Exploring the rate-limiting steps in visual phototransduction recovery by bottom-up kinetic modeling

Phototransduction in vertebrate photoreceptor cells represents a paradigm of signaling pathways mediated by G-protein-coupled receptors (GPCRs), which share common modules linking the initiation of the cascade to the final response of the cell. In this work, we focused on the recovery phase of the visual photoresponse, which is comprised of several interacting mechanisms. We employed current biochemical knowledge to investigate the response mechanisms of a comprehensive model of the visual phototransduction pathway. In particular, we have improved the model by implementing a more detailed representation of the recoverin (Rec)-mediated calcium feedback on rhodopsin kinase and including a dynamic arrestin (Arr) oligomerization mechanism. The model was successfully employed to investigate the rate limiting steps in the recovery of the rod photoreceptor cell after illumination. Simulation of experimental conditions in which the expression levels of rhodospin kinase (RK), of the regulator of the G-protein signaling (RGS), of Arr and of Rec were altered individually or in combination revealed severe kinetic constraints to the dynamics of the overall network. Our simulations confirm that RGS-mediated effector shutdown is the rate-limiting step in the recovery of the photoreceptor and show that the dynamic formation and dissociation of Arr homodimers and homotetramers at different light intensities significantly affect the timing of rhodopsin shutdown. The transition of Arr from its oligomeric storage forms to its monomeric form serves to temper its availability in the functional state. Our results may explain the puzzling evidence that overexpressing RK does not influence the saturation time of rod cells at bright light stimuli. The approach presented here could be extended to the study of other GPCR signaling pathways.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Monte Carlo study of a kinetic lattice model with random diffusion of disorder

We report Monte Carlo results for a nonequilibrium Ising-like model in two and three dimensions. Nearest-neighbor interactions J change sign randomly with time due to competing kinetics. There follows a fast and random, i.e., spin-configuration-independent diffusion of Js, of the kind that takes place in dilute metallic alloys when magnetic ions diffuse. The system exhibits steady states of the ferromagnetic (antiferromagnetic) type when the probability p that J>0 is large (small) enough. No counterpart to the freezing phenomena found in quenched spin glasses occurs. We compare our results with existing mean-field and exact ones, and obtain information about critical behavior.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Electrochemically promoted carbon-halide bond cleavage in 4-nitrobenzyl halides

This manuscript reports the study of the carbon-halide bond cleavage in 4-nitrobenzyl halides, taking special attention to the iodide and fluoride derivatives. The electrochemical reduction mechanism has been disclosed for both compounds by terms of cyclic voltammetry and controlled potential electrolysis. In the case of 4-nitrobenzyl iodide, a first one electron irreversible wave leads to the corresponding 4-nitrobenzyl radical and iodide. However, in the case of 4-nitrobenzyl fluoride, a first one-electron reversible wave appears at –1.02 vs. SCE followed by one electron irreversible wave. In this second electron transfer process, the cleavage of the C-F bond is taking place, so the bond cleavage reaction occurs at the dianion level. To disclose and understand the electrochemical reduction mechanisms that allows to obtain important thermodynamic and kinetic data that would help in the understanding of C-X bond cleavage. This type of bond dissociation reactions are involved in the metabolism pathways of the human body.

Modelització de la producció de melanina a partir de polifenol oxidasa d'Agaricus bisporus

Les melanines són un grup heterogeni de polímers producte de reaccions enzimàtiques en els teixits vegetals que contenen compostos fenòlics o polifenòlics. Estudis recents han descobert algunes propietats benèfiques de les melanines sobre la salut, tals com antioxidants, antiinflamatòries, immunològiques i propietats anti-tumorals. Així, no només la seva eliminació ha de ser examinada, sinó que també podria considerar-se la seva addició a aliments funcionals de nova creació. D’aquesta manera, es requereix conèixer el mecanisme cinètic de la lanogènesi abans de la seva possible utilització industrial. S’ha desenvolupat un model cinètic per explicar la formació de melanina a partir de L-tirosina utilitzant polifenol oxidasa d’Agaricus bisporus i monitoritzant l'absorbància de la solució. Aquesta expressió permet descriure la formació de melanina en funció del temps de reacció i obtenir alguns paràmetres importants que defineixen el producte, com el coeficient d'extinció. L’absorbància comença a créixer després d'un període de latència en què es produeixen productes intermedis incolors. El coeficient d'extinció dels productes resultants no és un valor constant, perquè depèn de les condicions de cada experiment. La tirosinasa tingué un menor efecte catalitzador sobre la L-tirosina (primera reacció que catalitza), que sobre L-DOPA (segona reacció).

