1,720,970 research outputs found
Sensitivity analysis of the reaction occurrence and recurrence times in steady-state biochemical networks
No full textContinuous-time stationary Markov jump processes among discrete sites are encountered in disparate biochemical ambits. Sites and connecting dynamical events form a ‘network’ in which the sites are the available system's states, and the events are site-to-site transitions, or even neutral processes in which the system does not change site but the event is however detectable. Examples include conformational transitions in single biomolecules, stochastic chemical kinetics in the space of the molecules copy numbers, and even macroscopic steady-state reactive mixtures if one adopts the viewpoint of a tagged molecule (or even of a molecular moiety) whose state may change when it is involved in a chemical reaction. Among the variety of dynamical descriptors, here we focus on the first occurrence times (starting from a given site) and on the recurrence times of an event of interest. We develop the sensitivity analysis for the lowest moments of the statistical distribution of such times with respect to the rate constants of the network. In particular, simple expressions and inequalities allow us to establish a direct relationship between selective variation of rate constants and effect on average times and variances. As illustrative cases we treat the substrate inhibition in enzymatic catalysis in which a tagged enzyme molecule jumps between three states, and the basic two-site model of stochastic gene expression in which the single gene switches between active and inactive forms
Dissipation-recurrence inequalities at the steady state
No full textFor Markov jump processes in out-of-equilibrium steady state, we present inequalities which link the average rate of entropy production with the timing of the site-to-site recurrences. Such inequalities are upper bounds on the average rate of entropy production. The combination with the finite-time thermodynamic uncertainty relation (a lower bound) yields inequalities of the pure kinetic kind for the relative precision of a dynamical output. After having derived the main relations for the discrete case, we sketch the possible extension to overdamped Markov dynamics on continuous degrees of freedom, treating explicitly the case of one-dimensional diffusion in tilted periodic potentials; an upper bound on the average velocity is derived, in terms of the average rate of entropy production and the microscopic diffusion coefficient, which corresponds to the finite-time thermodynamic uncertainty relation in the limit of vanishingly small observation time
Intrinsic timing in classical master equation dynamics from an extended quadratic format of the evolution law
No full textThe paradigm of Markov jump process is widely employed in disparate contexts, like for instance in ecology, epidemiology and chemistry, any time the state-space is discrete and a tracked entity (the system) stochastically jumps from site to site. The classical master equation describes the system's evolution in terms of site occupation probabilities starting from a given initial condition associated with the initial knowledge about the system. For the master equation of Markov processes admitting stationary occupation probabilities, it is here derived an equivalent quadratic format in an extended space of mutually interrelated variables having physical dimension of inverse of time. The evolution in the probability space is thus mirrored by the evolution in the extended space. This universal format potentially allows one to unveil general traits underlying the master equation dynamics. Here we specifically consider the emergence of an intrinsic rate which, behaving as a state function in the probability space, introduces a timing during the relaxation process. This specific feature has to be taken an empirical discovery which derives from the analysis of numerical calculations; a possible direction towards a formal proof is however proposed. The conjecture made here is that such intrinsic timing is a typical trait (i.e., normally present) of the Markov jump processes
Fluctuating systems driven between nonequilibrium states: Extractability of work and constraints on the final distribution
No full textThis work deals with fluctuating systems taken out-of-equilibrium by some “activating event”, and then driven by acting upon selected parameters. First we establish general conditions under which an average amount of work can be extracted during the driven transformation; this is what we term extractability of work. Second, from the premise that work is extracted on average, we derive a mutual bound between a measure of the final system’s disequilibrium, the free energy variation, and the average amount of energy involved in the activation phase. As a special case, we consider the situation in which the disequilibrium is quantified by the polarization over an a
priori unbiased periodic degree of freedom
Tagged-moiety viewpoint of chemical reaction networks
No full textIn this work we consider mass action chemical reaction networks, either closed or open, and focus on the hopping path that a tagged moiety makes from molecule to molecule because of the occurrence of the reactions. We develop the tool for simulating the stochastic paths by means of a Gillespie-like algorithm and provide examples of the master equation counterpart for simple archetype problems of general interest. Both stationary and transient conditions are taken into account. An explanatory case is adopted to illustrate the approach
Inequalities for overdamped fluctuating systems
No full textIn many ambits of the chemical sciences it happens to deal with complex systems udergoing thermal fluctuations in the overdamped regime of the motion (i.e., multidimensional diffusive processes). Although such stochastic dynamics are well specified in terms of the Fokker–Planck–Smoluchowski equation for the time-dependent probability density, the solution becomes rapidly unfeasible as the number of degrees of freedom increases beyond a few units. Here we present a strategy, based on inequalities for “completely monotone decreasing” functions viewed as convex functions of time, to by-pass such a difficulty and aimed to achieve only bounds (but with low computational effort) on some quantities that pertain the system’s dynamics. Namely, we derive (i) a lower bound for the maximum value of the probability density that develops from a given initial condition, and (ii) a lower bound on the correlation time for a generic self-correlation function. The former bound is quantified by means of simple operations on the initial condition, while the latter is gained by the knowledge of an initial “piece” of correlation function to be supplied, for instance, by molecular or Brownian dynamics simulations. Some practical applications are discussed
