A thermodynamical study of the clockwork hypothesis proposed by E. Schrödinger

In the present study, the 'clockwork' hypothesis proposed by Schr?dinger was examined from the viewpoint of thermodynamics. Firstly, noticing a unidirectional transfer of entropy in a heat engine, the logic was briefly explained about a close relation between this entropy transfer and an irreversible cycle performed by a working body. Next, paying attention to two fundamental differences between a heat engine and a biological system, we considered an isolated system Asigma consisting of three one-component systems (Ai, A, Ao) and noted a case that the same molecules as the component ones flowed quasistatically into Ai from the outside. Then, the unidirectional flows of the molecules, energy and entropy, which were induced by the above inflow in Asigma, were formulated on the basis of the equilibrium thermodynamics for an open system. Furthermore, it was clarified that the fundamental equation for these flows is the Schr?dinger inequality and that the necessary-sufficient condition for this inequality is the existence of an irreversible cycle performed by A. Here A corresponds to a working body in a heat engine. It was, thus, concluded that the 'clockwork' hypothesis by Schr?dinger is considered to be reasonable for a biological system composed of various irreversible subsystems.     

A note on the thermodynamics and kinetics of open and steady state systems

Some conclusions of irreversible thermodynamics are summarized. It is shown that θ, the rate of irreversible entropy production, is not minimized in the steady state. It is also postulated that multiple steady states are possible in nonlinear kinetic systems, giving rise to situations of possible biological interest. The necessity of examining particular kinetic models is mentioned.     

Biomathematics on the Basis of Thermodynamics

Mathematical terms as e.g. total differential and partial derivative play a specific role in classic thermodynamics. In this connection we ask for the existence of a thermodynamical biomathematics in consequence of the large biological importance of the thermodynamics of irreversible processes in open systems. In spite of our present limited knowledge we answer this question positive by means of theoretical considerations and practical examples.     

Thermodynamically feasible kinetic models of reaction networks

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.     

Thermodynamics of natural selection III: Landauer's principle in computation and chemistry

This is the third in a series of three papers devoted to energy flow and entropy changes in chemical and biological processes, and their relations to the thermodynamics of computation. The previous two papers have developed reversible chemical transformations as idealizations for studying physiology and natural selection, and derived bounds from the second law of thermodynamics, between information gain in an ensemble and the chemical work required to produce it. This paper concerns the explicit mapping of chemistry to computation, and particularly the Landauer decomposition of irreversible computations, in which reversible logical operations generating no heat are separated from heat-generating erasure steps which are logically irreversible but thermodynamically reversible. The Landauer arrangement of computation is shown to produce the same entropy-flow diagram as that of the chemical Carnot cycles used in the second paper of the series to idealize physiological cycles. The specific application of computation to data compression and error-correcting encoding also makes possible a Landauer analysis of the somewhat different problem of optimal molecular recognition, which has been considered as an information theory problem. It is shown here that bounds on maximum sequence discrimination from the enthalpy of complex formation, although derived from the same logical model as the Shannon theorem for channel capacity, arise from exactly the opposite model for erasure.     

A mathematical model for the freezing process in biological tissue

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.     

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].     

Revisiting the Thermodynamic Theory of Optimal ATP Stoichiometries by Analysis of Various ATP-Producing Metabolic Pathways

The stoichiometry of ATP-producing metabolic pathways had been analysed theoretically by several authors by using evolutionary arguments and optimality principles. Waddell et al. (Biochem Educ 27:12–13, 1999) analysed (lactate-producing) glycolysis and used linear irreversible thermodynamics. The result was that half of the free-energy difference should be converted into free-energy of ATP and the remaining half should be used to drive the pathway. The calculated stoichiometry is in agreement with the observed yield of two moles of ATP per mole of glucose. Using the same approach, we here analyse eight other metabolic pathways. Although the deviation is not very large, the calculated values do not fit as nicely as for glycolysis as leading to lactate. For example, for O₂ respiration, the theoretical ATP yield equals 27.9. The real value varies among organisms between 26 and 38. For mixed-acid fermentation in Escherichia coli, the theoretical and experimental values are 2.24 and 2, respectively. For arginine degradation in M. pneumoniae, the calculated value is 2.43 mol of ATP, while in vivo only one mole is produced. During evolution, some pathways may not have reached their optimal ATP net production because energy yield is not their only function. Moreover, it should be acknowledged that the approach by linear irreversible thermodynamics is a rough approximation.     

