Dynamical properties of Discrete Reaction Networks

Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying discrete nondeterministic transitions of stochastic models of reaction networks. In that sense, a proof of non-reachability in a given DRN has immediate implications for any concrete stochastic model based on that DRN, independent of the choice of kinetic laws and constants. Moreover, if we assume that stochastic kinetic rates are given by the mass-action law (or any other kinetic law that gives non-vanishing probability to each reaction if the required number of interacting substrates is present), then reachability properties are equivalent in the two settings. The analysis of two types of global dynamical properties of DRNs is addressed: irreducibility, i.e., the ability to reach any discrete state from any other state; and recurrence, i.e., the ability to return to any initial state. Our results consider both the verification of such properties when species are present in a large copy number, and in the general case. The necessary and sufficient conditions obtained involve algebraic conditions on the network reactions which in most cases can be verified using linear programming. Finally, the relationship of DRN irreducibility and recurrence with dynamical properties of stochastic and continuous models of reaction networks is discussed.     

A model of intracellular transport of particles in an axon

In this paper we develop a model of intracellular transport of cell organelles and vesicles along the axon of a nerve cell. These particles are moving alternately by processive motion along a microtubule with the aid of motor proteins, and by diffusion. The model involves a degenerate system of diffusion equations. We prove a maximum principle and establish existence and behavior of a unique solution. Numerical results show how the transportation of mass depends on the relevant parameters of the model.     

Homotopy methods for counting reaction network equilibria

Dynamical system models of complex biochemical reaction networks are usually high-dimensional, non-linear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases multiple equilibria exist if and only if special relationships between these parameters are satisfied. We describe methods based on homotopy invariance of degree which allow us to determine the number of equilibria for complex biochemical reaction networks and how this number depends on parameters in the model.     

Simulation and verification of P systems through communicating X-machines

The aim of this paper is to prove the suitability of a parallel distributed computational model, communicating X-machines, to simulate in a natural way a well established model of molecular computation, P systems, and to present some further benefits of the approach allowing us to check for some formal properties. A set of rules to transform any P system with symbol-objects into a communicating X-machine model is presented and a variation of temporal logic for X-machines is briefly discussed, which facilitates model checking of desired properties of the system. Finally, the benefits resulting from the transformation are discussed.     

Expression of 5-lipoxygenase and 15-lipoxygenase in rheumatoid arthritis synovium and effects of intraarticular glucocorticoids

Introduction  

It was previously shown that lipoxygenase (LO) pathways are important in the rheumatoid arthritis (RA) inflammatory process and that synovial fluid from RA patients contains high amounts of leukotrienes. We therefore aimed to investigate the 5-LO and 15-LO-1 expression pattern in RA and ostheoarthritis (OA) synovial tissue and to study the effect of intraarticular glucocorticoid (GC) therapy on enzyme expression.     

The basal permeability to water of human red blood cells evaluated by a nuclear magnetic resonance technique

The characteristics of water diffusional permeability (P) of human red blood cells were studied on isolated erythrocytes by a doping nuclear magnetic resonance technique. In order to estimate the basal permeability the maximal inhibition of water diffusion was induced by exposure of red blood cells to p-chloromercuribenzene sulfonate (PCMBS) under various conditions (concentration, duration, temperature). The lowest values of P were around 0.7×10^–3 cm s^–1 at 10°C, 1.2×10^–3 cm s^–1 at 15°C, 1.4×10^–3 cm s^–1 at 20°C, 1.8×10^–3 cm s^–1 at 25°C, 2.1×10^–3 cm s^–1 at 30°C and 3.5×10^–3 cm s^–1 at 37°C. The mean value of the activation energy of water diffusion (E_a,d) was 25 kJ/mol for control and 43.7 kJ/mol for PCMBS-inhibited erythrocytes. The values of P and E_a,d obtained after induction of maximal inhibition of water diffusion by PCMBS can be taken as references for the basal permeability to water of the human red blood cell membrane.     

Myeloperoxidase,a possible biomarker for the early diagnosis of cardiac diastolic dysfunction with preserved ejection fraction

The current study was conducted on a sample of 91 patients diagnosed with diastolic dysfunction (DD) with preserved systolic function caused by a painful chronic ischaemic cardiopathy – angina pectoris stable at the effort. The diagnosis was established following anamnesis, electrocardiogram, and echocardiography. Myeloperoxidase (MPO) serum levels were assessed in all patients and then these values were correlated with some of the echocardiography parameters that proved the mentioned diagnosis.

In conclusion, the execution of this investigation triad (electrocardiogram, echocardiography, and MPO) allows:

• Stratifying the patients depending on the disease risk by early detecting of any possible DD with preserved systolic function.

• The use of the MPO increased circulating levels as a biomarker for diagnosis and risk due to the statistically significant correlation between those and the results of the other two aforementioned paraclinical investigation.