Here are the notes from Florian Berger's lecture on Theoretical Biophysics. Here he discusses why numbers and units are important, especially in biology. In addition, he shows some of his own research.
What is the advantage of having numbers in biology?
Data information knowledge understanding
Data + context = information
Information + experience + intuition = knowledge
Knowing or realizing the cause of something =
understanding
The more chocolate you eat, the more Nobel prize
winners there are per country. This shows correlation vs
causality. The correlation is money, the richer the
country the more chocolate is consumed (luxury item).
Physics provides a framework to explain the causes behind natural phenomena. Numbers
and mathematics provide consistent logic. This could establish causal relations.
Scientists measure things. They measure quantities with numbers in units. A measurement is
always a comparison, you compare it to something that you already know. Different
quantities can have the same units: width, length, height, distance, etc. But there are also
often quantities that have combined units such as area, volume, or velocity.
Two tricks for units:
- You can only add or subtract quantities with SAME units. You can’t add distance to
the velocity;
- The argument of some functions must be unitless. Everything that you put into a
function (such as x) can’t have a unit (sin(x), cos(x), etc.).
This formula shows exponential growth. With the first trick, you
can write the equation, so there is a subtraction so they have the
same unit. But the exponent is a function so it does not have a
unit. The K and T have a unit of 1 (K*T=1), so K has the unit 1/T.
This formula shows the membrane potential. The unit of V is volt
and the unit of F is J/mol V if R = J/Kmol and T = K and z is unitless.
Because you can rewrite the formula like F = R*T/Z*V and you can
fill in the units that are known.
To get rid of mol, you use the Avogrado constant Na = 1/mol.
Because RT = J/mol and dividing that by mol gets J.
A cell uses the free energy of ATP hydrolysis. Motor proteins
use this free energy and they fuse this into a mechanic
power. This equation shows how you get the free energy.
When the equilibrium constant is known, plus how much ATP
and ADP is in the cell, the free energy G can be calculated. This is around G = 25 KT.
A molecular motor uses 1 ATP per 10 nm step. But what is the maximal force production of a
molecular motor? 1 ATP generates a maximum energy of 25KT. The unit of deltaG is the
energy, so it could be J or N*m. So the energy is a force * distance. The typical force can be
determined: F = deltaG / deltaX. So the force is the energy divided by distance. The distance
is 10nm, so the force can be calculated: F = 25KbT / 10nm = 10 pN. This is the maximum
force when a motor hydrolyses 1 ATP.
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