Thermodynamics and kinetics of a molecular motor ensemble

If, contrary to conventional models of muscle, it is assumed that molecular forces equilibrate among rather than within molecular motors, an equation of state and an expression for energy output can be obtained for a near-equilibrium, coworking ensemble of molecular motors. These equations predict clear, testable relationships between motor structure, motor biochemistry, and ensemble motor function, and we discuss these relationships in the context of various experimental studies. In this model, net work by molecular motors is performed with the relaxation of a near-equilibrium intermediate step in a motor-catalyzed reaction. The free energy available for work is localized to this step, and the rate at which this free energy is transferred to work is accelerated by the free energy of a motor-catalyzed reaction. This thermodynamic model implicitly deals with a motile cell system as a dynamic network (not a rigid lattice) of molecular motors within which the mechanochemistry of one motor influences and is influenced by the mechanochemistry of other motors in the ensemble.     

Regulatory functions of allosteric enzymes in far-from-equilibrium systems

A theoretical study is made on catalytic activities of allosteric enzymes in non-equilibrium systems. It is demonstrated that the amount of chemical flow catalyzed by allosteric enzymes in systems maintained far-from-equilibrium can be qualitatively different from that familiar in the near-equilibrium situations. To be more specific, a study is made of a system containing two chemical species, S and P, and an allosteric enzyme, E, which catalyzes the reaction of the interconversion between them. This system interacts with its environment in a way characterized by a set of controlled parameters. By this interaction the system is maintained far-from-equilibrium. More than one steady state is possible for a certain range of controlled parameters. For continuous changes of the controlled parameters, discontinuous transitions between the multiple steady states can occur. This new aspect of the enzyme kinetics of allosteric proteins may play a role in the regulation of metabolic flows within living cells.     

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.     

Artificial neural network based soft estimator for estimation of transducer static nonlinearity

In this work, the development of an Artificial Neural Network (ANN) based soft estimator is reported for the estimation of static-nonlinearity associated with the transducers. Under the realm of ANN based transducer modeling, only two neural models have been suggested to estimate the static-nonlinearity associated with the transducers with quite successful results. The first existing model is based on the concept of a functional link artificial neural network (FLANN) trained with mu-LMS (Least Mean Squares) learning algorithm. The second one is based on the architecture of a single layer linear ANN trained with alpha-LMS learning algorithm. However, both these models suffer from the problem of slow convergence (learning). In order to circumvent this problem, it is proposed to synthesize the direct model of transducers using the concept of a Polynomial-ANN (polynomial artificial neural network) trained with Levenberg-Marquardt (LM) learning algorithm. The proposed Polynomial-ANN oriented transducer model is implemented based on the topology of a single-layer feed-forward back-propagation-ANN. The proposed neural modeling technique provided an extremely fast convergence speed with increased accuracy for the estimation of transducer static nonlinearity. The results of convergence are very stimulating with the LM learning algorithm.     

Energetics of syntrophic propionate oxidation in defined batch and chemostat cocultures

Propionate consumption was studied in syntrophic batch and chemostat cocultures of Syntrophobacter fumaroxidans and Methanospirillum hungatei. The Gibbs free energy available for the H(2)-consuming methanogens was <-20 kJ mol of CH(4)(-1) and thus allowed the synthesis of 1/3 mol of ATP per reaction. The Gibbs free energy available for the propionate oxidizer, on the other hand, was usually >-10 kJ mol of propionate(-1). Nevertheless, the syntrophic coculture grew in the chemostat at steady-state rates of 0.04 to 0. 07 day(-1) and produced maximum biomass yields of 2.6 g mol of propionate(-1) and 7.6 g mol of CH(4)(-1) for S. fumaroxidans and M. hungatei, respectively. The energy efficiency for syntrophic growth of S. fumaroxidans, i.e., the biomass produced per unit of available Gibbs free energy was comparable to a theoretical growth yield of 5 to 12 g mol of ATP(-1). However, a lower growth efficiency was observed when sulfate served as an additional electron acceptor, suggesting inefficient energy conservation in the presence of sulfate. The maintenance Gibbs free energy determined from the maintenance coefficient of syntrophically grown S. fumaroxidans was surprisingly low (0.14 kJ h(-1) mol of biomass C(-1)) compared to the theoretical value. On the other hand, the Gibbs free-energy dissipation per mole of biomass C produced was much higher than expected. We conclude that the small Gibbs free energy available in many methanogenic environments is sufficient for syntrophic propionate oxidizers to survive on a Gibbs free energy that is much lower than that theoretically predicted.     

