Thermodynamics and kinetics of the FoF1-ATPase: application of the probability isotherm

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255-318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667-2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

Perspective - life and death of a photon: an intuitive non-equilibrium thermodynamic distinction between photochemistry and thermochemistry

Neither the thermodynamically determined probability isotherm nor its kinetically manifest rate isotherm can be applied to photo-absorptive reactions such that the participants, including photons, may be treated as if they were chemical reactants. Photons and chemical reactants differ from each other fundamentally: firstly, a photon's energy is absolute and, in all instances of practical relevance to the present paper, independent of its surrounding electrochemical field, while the energy of a chemical reactant is relative and defined by its surrounding field; secondly, while both photons and chemical reactants can and do engage in entropy creation, only chemical reactants can engage in entropy exchange. Clarification of these differences requires identification and abandonment of fundamental historical errors in photochemical thought deriving from inappropriate overreach of analogies drawn between light and ideal gases, and including: treatment of photo-absorption as a reversible chemical reaction; attribution to light of thermal potential, or temperature (as distinct from the idealised abstraction of a 'temperature signature'); attribution to light of exchangeable entropy content. We begin by addressing widespread misapprehensions concerning the perennially misunderstood concept of entropy and the frequently overlooked distinction between entropy creation and entropy exchange. Armed with these clarifications, we arrive at a useful perspective for understanding energy absorption and transfer in photosynthetic processes which, through the chemical 'kidnapping' of metastable excited states within structured metabolic pathways, achieves outcomes which the Second Law denies to thermal chemical reactions.

An Equivocal Final Link - Quantitative Determination of the Thermodynamic Efficiency of ATP Hydrolysis - Sullies the Chain of Electric, Ionic, Mechanical and Metabolic Steps Underlying Cardiac Contraction

Each beat of the heart completes the final step in a sequence of events commencing with electrical excitation-triggered release of Ca2+ from the sarcoplasmic reticulum which, in turn, triggers ATP-hydrolysis-dependent mechanical contraction. Given that Thermodynamics is inherently detail-independent, the heart can be thus be viewed as a mechanical pump - the generator of pressure that drives blood through the systemic and pulmonary circulations. The beat-to-beat pressure-volume work (W) of the heart is relatively straightforward to measure experimentally. Given an ability to measure, simultaneously, the accompanying heat production or oxygen consumption, it is trivial to calculate the mechanical efficiency: ε = W/ΔH where ΔH is the change of enthalpy: (W + Q), Q representing the accompanying production of heat. But it is much less straightforward to measure the thermodynamic efficiency: η = W/ΔG ATP , where ΔG ATP signifies the Gibbs Free Energy of ATP hydrolysis. The difficulty arises because of uncertain quantification of the substrate-dependent yield of ATP - conveniently expressed as the P/O2 ratio. P/O2 ratios, originally ("classically") inferred from thermal studies, have been considerably reduced over the past several decades by re-analysis of the stoichiometric coefficients separating sequential steps in the electron transport system - in particular, dropping the requirement that the coefficients have integer values. Since the early classical values are incompatible with the more recent estimates, we aim to probe this discrepancy with a view to its reconciliation. Our probe consists of a simple, thermodynamically constrained, algebraic model of cardiac mechano-energetics. Our analysis fails to reconcile recent and classical estimates of PO2 ratios; hence, we are left with a conundrum.

Elastic coupling power stroke mechanism of the F1-ATPase molecular motor

The angular velocity profile of the 120° F₁-ATPase power stroke was resolved as a function of temperature from 16.3 to 44.6 °C using a Δμ_ATP = -31.25 k_BT at a time resolution of 10 μs. Angular velocities during the first 60° of the power stroke (phase 1) varied inversely with temperature, resulting in negative activation energies with a parabolic dependence. This is direct evidence that phase 1 rotation derives from elastic energy (spring constant, κ = 50 k_BT·rad^-2). Phase 2 of the power stroke had an enthalpic component indicating that additional energy input occurred to enable the γ-subunit to overcome energy stored by the spring after rotating beyond its 34° equilibrium position. The correlation between the probability distribution of ATP binding to the empty catalytic site and the negative E_a values of the power stroke during phase 1 suggests that this additional energy is derived from the binding of ATP to the empty catalytic site. A second torsion spring (κ = 150 k_BT·rad^-2; equilibrium position, 90°) was also evident that mitigated the enthalpic cost of phase 2 rotation. The maximum ΔG^ǂ was 22.6 k_BT, and maximum efficiency was 72%. An elastic coupling mechanism is proposed that uses the coiled-coil domain of the γ-subunit rotor as a torsion spring during phase 1, and then as a crankshaft driven by ATP-binding-dependent conformational changes during phase 2 to drive the power stroke.

Thermodynamic analysis questions claims of improved cardiac efficiency by dietary fish oil

Studies in the literature describe the ability of dietary supplementation by omega-3 fish oil to increase the pumping efficiency of the left ventricle. Here we attempt to reconcile such studies with our own null results. We undertake a quantitative analysis of the improvement that could be expected theoretically, subject to physiological constraints, by posing the following question: By how much could efficiency be expected to increase if inefficiencies could be eliminated? Our approach utilizes thermodynamic analyses to investigate the contributions, both singly and collectively, of the major components of cardiac energetics to total cardiac efficiency. We conclude that it is unlikely that fish oils could achieve the required diminution of inefficiencies without greatly compromising cardiac performance.

A facilitated diffusion model constrained by the probability isotherm: a pedagogical exercise in intuitive non-equilibrium thermodynamics

This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis-Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis-substrate binding, cis→trans bound enzyme shuttling, trans-substrate dissociation and trans→cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive 'tuning' of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force-flux relations, with only a minority of cases having their quasi-linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme's being thermodynamically 'tuned' to its particular task, dependent on the cis- and trans-substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport.