Clas Blomberg - Physics of life-Elsevier Science (2007)

12 Part I. General introduction
The mentioned formalism describes averages of quantities defined from the low-level
atomic description. As large-scale systems, fluctuations, variations around the averages play
a relatively small role. Most is given by the averages (“law of large numbers”).
In biological systems, the situation is more complex as we can identify several intermediate
levels, which can be considered as “mesosystems”, systems considerably lower than the pure
atoms, but not sufficient large to make fluctuation effects negligible.
First, we have the macromolecules, in particular the proteins. They contain a relatively
large number of atoms and can well be treated by statistical physical methods. Much of the
atomic energies, in particular those that are related to vibrational modes of the atoms get
within short timescales equilibrium distributions. The molecules as a whole are influenced
by atomic forces, both from their own constituents as surrounding entities. At these scales,
fluctuations are relevant at scales that are large compared to the atomic time and length scales,
but still small enough to play an important role in the dynamics of cells.
The archetype example of this kind of fluctuation effect is Brownian motion, the irregular
diffusional motion of large particles driven by variations of the forces of the environment.
Motions of protein molecules in any solvent, and in particular in a cell can well be considered
as a type of Brownian motion. Further, what from the high-level view appear as irregular
energy influences also provide changes of the molecules such as opening and re-arranging
protein structures. These imply what can be apprehended as relatively improbable effects.
They are infrequent in the low-level timescales, but this confirms our important picture: The
protein structures are stable during relatively long times, but now and then, they meet infrequent,
improbable influences, which lead to changes.
Atomic variations influence the macromolecule dynamics, the structure changes as well
as their movements. These also have an effect in a cell and by that for an entire organism.
The properties of biological systems depend to a high degree on the actions of macromolecules
and cellular compartments, and these are governed by what can be interpreted as
random effects due to uncontrolled motions at the lowest, atomic scale.
Now to another point. Physicists like analogies. Ideas behind some theoretical description
of a certain problem can be relevant for quite a different kind of system. Concepts can then
be overtaken and the analogy can provide illuminating aspects. Such views have often been
very powerful for developing methods in new fields.
Models that have played an important role as analogies concern molecular moments and
magnetic interactions. The simplest models have magnetic moments ordered along a line
(one-dimensional (1D)), in a square lattice (2D), or in an ordered 3D crystal structure. The
magnetic moments can point in different directions and represent the low-level structure of
a large magnetic system where the total magnetisation is given by the sum of the individual
molecular moments. An entropy is defined from the number of combinations of individual
spins that lead to the same total magnetisation.
Then, one adds interactions between neighbouring atomic moments. In the simplest case,
there is a gain in energy if neighbouring moments point in the same directions. This means
that the energy is lower the more one direction of moments dominate. If we then consider the
entropy, i.e. the number of distributions of the individual moments that provide a certain
energy, this is largest when there is an equal amount of moments in all directions.
For systems held at a certain temperature, the relevant concept is the free energy that contains
both energy and entropy, and these two parts provide two different tendencies. Energy