Stochastic thermodynamics of chemical reaction networks

For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations like a generalized Jarzynski relation and a generalized Clausius inequality are discussed. We illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.Comment: 14 pages, 2 figures, accepted for publication in J. Chem. Phy

Idiopathic Recurrent Calcium Urolithiasis (IRCU): variation of fasting urinary protein is a window to pathophysiology or simple consequence of renal stones in situ? A tripartite study in male patients providing insight into oxidative metabolism as possible driving force towards alteration of urine composition, calcium salt crystallization and stone formation*

<p>Abstract</p> <p>Background</p> <p>In IRCU it is uncertain whether variation of urinary protein, especially non-albumin protein (NAlb-P), is due to the presence of stones or reflects alteration of oxidative metabolism.</p> <p>Aims</p> <p>To validate in a tripartite cross-sectional study of 187 ambulatory male patients, undergoing a standardized laboratory programme, whether stones impact on N-Alb-P or the state of oxidative metabolism interferes with IRCU pathophysiology.</p> <p>Methods</p> <p>In part 1 the strata low and high of fasting urinary excretion rate per 2 h of N-Alb-P, malonedialdehyde, hypoxanthine, xanthine, pH and other urine components were compared, and association with renal stones in situ evaluated; in part 2 the co-variation of oxidatively modulated environment, fasting urinary pH, calcium (Ca) salt crystallization risk and the number of patients with stones in situ was examined; in part 3, the nucleation of Ca oxalate and Ca phosphate was tested in undiluted postprandial urine of patients and related to the state of oxidative metabolism.</p> <p>Results</p> <p>In part 1, N-Alb-P excretion > 4.3 mg was associated with increase of blood pressure, excretion of total protein, hypoxanthine (a marker of tissue hypoxia), malonedialdehyde (a marker of lipid peroxidation), sodium, magnesium, citrate, uric acid, volume, pH, and increase of renal fractional excretion of both NAlb-P and uric acid; when stones were present, urinary pH was elevated but other parameters were unaffected. Significant predictors of N-Alb-P excretion were malonedialdehyde, fractional N-Alb-P and hypoxanthine. In part 2, urine pH > 6.14 was associated with unchanged blood pressure and plasma vasopressin, increase of blood pH, urinary volume, malonedialde hyde, fractional excretion of N-Alb-P, uric acid, Ca phosphate, but not Ca oxalate, supersaturation; this spectrum was accompanied by decrease of concentration of urinary total and free magnesium, total and complexed citrate, plasma uric acid (in humans the major circulating antioxidant) and insulin; the number of stone-bearing patients was increased. Significant predictors of urine pH were body mass index, plasma insulin and uric acid (negative), and urinary xanthine (positive). In part 3 low plasma uric acid, not high urinary malonedialdehyde or high ratio malonedialdehyde/uric acid was significantly associated with diminished Ca but not oxalate tolerance, with the first nucleating crystal type being mostly Ca phosphate (hydroxyapatite), in the rest Ca oxalate dihydrate; uricemia correlated marginally positively (p = 0.055) with Ca tolerance of urine, stronger with blood pressure and insulin, and negatively with urinary xanthine, fractional N-Alb-P, volume, sodium.</p> <p>Conclusions</p> <p>In IRCU 1) not renal stones in situ, but disturbed oxidative metabolism apparently modulates nephron functionality, ending up in higher renal NAlb-P release, urinary volume, sodium and pH of fasting urine; 2) etiologically unknown decline of uricemia may represent antioxidant deficiency and cause a risk of hydroxyapatite crystallization and stone formation in a weakly acidic or alkaline inhibitor-deficient and NAlb-P-rich milieu; 3) several observations, linking oxidative and systemic metabolism, are compatible with Ca stone initiation beyond tubules.</p

Magnon-driven quantum-dot heat engine

We investigate a heat- to charge-current converter consisting of a single-level quantum dot coupled to two ferromagnetic metals and one ferromagnetic insulator held at different temperatures. We demonstrate that this nano engine can act as an optimal heat to spin-polarized charge current converter in an antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel case. We discuss the maximal output power of the device and its efficiency.Comment: 6 pages, 4 figures, published version, selected as Editor's choic

