The Significance of Non-ergodic
Property of Statistical Mechanics Systems
for Understanding Resting State of a Living Cell
D. V. Prokhorenko1 and V. V. Matveev2
1Institute of Spectroscopy, Russian Academy of Sciences,
142190 Moscow Region, Troitsk, RUSSIA;
2Institute of Cytology, Russian Academy of Sciences, 194064
Saint Petersburg, RUSSIA
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Abstract
A better grasp of the physical foundations of life is necessary before we can
understand the processes occurring inside a living cell. In his physical theory
of the cell, American physiologist Gilbert Ling introduced an important notion
of the resting state of the cell. He describes this state as an independent
stable thermodynamic state of a living substance in which it has stored all the
energy it needs to perform all kinds of biological work. This state is
characterized by lower entropy of the system than in an active state. The main
contribution to this reduction in entropy is made by the cellular water (the
dominant component with a concentration of 44 M) which remains in a bound
quasi-crystallized state in a resting cell. When the cell becomes active the
water gets desorbed and the system’s entropy goes up sharply while the free
energy of the system decreases as it is used up for biological work. However,
Ling’s approach is primarily qualitative in terms of thermodynamics and it
needs to be characterized more specifically. To this end, we propose a new
thermodynamic approach to studying Ling’s model of the living cell (Ling’s
cell), the centrepiece off which is the non-ergodicity property which has
recently been proved for a wide range of systems in statistical mechanics (Prokhorenko,
2009). In many ways this new thermodynamics overlaps with the standard
quasi-stationary thermodynamics and is therefore compatible with the principles
of the Ling cell, however a number of new specific results take into account the
existence of several non-trivial motion integrals communicating with each other,
whose existence follows from the nonergodicity of the system (Ling’s cell).
These results allowed us to develop general thermodynamic approaches to
explaining some of the well-known physiological phenomena, which can be used for
further physical analysis of these phenomena using specific physical models.
Keywords : Ling’s Association-Induction Hypothesis; thermodynamic; entropy;
Non-ergodic
1 Introduction
The living state of a substance has always attracted the attention of
physicists. And indeed, only a clear understanding of the thermodynamic
characteristics of the living matter can give us insight into the processes that
occur in living organisms. However, despite the fact that there is a lot of
interest in this problem, this field can’t be said to be developing by leaps and
bounds.
Before proceeding with our analysis we have to establish its boundaries and
conditions. There are two very different approaches to the thermodynamics of
living systems: one based on the thermodynamics of equilibrium process (Ling
1962, 2001, 1997, Bauer 1935) and the other on thermodynamics of non-equilibrium
processes (Prigogin, 1968). Shroedinger’s research in this area (Schroedinger,
1994) differs from both of these.
An obscure Russian scientist of Hungarian descent Ervin Bauer (Bauer, 1935) was
probably the first to suggest that the living state should be regarded as an
unstable equilibrium. Treating the physical state of living substance in this
way allowed him to draw a number of interesting conclusions and generalizations,
but on the whole the most part of research was purely theoretical.
According to Ling (Ling, 1962, 2001, 1997), whose position is of special
interest to us, the minimal cell in the physical sense is a complex comprising
protein in an unfolded configuration and water with ions. The most significant
characteristic of this complex is the state of water in it; it is absorbed by
the protein in the form of a multi-layered structure that surrounds it along the
entire length of the polypeptide. This ’coat’ consisting of water molecules is
stabilized by hydrogen links that are stronger than the hydrogen links in
volumetric water. This increase in strength is a result of an increase in the
dipole moment of the water molecules under the influence of other dipoles that
are stronger than water such as the functional groups in the peptide link bound
(NH and CO). The polarization of water molecules explains both their strong
binding by the polypeptide frame of the protein and the multilayered absorption
of water on the surface of the unfolded protein. According to Ling, almost all
the water in a the cell is in a bound state. Because, in terms of the number of
molecules, water is the most abundant compound inside the cell, its transition
into a quasi-crystal state results in a significant fall in the entropy of the
cell. This lower entropy is what brings about the rise in the amount of free
energy of the resting living cell.
The introduction of the concept of a resting state is one of Ling’s
achievements. It’s this state that is used as the reference point for all the
physical and chemical processes that take place inside the cell. When a cell is
activated by an external stimulant or some other signal, it changes its state
from resting to active. The active state is characterized by the disintegration
of the water-protein-ions complex. The bound water breaks free and the system’s
entropy increases. The free energy of the resting state is released and is used
up for all kinds of biological work. This is the Ling model of the living cell
(Ling’s cell) that will be the focus of our analysis.
According to Ling, a cell can remain resting without exchanging energy or
substances with the external environment. The cell just maintains diffusion
equilibrium with the environment. This view directly contradicts Prigozhin’s
approach according to which a living cell can only maintain its organization as
long as it keeps exchanging substance and energy with the environment on a
continuous basis. In other words, a cell can be likened to a burning candle
flame; the flame will remain ’alive’ only as long as there is sufficient supply
of fuel and oxidizer.
Ling believes that such understanding of the thermodynamics of life is
completely inadequate in the case of a living cell. His calculations demonstrate
that if a continuous inflow of energy was really necessary for the
experimentally observed exchange of Na+ ions between a resting cell and the
environment (as is postulated in the traditional mechanism), the cell would
simply be incapable to produce the necessary amounts of energy (Ling, 1997) and
therefore the universally adopted model of ion transport contradicts the energy
preservation law. Ling’s other argument proceeds as follows; if a living cell
and a burning candle were to be frozen to the temperature of liquid nitrogen,
both the flame and the life in the cell will ’go out’, but if they’re heated
back to room temperature, the flame won’t start burning again, but the life
processes in the cell will resume.
The contradictions between the thermodynamic approaches to the phenomenon of
life are so pronounced that the need for further research in this field is
self-evident. The purpose of this paper is the demonstrate that the property of
non-ergodicity that has recently been proved for a large number of systems in
statistical mechanics can help better understand the nature of the resting state
of a Ling’s cell and supports his understanding of the living cell’s
thermodynamics.
One feature of this approach is that it suggests that the resting state of a
Ling’s cell should be considered to be a non-equilibrium stationary state, whose
existence is a direct consequence of the non-ergodicity property that we
postulate for Ling’s cells. In this approach thermodynamics of non-equilibrium
stationary states must be constructed (analogous to the standard
quasi-stationary thermodynamics) to explain why biological work becomes possible
in the context of the proposed approach (biological work here means any changes
in the cell that have a biological significance and that use up energy, for
instance muscle contraction). There is no real contradiction between Ling’s
stationary resting state and the obviously continuous metabolism necessary to
maintain life, because a real cell constantly changes its state from active to
resting and back. Metabolism and energy are needed to go back to a resting state
rather than maintain it.
Non-ergodicity means that there exist non-trivial first integrals of the system
(i.e. that are invariant under the Heisenberg and Hamilton motion equations).
Because by definition we consider these first integrals to be real, then, in the
case of quantum mechanics, they must be represented by selfadjoint operators and
be experimentally observable values. It’s then only natural to ask how come they
can only be observed in biological systems (as is shown below) as well as in
liquid helium and superconductors, systems that are as far from biological as
can be? When answering this question we come across a certain mathematical
similarity between the super-fluid state of helium and the resting state of the
Ling cell, and this similarity helps us better understand the physics of the
living state.
The main result of this paper is that by looking at the Ling cell as a non-ergodic
system we were able to propose a common physical mechanism for various
physiological phenomena, which were previously explained with the help of
separate mechanisms barely related to each other. The main goal of physics in
physiology must be to find out the thermodynamic nature of an active living
cell, i.e. the source of all the manifestations of life. With this goal in mind
we only discuss some of the characteristics of the Ling cell and provide only a
most general physical description for them. We demonstrate, for example, that
when a Ling’s cell is activated it emits heat rather than absorbs it. When we
consider the properties of the physical model we use, it becomes perfectly clear
why it is that unfolded proteins that make up the structural foundation of a
resting Ling’s cell, begin to fold when it goes active, why potassium ions exit
the cell into the environment and why an active cell changes its size (usually
it shrinks) and what makes a cell dead. It is not our goal in this paper to
compare the results we obtain for the Ling’s cell with the properties of a real
living cell.
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Web-Links
Ling
G.N.
A Physical Theory of the Living State: The Association-Induction Hypothesis.
Blaisdell. New York, 1962.
Ling G.N.
In search of the physical basis of life. Plenum Press, New York, London,
1984.
Ling G.N.
A Revolution in the Physiology of the Living Cell, 1992.
Selected Ling's
works.
The Journal "Physiological
Chemistry and Physics and Medical NMR".
Russian
edition of the book:
Ling, G.N. (2001). Life at the Cell and Below-Cell Level. The Hidden History of
a Fundamental Revolution in Biology, Pacific Press, New York.
Pollack G.H. Water, Energy and Life.
(Lecture).