Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page

Generally covariant state-dependent diffusion

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously defined. They typically do not relax to equilibrium steady states even in the absence of extenal forces. Assuming both coordinate covariance and gauge invariance, we derive a second-order Langevin equation with state-dependent diffusion matrix and vanishing environmental forces. It differs from previous proposals but nevertheless entails the Einstein relation, a Maxwellian conditional steady state for the velocities, and the equipartition theorem. The over-damping limit leads to a stochastic differential equation in state space that cannot be interpreted as a pure differential (Ito, Stratonovich or else). At odds with the latter interpretations, the corresponding Fokker-Planck equation admits an equilibrium steady state; a detailed comparison with other theories of state-dependent diffusion is carried out. We propose this as a theory of diffusion in a heat bath with varying temperature. Besides equilibrium, a crucial experimental signature is the non-uniform steady spatial distribution.Comment: 24 page

Nonequilibrium thermodynamics as a gauge theory

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been amende

Fluctuation relations for a few observable currents at their own beat

Coarse-grained models are widely used to explain the effective behavior of partially observable physical systems with hidden degrees of freedom. Reduction procedures in state space typically disrupt Markovianity and a fluctuation relation cannot be formulated. A recently developed framework of transition-based coarse-graining gave rise to a fluctuation relation for a single current, while all others are hidden. Here, we extend the treatment to an arbitrary number of observable currents. Crucial for the derivation are the concepts of mixed currents and their conjugated effective affinities, that can be inferred from the time series of observable transitions. We also discuss the connection to generating functions, transient behavior, and how our result recovers the fluctuation relation for a complete set of currents.Comment: 36 pages, 11 figure

Brownian Carnot engine

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of microscopic Carnot engines is still lacking. Here we report on an experimental realization of a Carnot engine with a single optically trapped Brownian particle as working substance. We present an exhaustive study of the energetics of the engine and analyze the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency -an insight that could inspire novel strategies in the design of efficient nano-motors.Comment: 7 pages, 7 figure

Spontaneous renal artery dissection diagnosed by unenhanced magnetic resonance angiography: case report

A 47-year-old patient is presented who was admitted to the emergency department with complaints of right-sided flank pain and hypertension. His creatinine and glomerular filtration rate were 2.5 mg/dl and 37 ml/min respectively, so that contrast media administration was contraindicated. The unenhanced magnetic resonance angiography image obtained with 3D in-flow inversion recovery sequence showed right renal artery dissection, without aortic dissection. Selective renal angiography confirmed the diagnosis and a stent was placed in the renal artery. The patient was free of pain after stenting, with normalized laboratory values and blood pressure. Copyright © 2012 S. Karger AG, Basel

Laboratory study on the mobility of major species in fly ash–brine co-disposal systems: up-flow percolation test

Apart from the generation of fly ash, brine (hyper-saline wastewater) is also a waste material generated in South African power stations as a result of water re-use. These waste materials contain major species such as Al, Si, Na, K, Ca, Mg, Cl and SO4. The co-disposal of fly ash and brine has been practiced by some power stations in South Africa with the aim of utilizing the fly ash to capture the salts in brine. The effect of the chemical interaction of the species contained in both fly ash and brine, when co-disposed, on the mobility of species in the fly ash–brine systems is the focus of this study. The up-flow percolation test was employed to determine the mobility of some major species in the fly ash–brine systems. The results of the analysed eluates from the up-flow percolation tests revealed that some species such as Al, Ca and Na were leached from the fly ash into the brine solution while some species such as Mg, Cl and SO4 were removed to some extent from the brine solution during the interaction with fly ash. The pH of the up-flow percolation systems was observed to play a significant role on the mobility of major species from the fly ash–brine systems. The study showed that some major species such as Mg, Cl and SO4 could be removed from brine solution using fly ash when certain amount of brine percolates through the ash.Web of Scienc

68Ga-PSMA PET/CT in recurrent prostate cancer after radical prostatectomy using PSMA-RADS version 2.0

Background: 68Ga-PSMA PET/CT is superior to standard-of-care imaging for detecting regional and distant metastatic recurrent prostate cancer. The objective of our study was to evaluate the performance of 68Ga-PSMAPET/CT in our patient population, using the new PSMA-RADS version 2.0. Methods: A total of 128 patients scanned with 68Ga-PSMA PET/CT for detection of recurrence after RP were analyzed with PSMA-RADS version 2.0. For the analysis of the detection rate, categories PSMA-RADS 3 to 5 were considered as “positive for malignancy” and 1–2 as “negative”. Results: According to PSMA-RADS v2.0, we classified patients as follows: 23 patients without PSMA-RADS because they were negative; PSMA-RADS 1: 10 patients; PSMA-RADS 2: 4 patients; PSMA-RADS 3A: 11 patients; PSMA-RADS 3B: 2 patients; PSMA-RADS 3C: 2 patients; PSMA-RADS 3D: 2 patients; PSMA-RADS 4: 13 patients; PSMA-RADS 5: 61 patients. Conclusions: The overall detection rate of 68Ga-PSMA PET/CT was 71%. By dividing the patients into fourgroups according to PSA level before examination, we obtained the following detection rates: PSA < 0.2 ng/mL 38%; 0.2 ≤ PSA < 0.5 ng/mL 57%; 0.5 ≤ PSA ≤ 1 ng/mL 77%; and PSA > 1 ng/mL 95%. Conclusion: Using PSMA-RADS version 2.0, we obtained detection rate values comparable with recent literature both in absolute terms and in relation to different PSA levels

Imaging for acute pelvic pain in pregnancy

Acute pelvic pain in pregnancy presents diagnostic and therapeutic challenges. Standard imaging techniques need to be adapted to reduce harm to the foetus from X-rays because of their teratogenic and carcinogenic potential. Ultrasound remains the primary imaging investigation of the pregnant abdomen. Magnetic resonance imaging (MRI) has been shown to be useful in the diagnosis of gynaecological and obstetric problems during pregnancy and in the setting of acute abdomen during pregnancy. MRI overcomes some of the limitations of ultrasound, mainly the size of the gravid uterus. MRI poses theoretical risks to the foetus and care must be taken to minimise these with the avoidance of contrast agents. Teaching Points • Ultrasound and MRI are the preferred investigations for acute pelvic pain during pregnancy. • Ultrasound remains the primary imaging investigation because of availability and portability. • MRI helps differentiate causes of acute pelvic pain when ultrasound is inconclusive

Coplanarity of rooted spanning-tree vectors

Employing a recent technology of tree surgery we prove a ``deletion-constriction\u27\u27 formula for products of rooted spanning trees on weighted directed graphs that generalizes deletion-contraction on undirected graphs. The formula implies that, letting $τ_x^\varnothing$, $τ_x^+$, and $τ_x^-$ be the rooted spanning tree polynomials obtained respectively by removing an edge in both directions or by forcing the tree to pass through either direction of that edge, the vectors $(τ_x^\varnothing, τ_x^+, τ_x^-)$ are coplanar for all roots $x$. We deploy the result to give an alternative derivation of a recently found mutual linearity of stationary currents of Markov chains. We generalize deletion-constriction and current linearity among two edges, and conjecture that similar results may hold for arbitrary subsets of edges.21 pages, 3 figure