Glacial-interglacial changes in bottom-water oxygen content on the Portuguese margin

During the last and penultimate glacial maxima, atmospheric CO2 concentrations were lower than present, possibly in part because of increased storage of respired carbon in the deep oceans. The amount of respired carbon present in a water mass can be calculated from its oxygen content through apparent oxygen utilization; the oxygen content can in turn be calculated from the carbon isotope gradient within the sediment column. Here we analyse the shells of benthic foraminifera occurring at the sediment surface and the oxic/anoxic interface on the Portuguese Margin to reconstruct the carbon isotope gradient and hence bottom-water oxygenation over the past 150,000 years. We find that bottom-water oxygen concentrations were 45 and 65 μmol kg−1 lower than present during the last and penultimate glacial maxima, respectively. We calculate that concentrations of remineralized organic carbon were at least twice as high as today during the glacial maxima. We attribute these changes to decreased ventilation linked to a reorganization of ocean circulation and a strengthened global biological pump. If the respired carbon pool was of a similar size throughout the entire glacial deep Atlantic basin, then this sink could account for 15 and 20 per cent of the glacial PCO2 drawdown during the last and penultimate glacial maxima

Prior-predictive value from fast growth simulations

Building on a variant of the Jarzynski equation we propose a new method to numerically determine the prior-predictive value in a Bayesian inference problem. The method generalizes thermodynamic integration and is not hampered by equilibration problems. We demonstrate its operation by applying it to two simple examples and elucidate its performance. In the case of multi-modal posterior distributions the performance is superior to thermodynamic integration.Comment: 8 pages, 11 figure

Engineered swift equilibration of a Brownian particle

A fundamental and intrinsic property of any device or natural system is its relaxation time relax, which is the time it takes to return to equilibrium after the sudden change of a control parameter [1]. Reducing $tau$ relax , is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on driving have been recently demonstrated [2, 3], for isolated quantum and classical systems [4--9]. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol,named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro and nano devices, where the reduction of operation time represents as substantial a challenge as miniaturization [10]. The concepts of equilibrium and of transformations from an equilibrium state to another, are cornerstones of thermodynamics. A textbook illustration is provided by the expansion of a gas, starting at equilibrium and expanding to reach a new equilibrium in a larger vessel. This operation can be performed either very slowly by a piston, without dissipating energy into the environment, or alternatively quickly, letting the piston freely move to reach the new volume

Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions

We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven with a constant rate. The time evolution of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the performed work during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility.Comment: 21 pages, 7 figure

Idiopathic recurrent calcium urolithiasis (IRCU): pathophysiology evaluated in light of oxidative metabolism, without and with variation of several biomarkers in fasting urine and plasma - a comparison of stone-free and -bearing male patients, emphasizing mineral, acid-base, blood pressure and protein status