Ecological complexity for unifying ecological theory across scales: A field ecologist's perspective

The evening session in ecological complexity at the last Joint Meeting of the International Association for Ecology (INTECOL) and the Ecological Society of America (ESA) held in Montreal was an occasion to evaluate the pertinence and upcoming challenges of the complex systems approach (CSA) applied to ecology. Through concepts such as the interaction topology among biological objects, the phenotypic integration of individual traits, the meaning of biological objects and complexity measures in space and time, the management of human dominated ecosystems, and non-equilibrium thermodynamics as a paradigm for the development of ecosystems, the panel members covered some of the most active areas of research in ecological complexity. However, for many ecologists, and particularly field ecologists, a comprehensive framework clearly emphasizing how and why the CSA provides a unique corpus for studying ecosystem functions is missing. The purpose of this article is thus to provide an overview of the different themes visited during the evening session and to emphasize the distinctiveness of the CSA as an alternative to contemporary ecological issues. Examples from functional ecology and food webs are given to support the discussion.     

Theoretical analysis of Lumry-Eyring models in differential scanning calorimetry

A theoretical analysis of several protein denaturation models (Lumry-Eyring models) that include a rate-limited step leading to an irreversibly denatured state of the protein (the final state) has been carried out. The differential scanning calorimetry transitions predicted for these models can be broadly classified into four groups: situations A, B, C, and C′. (A) The transition is calorimetrically irreversible but the rate-limited, irreversible step takes place with significant rate only at temperatures slightly above those corresponding to the transition. Equilibrium thermodynamics analysis is permissible. (B) The transition is distorted by the occurrence of the rate-limited step; nevertheless, it contains thermodynamic information about the reversible unfolding of the protein, which could be obtained upon the appropriate data treatment. (C) The heat absorption is entirely determined by the kinetics of formation of the final state and no thermodynamic information can be extracted from the calorimetric transition; the rate-determining step is the irreversible process itself. (C′) same as C, but, in this case, the rate-determining step is a previous step in the unfolding pathway. It is shown that ligand and protein concentration effects on transitions corresponding to situation C (strongly rate-limited transitions) are similar to those predicted by equilibrium thermodynamics for simple reversible unfolding models. It has been widely held in recent literature that experimentally observed ligand and protein concentration effects support the applicability of equilibrium thermodynamics to irreversible protein denaturation. The theoretical analysis reported here disfavors this claim.     

Plasma membrane water permeabilities of human oocytes: the temperature dependence of water movement in individual cells.

Membrane water permeability values were measured in individual fresh human pre-ovulatory oocytes using real time microscopy in a microscope diffusion chamber. The cells were exposed to anisosmotic conditions, their volume responses measured, and from these data the Lp values were computed employing the Kedem-Katchalsky analyses of irreversible thermodynamics. Lp values were measured at four temperatures for each oocyte between 37 degrees C and 10 degrees C, and the temperature-related Arrhenius activation energy (Ea) calculated. It was apparent that individual oocytes exhibited a wide range of Lp values; at 37 degrees C Lp values ranged between 0.33 and 1.80 microns/atm/min. However, each oocyte exhibited the expected inverse linear correlation between Lp and temperature, with high linear correlations (R2 values between 0.73 and 0.96). A mean value for Ea of 8.61 +/- 5.11 Kcal/mol was computed. It is apparent that pre-ovulatory human oocytes express a range of biological diversity in terms of membrane water transport, and this fact needs to be considered when attempting to formulate cryopreservation protocols for storage of these oocytes.     

