Thermodynamically consistent model calibration in chemical kinetics

<p>Abstract</p> <p>Background</p> <p>The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function.</p> <p>Results</p> <p>We introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an <it>open </it>biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from <url>http://www.cis.jhu.edu/~goutsias/CSS lab/software.html</url>. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database.</p> <p>Conclusions</p> <p>TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting.</p

The Influence of Thermal Pressure on Equilibrium Models of Hypermassive Neutron Star Merger Remnants

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state, angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (~5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically-symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear equations of state, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parametrized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.Comment: 20 pages, 12 figures. Accepted for publication in Ap

From hadrons to quarks in neutron stars: a review

We review the equation of state of matter in neutron stars from the solid crust through the liquid nuclear matter interior to the quark regime at higher densities. We focus in detail on the question of how quark matter appears in neutron stars, and how it affects the equation of state. After discussing the crust and liquid nuclear matter in the core we briefly review aspects of microscopic quark physics relevant to neutron stars, and quark models of dense matter based on the Nambu--Jona-Lasinio framework, in which gluonic processes are replaced by effective quark interactions. We turn then to describing equations of state useful for interpretation of both electromagnetic and gravitational observations, reviewing the emerging picture of hadron-quark continuity in which hadronic matter turns relatively smoothly, with at most only a weak first order transition, into quark matter with increasing density. We review construction of unified equations of state that interpolate between the reasonably well understood nuclear matter regime at low densities and the quark matter regime at higher densities. The utility of such interpolations is driven by the present inability to calculate the dense matter equation of state in QCD from first principles. As we review, the parameters of effective quark models -- which have direct relevance to the more general structure of the QCD phase diagram of dense and hot matter -- are constrained by neutron star mass and radii measurements, in particular favoring large repulsive density-density and attractive diquark pairing interactions. We describe the structure of neutron stars constructed from the unified equations of states with crossover. Lastly we present the current equations of state -- called "QHC18" for quark-hadron crossover -- in a parametrized form practical for neutron star modeling.Comment: v2, 42 pages, 36 figures, 3 tables; to be published in Reports on Progress in Physics; new sections for cooling, X-ray analyses, and gravitational waves are added; the results for tidal deformability are included; equations of state and the numerical tables are updated; v3, typos corrected in eq.

Effective fluctuation and response theory

The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond equilibrium. All these results rely on the crucial assumption that the observer has complete information about the system. Such a precise control is difficult to attain, hence the following questions are compelling: Will an observer who has marginal information be able to perform an effective thermodynamic analysis? Given that such observer will only establish local equilibrium amidst the whirling of hidden degrees of freedom, by perturbing the stalling currents will he/she observe equilibrium-like fluctuations? We model the dynamics of open systems as Markov jump processes on finite networks. We establish that: 1) While marginal currents do not obey a full-fledged fluctuation relation, there exist effective affinities for which an integral fluctuation relation holds; 2) Under reasonable assumptions on the parametrization of the rates, effective and "real" affinities only differ by a constant; 3) At stalling, i.e. where the marginal currents vanish, a symmetrized fluctuation-dissipation relation holds while reciprocity does not; 4) There exists a notion of marginal time-reversal that plays a role akin to that played by time-reversal for complete systems, which restores the fluctuation relation and reciprocity. The above results hold for configuration-space currents, and for phenomenological currents provided that certain symmetries of the effective affinities are respected - a condition whose range of validity we deem the most interesting question left open to future inquiry. Our results are constructive and operational: we provide an explicit expression for the effective affinities and propose a procedure to measure them in laboratory.Comment: 41 pages. Comments are welcome

Ocean ensemble forecasting. Part I: Ensemble Mediterranean winds from a Bayesian hierarchical model

A Bayesian hierarchical model (BHM) is developed to estimate surface vector wind (SVW) fields and associated uncertainties over the Mediterranean Sea. The BHM–SVW incorporates data-stage inputs from analyses and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) and SVW retrievals from the QuikSCAT data record. The process-model stage of the BHM–SVW is based on a Rayleigh friction equation model for surface winds. Dynamical interpretations of posterior distributions of the BHM–SVW parameters are discussed. Ten realizations from the posterior distribution of the BHM–SVW are used to force the data-assimilation step of an experimental ensemble ocean forecast system for the Mediterranean Sea in order to create a set of ensemble initial conditions. The sequential data-assimilation method of the Mediterranean forecast system (MFS) is adapted to the ensemble implementation. Analyses of sample ensemble initial conditions for a single data-assimilation period in MFS are presented to demonstrate the multivariate impact of the BHM–SVW ensemble generation methodology. Ensemble initial-condition spread is quantified by computing standard deviations of ocean state variable fields over the ten ensemble members. The methodological findings in this article are of two kinds. From the perspective of statistical modelling, the process-model development is more closely related tophysicalbalances than inpreviousworkwithmodels for the SVW.Fromthe ocean forecast perspective, the generation of ocean ensemble initial conditions via BHM is shown to be practical for operational implementation in an ensemble ocean forecast system. Phenomenologically, ensemble spread generated via BHM–SVW occurs on ocean mesoscale time- and space-scales, in close association with strong synoptic-scale wind-forcing events. A companion article describes the impacts of the BHM–SVW ensemble method on the ocean forecast in comparisons with more traditional ensemble methods

A theoretical and computational study of the mechanics of biomembranes at multiple scales

Lipid membranes are thin objects that form the main separation structure in cells. They have remarkable mechanical properties; while behaving as a solid shell against bending, they exhibit in-plane fluidity. These two aspects of their mechanics are not only interesting from a physical viewpoint, but also fundamental for their biological function. Indeed, the equilibrium shapes of different organelles in the cell rely on the bending elasticity of lipid membranes. On the other hand, the in-plane fluidity of the membrane is essential in functions such as cell motility, mechano-adaptation, or for the lateral diffusion of proteins and other membrane inclusions. The bending rigidity of membranes can be motivated from microscopic models that account for the stress distribution across the membrane thickness. In particular, the microscopic stress across the membrane is routinely computed from molecular dynamics simulations to investigate how different microscopic features, such as the addition of anesthetics or cholesterol, affect their effective mechanical response. The microscopic stress bridges the gap between the statistical mechanics of a set of point particles, the atoms in a molecular dynamics simulation, and continuum mechanics models. However, we lack an unambiguous definition of the microscopic stress, and different definitions of the microscopic stress suggest different connections between molecular and continuum models. In the first Part of this Thesis, we show that many of the existing definitions of the microscopic stress do not satisfy the most basic balance laws of continuum mechanics, and thus are not physically meaningful. This striking issue has motivated us to propose a new definition of the microscopic stress that complies with these fundamental balance laws. Furthermore, we provide a freely available implementation of our stress definition that can be computed from molecular dynamics simulations (mdstress.org). Our definition of the stress along with our implementation provides a foundation for a meaningful analysis of molecular dynamics simulations from a continuum viewpoint. In addition to lipid membranes, we show the application of our methodology to other important systems, such as defective crystals or fibrous proteins. In the second part of the Thesis, we focus on the continuum modeling of lipid membranes. Because these membranes are continuously brought out-of-equilibrium by biological activity, it is important to go beyond curvature elasticity and describe the internal mechanisms associated with bilayer fluidity. We develop a three-dimensional and non-linear theory and a simulation methodology for the mechanics of lipid membranes, which have been lacking in the field. We base our approach on a general framework for the mechanics of dissipative systems, Onsager's variational principle, and on a careful formulation of the kinematics and balance principles for fluid surfaces. For the simulation of our models, we follow a finite element approach that, however, requires of unconventional dicretization methods due to the non-linear coupling between shape changes and tangent flows on fluid surfaces. Our formulation provides the basis for further investigations of the out-of-equilibrium chemo-mechanics of lipid membranes and other fluid surfaces, such as the cell cortex.Las membranas lipídicas son estructuras delgadas que forman la separación fundamental de las células. Tienen propiedades físicas notables: mientras que se comportan como láminas delgadas sólidas frente a curvatura, presentan fluidez interfacial. Estos dos aspectos de su mecánica son interesantes desde un punto de vista físico e ingenieril, pero además son fundamentales para su función biológica. Las formas de equilibrio de diferentes organelos celulares dependen de la elasticidad frente a curvatura de la membrana lipídica. Por otro lado, la fluidez interfacial es esencial en funciones como la movilidad celular, la adaptación mecánica a deformaciones, o para la difusión lateral de proteínas. La elasticidad frente a curvatura de las membranas lipídicas puede motivarse a través de modelos microscópicos que tienen en cuenta la distribución de esfuerzos a lo largo del espesor de la membrana. En particular, el tensor de esfuerzos microscópico se calcula habitualmente en simulaciones de dinámica molecular a lo largo del espesor de la membrana para investigar cómo diferentes características microscópicas, como la adición de anestésicos o colesterol, afecta la respuesta mecánica efectiva. El tensor de esfuerzos microscópico tiende un puente entre la mecánica estadística de un conjunto de partículas puntuales, los átomos de una simulación de dinámica molecular, y modelos de mecánica de medios continuos. Sin embargo, no disponemos de una definición única del tensor de esfuerzos microscópico, y diferentes definiciones dan lugar a diferentes interpretaciones de la conexión entre modelos moleculares y continuos. En la primera parte de la tesis, mostramos que muchas de las definiciones del tensor de esfuerzos microscópico no satisfacen las leyes más básicas de la mecánica de medios continuos, y por tanto no son físicamente relevantes. Este problema nos ha motivado a proponer una nueva definición del tensor de esfuerzos microscópicos que cumpla las leyes fundamentales de la mecánica de medios continuos por construcción. Además, hemos desarrollado (y puesto a disposición del público libremente) una implementación numérica de nuestra definición del tensor de esfuerzos microscópico que puede calcularse mediante simulaciones de dinámica molecular (mdstress.org). Nuestra definición del tensor de esfuerzos, así como nuestra implementación del mismo, proporcionan una base sólida para el análisis de simulaciones de dinámica molecular desde un punto de vista continuo. Además de membranas lipídicas, mostramos la aplicación de nuestro método en otros sistemas relevantes, como cristales con defectos o proteínas fibrosas. En la segunda parte de esta tesis nos hemos focalizado en el modelado continuo de membranas lipídicas. Ya que estas membranas están constantemente sufriendo actividad biológica que las lleva fuera de equilibrio, es importante tener en cuenta no sólo la elasticidad de curvatura, sino también los grados de libertad internos asociados a la fluidez de la membrana. Para ello, desarrollamos un nuevo marco teórico y computacional general, tridimensional y no-lineal, para la mecánica de membranas lipídicas. Nuestro enfoque se basa en un marco general para la mecánica de sistemas disipativos, el principio variacional de Onsager, y en una formulación cuidadosa de la cinemática y las ecuaciones de balance para superficies fluídas. Para la simulación de nuestros modelos, seguimos una aproximación basada en elementos finitos que, sin embargo, requiere de métodos no convencionales debido al acoplamiento no-lineal entre cambios de forma y los campos de velocidad tangentes en superficies fluídas. Nuestra formulación proporciona la base para futuras investigaciones de la quimiomecánica fuera de equilibrio de membranas lipídicas y otras superficies fluídas, como el cortex celula