Richard Neher

Biozentrum, University of Basel

- Motions of planets and moons can be predicted with extreme accuracy
- Behavior of atoms, particles, electrons etc can be controlled, predicted, and exploited
- Unintuitive behavior is captured by physical theories

- Laws of physics connect fundamental particles and forces.
- Or describe homogenous matter.
- Biology is neither.

- Biological systems evolved -- layering complexity
- Cells consist of 10s of thousands of molecular species, interacting in complicated ways
- Biology is always in flux.

- How rapidly does a protein move from one end of the cell to another?
- How many ribosomes/signaling molecules are in a cell?
- 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?
- How many human cells are in your body?
- How many other cells?

**Not:**Gene X causes Y**But:**20% faster diffusion of gene X extends the gradient by $20\mu m$

- length
- weight
- energy
- current
- force
- temperature
- ....

- 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

- 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 for a particular purpose.
- Everyday units are often inconvienent for biological processes
- We can pick units to make things as simple as possible

Take Newton's law:

$$ F = m \times a$$ $$ \mathrm{Force} = \mathrm{mass} \times \mathrm{acceleration}$$

This equation relates quantities of different dimensions to each other.

**The law is valid in any system of units!**

Units are chosen by humans, the law itself is fundamental.

$$ F = m \times a$$ $$ \mathrm{Force} = \mathrm{mass} \times \mathrm{acceleration}$$

This equation relates quantities of different dimensions to each other.

In our conventional unit system the different quantities have the units:

$$ \mathrm{[Newton]} = \mathrm{[Kilogram]} \times \mathrm{[meter/second^2]}$$

thereby defining the unit of force "Newton".

$$ \mathrm{[Newton]} = \mathrm{[Kilogram]} \times \mathrm{[meter/second^2]}$$

thereby defining the unit of force "Newton".

Units are chosen by humans, the law itself is fundamental.

Consider the gravitational law:

$$ F \sim \frac{m_1 m_2}{r^2}$$ $$ \mathrm{Force} \sim \mathrm{mass^2}/\mathrm{length^2}$$

The quantities left and right do**not** have the same dimensions!
This relation tells us how the force changes when masses or distance change, but not what the absolute value of the force is.

$$ F \sim \frac{m_1 m_2}{r^2}$$ $$ \mathrm{Force} \sim \mathrm{mass^2}/\mathrm{length^2}$$

The quantities left and right do

The missing link is established by the gravitational constant $G$:

$$ F = G\frac{m_1 m_2}{r^2}\quad \mathrm{with} \quad G \approx 6.67 \frac{m^3}{kg\,s}$$

The value of $G$ depends on the system of units we use.

$$ F = G\frac{m_1 m_2}{r^2}\quad \mathrm{with} \quad G \approx 6.67 \frac{m^3}{kg\,s}$$

The value of $G$ depends on the system of units we use.

- Laws of physics yield quantitative and predictive relationships and constraints for biology
- Computer programming is essential to explore quantitative relationships and handle data
- Units are absolutely critical to get right:

If you calculate a*length*and the result is in*seconds*something went seriously wrong - Checking your units will catch many obvious mistakes.
- Choosing your units wisely will make many calculations easier