Thermodynamic stability of ecosystems

The stability of ecosystems during periods of stasis in their macro-evolutionary trajectory is studied from a non-equilibrium thermodynamic perspective. Individuals of the species are considered as units of entropy production and entropy exchange in an open thermodynamic system. Within the framework of the classical theory of irreversible thermodynamics, and under the condition of constant external constraints, such a system will naturally evolve toward a globally stable thermodynamic stationary state. It is thus suggested that the ecological steady state, or stasis, is a particular case of the thermodynamic stationary state, and that the evolution of community stability through natural selection is a manifestation of non-equilibrium thermodynamic directives. Furthermore, it is argued that punctuation of stasis leading to ecosystem succession, may be a manifestation of non-equilibrium "phase transitions" brought on by a change of external constraints through a thermodynamic critical point.     

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.     

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.     

Mathematical modelling of glycolysis and adenine nucleotide metabolism of human erythrocytes. I. Reaction-kinetic statements, analysis of in vivo state and determination of starting conditions for in vitro experiments

A mathematical model of energy metabolism of human red cells is presented, which includes besides the glycolytic reactions the adenine nucleotide metabolism. The model is based on the network of chemical reactions, the thermodynamic equilibrium constants of fast reversible reactions and on the kinetic equations for irreversible enzyme reactions. The model consists of a system of 16 differential equations and allows the mathematical evaluation of metabolic levels in the steady state of energy metabolism corresponding to the in vivo state erythrocytes with the kinetic data for the enzymes derived from in vitro experiments. The dependence of the levels of metabolites in the steady state on the activity of some enzymes is analysed to characterize the regulatory properties of the system. The comparison of the steady state levels of the model with experimental data makes it possible to estimate values of some controversial enzyme parameters. Estimates of the kinetic parameters of the following intracellular processes are presented: 1) rate constant of AMP-phosphatase, 2) maximum rate of adenylate deaminase, 3) activity of adenine phosphoribosylpyrophosphate transferase and 4) adenosine transport through the cell membrane. The simulation of the preparatory phase before incubation of erythrocytes indicates, that the model also permits to compute the time course of changes of levels of metabolites. To solve the initial problem the stiff differential equation system is integrated numerically by an efficient program without the application of the quasi-steady-state approximation.     

A prediction of mRNA hybridization kinetics based on polypeptide abundances

An oscillating chemical reaction dealt with in this paper is the Brusselator, which is capable of generating a limit cycle oscillation beyond instability point. The rate equations of this reaction scheme are solved by two-time scale method. An evolution criterion is derived for the limit cycle to first order approximation. The time average of entropy change over the period of the limit cycle takes a definite negative value, which is dependent not on the initial conditions but on the external parameters bringing the kinetic behaviour of the system under control. It can be expressed as the product of two quantities. The first, which is kinetic in character, is the areal velocity of the limit cycle. The second, which is thermodynamic in character, is the rotation of anti-symmetric flow with respect to thermodynamic force. It is shown that the latter is equivalent to the irreversible circulation of fluctuation.     

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.     

Mass balance and thermodynamic description of solid state fermentation of lignocellulosics byPleurotus ostreatus for animal feed production

This study was focused primarily on the degradation of lignin in water hyacinth and barley straw for animal-feed production. The experiment was performed in a 1.5-L Applikon fermenter for 30 days, varying the air flow rate from 0.022 VVM/0.047 VMM to 0.048 VVM/0.102 VMM. A novel approach was introduced for prediction of a kinetic model by using instantaneous respiratory quotient (RQ) measurements and steady state elemental balances. Growth kinetics were determined for the fungus in a 30-day fermentation with a mixture of barley straw and water hyacinth as the substrate. The instantaneous heat-interaction profile was predicted from steady state balances. Fermentation data were checked for consistency using the entropy balance inequality, and thermodynamic efficiency was calculated to show that degradation of lignocellulosics byPleurotus ostreatus followed more than one metabolic pathway during the course of the fermentation. Growth ofP. ostreatus on lignocellulosics, such as water hyacinth and barley straw, was di-auxic or possibly tri-auxic during the 30 days of fermentation.     

Thermodynamics of Random Reaction Networks

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.     

Far from equilibrium synthesis of small polymer chains and chemical evolution

Summary A number of simple models for the synthesis of small polymers are considered. The role of autocatalysis and primitive template processes is examined. It is shown that far from equilibrium such systems may exhibit multiple steady state or sigmoidal transitions, favouring the enhancement of the (oligomer/monomer) ratio in the medium. A thermodynamic analysis in the non-linear range shows that the molar entropy production passes through a maximum when the system undergoes the non-equilibrium transition. The results are discussed in connection with the problems of prebiotic synthesis and developmental biology.     

Kinetic analysis of the transient phase and steady state of open multicyclic enzyme cascades

This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.     

Specific features in realization of the principle of minimum energy dissipation during individual development

Realization of the principle of minimum energy dissipation (Prigogine??s theorem) during individual development has been analyzed. This analysis has suggested the following reformulation of this principle for living objects: when environmental conditions are constant, the living system evolves to a current steady state in such a way that the difference between entropy production and entropy flow (?? _u function) is positive and constantly decreases near the steady state, approaching zero. In turn, the current steady state tends to a final steady state in such a way that the difference between the specific entropy productions in an organism and its environment tends to be minimal. In general, individual development completely agrees with the law of entropy increase (second law of thermodynamics).     

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism

The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.     

Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations

The steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network. A detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions. The characteristics of the dissipative structures are discussed and it is shown that the observed behavior depends strongly on both the boundary and initial conditions. The theoretical expressions are limited to the neighborhood of the marginal stability point. Computer simulations allow not only the verification of their predictions but also the investigation of the behavior of the system for larger deviations from the instability point. It is shown that new features such as multiplicity of solutions and secondary bifurcations can appear in this region.     

The steady state kinetics of some biological systems: III. Thermodynamic aspects

Some thermodynamic aspects of steady systems are considered. The time rates of changes, “flux”, of various thermodynamic quantities are formulated. In particular the free energy flux in the steady state, the difference between the free energy flux in the steady and time dependent states and the change in free energy flux upon transition between steady states are discussed. Equations are derived which exhibit the formal similarities and differences between the free energy flux and the conventional free energy change. The temperature dependence of the steady state rate is examined and conditions for “mastery” by a single step discussed. A brief discussion of the role ofrate in the coupling of exergonic and endergonic reactions is given.     

Increased entropy production in diaphragm muscle of PPAR alpha knockout mice

Peroxisome proliferator activated receptor alpha (PPAR alpha) regulates fatty acid beta-oxidation (FAO) and plays a central role in the metabolic and energetic homeostasis of striated muscles. The thermodynamic consequences of the absence of PPAR alpha were investigated in diaphragm muscle of PPAR alpha knockout mice (KO). Statistical mechanics provides a powerful tool for determining entropy production, which quantifies irreversible chemical processes generated by myosin molecular motors and which is the product of thermodynamic force A/T (chemical affinity A and temperature T) and thermodynamic flow (myosin crossbridge (CB) cycle velocity upsilon). The behavior of both wild type (WT) and KO diaphragm was shown to be near-equilibrium and in a stationary state, but KO was farther from equilibrium than WT. In KO diaphragm, a substantial decrease in contractile function was associated with an increase in both A/T and upsilon and with profound histological injuries such as contraction band necrosis. There were no changes in PPAR delta and gamma expression levels or myosin heavy chain (MHC) patterns. In KO diaphragm, a marked increase in entropy production (A/T x upsilon) accounted for major thermodynamic dysfunction and a dramatic increase in irreversible chemical processes during the myosin CB cycle.     

Kinetics of a model of autocatalysis, coupling of a reaction in which the enzyme acts on one of its substrates.

A global kinetic analysis is presented of a model of an enzyme autocatalytic process, to which a reaction is coupled, in which the enzyme acts upon one of its substrates. The kinetic equations of both the transient phase and the steady state are derived for this mechanism. In addition, we determine the corresponding kinetic equations for several particular cases which are characterized by certain relations between the rate constants. Finally, a kinetic data analysis is proposed for one of these particular cases. It can easily be extended to any of the other cases.     

Transient kinetics of thermodynamic buffering

The transient response of mitochondrial ATP production towards perturbations was studied by analyzing the trajectories leading from arbitrary initial conditions of the adenine nucleotide pool to the final steady state. These trajectories were calculated from differential equations based on linear relations between flows and thermodynamic forces of the adenylate kinase system including oxidative phosphorylation. The motion of the system along the trajectories consists of two phases: (1) a rapid phase leading from initial states to a common relaxation curve; and (2) a slow phase leading along the relaxation curve to the final steady state. The first phase corresponds to a motion close to the loci of constant adenylic energy charge. In line with this observation is the finding that the energy charge is a constant of motion of the adenylate kinase reaction. The second phase corresponds to a motion along a relaxation curve characterized by minimal Lyapunov exponents in the concentration space of the adenine nucleotides. Thus, both phases of the transient kinetics can be approximated in terms of thermodynamic functions to a high degree of precision. Incubations with isolated rat liver mitochondria were in excellent agreement with the theoretical predictions. In summary, these studies show that the adenylate kinase system not only optimizes the efficiency of oxidative phosphorylation through thermodynamic buffering but, in addition, also deeply influences the transient response of the whole system.     

Oscillatory isozymes as the simplest model for coupled biochemical oscillators

We analyze a simple model for two autocatalytic reactions catalyzed by two distinct isozymes transforming, with different kinetic properties, a given substrate into the same product. This two-variable system can be viewed as the simplest model of chemically coupled biochemical oscillators. Phase-plane analysis indicates how the kinetic differences between the two enzymes give rise to complex oscillatory phenomena such as the coexistence of a stable steady state and a stable limit cycle, or the co-existence of two simultaneously stable oscillatory regimes (birhythmicity). The model allows one to verify a previously proposed conjecture for the origin of birhythmicity. In other conditions, the system admits multiple oscillatory domains as a function of a control parameter whose variation gives rise to markedly different types of oscillations. The latter behavior provides an explanation for the occurrence of multiple modes of oscillations in thalamic neurons.     

Thermodynamic analysis of protein interactions with biosensor technology

A methodology using biosensor technology for combined kinetic and thermodynamic analysis of biomolecular interactions is described. Rate and affinity constants are determined with BIAcore. Thermodynamics parameters, changes in free energy, enthalpy and entropy, are evaluated from equilibrium data and by using rate constants and transition state theory. The methodology using van't Hoff theory gives complementary information to microcalorimetry, since only the direct binding is measured with BIAcore whereas microcalorimetry measures all components, including e.g. hydration effects. Furthermore, BIAcore gives possibilities to gain new information by thermodynamic analysis of the rate constants.