Functional analysis of Fontan energy dissipation

We formalize the hydrodynamic energy dissipation in the total cavopulmonary connection (TCPC) using dimensional analysis and examine the effect of governing flow variables; namely, cardiac output, flow split, body surface area, Reynolds number, and certain geometric characteristics. A simplistic and clinically useful mathematical model of the dependence of energy dissipation on the governing variables is developed. In vitro energy loss data corresponding to six patients' anatomies validated the predicted dependency of each variable and was used to develop a predictive, semi-empirical energy dissipation model of the TCPC. It is shown that energy dissipation is a cubic function of pulmonary flow split in the physiological range. Furthermore, non-dimensional energy dissipation, which is a measure of resistance of the connection, is dependent on Reynolds number and geometrical factors alone. Non-dimensional energy dissipation decreases with Reynolds number as Re(-0.25) (R(2)>0.95). In addition, for high Reynolds numbers, within physiological exercise limits, dissipation strongly correlates to minimum PA area as a power law decay with an exponent of -5/4 (R(2)>0.88). This study presents a simple analytical form of energy dissipation rate in complex patient-specific TCPCs that accurately captures the effect of cardiac output, flow split, body surface area, Reynolds number, and pulmonary artery size within physiological limits. Further studies with larger sample sizes are necessary for incorporating finer geometrical parameters such as vessel curvatures and offsets.     

Complexing capacity scales and “energy-rich” bonds

Stability constants for equilibria between copper(II) and chelating ligands are analyzed for comparison with equilibria involving “energy-rich” bonds in biochemical reactions. Equilibria between copper(II) and α-aminoacids and between copper(II) and aminoethanols give a consistent explanation of the experimental behavior only if both processes of deprotonation and complexation are considered at the same time. At pH = 7 the free-energy changes are close to the free energy for hydrolysis of ATP to ADP. The same holds for free-energy changes for equilibria between copper(II), proton, and oligopeptides. It is also shown that the free-energy changes for equilibria between nickel(II), proton, and oligopeptides are near the value of the free energy of hydrolysis of glycerol-3-phosphate.     

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.     

Autonomic energy conversion. I. The input relation: phenomenological and mechanistic considerations

The differences between completely and incompletely coupled linear energy converters are discussed using suitable electrochemical cells as examples. The output relation for the canonically simplest class of self-regulated incompletely coupled linear energy converters has been shown to be identical to the Hill force-velocity characteristic for muscle. The corresponding input relation (the “inverse” Hill equation) is now derived by two independent methods. The first method is a direct transformation of the output relation through the phenomenological equations of the converter; Onsager symmetry has no influence on the result. The second method makes use of a model system, a hydroelectric device with a regulator mechanism which depends only on the operational limits of the converter (an electro-osmosis cell operated in reverse) and on the load. The inverse Hill equation is shown to be the simplest solution of the regulator equation. An interesting and testable series of relations between input and output parameters arises from the two forms of the Hill equation. For optimal regulation the input should not be greatly different in the two limiting stationary states (level flow and static head). The output power will then be nearly maximal over a considerable range of load resistance, peak output being obtained at close to peak efficiency.     

Viscous energy dissipation for steady flow in models of arterial bifurcations

In this paper the viscous energy dissipation in a series of glass model symmetric bifurcations—typical of human vascular branching—was studied. The bifurcations studied have included angles of 75°, 100° and 125° and total output/input area ratios of 0.73, 1.07 and 1.33. The flowrate range studied corresponded to parent tube Reynolds numbers in the range 100–1000.Pressure and flow measurements were made using a highly sensitive variable reluctance pressure transducer and electromagnetic flowmeter. The measurements were made in such a way as to indicate the net effect of the bifurcation.It was found that a dimensionless form of the viscous dissipation had a constant value for all the geometries investigated up to a Reynolds number of 800. Above this, for an angle of 125°, the measured energy dissipation increased. An analytical model based on entry flow principles showed good agreement with measured values except at an area ratio of 0.73. The reasons for this are discussed with the physiological implications of the results.     

Calorimetry with heat flux transducers: comparison with a suit calorimeter

Regional and total body heat loss rates of human subjects at rest were measured simultaneously by means of an array of heat flux transducers and with a tube suit calorimeter. Conditions ranged from thermal comfort to strong cooling. A high degree of correlation was found between heat loss rates determined by the two independent techniques. For the head and arms, the transducer array system measured less heat loss than the suit. For the torso and legs, measurements by the two methods were equivalent. For the whole body, the transducer system yielded a heat loss rate 87% of the suit calorimeter value.     

Viscous energy dissipation in a model of the human bronchial tree

The viscous energy dissipation in a two generation model of the human bronchial tree is determined from inspiratory velocity and static pressure data obtained for large Reynolds numbers (10⁴ < Re < 10⁵). This dissipation is found to be an increasing function of both Re and distance downstream from the inlet of the model. The ratio of the dissipation in the model to the energy dissipation in an equivalent straight pipe system is determined. This ratio, Z^*, for the model is compared to values in the literature for lower (laminar) Re. There is more dissipation in the branched model than in a straight pipe (Z^* > 1) and turbulence keeps Z^* at roughly a fixed value for large Reynolds numbers (10⁴ < Re < 10⁵). Z^* values for curved pipes are also compared to the branching system values. It is found that the energy dissipation for the branched model behaves similarly to that in curved pipes.     