<p>Abstract</p> <p>Background</p> <p>IRCU is traditionally considered as lifestyle disease (associations with, among others, overweight, obesity, hypertension, type-2 diabetes), arising from excess, in 24 h urine, of calcium (Ca) salts (calcium oxalate (CaOx), calcium phosphate (CaPi)), supersaturation of, and crystallization in, tubular fluid and urine, causing crystal-induced epithelial cell damage, proteinuria, crystal aggregation and uroliths.</p> <p>Methods</p> <p>Another picture emerges from the present uncontrolled study of 154 male adult IRCU patients (75 stone-bearing (SB) and 79 age-matched stone-free (SF)), in whom stone-forming and other parameters in fasting urine and plasma were contrasted with five biomarkers (see footnote) of oxidative metabolism (OM), without and with variation of markers.</p> <p>Results</p> <p>1) In SB vs. SF unstratified OM biomarkers were statistically unchanged, but the majority of patients was overweight; despite, in SB vs. SF urine pH, total and non-albumin protein concentration were elevated, fractional urinary uric acid excretion and blood bicarbonate decreased, whereas urine volume, sodium, supersaturation with CaOx and CaPi (as hydroxyapatite) were unchanged; 2) upon variation of OM markers (strata below and above median) numerous stone parameters differed significant!)', among others urine volume, total protein, Ca/Pi ratio, pH, sodium, potassium, plasma Ca/Pi ratio and parathyroid hormone, blood pressure, renal excretion of non-albumin protein and other substances; 3) a significant shift from SF to SB patients occurred with increase of urine pH, decrease of blood bicarbonate, and increase of diastolic blood pressure, whereas increase of plasma uric acid impacted only marginally; 4) in both SF and SB patients a strong curvilinear relationship links a rise of urine Ca/Pi to urine Ca/Pi divided by plasma Ca/Pi, but in SB urine Ca/Pi failed to correlate significantly with urine hydroxyapatite supersaturation; 5) also in SB, plasma Ca/Pi and urinary nitrate were negatively correlated, whereas in SF plasma Ca/Pi ratio, PTH and body mass index correlated positively; 6) multivariate regression analysis revealed that PTH, body mass index and nitrate together could explain 22 (p = 0.002) and only 7 (p = 0.06) per cent of variation of plasma Ca/Pi in SF and SB, respectively</p> <p>Conclusions</p> <p>In IRCU a) numerous constituents of fasting urine, plasma, blood and blood pressure change in response to variation of OM biomarkers, suggesting involvement of OM imbalance as factor in functional deterioration of tissue; b) in the majority of patients a positive exponential relationship links urine Ca/Pi to urine Ca/Pi divided by plasma Ca/Pi, presumably to accumulate Ca outside tubular lumen, thereby minimizing intratubular and urinary Ca salt crystallization; c) alteration of interactions of low urine nitrate, PTH and Ca/Pi in plasma may be of importance in formation of new Ca stone and co-regulation of dynamics of blood vasculature; d) overweight, combined with OM-modified renal interstitial environment appears to facilitate these processes, carrying the risk that CaPi mineral develops within or/and close to blood vessel tissue, and spreads towards urothelium.</p> <p>For future research focussing on IRCU pathogenesis studies are recommended on the role of affluent lifestyle mediated renal ischemia, mild hypertensive nephropathy, rise of uric acid precursor oxypurines and uricemia, clarifying also why loss of significance of interrelationships of OM biomarkers with traditional Ca stone risk factors is characteristic for SB patients.</p> <p>OM biomarkers</p> <p>Plasma uric acid - Discussed as scavenger of reactive oxygen species, but also as donator (via the xanthine oxido-reductase reaction)</p> <p>Urinary malonedialdehydc - Accepted as indicator of peroxidation of lipids within biological cell membranes</p> <p>Urinaiy nitrate - Accepted as indicator of vasodilation-mediating nitric oxide production by blood vessel endothelium</p> <p>Urinary malonedialdehyde/Plasma uric acid - Tentative markers of oxidant/antioxidant imbalance</p> <p>Urinary nitrate/Plasma uric acid - Tentative markers of oxidant/antioxidant imbalance</p

A minimal model of an autonomous thermal motor

We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a non- vanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the B\"uttiker-Landauer model [1-3] for a single particle diffusing in an environment with position dependent temperature. By using numerical calculations of the Fokker-Planck equation and simulations of the Langevin equations we study the model for arbitrary coupling, retrieving many features of the strong coupling limit. In particular, directed transport emerges even for symmetric potentials. For distinct heat reservoirs the heat currents are well-defined quantities allowing a study of the motor efficiency. We show that the optimal working regime occurs for moderate coupling. Finally, we introduce a model with discrete phase space which captures the essential features of the continuous model, can be solved in the limit of weak coupling, and exhibits a larger efficiency than the continuous counterpart.Comment: Revised version. Extended discussion on the discrete model. To appear in EP

Efficiency of Free Energy Transduction in Autonomous Systems

We consider the thermodynamics of chemical coupling from the viewpoint of free energy transduction efficiency. In contrast to an external parameter-driven stochastic energetics setup, the dynamic change of the equilibrium distribution induced by chemical coupling, adopted, for example, in biological systems, is inevitably an autonomous process. We found that the efficiency is bounded by the ratio between the non-symmetric and the symmetrized Kullback-Leibler distance, which is significantly lower than unity. Consequences of this low efficiency are demonstrated in the simple two-state case, which serves as an important minimal model for studying the energetics of biomolecules.Comment: 4 pages, 4 figure