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

Chapter 4. Basics of classical (Newtonian) dynamics 25
will be variations, but the variations are kept in a certain range. There is a universal measure
of this, related to temperature. The higher the temperature, the higher is the average
velocity and kinetic energy of the molecules. The average kinetic energy of the molecules
is proportional to the absolute temperature and is equal to 3k B T/2, where k B is Boltzmann’s
constant, 1.38 10 23 J/K. (We speak about atomic quantities now, and this is an appropriate
measure of the atomic energies.) The spreading and equalization of energy is what we
apprehend as “tendency towards equilibrium” and we will interpret the equalized state with
molecular kinetic energies around 3k B T/2 as “thermal equilibrium”. What is important, and
which we will discuss further in a later section is that this comprises an irreversible process.
Energy is spread out and equalized as this is the most probable process.
Water is, of course, denser than air, but the main principles of damping and spreading of
energy remain the same. The elementary encounters appear on still smaller scales, and the
establishing of a thermal equilibrium with molecular energies in the described manner
is still valid but can appear faster than in air. This has important consequences for biological
processes, which normally are much slower than the establishing of equilibrium.
Biological processes may be around 10 6 –10 3 sec or often larger as compared to maybe
10 9 sec for the main energy equalization. In turn, this means that we generally can apprehend
the watery biological systems as being in an essential equilibrium with a definite temperature.
(We will later take up these concepts in more detail.) This facilitates much of the
arguments.
These ideas are basic when we go to phenomena in a cell. There are molecules that move
and interact via forces and bind together. There is kinetic energy, but also rotational and, to a
large extent, vibration energies. The large molecules are kept together and attain firm structures
due to forces, to interactions, and they can move in various ways. Energy is supplied
and to some extent spread out to accomplish a kind of thermal equilibrium with a definite
temperature. One peculiar feature when we go to living systems is that the systems often
are quite small. A cell is in itself relatively small, and when we go down to the molecules they
are still much smaller. One can say that they often comprises a kind of intermediate stage
between what we refer to as properly microscopic, the one where we distinguish the basic
atoms and what we see as macroscopic, the large scale we have around us. Of course, large
individuals like us are clearly macroscopic, most of the interesting processes appear on such
an intermediate scale, what one often refers to as “meso-scopic”. Then we may be much
larger than the single atoms, but small enough that the probabilistic principles become relevant.
We often cannot say that the molecular energies are 3k B T/2, but should rather say that
they are around that value, and we have to be cautious about variations, what we will refer
to as fluctuations. More about that in separate sections.
We shall go further with the basic dynamics and we cannot avoid quantum mechanics. That
turns out as the (at least for our purposes) lowest kind of stage where the classical mechanics
is no longer appropriate. Quantum mechanics makes things more complicated but, in order
to understand the molecular level correctly, one needs a descriptions of how molecules are
kept together and of the forces between molecules and between molecule groups. Quantum
mechanics is needed for everything that involves electrons, but when considering the molecular
objects as entities, classical concepts are quite appropriate for discussing molecular
dynamics.