Full Exploration of the Diels–Alder Cycloaddition on Metallofullerenes M3N@C80 (M=Sc, Lu, Gd): The D5h versus Ih Isomer and the Influence of the Metal Cluster

In this work a detailed investigation of the exohedral reactivity of the most important and abundant endohedral metallofullerene (EMF) is provided, that is, Sc3N@Ih-C80 and its D5h counterpart Sc3N@D5h-C80, and the (bio)chemically relevant lutetium- and gadolinium-based M3N@Ih/D5h-C80 EMFs (M=Sc, Lu, Gd). In particular, we analyze the thermodynamics and kinetics of the Diels–Alder cycloaddition of s-cis-1,3-butadiene on all the different bonds of the Ih-C80 and D5h-C80 cages and their endohedral derivatives. First, we discuss the thermodynamic and kinetic aspects of the cycloaddition reaction on the hollow fullerenes and the two isomers of Sc3N@C80. Afterwards, the effect of the nature of the metal nitride is analyzed in detail. In general, our BP86/TZP//BP86/DZP calculations indicate that [5,6] bonds are more reactive than [6,6] bonds for the two isomers. The [5,6] bond D5h-b, which is the most similar to the unique [5,6] bond type in the icosahedral cage, Ih-a, is the most reactive bond in M3N@D5h-C80 regardless of M. Sc3N@C80 and Lu3N@C80 give similar results; the regioselectivity is, however, significantly reduced for the larger and more electropositive M=Gd, as previously found in similar metallofullerenes. Calculations also show that the D5h isomer is more reactive from the kinetic point of view than the Ih one in all cases which is in good agreement with experiments

Driven fragmentation of granular gases

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the longvelocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f (c)~exp (−cⁿ), with n ≈1.2, regarding less the fragmentation mechanisms

Tensile strength characteristics of polypropylene composites reinforced with stone groundwood fibers from softwood

The behavior of stone groundwood / polypropylene injection-molded composites was evaluated with and without coupling agent. Stone groundwood (SGW) is a fibrous material commonly prepared in a high yield process and mainly used for papermaking applications. In this work, the use of SGW fibers was explored as a reinforcing element of polypropylene (PP) composites. The surface charge density of the composite components was evaluated, as well as the fiber’s length and diameter inside the composite material. Two mixing extrusion processes were evaluated, and the use of a kinetic mixer, instead of an internal mixer, resulted in longer mean fiber lengths of the reinforcing fibers. On the other hand, the accessibility of surface hydroxyl groups of stone groundwood fibers was improved by treating the fibers with 5% of sodium hydroxide, resulting in a noticeable increase of the tensile strength of the composites, for a similar percentage of coupling agent. A new parameter called Fiber Tensile Strength Factor is defined and used as a baseline for the comparison of the properties of the different composite materials. Finally the competitiveness of stone groundwood / polypropylene / polypropylene-co-maleic anhydride system, which compared favorably to sized glass-fiber / polypropylene GF/PP and glass-fiber / polypropylene / polypropylene-co-maleic anhydride composite formulations, was quantified by means of the fiber tensile strength factor

Irreversible thermodynamics of Poisson processes with reaction

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics

Calorimetry of dehydrogenation and dangling-bond recombination in several hydrogenated amorphous silicon materials

Differential scanning calorimetry (DSC) was used to study the dehydrogenation processes that take place in three hydrogenated amorphous silicon materials: nanoparticles, polymorphous silicon, and conventional device-quality amorphous silicon. Comparison of DSC thermograms with evolved gas analysis (EGA) has led to the identification of four dehydrogenation processes arising from polymeric chains (A), SiH groups at the surfaces of internal voids (A'), SiH groups at interfaces (B), and in the bulk (C). All of them are slightly exothermic with enthalpies below 50 meV/H atoms , indicating that, after dissociation of any SiH group, most dangling bonds recombine. The kinetics of the three low-temperature processes [with DSC peak temperatures at around 320 (A),360 (A'), and 430°C (B)] exhibit a kinetic-compensation effect characterized by a linea relationship between the activation entropy and enthalpy, which constitutes their signature. Their Si-H bond-dissociation energies have been determined to be E (Si-H)0=3.14 (A), 3.19 (A'), and 3.28 eV (B). In these cases it was possible to extract the formation energy E(DB) of the dangling bonds that recombine after Si-H bond breaking [0.97 (A), 1.05 (A'), and 1.12 (B)]. It is concluded that E(DB) increases with the degree of confinement and that E(DB)>1.10 eV for the isolated dangling bond in the bulk. After Si-H dissociation and for the low-temperature processes, hydrogen is transported in molecular form and a low relaxation of the silicon network is promoted. This is in contrast to the high-temperature process for which the diffusion of H in atomic form induces a substantial lattice relaxation that, for the conventional amorphous sample, releases energy of around 600 meV per H atom. It is argued that the density of sites in the Si network for H trapping diminishes during atomic diffusion

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems