Phenomenon of Life: Between Equilibrium and Non-Linearity

A model of ordering applicable to biological evolution is presented. It is shown that a steady state (more precisely approaching to a steady state) system of irreversible processes, under conditions of disproportionation of entropy, produces a lower-entropy product, that is, ordering. The ordering is defined as restricting of degrees of freedom: freedom of motion, interactions etc. The model differs from previous ones in that it relates the ordering to processes running not far from equilibrium, described in the linear field of non-equilibrium thermodynamics. It is shown that a system, which includes adenosine triphosphate (ATP) to adenosine diphosphate (ADP) conversion meets the demands of the physical model: it provides energy maintaining steady state conditions, and hydrolysis of ATP proceeding with consumption of water can be tightly conjugated with the most important reactions of synthesis of organic polymers (peptides, nucleotide chains etc.), which proceed with release of water. For these and other reasons ATP seems to be a key molecule of prebiotic evolution. It is argued that the elementary chemical reaction proceeding under control of an enzyme is not necessarily far from equilibrium. The experimental evidence supporting this idea, is presented. It is based on isotope data. Carbon isotope distribution in biochemical systems reveals regularity, which is inherent to steady state systems of chemical reactions, proceeding not far from equilibrium. In living organisms this feature appears at the statistical level, as many completely irreversible and non-linear processes occur in organisms. However not-far-from-equilibrium reactions are inherent to biochemical systems as a matter of principle. They are reconcilable with biochemical behavior. Extant organisms are highly evolved entities which, however, show in their basis the same features, as the simplest chemical systems must have had been involved in the origin of life. Some consequences following from the model, which may be significant for understanding the origin of life and the mechanism of biological evolution, are pointed out.     

On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems.     

How Does the Plant Plasma Membrane H+-ATPase Pump Protons?

The plasma membrane H⁺-ATPase couples ATP hydrolysis to protontransport thereby establishing the driving force for solutetransport into and out of plant cells. As such, this enzymeparticipates in a number of cellular processes important tothe overall physiology of plants. From biochemical studies andthe recent application of molecular approaches, the enzyme reactionmechanism and structure of this protein have been characterized.However, our basic understanding of how this enzyme links theendergonic reaction of ATP hydrolysis to proton translocationis far from complete. In this review, several significant questionsregarding the energy coupling mechanism will be addressed interms of information available on the plant plasma membraneH⁺-ATPase and from studies on other P-type transport ATPases.These questions focus on the chemical nature of proton translocation,how this is linked or driven by the ATP hydrolysis reactionand what role, if any, K⁺ has in the transport process. Key words: Energy coupling, membranes, bioenergetics, ion transport, P-type transport ATPase     

Models of growth, self-reproduction and autoregulation based on consideration of reaction vessels with distensible, semipermeable walls]

We constructed non-equilibrium thermodynamics of the open physical-chemical irreversible processes in reactors with the strain semipermeable walls. This thermodynamics does not use the reciprocal relations of Onsager, so it may be applied when the stability stationary state is far from equilibrium. One of a general consequences of this thermodynamics is the statement: coordinated growth and self-reproduction are possible near the absolute equilibrium of the dissolvent and near the absolute stability stationary state of all chemicals with the absolute conservation of the differential equations of chemical kinetics. The supposition of ideal mixing is unnecessary; this condition is fulfilled automatically with diffusion. Growth and self-reproduction are not connected with positive eigenvalue of the differential equation of chemical kinetics. It is possible to construct a model of autoregulation and differentiation with this thermodynamics. The uniquness of such autoregulation follows from the mathematical theory [1]. The mathematical foundation of this thermodynamics is given in [1].     

