Thermodynamics of Terrestrial Evolution

The causal element of biological evolution and development can be understood in terms of a potential function which is generalized from the variational principles of irreversible thermodynamics. This potential function is approximated by the rate of entropy production in a configuration space which admits of macroscopic excursions by fluctuation and regression as well as microscopic ones. Analogously to Onsager's dissipation function, the potential takes the form of a saddle surface in this configuration space. The path of evolution following from an initial high dissipation state within the fixed constraint provided by the invariant energy flux from the sun tends toward the stable saddle point by a series of spontaneous regressions which lower the entropy production rate and by an alternating series of spontaneous fluctuations which introduce new internal constraints and lead to a higher entropy production rate. The potential thus rationalizes the system's observed tendency toward "chemical imperialism" (high dissipation) while simultaneously accommodating the development of "dynamic efficiency" and complication (low dissipation).     

Entropy consumption in primary photosynthesis

Knox and Parson have objected to our previous conclusion on possible negative entropy production during primary photochemistry, i.e., from photon absorption to primary charge separation, by considering a pigment system in which primary photochemistry is not specifically considered. This approach does not address our proposal. They suggest that when a pigment absorbs light and passes to an excited state, its entropy increases by hν/T. This point is discussed in two ways: (i) from considerations based on the energy gap law for excited state relaxation; (ii) using classical thermodynamics, in which free energy is introduced into the pigment (antenna) system by photon absorption. Both approaches lead us to conclude that the excited state and the ground state are isoentropic, in disagreement with Knox and Parson. A discussion on total entropy changes specifically during the charge separation process itself indicates that this process may be almost isoentropic and thus our conclusions on possible negentropy production associated with the sequence of reactions which go from light absorption to the first primary charge separation event, due to its very high thermodynamic efficiency, remain unchanged.     

Entropy consumption in primary photosynthesis

Knox and Parson have objected to our previous conclusion on possible negative entropy production during primary photochemistry, i.e., from photon absorption to primary charge separation, by considering a pigment system in which primary photochemistry is not specifically considered. This approach does not address our proposal. They suggest that when a pigment absorbs light and passes to an excited state, its entropy increases by hnu/T. This point is discussed in two ways: (i) from considerations based on the energy gap law for excited state relaxation; (ii) using classical thermodynamics, in which free energy is introduced into the pigment (antenna) system by photon absorption. Both approaches lead us to conclude that the excited state and the ground state are isoentropic, in disagreement with Knox and Parson. A discussion on total entropy changes specifically during the charge separation process itself indicates that this process may be almost isoentropic and thus our conclusions on possible negentropy production associated with the sequence of reactions which go from light absorption to the first primary charge separation event, due to its very high thermodynamic efficiency, remain unchanged.     

Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

Pupillometric evidence for the decoupling of attention from perceptual input during offline thought

Accumulating evidence suggests that the brain can efficiently process both external and internal information. The processing of internal information is a distinct "offline" cognitive mode that requires not only spontaneously generated mental activity; it has also been hypothesized to require a decoupling of attention from perception in order to separate competing streams of internal and external information. This process of decoupling is potentially adaptive because it could prevent unimportant external events from disrupting an internal train of thought. Here, we use measurements of pupil diameter (PD) to provide concrete evidence for the role of decoupling during spontaneous cognitive activity. First, during periods conducive to offline thought but not during periods of task focus, PD exhibited spontaneous activity decoupled from task events. Second, periods requiring external task focus were characterized by large task evoked changes in PD; in contrast, encoding failures were preceded by episodes of high spontaneous baseline PD activity. Finally, high spontaneous PD activity also occurred prior to only the slowest 20% of correct responses, suggesting high baseline PD indexes a distinct mode of cognitive functioning. Together, these data are consistent with the decoupling hypothesis, which suggests that the capacity for spontaneous cognitive activity depends upon minimizing disruptions from the external world.     

Efficiency of free energy transfer and entropy production in photosynthetic systems

The diagram method for the calculation of entropy production and efficiency associated with very first steps of photosynthetic mechanism is developed. By using one simple model for the bacteriorhodopsin light activated proton pump action, it is shown that in the steady state of biological interest, both entropy production and efficiency of transfer of light energy are maximal for the same optimal values of kinetic constants.     

Maximization principles and daisyworld

We investigate whether the equilibrium time-averaged state of a self-organizing system with many internal degrees of freedom, 2D-daisyworld, can be described by optimizing a single quantity. Unlike physical systems where a principle of maximum energy production has been observed, daisyworld follows evolutionary dynamics rather than Hamiltonian dynamics. We find that this is sufficient to invalidate the maximum entropy production principle, finding instead a different principle, that the system self-organizes to a state which maximizes the amount of life.     

A theoretical prediction of the normal cardiac oxygen consumption

A model is described from which the entropy production associated with the process of transporting oxygen and carbon dioxide between the lungs and the muscles of the body can be calculated. The two entropy sources which are assumed to be the dominant ones for this process are the entropy production associated with the metabolism of the heart and the entropy production associated with the diffusion of oxygen and carbon dioxide into and out of the blood. The hypothesis that the observed blood flow is the one for which a given amount of oxygen and carbon dioxide is transported between the lungs and the muscles with minimum total entropy production is used to predict the value of the slope of the cardiac oxygen consumption vs. blood flow curve. At a blood flow of 15 liters/min, the predicted value of the slope of this curve is 1.2 ml/liter.     

