A case study of zeolitization process: 'Tufo Rosso a Scorie Nere' (Vico Volcano, Italy). Inferences for a general model

This paper focuses on the authigenic mineralization processes acting on 'Tufo Rosso a Scorie Nere' (TRS), i.e. one of the main pyroclastic units of the Vico stratovolcano (Latium, Italy). The pyroclastic deposits appear in general massive and made of 'black vitreous vesiculated juvenile scoriae', immersed in an ashy matrix lithified after zeolitization processes. The main minerals are chabazite and phillipsite, and the zeolitic content is locally variable, reaching 68 % wt. Zeolites grow replacing both amorphous fraction and pre-existing phases, occurring inside both matrix and scoriae. Concerning scoriae, zeolitization moves from the rim to the core of the scoriaceous fragment as a function of (a) temperature of the fluids and (b) permeability (primary or secondary). Composition of parental fresh glass and that of zeolitized rocks is compatible with trachyte chemistry, lightly undersaturated in SiO2, and the alteration processes modified the parental rock chemical features. Zeolites genesis is ascribed to a 'geoautoclave-like system', and zeolites display a Si/Al ratio similar to that of the parental glasses. TRS presents promising mineralogical characteristics as supplementary cementitious material in the production of mixed cements

Discrepancies between extinction events and boundary equilibria in reaction networks

Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In particular, the deterministic model consists of an autonomous system of differential equations, whereas the stochastic system is a continuous-time Markov chain. Connections between the two modeling regimes have been studied since the seminal paper by Kurtz (J Chem Phys 57(7):2976–2978, 1972), where the deterministic model is shown to be a limit of a properly rescaled stochastic model over compact time intervals. Further, more recent studies have connected the long-term behaviors of the two models when the reaction network satisfies certain graphical properties, such as weak reversibility and a deficiency of zero. These connections have led some to conjecture a link between the long-term behavior of the two models exists, in some sense. In particular, one is tempted to believe that positive recurrence of all states for the stochastic model implies the existence of positive equilibria in the deterministic setting, and that boundary equilibria of the deterministic model imply the occurrence of an extinction event in the stochastic setting. We prove in this paper that these implications do not hold in general, even if restricting the analysis to networks that are bimolecular and that conserve the total mass. In particular, we disprove the implications in the special case of models that have absolute concentration robustness, thus answering in the negative a conjecture stated in the literature in 2014

Uniform approximation of solutions by elimination of intermediate species in deterministic reaction networks

Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a setting, based on ordinary differential equations, in which the presence of intermediate species has little effect on the overall dynamics of a biological system. The result provides a method to perform model reduction by elimination of intermediate species. We study the problem in a multiscale setting, where the species abundances as well as the reaction rates scale to different orders of magnitudes. The different time and concentration scales are parameterized by a single parameter N. We show that a solution to the original reaction system is uniformly approximated on compact time intervals to a solution of a reduced reaction system without intermediates and to a solution of a certain limiting reaction systems, which does not depend on N. Known approximation techniques such as the theorems by Tikhonov and Fenichel cannot readily be used in this framework

Elimination of intermediate species in multiscale stochastic reaction networks

We study networks of biochemical reactions modelled by continuous time Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis-Menten mechanism. Such species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to observe experimentally. We provide conditions under which the Markov process of a multiscale reaction network with intermediate species is approximated by the Markov process of a simpler reduced reaction network without intermediate species. We do so by embedding the Markov processes into a one-parameter family of processes, where reaction rates and species abundances are scaled in the parameter. Further, we show that there are close links between these stochastic models and deterministic ODE models of the same networks

Product-form poisson-like distributions and complex balanced reaction systems

Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on Nn. Here we provide a fundamental characterization that connects structural properties of a network to its dynamical features. Specifically, we define the notion of "stochastically complex balanced systems" in terms of the network's stationary distribution and provide a characterization of stochastically complex balanced systems, parallel to that established in the 1970s and 1980s for deterministic reaction networks. Additionally, we establish that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Further, we prove a stochastic version of the "deficiency zero theorem" and show that any (not only complex balanced) deficiency zero reaction network has a product-form Poisson-like stationary distribution on all irreducible components. Finally, we provide sufficient conditions for when a product-form Poisson-like distribution on a single (or all) component(s) implies the network is complex balanced, and we explore the possibility to characterize complex balanced systems in terms of product-form Poisson-like stationary distributions

Graphically balanced equilibria and stationary measures of reaction networks

The graph-related symmetries of a reaction network give rise to certain special equilibria (such as complex balanced equilibria) in deterministic models of dynamics of the reaction network. Correspondingly, in the stochastic setting, when modeled as a continuous time Markov chain, these symmetries give rise to certain special stationary measures. Previous work by Anderson, Craciun, and Kurtz [Bull Math. Biol., 72 (2010), pp. 1947-1970] identified stationary distributions of a complex balanced network; later, Cappelletti and Wiuf [SIAM J. Appl. Math., 76 (2016), pp. 411-432] developed the notion of complex balancing for stochastic systems. We define and establish the relations between reaction balanced measure, complex balanced measure, reaction vector balanced measure, and cycle balanced measure and prove that with mild additional hypotheses, the former two are stationary distributions. Furthermore, in the spirit of an earlier work by Joshi [Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), pp. 1077-1105] we give sufficient conditions under which detailed balance of the stationary distribution of Markov chain models implies the existence of positive detailed balance equilibria for the related deterministic reaction network model. Finally, we provide a complete map of the implications between balancing properties of deterministic and corresponding stochastic reaction systems, such as complex balance, reaction balance, reaction vector balance, and cycle balance