Nonequilibrium chemical potentials and free energies for enzyme-catalyzed reactions

Using the statistical theory of nonequilibrium thermodynamics we explore the nature of nonequilibrium corrections to chemical potentials in simple enzyme-catalyzed reactions. The statistical definition of the chemical potential, which pertains to systems that are at stable steady states, is applied to the Michaelis-Menten reaction scheme in a cellular-sized compartment that communicates with out-side reservoirs. Calculations based on the kinetic parameters for hexokinase and triose phosphate isomerase show that substantial corrections to the chemical potential of product (the order of 25 mV) are possible if the reaction is sufficiently far from equilibrium. The dependence of the corrections to the chemical potentials on the size of the cellular compartment are explored, and the relevance of the corrections for understanding the thermodynamics of metabolites is discussed.     

Observation of broken detailed balance in polymorphic transformation of bacterial flagellar filament

Living systems operate far from thermodynamic equilibrium, which usually manifests as broken detailed balance at the molecular scale. At larger scales with collective function of many molecules, the presence of non-equilibrium thermodynamics may not be evident. In bacterial motility, the switching dynamics of the flagellar rotary motor was recently discovered to be operating in non-equilibrium. However, the resulting motility pattern at the mesoscale, the run-and-tumble behavior, was normally considered to be a Poisson process that can be described by a two-state equilibrium model. Here, we studied the details of the run-and-tumble behavior by following the polymorphic transformation of the flagellar filaments, observing broken detailed balance that reveals its non-equilibrium nature. Evaluation of entropy production provided a direct measure of the lack of detailed balance and a quantification of the rate of energy dissipation for bacterial run-and-tumble regulation.     

The Glansdorff-Prigogine thermodynamic stability criterion in the light of Lyapunov's theory.

The significance of thermodynamic coupling in chemical reactions—which recently has been questioned on thermodynamic grounds—is examined from the point of view of kinetics. It is shown that considerations of stoichiometry lead to a meaningful definition of velocity for elementary and certain elementary-complex reactions, whereas the non-equilibrium thermodynamic definition of reaction velocity is ambiguous in multireaction systems. Based on rate laws which include the effects of nonideality, it is proven that elementary-type reactions are not coupled thermodynamically and concluded that thermodynamic coupling has no kinetic significance. A discussion is given to show that this result is compatible with coupling in both biochemical systems and oscillating reactions.     

Energy transduction in lactic acid bacteria

Abstract: In the discovery of some general principles of energy transduction, lactic acid bacteria have played an important role. In this review, the energy transducing processes of lactic acid bacteria are discussed with the emphasis on the major developments of the past 5 years. This work not only includes the biochemistry of the enzymes and the bioenergetics of the processes, but also the genetics of the genes encoding the energy transducing proteins. The progress in the area of carbohydrate transport and metabolism is presented first. Sugar translocation involving ATP-driven transport, ion-linked cotransport, heterologous exchange and group translocation are discussed. The coupling of precursor uptake to product product excretion and the linkage of antiport mechanisms to the deiminase pathways of lactic acid bacteria is dealt with in the second section. The third topic relates to metabolic energy conservation by chemiosmotic processes. There is increasing evidence that precursor/product exchange in combination with precursor decarboxylation allows bacteria to generate additional metabolic energy. In the final section transport of nutrients and ions as well as mechanisms to excrete undesirable (toxic) compounds from the cells are discussed.     

Basic statistical recipes for the emergence of biochemical discernment

An essential step towards understanding life would be to identify the very basic mechanisms responsible for the discerning behaviour of living biochemical systems, absent from randomly reacting chemical soups. One intuitively feels that this question goes beyond the particular nature of the biological molecules and should relate to general physical principles. The pre-eminent physicist Ludwig Boltzmann early envisioned life as a struggle for entropy, in concordance with the subsequent principle of self-organization out of equilibrium. Re-examination of elementary steady state biochemical systems from a statistical perspective supports this view and shows that sigmoidal responses arising from microstates elimination, are sufficient to explain innermost characteristics of life, including its capacity to convert random molecular interactions into accurate biological reactions. A primary operating strategy to achieve this goal is the introduction of time-irreversible transitions in molecular state conversion cycles by injection of free energy, which confers decisional capacity to single macromolecules. Selected examples from various fields of molecular biology such as enzymology and gene expression, are provided to show that these non-equilibrium steady state mechanisms remain important in contemporary biochemical systems. But in addition, information archiving allowed the emergence of the time-reversible counterparts of these mechanisms, mediated by evolutionary pre-organized macromolecular complexes capable of generating discernment in a non-dissipative manner.     

Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics

During the last 15 years, scientists have developed methods that permit the direct mechanical manipulation of individual molecules. Using this approach, they have begun to investigate the effect of force and torque in chemical and biochemical reactions. These studies span from the study of the mechanical properties of macromolecules, to the characterization of molecular motors, to the mechanical unfolding of individual proteins and RNA. Here I present a review of some of our most recent results using mechanical force to unfold individual molecules of RNA. These studies make it possible to follow in real time the trajectory of each molecule as it unfolds and characterize the various intermediates of the reaction. Moreover, if the process takes place reversibly it is possible to extract both kinetic and thermodynamic information from these experiments at the same time that we characterize the forces that maintain the three-dimensional structure of the molecule in solution. These studies bring us closer to the biological unfolding processes in the cell as they simulate in vitro, the mechanical unfolding of RNAs carried out in the cell by helicases. If the unfolding process occurs irreversibly, I show here that single-molecule experiments can still provide equilibrium, thermodynamic information from non-equilibrium data by using recently discovered fluctuation theorems. Such theorems represent a bridge between equilibrium and non-equilibrium statistical mechanics. In fact, first derived in 1997, the first experimental demonstration of the validity of fluctuation theorems was obtained by unfolding mechanically a single molecule of RNA. It is perhaps a sign of the times that important physical results are these days used to extract information about biological systems and that biological systems are being used to test and confirm fundamental new laws in physics.     

Relating a calcium indicator signal to the unperturbed calcium concentration time-course

Carbohydrate restriction as a strategy for control of obesity is based on two effects: a behavioral effect, spontaneous reduction in caloric intake and a metabolic effect, an apparent reduction in energy efficiency, greater weight loss per calorie consumed. Variable energy efficiency is established in many contexts (hormonal imbalance, weight regain and knock-out experiments in animal models), but in the area of the effect of macronutrient composition on weight loss, controversy remains. Resistance to the idea comes from a perception that variable weight loss on isocaloric diets would somehow violate the laws of thermodynamics, that is, only caloric intake is important ("a calorie is a calorie"). Previous explanations of how the phenomenon occurs, based on equilibrium thermodynamics, emphasized the inefficiencies introduced by substrate cycling and requirements for increased gluconeogenesis. Living systems, however, are maintained far from equilibrium, and metabolism is controlled by the regulation of the rates of enzymatic reactions. The principles of nonequilibrium thermodynamics which emphasize kinetic fluxes as well as thermodynamic forces should therefore also be considered. Here we review the principles of nonequilibrium thermodynamics and provide an approach to the problem of maintenance and change in body mass by recasting the problem of TAG accumulation and breakdown in the adipocyte in the language of nonequilibrium thermodynamics. We describe adipocyte physiology in terms of cycling between an efficient storage mode and a dissipative mode. Experimentally, this is measured in the rate of fatty acid flux and fatty acid oxidation. Hormonal levels controlled by changes in dietary carbohydrate regulate the relative contributions of the efficient and dissipative parts of the cycle. While no experiment exists that measures all relevant variables, the model is supported by evidence in the literature that 1) dietary carbohydrate, via its effect on hormone levels controls fatty acid flux and oxidation, 2) the rate of lipolysis is a primary target of insulin, postprandial, and 3) chronic carbohydrate-restricted diets reduce the levels of plasma TAG in response to a single meal. In summary, we propose that, in isocaloric diets of different macronutrient composition, there is variable flux of stored TAG controlled by the kinetic effects of insulin and other hormones. Because the fatty acid-TAG cycle never comes to equilibrium, net gain or loss is possible. The greater weight loss on carbohydrate restricted diets, popularly referred to as metabolic advantage can thus be understood in terms of the principles of nonequilibrium thermodynamics and is a consequence of the dynamic nature of bioenergetics where it is important to consider kinetic as well as thermodynamic variables.     

