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 and exploited
- Unintuitive behavior is captured by physical theories

- Laws of physics connect fundamental particles and forces.
- Physics often describe homogenous or simple matter.

- Biological systems evolved -- layering complexity
- Cells consist 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.
- Everyday units are often inconvienent for biological processes
- We can pick units to make things as simple as possible

Take Newton's law:

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

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.

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

Relates quantities of different dimensions to each other.

Common units for the quantities involved are:

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

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!

Links force to masses and distance, 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

Links force to masses and distance, but not what the absolute value of the force is.

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

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

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

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

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