PoL I: Quantitative problems, dimensions, and units


Richard Neher
Biozentrum, University of Basel


slides at neherlab.org/PoLI_2024_week01_UnitsAndLaws.html

So far in this course ...

  • Thermodynamics and statistical mechanics
  • Protein folding
  • Reaction kinetics
  • Ligand binding

What about topics like ...

  • Gene regulation
  • Developmental biology
  • Cell biology
  • ....

Mathematics is extremely effective in physics

  • Motions of planets and moons can be predicted with extreme accuracy
  • Behavior of atoms, particles, electrons etc can be controlled and exploited
  • Behavior that is unintuitive to us is captured well by the laws of physics

The strange behavior of rotating objects

Biology is much more complex than Physics

Physics is most effective in simple and controlled systems
  • Laws of physics connect fundamental particles and forces.
  • These laws explain properties of simple systems and homogeneous matter
  • Good understanding of systems at equilibrium or isolated systems
  • These laws also govern complex systems, but the connection between the laws and the behavior is hard to decipher

Biological complexity
  • Biological systems evolved -- layering complexity
  • Cells consist of thousands of molecular species, interacting in complicated ways
  • Biology is always in flux.

Physics vs Biology

Wikipedia, by Brews Oshare
  • Equations that govern the dynamics
  • Exact predictions of future configuration
Wikipedia, by cybertory
  • Long, but incomplete, list of components
  • Only qualitative description of interactions

From description to quantitative understanding!

Quantitative questions

  • How many human cells are in your body?
  • How many other cells?
  • How many ribosomes/signaling molecules are in a cell?
  • How do genes regulate each other?
  • How rapidly does a protein move from one end of the cell to another?
  • What fraction of transcription factors is bound to DNA?
  • What are the speed limits for biochemical reactions?
  • How are polarities and developmental gradients set up?
  • Not: Gene X causes Y
  • But: 20% faster diffusion of gene X extends the gradient by $20\mu m$

Dimensions and units

Dimensions
  • length
  • weight
  • energy
  • current
  • force
  • temperature
  • ....
Units:
  • length: meters, miles, feet, Angstrom
  • weight: grams, stones,
  • energy: Joules, calories
  • current: ampere
  • force: Newton
  • temperature: Celsius, Kelvin
  • ....
  • Dimensions describe the nature of a quantity
  • Units are conventions to measure them

Comparing quantities

  • Only quantities of the same dimension can be compared: length $X$ is greater than length $Y$ etc. There is no sense is which length $X$ can be greater than weight $Y$.
  • Units are conventions -- there is nothing fundamental about them.
  • Some unit systems are more convenient than others.
  • Everyday units are often inconvienent for biological processes
  • We can pick units to make things as simple as possible

Aim: Enable you to reason quantitatively about biological problems!