Mechanism of transport and storage of neurotransmitters

This review will focus on the bioenergetics, mechanism, and molecular basis of neurotransmitter transport. As indicated in the next section, these processes play an important role in the overall process of synaptic transmission. During the last few years, direct evidence has been obtained that these processes are coupled chemiosmotically, i.e., the accumulation of neurotransmitters is driven by ion gradients. Two types of neurotransmitter transport systems have been identified: sodium-coupled systems located in the synaptic plasma membrane of nerves (and sometimes in the plasma membrane of glial cells) and proton-coupled systems which are part of the membrane of intracellular storage organelles. From a bioenergetic point of view, the sodium-coupled systems are especially interesting, since it has recently been discovered that many systems require other ions in addition to sodium. It has now been demonstrated in several cases that, besides sodium ions, these additional ions, such as chloride and potassium, serve as additional coupling ions. These systems will be reviewed here in considerable detail with emphasis on the role of the additional ions. In the second part of the review we shall focus on neurotransmitter transport into storage organelles. Although both sodium and proton coupled systems have been reviewed in the past, there has been a shift from a kinetic and thermodynamic to a biochemical approach. In fact, a few transporters have been identified and functionally reconstituted. These developments have of course been incorporated in this review.     

On the admittance of membranes associated with channel conduction. Application to channels at non-equilibrium steady state

The small-signal admittance of membranes associated with channel conduction is derived for a general channel model. A general channel model is represented by a set of chemical reactions with each species of the reactions representing a channel state. The membrane admittance is shown to be related to the phenomenological relaxation matrix of the reactions. If the kinetic reactions are at a non-equilibrium steady state, the relaxation matrix may have complex eigenvalues and the equivalent circuit of the membrane admittance may contain RLC or RLC-like branches. For equilibrium kinetic systems, on the other hand, the equivalent circuit contains only RL or RC branches. Thus, the membrane admittance of equilibrium channels is quite different from that of non-equilibrium channels. In particular, we show that the low frequency feature in the admittance of squid axons as observed by Fishman, Poussart, Moore &; Siebenga (1977) can be obtained easily from a non-equilibrium cycling steady-state model.     

Metabolic energy conservation for fermentative product formation

Microbial production of bulk chemicals and biofuels from carbohydrates competes with low-cost fossil-based production. To limit production costs, high titres, productivities and especially high yields are required. This necessitates metabolic networks involved in product formation to be redox-neutral and conserve metabolic energy to sustain growth and maintenance. Here, we review the mechanisms available to conserve energy and to prevent unnecessary energy expenditure. First, an overview of ATP production in existing sugar-based fermentation processes is presented. Substrate-level phosphorylation (SLP) and the involved kinase reactions are described. Based on the thermodynamics of these reactions, we explore whether other kinase-catalysed reactions can be applied for SLP. Generation of ion-motive force is another means to conserve metabolic energy. We provide examples how its generation is supported by carbon-carbon double bond reduction, decarboxylation and electron transfer between redox cofactors. In a wider perspective, the relationship between redox potential and energy conservation is discussed. We describe how the energy input required for coenzyme A (CoA) and CO₂ binding can be reduced by applying CoA-transferases and transcarboxylases. The transport of sugars and fermentation products may require metabolic energy input, but alternative transport systems can be used to minimize this. Finally, we show that energy contained in glycosidic bonds and the phosphate-phosphate bond of pyrophosphate can be conserved. This review can be used as a reference to design energetically efficient microbial cell factories and enhance product yield.     