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.     

An Indicator to Evaluate the Thermodynamic Maturity of Industrial Process Units in Industrial Ecology

The article suggests a measure to evaluate the thermodynamic maturity of industrial systems at the level of single process units. The measure can be quantified with reasonable confidence on the basis of entropy production as defined by irreversible thermodynamics theory. It quantifies, for one process unit, the distance between its actual state of operation and its state with minimum entropy production or optimum exergy efficiency, when the two states are constrained with a fixed production capacity of the process unit. We suggest that the minimum entropy production state is a mature state, or that processes that operate at this state are mature. We propose to call the measure "the thermodynamic maturity indicator" (π), and we define it as the ratio between the minimum entropy production and the actual entropy production. We calculated π on the basis of literature data for some examples of industrial process units in the chemical and process industry (i.e., heat exchanger, chemical reactor, distillation column, and paper drying machine). The proposed thermodynamic measure should be of interest for industrial ecology because it emerges from the entropy production rate, a dynamic function that can be optimized and used to understand the thermodynamic limit to improving the exergy efficiency of industrial processes. Although not a tool for replacing one process with another or comparing one technology to another, π may be used to assess actual operation states of single process units in industrial ecology.     

A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes

Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta-cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta-cell mass (positive feedback). The model predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia).     

Origin and evolution of life and intellect from the point of view of information processing]

Beginning of life and intellect on the Earth is determined by the fact that synthesis of semantic information about algorithms of chemical transformation for appointed classes of chemical compounds is not accompanied by the information synthesis, but is controlled by chance in genetic material. Genetic information as memorizing accidental choice always arises as a result of the environment interaction, when memorizing realization in the form of repeated reproduction occurs on the basis of processes radically different from those which created initial genetic chance. Such stepped synthesis of information has hierarchical character and it is described by entropy of different dimensions. Entropy is determined by conditional probabilities. Therefore as a form of life becomes complicated, the entropy is decreased within the limits of the given hierarchical step. The part of entropy depending on the number of elements of the system (cells, individuals, etc.) always increases in the memorizing process, i. e. life defines the maximum of entropy production (but not the minimum like in nature). This fact settles paradoxes of chance in Darwinism: as a result of entropy decrease within higher hierarchical step the simbiotic processes for more complex forms of life can arise with great probability. For instance, rapidity of evolution of human brain given by supplementary chance in the mechanism of fecundation under the conditions of biochemical pressure of androgenes both, on the brain development and on muscular force at the same time. Synthesis of information in the brain is determined by the same principles, but extremums of the thermo-dynamic potential (their analogues in logic) are based on an arbitrary system of axioms. As a whole life and intellect are not fluctuations pointed against entropy increases, but they arose according to spontaneous process of entropy development.     

Photosynthesis and negative entropy production

The widely held view that the maximum efficiency of a photosynthetic pigment system is given by the Carnot cycle expression (1-T/Tr) for energy transfer from a hot bath (radiation at temperature Tr) to a cold bath (pigment system at temperature T) is critically examined and demonstrated to be inaccurate when the entropy changes associated with the microscopic process of photon absorption and photochemistry at the level of single photosystems are considered. This is because entropy losses due to excited state generation and relaxation are extremely small (DeltaS < T/Tr) and are essentially associated with the absorption-fluorescence Stokes shift. Total entropy changes associated with primary photochemistry for single photosystems are shown to depend critically on the thermodynamic efficiency of the process. This principle is applied to the case of primary photochemistry of the isolated core of higher plant photosystem I and photosystem II, which are demonstrated to have maximal thermodynamic efficiencies of xi > 0.98 and xi > 0.92 respectively, and which, in principle, function with negative entropy production. It is demonstrated that for the case of xi > (1-T/Tr) entropy production is always negative and only becomes positive when xi < (1-T/Tr).     

Properties of membrane stationary states

Summary The flux of permeant species through a membrane is examined using discrete state stochastic models for the transport process within the membrane. While a membrane flux is maintained due to a concentration gradient between bathing solutions, the distribution of species within the membrane evolves to a time invariant configuration which can differ significantly from the equilibrium configuration. Some special properties of these stationary states are examined using linear, microcanonical models for the membrane transport process. Analysis of these models reveals properties which are masked by the phenomenological analysis of irreversible thermodynamics. For example, the models can be used to study the nature of multi-state relaxation within the membrane by observation of the time dependence of the net membrane flux when the membrane is perturbed from its stationary state distribution. Under some conditions, multi-state models will produce relaxation similar to that observed for single-state processes. The symmetry within the membrane is a critical factor for monitoring relaxation processes within the membrane. Because of the stationary nature of the membrane configuration, statistical thermodynamic variables can be defined for the membrane configuration. The total system is not in equilibrium since the baths must still be described by dissipation functions. In the stationary state, the configurational entropy of the membrane is lowered relative to equilibrium and is shown to depend quadratically on the time independent parameter (j/p) wherej is the membrane flux andp is a characteristic transition probability for intra-membrane transitions. The basic membrane system serves as a quantitative example of the entropy reduction possible in a stationary state system. An allosteric transition mediated by the stationary state configuration is examined as a means of utilizing this negentropy production.     

