The Significance of Non-ergodic Property of Statistical Mechanics Systems for Understanding Resting State of a Living Cell

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 characterised 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 14 M) which remains in a bound quasi-crystallised 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 characterised 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 of which is the non-ergodicity property which has recently been proved for a wide range of systems in statistical mechanics [7]. 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 non-ergodicity 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.

Coherent Behavior and the Bound State of Water and K+ Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

“…The term ‘metastable’ is used to indicate the stability of the high-energy character of the R-state, but also its potential to fall into lower-energy states, because it is very far from thermodynamic equilibrium (see [143] for details). However, as Ling [51] pointed out with his EMOC preparations, it is nevertheless a physical equilibrium, in need of neither pumping activity nor a continuous energy supply, as MT erroneously believed.…”

“…This means that the thermodynamics of Prigogine cannot be used to describe the R-state. Only very recently, Prokhorenko and Matveev [143] derived the thermodynamics of static (metastable) non-linear systems far from equilibrium . They were developed from first principles and immediately applied to Ling’s description of a cell’s R-state.…”

Two models of protoplasm microstructure of the living cell in resting state

“…Compatibility of the Ling's resting cell organization principles with analytical methods of modern theoretical physics was first shown in our previous work (Prokhorenko and Matveev, 2011). The base of our approach is the fact that the majority of statistical mechanics systems (including the most realistic ones) are non-ergodic that was proved by one of us (Prokhorenko, 2009).…”

“…The base of our approach is the fact that the majority of statistical mechanics systems (including the most realistic ones) are non-ergodic that was proved by one of us (Prokhorenko, 2009). The generalized thermodynamic analysis (generalized thermodynamics) of Ling's cell we proposed (Prokhorenko and Matveev, 2011) allowed us to explain (in framework of adopted boundary conditions) a number of physiological phenomena that occur when cell is in activated (excited) state: exothermicity of transition to excited state, change of cell volume, folding of natively unfolded proteins (which determine, by Ling, a main features of the resting state), efflux of cell K + and wider -major redistribution of physiologically important ions between the cell and its environment. However, we determined the sign (direction) only of these processes, there were no numerical evaluations.…”

“…Indeed, inequalities we have determined (Prokhorenko and Matveev, 2011) were based on the postulate of relative entropy maximum for the resting cell standing in the state of thermodynamic equilibrium with environment. However, an equilibrium with environment does not mean the equilibrium state (the absolute maximum of entropy) of a system; that's why the relative nature of the entropy maximum is indicated.…”