ATP synthesis and storage

Since 1929, when it was discovered that ATP is a substrate for muscle contraction, the knowledge about this purine nucleotide has been greatly expanded. Many aspects of cell metabolism revolve around ATP production and consumption. It is important to understand the concepts of glucose and oxygen consumption in aerobic and anaerobic life and to link bioenergetics with the vast amount of reactions occurring within cells. ATP is universally seen as the energy exchange factor that connects anabolism and catabolism but also fuels processes such as motile contraction, phosphorylations, and active transport. It is also a signalling molecule in the purinergic signalling mechanisms. In this review, we will discuss all the main mechanisms of ATP production linked to ADP phosphorylation as well the regulation of these mechanisms during stress conditions and in connection with calcium signalling events. Recent advances regarding ATP storage and its special significance for purinergic signalling will also be reviewed.     

Relationship between thermodynamic driving force and one-way fluxes in reversible processes

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and reverse fluxes and free energy for any chemical process operating in a steady state. This relationship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state in dilute solution, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.     

The Chemical Basis of Membrane Bioenergetics

All organisms rely on chemiosmotic membrane systems for energy transduction; the great variety of participating proteins and pathways can be reduced to a few universal principles of operation. This chemical basis of bioenergetics is reviewed with respect to the origin and early evolution of life. For several of the cofactors which play important roles in bioenergetic reactions, plausible prebiotic sources have been proposed, and it seems likely that these cofactors were present before elaborate protein structures. In particular, the hydrophobic quinones require only a membrane-enclosed compartment to yield a minimum chemiosmotic system, since they can couple electron transport and proton translocation in a simple way. It is argued that the central features of modern bioenergetics, such as the coupling of redox reactions and ion translocation at the cytoplasmic membrane, probably are ancient features which arose early during the process of biogenesis. The notion of a thermophile root of the universal phylogenetic tree has been discussed controversially, nevertheless, thermophiles are interesting model organisms for reconstructing the origin of chemiosmotic systems, since they are often acidophiles and anaerobic respirers exploiting iron–sulfur chemistry. This perspective can help to explain the prominent role of iron–sulfur proteins in extant biochemistry as well as the origin of both respiration and proton extrusion within the context of a possible origin of life in the vicinity of hot vents. Received: 6 June 2001 / Accepted: 16 October 2001     

Current noise in transport of hydrophobic ions through lipid bilayer membranes including diffusion polarization in the aqueous phase

An exact treatment of the current noise spectrum produced by transport of hydrophobic ions through membranes is presented, including the coupling of the diffusion processes through both the aqueous phase and the membrane. Both the equilibrium and the steady state noise spectra are computed. The theory contains previous results as limiting cases. The structure of the spectra is discussed with emphasis upon how noise measurements can be used to estimate kinetic parameters, especially the rate of desorption from the membrane. For this restricted model there is no low frequency divergence in the non-equilibrium current noise, i.e., for the model treated there is no 1/f noise.     

Single-molecule studies of complex systems: the replisome

A complete, system-level understanding of biological processes requires comprehensive information on the kinetics and thermodynamics of the underlying biochemical reactions. A wide variety of structural, biochemical, and molecular biological techniques have led to a quantitative understanding of the molecular properties and mechanisms essential to the processes of life. Yet, the ensemble averaging inherent to these techniques limits us in understanding the dynamic behavior of the molecular participants. Recent advances in imaging and molecular manipulation techniques have made it possible to observe the activity of individual enzymes and record "molecular movies" that provide insight into their dynamics and reaction mechanisms. An important future goal is extending the applicability of single-molecule techniques to the study of larger, more complex multi-protein systems. In this review, the DNA replication machinery will be used as an example to illustrate recent progress in the development of various single-molecule techniques and its contribution to our understanding of the orchestration of multiple enzymatic processes in large biomolecular systems.