Recasting the mass-action rate equations of open chemical reaction networks into a universal quadratic format
No full textRecasting the rate equations of mass-action chemical kinetics into universal formats s a potentially useful strategy to rationalize typical features that are observed in the space of the species concentrations. For example, a remarkable feature is the appearance of the so-called slow manifolds (subregions of the concentration space where the trajectories bundle), whose detection can be exploited to simplify the description of the slow part of the kinetics via model reduction and to understand how the chemical network approaches the stationary state. Here we focus on generally open chemical reaction networks with continuous injection of species at constant rates, that is, the situation of idealized biochemical networks and microreactors under well-mixing conditions and externally controllable input of chemicals. We show that a unique format of pure quadratic ordinary differential equations can be achieved, regardless of the nonlinearity of the kinetic scheme, by means of a suitable change and extension of the set of dynamical variables. Then we outline some possible employments of such a format, with special emphasis on a low-computational-cost strategy to localize the slow manifolds which are indeed observed also for open systems
Local Self-Assembly of Dissipative Structures Sustained by Substrate Diffusion
Full text linkThe coupling between energy-consuming molecular processes and the macroscopic dimension plays an important role in nature and in the development of active matter. Here, we study the temporal evolution of a macroscopic system upon the local activation of a dissipative self-assembly process. Injection of surfactant molecules in a substrate-containing hydrogel results in the local substrate-templated formation of assemblies, which are catalysts for the conversion of substrate into waste. We show that the system develops into a macroscopic (pseudo-)non-equilibrium steady state (NESS) characterized by the local presence of energy-dissipating assemblies and persistent substrate and waste concentration gradients. For elevated substrate concentrations, this state can be maintained for more than 4 days. The studies reveal an interdependence between the dissipative assemblies and the concentration gradients: catalytic activity by the assemblies results in sustained concentration gradients and, vice versa, continuous diffusion of substrate to the assemblies stabilizes their size. The possibility to activate dissipative processes with spatial control and create long lasting non-equilibrium steady states enables dissipative structures to be studied in the space-time domain, which is of relevance for understanding biological systems and for the development of active matter
Diffusive model to assess the release of chemicals from a material under intermittent release conditions
Full text linkWe consider the archetype situation of a chemical species that diffuses in a material and irreversibly escapes through the interface. In our setup, the interface switches between two states corresponding to ‘release phase’ (absorbing boundary) during which the species is released to the exterior, and ‘pause phase’ (reflecting boundary) during which the species is not released and its concentration profile inside the material partially relaxes back to uniformity. By combining numerical solution of the diffusion equation and statistical analysis of the outcomes, we derive upper and lower bounds and an empirical approximation for the amount of species released up to a certain time, in which the only information about the release-pause alternation schedule is the number of release phases and the average duration of a release phase. The methodology is developed thinking especially to dermal exposure assessment in the case of a slab-like homogeneous material irreversibly releasing chemicals during a number of contacts. However, upon proper extensions, this approach might be useful for inspecting other situations that are encountered, for instance, when dealing with leakage of chemicals in environmental contexts and regulatory toxicology
Plasma Treatment and Ozonation of Binary Mixtures: The Case of Maleic and Fumaric Acids
Full text linkWith respect to ozonation, plasma treatment involves direct contact between the discharge
and the contaminated water therefore benefting, in addition to ozone, also of short-lived
reactive species. This paper focuses on mechanistic aspects of water treatment based on
plasma activation (in-situ discharge) and ozonation (ex-situ discharge), using maleic acid
and fumaric acid as model substrates and dielectric barrier discharges (DBDs) for producing plasma and ozone. Both types of experiments were carried out at diferent pH values and degradation profles of residual concentration vs treatment time were compared in
experiments in which each acid was treated individually and in mixture with the other. It
was found that, under all conditions examined, plasma treatment was more efcient than
ozonation for both acids, and that fumaric acid was always more reactive than maleic acid.
Peculiar S-shaped degradation curves were obtained for the decay of maleic acid when
treated in mixture with fumaric acid under acidic and neutral pH conditions in ozonation
and in plasma experiments. This efect was not observed when maleic acid was treated
in mixture with phenol instead of fumaric acid. The experimental data are nicely ftted
with a simple kinetic model which assumes that a single reactive species, in steady state
concentration, is responsible for the attack initiating the pollutants degradation. Based on
the complete set of results obtained the conclusion is reached that, in the DBD reactor
used, under acidic and neutral pH conditions ozone plays a major role in the degradation of
maleic and fumaric acids also in direct plasma treatment
- …
