An enzyme, a transporter, or a team of immune cells can only work so fast. A saturating curve rises steeply at first, then levels off at a maximum. This one nonlinearity will matter for diabetes, fibrosis and aging. Models make predictions about dynamics, so you need dynamic measurements. For the network motif work, the lab built a library of about two thousand E. coli strains, each with a green fluorescent reporter fused to a different promoter, and measured promoter activity over time in living cells. Minimal model, prediction, experiment or data, refined model. Then around again. Sometimes a failure reveals a missing ingredient, and the model grows by exactly one piece, as we will see with insulin. The aim is the smallest model that explains many seemingly unrelated observations at once. Simplicity is not a license to ignore contradictory data: a model that fails a test has to be changed or abandoned. Sources: [isb-book](https://www.routledge.com/An-Introduction-to-Systems-Biology-Design-Principles-of-Biological-Circuits/Alon/p/book/9781439837177), [sysmed-notes](https://www.weizmann.ac.il/mcb/alon/courses/system-medicine-2022-2023), [zaslaver2006](https://doi.org/10.1038/nmeth895), [lab-site](https://www.weizmann.ac.il/mcb/alon/research).