Biological Physics Revision Lecture PDF

REVISION LECTURE of Biological Physics Richard Sear The biological physics part of the course has ten lectures. Below is a summary of these ten lectures, at the level of a key idea and equation per lecture. L1: Fermi estimation and why there is...

REVISION LECTURE of Biological Physics Richard Sear The biological physics part of the course has ten lectures. Below is a summary of these ten lectures, at the level of a key idea and equation per lecture. L1: Fermi estimation and why there is no King Kong Stress on femur mass × g stress = number of legs × femur cross-section due to limited strength of bone, stress ≲ 106 Pa. This limits size h of animals that can walk on land, because mass scales as h3 while load-bearing area of femurs increases only as h2. L2: Why we can’t walk on water To stand on water, surface tension force must be large enough to resist gravity, i.e., surface > force of gravity tension force Surface tension force is surface tension Γ times the total length of 4 legs in contact with water surface, force of gravity is mg. This inequality is true for water striders, not true for us, because again mass scales with size h as h3 while surface tension only increases as h1. L3: Dimensionless numbers: Why little droplets are round, while big ones are flattened Estimating the value of these dimensionless numbers allows you to estimate which one of two competing forces, or energies, or times,... dominates. For example the Bond number. gravity force Bo = surface tension force for Bo ≫ 1 gravity dominates — droplet flattened by gravity. Bo ≪ 1 surface tension wins and droplet almost spherical. L4: Diffusion, flow and why heart attacks kill The time to diffuse a distance λ increases as the square of the distance. λ2 tD ≃ D for D the diffusion constant. Time to move via flow at speed u λ tF ≃ u So diffusion is very fast across small distances such as across one of our cells, ∼ 10 micrometres, but is incredibly slow across a 1 metre human body. 1  The Péclet number is defined to be Time for diffusion of a molecule a distance λ Pe = Time for flow to carry a molecule a distance λ and λ2 /D uλ Pe = = λ/u D so is large for fast flow u, large distances λ and small diffusion constants D. When Pe ≫ 1 flow dominates diffusion, other way round when Pe ≪ 1. L5: Tiny motors in your muscles For any machine (any size) work done = force × distance for a nanomotor maximum force 10−19 J ∼ = 10−11 N of a nanomotor 10 nm as chemical reaction that powers one step of length 10 nm, releases ∼ 1 eV∼ 10−19 J. L6: Your DNA stores as much information as Google, and on/off switches made of genes and proteins As each base pair or monomer of DNA can store two bits: total information storage capacity of ∼ 6 billion bits of human genome your genome is about 3 billion monomers (bases) of DNA. Many biological processes, eg cell division (and hence cancer) rely on cell signalling and switches made from molecules that are inside cells. Can make switch from molecules, just need that 1. The input signal, eg concentraton of cell signalling molecules, must affect the output, eg production of a protein cP 2. Switch-like output, i.e., output that is either ON or OFF, can be obtained in a few ways. One way is by cooperative binding of, eg, four molecules together, not one. L7: The physics of airborne infectious diseases eg COVID-19, flu, tuberculosis (TB), etc Some infectious diseases are transmitted across the air in suspended particles (aerosols), for example the virus SARS-CoV-2 which causes COVID-19. In a room the fraction of the air that is second-hand, i.e., has gone through someone’s lungs and so may have picked up SARS-CoV-2, TB, etc, is Room air CO2 (ppm) − 400 f2nd ≃ 40, 000 because the concentration of CO2 in the Earth’s atmosphere is ∼ 400 ppm, while that in our breath is ∼ 40, 000 ppm. 2  Aerosol particles do fall under gravity with a speed u set by balance between gravity (mg) and the Stokes drag (6πηa), and for mucus particles this is about u ≃ 2 × 108 a2 a in m For droplets of radius a = 10 µm, u ≃ 2 cm s−1. Air currents in room can easily be cm s−1 , so can keep aerosol droplets suspended long enough to cross a room. L8: Simple model for cancer mortality The mortality rate for a particular cancer is defined as probability that person of age t years hC (t) = dies of that cancer at that age Assuming that K independent random mutations are needed to cause a lethal cancer 1 hC (t) ≃ rK tK−1 rt