Reassessment of Hammett σ as an effective parameter representing intermolecular interaction energy-links between traditional and modern QSAR approaches

The Hammett σ constant has for a long time been known to be one of most important linear free-energy related parameters that correlate with biological activity. It is a conventionally used electronic parameter in studies of enzymatic quantitative structure-activity relationships (QSAR). However, it is not necessarily obvious why σ represents variations in the free-energy change associated with the complex formation between a congeneric series of ligands with their target protein. So far, several powerful molecular calculations, such as the ab initio fragment molecular orbital (FMO) one, that are directly applicable to ligand-protein complexes have emerged. In this study, we comprehensively reevaluate experimentally derived parameter σ confirming it represents intermolecular interaction energy terms, by applying molecular orbital (MO) calculations to a simple ligand-protein complex model. The current results provide a rational and quantitative basis for bridging the gap between the traditional QSAR approach and 'the modern QSAR one', which involves the molecular calculations to evaluate the overall free-energy change for complex formation.     

Thermodynamic Analysis of Energy Transfer in Acidogenic Cultures

A global thermodynamic analysis, normally used for pure cultures, has been performed for steady‐state data sets from acidogenic mixed cultures. This analysis is a combination of two different thermodynamic approaches, based on tabulated standard Gibbs energy of formation, global stoichiometry and medium compositions. It takes into account the energy transfer efficiency, ?, together with the Gibbs free energy dissipation, ΔG_o, analysis of the different data. The objective is to describe these systems thermodynamically without any heat measurement. The results show that ? is influenced by environmental conditions, where increasing hydraulic retention time increases its value all cases. The pH effect on ? is related to metabolic shifts and osmoregulation. Within the environmental conditions analyzed, ? ranges from 0.23 for a hydraulic retention time of 20 h and pH 4, to 0.42 for a hydraulic retention time of 8 h and a pH ranging from 7–8.5. The estimated values of ΔG_o are comparable to standard Gibbs energy of dissipation reported in the literature. For the data sets analyzed, ΔG_o ranges from –1210 kJ/mol_x, corresponding to a stirring velocity of 300 rpm, pH 6 and a hydraulic retention time of 6 h, to –20744 kJ/mol_x for pH 4 and a hydraulic retention time of 20 h. For average conclusions, the combined approach based on standard Gibbs energy of formation and global stoichiometry, used in this thermodynamic analysis, allows for the estimation of Gibbs energy dissipation values from the extracellular medium compositions in acidogenic mixed cultures. Such estimated values are comparable to the standard Gibbs energy dissipation values reported in the literature. It is demonstrated that ? is affected by the environmental conditions, i.e., stirring velocity, hydraulic retention time and pH. However, a relationship that relates this parameter to environmental conditions was not found and will be the focus of further research.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Flow-force relationships for a six-state proton pump model: intrinsic uncoupling, kinetic equivalence of input and output forces, and domain of approximate linearity

General flow-force relations have been determined, by the Hill diagram method, for a six-state proton pump model with and without intrinsic uncoupling (molecular slipping). A computer-aided analysis of the resulting sigmoidal flow-force curves has been performed by using a set of physically meaningful rate constants. It is shown that gating effects and apparent irreversibility can arise from sigmoidicity. The regions of approximate linearity in the vicinity of inflection points, which may be far from equilibrium, have been examined with a view to characterization in terms of linear phenomenological equations, with due regard to the problems of kinetic equivalence of the forces and symmetry. The determination of thermodynamic parameters such as the degree of coupling, the phenomenological stoichiometry, and the efficiency in these regions is discussed, and their meaning is analyzed in relation to the parameters characterizing the Onsager domain close to equilibrium. The application of the phenomenological equations of near-equilibrium nonequilibrium thermodynamics to such regions is at best a simplification to be treated with great caution. A knowledge of the distance from equilibrium of the flow-controlling ranges of the forces (i.e., the ranges of approximate linearity) turns out to be crucial for the interpretation of thermodynamic parameters determined by manipulating one of the forces while the other remains constant, as well as for the interpretation of measurements of force ratios at static head. The latter approaches can give good estimates of the magnitude of the mechanistic stoichiometry and of the constant force if the pumps are highly coupled and are operating not far from equilibrium. The force-flow relationships are shown to be modified by intrinsic uncoupling, reflecting the regulatory influence of the forces on the extent and nature of the slip. Thus reaction slip increases, for example, as the force against which the proton pump operates increases. The possible physiological significance of regulated intrinsic uncoupling is discussed.