Maxent-Stress Optimization of 3D Biomolecular Models

Knowing a biomolecule\u27s structure is inherently linked to and a prerequisite for any detailed understanding of its function. Significant effort has gone into developing technologies for structural characterization. These technologies do not directly provide 3D structures; instead they typically yield noisy and erroneous distance information between specific entities such as atoms or residues, which have to be translated into consistent 3D models. Here we present an approach for this translation process based on maxent-stress optimization. Our new approach extends the original graph drawing method for the new application\u27s specifics by introducing additional constraints and confidence values as well as algorithmic components. Extensive experiments demonstrate that our approach infers structural models (i.e., sensible 3D coordinates for the molecule\u27s atoms) that correspond well to the distance information, can handle noisy and error-prone data, and is considerably faster than established tools. Our results promise to allow domain scientists nearly-interactive structural modeling based on distance constraints

Microsolvation of biomolecular models by microwave spectroscopy: structure and cooperative effects

Se han estudiado los complejos microsolvatados de diversas biomoléculas con el grupo amida, responsable del enlace peptídico. Estos complejos, en los que la molécula de interés está rodeada de un número limitado de moléculas de agua, pueden generarse en una expansión supersónica, y estudiarse usando espectroscopía de rotación. El análisis del espectro permite obtener las constantes de rotación de las especies presentes en la expansión supersónica, que están relacionadas con la estructura molecular. Esto permite caracterizar las interacciones que estabilizan los complejos y los efectos cooperativos que afectan al enlace de hidrógeno. Además, se ha demostrado que los parámetros de acoplamiento de cuadrupolo nuclear y de rotación interna sirven como sonda para evidenciar los efectos cooperativos que afectan a la estructura de la molécula microsolvatada y cuya influencia cambia con el grado de hidratación.Departamento de Química Física y Química InorgánicaDoctorado en Químic

Non-conformal coarse-grained potentials for water

Water is a notoriously difficult substance to model both accurately and efficiently. Here, we focus on descriptions with a single coarse-grained particle per molecule using the so-called Approximate Non-Conformal (ANC) and generalized Stockmayer potentials as the starting points. They are fitted using the radial density function and the density of the atomistic SPC/E model by downhill simplex optimization. We compare the results with monatomic water (mW), ELBA, as well as with direct Iterative Boltzmann Inversion (IBI) of SPC/E. The results show that symmetrical potentials result in non-transferable models, that is, they need to be reparametrized for new state-points. This indicates that transferability may require more complex models. Furthermore, the results also show that the addition of a point dipole is not sufficient to make the potentials accurate and transferable to different temperatures (300 K-500 K) and pressures without an appropriate choice of properties as targets during model optimization

Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced perpetual reaction, with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.Comment: 11 pages, 2 figures (v2 is now placed in proper context of the excellent 1962 paper by James Wei entitled "Axiomatic treatment of chemical reaction systems". In addition, section 4, on "Utility of steady state existence theorem" has been expanded.

Reconstruction of an in silico metabolic model of _Arabidopsis thaliana_ through database integration

The number of genome-scale metabolic models has been rising quickly in recent years, and the scope of their utilization encompasses a broad range of applications from metabolic engineering to biological discovery. However the reconstruction of such models remains an arduous process requiring a high level of human intervention. Their utilization is further hampered by the absence of standardized data and annotation formats and the lack of recognized quality and validation standards.

Plants provide a particularly rich range of perspectives for applications of metabolic modeling. We here report the first effort to the reconstruction of a genome-scale model of the metabolic network of the plant _Arabidopsis thaliana_, including over 2300 reactions and compounds. Our reconstruction was performed using a semi-automatic methodology based on the integration of two public genome-wide databases, significantly accelerating the process. Database entries were compared and integrated with each other, allowing us to resolve discrepancies and enhance the quality of the reconstruction. This process lead to the construction of three models based on different quality and validation standards, providing users with the possibility to choose the standard that is most appropriate for a given application. First, a _core metabolic model_ containing only consistent data provides a high quality model that was shown to be stoichiometrically consistent. Second, an _intermediate metabolic model_ attempts to fill gaps and provides better continuity. Third, a _complete metabolic model_ contains the full set of known metabolic reactions and compounds in _Arabidopsis thaliana_.

We provide an annotated SBML file of our core model to enable the maximum level of compatibility with existing tools and databases. We eventually discuss a series of principles to raise awareness of the need to develop coordinated efforts and common standards for the reconstruction of genome-scale metabolic models, with the aim of enabling their widespread diffusion, frequent update, maximum compatibility and convenience of use by the wider research community and industry

Properties of low-dimensional collective variables in the molecular dynamics of biopolymers

The description of the dynamics of a complex, high-dimensional system in terms of a low-dimensional set of collective variables Y can be fruitful if the low dimensional representation satisfies a Langevin equation with drift and diffusion coefficients which depend only on Y. We present a computational scheme to evaluate whether a given collective variable provides a faithful low-dimensional representation of the dynamics of a high-dimensional system. The scheme is based on the framework of finite-difference Langevin-equation, similar to that used for molecular-dynamics simulations. This allows one to calculate the drift and diffusion coefficients in any point of the full-dimensional system. The width of the distribution of drift and diffusion coefficients in an ensemble of microscopic points at the same value of Y indicates to which extent the dynamics of Y is described by a simple Langevin equation. Using a simple protein model we show that collective variables often used to describe biopolymers display a non-negligible width both in the drift and in the diffusion coefficients. We also show that the associated effective force is compatible with the equilibrium free--energy calculated from a microscopic sampling, but results in markedly different dynamical properties

Conditions for duality between fluxes and concentrations in biochemical networks

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality. That is, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes