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

A finite strain thermo-mechanically coupled material model for semi-crystalline polymers

In this work, a thermo-mechanically coupled constitutive model for semicrystalline polymers is derived in a thermodynamically consistent manner. In general, the macroscopic material behaviour of this class of materials is dictated by the underlying microstructure, i.e. by the distribution and structure of crystalline regimes, which form up after cooling from the amorphous melt. In order to account for the latter, the total degree of crystallinity is incorporated as an internal variable and its evolution is prescribed by means of a non-isothermal crystallisation kinetics model. The numerically efficient and robust framework is characterised based on experimental data for Polyamide 6 and shows a promising potential to predict the hyperelastic, visco-plastic material behaviour at various temperature

The Small Unit Cell Reconstructions of SrTiO3 (111)

We analyze the basic structural units of simple reconstructions of the (111) surface of SrTiO3 using density functional calculations. The prime focus is to answer three questions: what is the most appropriate functional to use; how accurate are the energies; what are the dominant low-energy structures and where do they lie on the surface phase diagram. Using test calculations of representative small molecules we compare conventional GGA with higher-order methods such as the TPSS meta-GGA and on-site hybrid methods PBE0 and TPSSh, the later being the most accurate. There are large effects due to reduction of the metal d oxygen sp hybridization when using the hybrid methods which are equivalent to a dynamical GGA+U, which leads to rather substantial improvements in the atomization energies of simple calibration molecules, even though the d-electron density for titanium compounds is rather small. By comparing the errors of the different methods we are able to generate an estimate of the theoretical error, which is about 0.25eV per 1x1 unit cell, with changes of 0.5-1.0 eV per 1x1 cell with the more accurate method relative to conventional GGA. An analysis of the plausible structures reveals an unusual low-energy TiO2-rich configuration with an unexpected distorted trigonal biprismatic structure. This structure can act as a template for layers of either TiO or Ti2O3, consistent with experimental results as well as, in principle, Magnelli phases. The results also suggest that both the fracture surface and the stoichiometric SrTiO3 (111) surface should spontaneously disproportionate into SrO and TiO2 rich domains, and show that there are still surprises to be found for polar oxide surfaces.Comment: 14 pages, 4 Figure

Tetrathiafulvalene: A Gate to the Mechanochemical Mechanisms of Electron Transfer Reactions

This report describes aspects of our previous studies of the mechanochemical synthesis of charge transfer complexes of the electron donor tetrathiafulvalene, which are relevant to the use of laboratory X-ray powder diffraction for ex situ monitoring of mechanochemical reactions toward investigating their mechanisms. In particular, the reaction of tetrathiafulvalene and chloranil was studied under neat mechanochemical conditions and liquid-assisted grinding with diethyl ether (1 μL/mg). The product in both cases is the green tetrathiafulvalene chloranil polymorph and the mechanism of the redox reaction is presumably the same. However, while the kinetic profile of the neat mechanochemical synthesis was fitted with a second-order rate law, that of the overall faster liquid-assisted grinding reaction was fitted with the Ginstling-Brounshtein 3D diffusion-controlled model. Hence, the diffusional processes and mass transfer bringing the reactants together and separating them from products must be different. Diffraction measurements sensitive to crystalline phases and amorphous material, combined with in situ monitoring by spectroscopic techniques, will ultimately afford a better understanding of mechanochemical reaction mechanisms, a hot topic in mechanochemistry

Structural Properties, Order-Disorder Phenomena and Phase Stability of Orotic Acid Crystal Forms

Orotic acid (OTA) is reported to exist in the anhydrous (AH), monohydrate (Hy1) and dimethylsulfoxide monosolvate (SDMSO) forms. In this study we investigate the (de)hydration/desolvation behavior, aiming at an understanding of the elusive structural features of anhydrous OTA by a combination of experimental and computational techniques, namely, thermal analytical methods, gravimetric moisture (de)sorption studies, water activity measurements, X-ray powder diffraction, spectroscopy (vibrational, solid-state NMR), crystal energy landscape and chemical shift calculations. The Hy1 is a highly stable hydrate, which dissociates above 135°C and loses only a small part of the water when stored over desiccants (25°C) for more than one year. In Hy1, orotic acid and water molecules are linked by strong hydrogen bonds in nearly perfectly planar arranged stacked layers. The layers are spaced by 3.1 Å and not linked via hydrogen-bonds. Upon dehydration the X-ray powder diffraction and solid-state NMR peaks become broader indicating some disorder in the anhydrous form. The Hy1 stacking reflection (122) is maintained, suggesting that the OTA molecules are still arranged in stacked layers in the dehydration product. Desolvation of SDMSO, a non-layer structure, results in the same AH phase as observed upon dehydrating Hy1. Depending on the desolvation conditions different levels of order-disorder of layers present in anhydrous OTA are observed, which is also suggested by the computed low energy crystal structures. These structures provide models for stacking faults as intergrowth of different layers is possible. The variability in anhydrate crystals is of practical concern as it affects the moisture dependent stability of AH with respect to hydration