Living organisms from Prigogine’s perspective: an opportunity to introduce students to biological entropy balance

All living structures, from archaea to human, are open thermodynamic systems analysed through nonequilibrium thermodynamics. Nonequilibrium thermodynamics is a field with important applications to life sciences, which is very often left out of life science courses. A three-step method is suggested to make an easy introduction of nonequilibrium thermodynamics to life science students. The first step is to introduce the Prigogine equation dS = d_eS + d_iS, and explain the meaning of the entropy exchange with the surroundings d_eS and internal entropy generation in the system d_iS. The second step is to show that the Prigogine equation is connected to the equilibrium thermodynamics already known to students. This can be done by deriving the Clausius inequality dS ≥ dq/T, from the Prigogine equation applied to reversible and irreversible processes in closed systems. Reversible and irreversible processes are discussed separately and the results are then combined into the Clausius inequality. The third step is to introduce the fact that the Prigogine equation has a variety of applications in life sciences. This would give the students an opportunity to understand the entropy balance of physiological processes in cells and organisms. The import and accumulation of entropy, entropy generation, and entropy export could be made easier for students to adopt.     

Multiple membrane systems as biological models

Summary The current-voltage equations for double, triple, and quadruple membrane systems are derived in closed form from the flow equations of irreversible thermodynamics. Numerical examples show that the behavior of these systems is very similar to that of nerve and muscle membranes. Multiple membrane systems exhibit resting potentials which do not have a characteristic Nernst concentration dependence; nonpermeant ions play a significant role in this nonlogarithmic behavior. Furthermore, multiple membrane systems have rectification properties similar to those of biological membranes. The direction of rectification is determined by the polarity of the membrane systems, not by the ionic concentrations in the bathing solutions.     

Über die Nachrichtenaufnahme durch biologische Receptoren

Summary The Hodgkin-Huxley theory of ion fluxes across membranes during excitation is extended to explain the graduated depolarisation (receptor potential) of sensory cell membranes. Electric circuit equivalents of living membranes are developed. Driving forces and velocity coefficients are represented by means of electric parameters. From this model active and passive ionic fluxes can be calculated quantitatively on the basis of transport equations derived from irreversible thermodynamics. Thus the circuit equivalent may be used as an analog computer. Electric receptor models allow a reproduction of all potential curves which have been derived in electrophysiological experiments on PD-receptors. The results obtained by the use of this model agree with the results obtained in biological experiments under various conditions of stimuli. The significance of solution compartments for intra-and extracellular ions in relation to the time functions of various conditions are discussed in detail. This models are of heuristic value in experimental research. In combination with neuron networks they can be used for the analysis of information theoretical problems.     

Mining Rare Associations between Biological Ontologies

The constantly increasing volume and complexity of available biological data requires new methods for their management and analysis. An important challenge is the integration of information from different sources in order to discover possible hidden relations between already known data. In this paper we introduce a data mining approach which relates biological ontologies by mining cross and intra-ontology pairwise generalized association rules. Its advantage is sensitivity to rare associations, for these are important for biologists. We propose a new class of interestingness measures designed for hierarchically organized rules. These measures allow one to select the most important rules and to take into account rare cases. They favor rules with an actual interestingness value that exceeds the expected value. The latter is calculated taking into account the parent rule. We demonstrate this approach by applying it to the analysis of data from Gene Ontology and GPCR databases. Our objective is to discover interesting relations between two different ontologies or parts of a single ontology. The association rules that are thus discovered can provide the user with new knowledge about underlying biological processes or help improve annotation consistency. The obtained results show that produced rules represent meaningful and quite reliable associations.     

A cooperative model for ligand binding to biological macromolecules as applied to oxygen carriers

This paper presents a model describing the thermodynamics of cooperative ligand binding to multimeric biological macromolecules and integrating some of the features of the two-state and induced-fit models. The protein is taken to be partitioned into a number of noninteracting functional constellations, each one existing in two possible quaternary conformations. Furthermore, the model postulates that a functional constellation is organized in several subsets of sites (called cooperons), in which subunits interact according to an induced-fit mechanism. In the present version the number of subunits forming a cooperon has been limited to two and the total number of parameters used for fitting experimental data is four, all having a precise physical meaning. Although the present application is limited to oxygen-carrying proteins (hemoglobins, hemocyanins, erythrocruorins), the model appears suitable to describe other biological macromolecules with functional interactions.