A maximum entropy criterion of filtering and coding for stationary autoregressive signals: Its physical interpretations and suggestions for its application to neural information transmission

The operations of encoding and decoding in communication agree with filtering operations of convolution and deconvolution for Gaussian signal processing. In an analogy with power transmission in thermodynamics, an autoregressive model of information transmission is proposed for representing a continuous communication system which requires a pair of an internal noise source and a signal source to encode or decode a message. In this model transinformation (informational entropy) equals the increase in stationary nonequilibrium organization formed through the amplification of white noise by a positive feedback system. The channel capacity is finite due to the existence of inherent noise in the system. The maximum entropy criterion in information dynamics corresponds to the 2^nd law of thermodynamics. If the process is stationary, the communication system is invertible, and has the maximum efficiency of transformation. The total variation in informational entropy is zero in the cycle of the invertible system, while in the noninvertible system the entropy of decoding is less than that of encoding. A noisy autoregressive coding which maximizes transinformation is optimum, but is also ideal.     

Entropy involved in fidelity of DNA replication

Information has an entropic character which can be analyzed within the framework of the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. Here, we introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.     

Working memory dynamics and spontaneous activity in a flip-flop oscillations network model with a Milnor attractor

Many cognitive tasks require the ability to maintain and manipulate simultaneously several chunks of information. Numerous neurobiological observations have reported that this ability, known as the working memory, is associated with both a slow oscillation (leading to the up and down states) and the presence of the theta rhythm. Furthermore, during resting state, the spontaneous activity of the cortex exhibits exquisite spatiotemporal patterns sharing similar features with the ones observed during specific memory tasks. Here to enlighten neural implication of working memory under these complicated dynamics, we propose a phenomenological network model with biologically plausible neural dynamics and recurrent connections. Each unit embeds an internal oscillation at the theta rhythm which can be triggered during up-state of the membrane potential. As a result, the resting state of a single unit is no longer a classical fixed point attractor but rather the Milnor attractor, and multiple oscillations appear in the dynamics of a coupled system. In conclusion, the interplay between the up and down states and theta rhythm endows high potential in working memory operation associated with complexity in spontaneous activities.

Kinetics of the interaction of dihydroalprenolol with beta-adrenergic receptors in rat cerebral cortex

Time and temperature dependence of the binding of 3H-dihydroalprenolol (3H-DHA) to beta-adrenergic receptors in rat cerebral cortex is described. The kinetic data obtained suggest that 3H-DHA binding proceeds through a two-step reaction scheme consisting of a bimolecular association step followed by an unimolecular internal conversion of the radioligand receptor complex (isomerisation). Equilibrium thermodynamic analysis provided evidence that the over-all binding process is associated with a small decrease in enthalpy and a substantial increase in entropy. Within the framework of the two-step binding kinetics, the evaluation of the temperature dependence by the van't Hoff analysis resulted in values for thermodynamic parameters for the single equilibrium steps. The data suggest that the association step can be considered as a bimolecular hydrophobic interaction which is mainly entropy-driven due to the release of structural water, while the isomerisation step is accompanied by a large negative change in both enthalpy and entropy. The large negative change in the activation entropy for the forward reaction of the isomerisation step, obtained from evaluation of Arrhenius plots, indicates an internal conversion to a highly ordered receptor-ligand complex, while the low activation energy points to a small threshold energy for reaching this structure. Thus, these result support a previous assumption that the hydrophobic center of an adrenergic antagonist interacts with the receptor by entering a pocket (Cherksey et al. 1981).     

The strategy of ecosystem development: specific dissipation as an indicator of ecosystem maturity

The ratio of entropy generation rate to entropy embodied in structures relatively to the surroundings can be considered as an indicator of the ability of a self-organizing dissipative system to maintain itself far from equilibrium by pumping out entropy. The higher the ratio (which may be called the specific entropy production or the specific dissipation of a system), the lower the capacity of a system to convert the incoming low-entropy energy into internal organization. It appears that the ratio attains special significance for interpreting the evolution of biological systems, as the maximum expression of self-organizing systems, from the sub-cellular to the ecosystem scale. This paper proposes specific dissipation, written as the ratio of biological entropy production to exergy stored in the living biomass, as a thermodynamic orientor as well as an indicator of the development state of ecological systems. After having presented a method for estimating the specific dissipation in lakes, the adequacy of the proposed indicator is discussed and also tested by comparing its response to those of some classical ecological attributes (successional sequences of species, biodiversity, individual body size, structural organization and generation time of organisms) throughout the seasonal progression of the plankton community in Lake Trasimeno (Umbria, Italy). The results support the hypothesis that the minimization of specific dissipation is a primary criterion of evolution of ecological systems and also sustain the use of specific dissipation as an indicator of ecological maturity.