Growth of Rhodococcus sp. strain BCP1 on gaseous n-alkanes: New metabolic insights and transcriptional analysis of two soluble di-iron monooxygenase genes

Rhodococcus sp. strain BCP1 was initially isolated for its ability to grow on gaseous n-alkanes, which act as inducers for the co-metabolic degradation of low-chlorinated compounds. Here, both molecular and metabolic features of BCP1 cells grown on gaseous and short-chain n-alkanes (up to n-heptane) were examined in detail. We show that propane metabolism generated terminal and sub-terminal oxidation products such as 1- and 2-propanol, whereas 1-butanol was the only terminal oxidation product detected from n-butane metabolism. Two gene clusters, prmABCD and smoABCD-coding for Soluble Di-Iron Monooxgenases (SDIMOs) involved in gaseous n-alkanes oxidation-were detected in the BCP1 genome. By means of Reverse Transcriptase-quantitative PCR (RT-qPCR) analysis, a set of substrates inducing the expression of the sdimo genes in BCP1 were assessed as well as their transcriptional repression in the presence of sugars, organic acids, or during the cell growth on rich medium (Luria-Bertani broth). The transcriptional start sites of both the sdimo gene clusters were identified by means of primer extension experiments. Finally, proteomic studies revealed changes in the protein pattern induced by growth on gaseous- (n-butane) and/or liquid (n-hexane) short-chain n-alkanes as compared to growth on succinate. Among the differently expressed protein spots, two chaperonins and an isocytrate lyase were identified along with oxidoreductases involved in oxidation reactions downstream of the initial monooxygenase reaction step

Rhodococcus aetherivorans BCP1 as cell factory for the production of intracellular tellurium nanorods under aerobic conditions

Background: Tellurite (TeO32-) is recognized as a toxic oxyanion to living organisms. However, mainly anaerobic or facultative-anaerobic microorganisms are able to tolerate and convert TeO32- into the less toxic and available form of elemental Tellurium (Te0), producing Te-deposits or Te-nanostructures. The use of TeO32--reducing bacteria can lead to the decontamination of polluted environments and the development of "green-synthesis" methods for the production of nanomaterials. In this study, the tolerance and the consumption of TeO32- have been investigated, along with the production and characterization of Te-nanorods by Rhodococcus aetherivorans BCP1 grown under aerobic conditions. Results: Aerobically grown BCP1 cells showed high tolerance towards TeO32- with a minimal inhibitory concentration (MIC) of 2800μg/mL (11.2mM). TeO32- consumption has been evaluated exposing the BCP1 strain to either 100 or 500μg/mL of K2TeO3 (unconditioned growth) or after re-inoculation in fresh medium with new addition of K2TeO3 (conditioned growth). A complete consumption of TeO32- at 100μg/mL was observed under both growth conditions, although conditioned cells showed higher consumption rate. Unconditioned and conditioned BCP1 cells partially consumed TeO32- at 500μg/mL. However, a greater TeO32- consumption was observed with conditioned cells. The production of intracellular, not aggregated and rod-shaped Te-nanostructures (TeNRs) was observed as a consequence of TeO32- reduction. Extracted TeNRs appear to be embedded in an organic surrounding material, as suggested by the chemical-physical characterization. Moreover, we observed longer TeNRs depending on either the concentration of precursor (100 or 500μg/mL of K2TeO3) or the growth conditions (unconditioned or conditioned grown cells). Conclusions:Rhodococcus aetherivorans BCP1 is able to tolerate high concentrations of TeO32- during its growth under aerobic conditions. Moreover, compared to unconditioned BCP1 cells, TeO32- conditioned cells showed a higher oxyanion consumption rate (for 100μg/mL of K2TeO3) or to consume greater amount of TeO32- (for 500μg/mL of K2TeO3). TeO32- consumption by BCP1 cells led to the production of intracellular and not aggregated TeNRs embedded in an organic surrounding material. The high resistance of BCP1 to TeO32- along with its ability to produce Te-nanostructures supports the application of this microorganism as a possible eco-friendly nanofactory

Stochastically modeled weakly reversible reaction networks with a single linkage class

It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so long as the initial condition has strictly positive components). It is conjectured that the stochastically modeled analogs of these systems are positive recurrent. We prove this conjecture in the affirmative under the following additional assumptions: (i) the system is binary, and (ii) for each species, there is a complex (vertex in the associated reaction diagram) that is a multiple of that species. To show this result, a new proof technique is developed in which we study the recurrence properties of the n-step embedded discrete-time Markov chain

Addition of flow reactions preserving multistationarity and bistability

We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology