Native aggregation in cell physiology


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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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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Dr. Vladimir Matveev
Institute of Cytology, Lab of Cell Physiology
Russian Academy of Sciences
194064, St.Petersburg, Tikhoretsky Avenue 4,
E-mail: vladimir.matveev @ gmail.com