Chaotic model and memory in single calcium-activated potassium channel kinetics

Ion channels are pores formed by proteins and responsible for carrying ion fluxes through cellular membranes. The ion channels can assume conformational states thereby controlling ion flow. Physically, the conformational transitions from one state to another are associated with energy barriers between them and are dependent on stimulus, such as, electrical field, ligands, second messengers, etc. Several models have been proposed to describe the kinetics of ion channels. The classical Markovian model assumes that a future transition is independent of the time that the ion channel stayed in a previous state. Others models as the fractal and the chaotic assume that the rate of transitions between the states depend on the time that the ionic channel stayed in a previous state. For the calcium activated potassium channels of Leydig cells the R/S Hurst analysis has indicated that the channels are long-term correlated with a Hurst coefficient H around 0.7, showing a persistent memory in this kinetic. Here, we applied the R/S analysis to the opening and closing dwell time series obtained from simulated data from a chaotic model proposed by L. Liebovitch and T. Toth [J. Theor. Biol. 148, 243 (1991)] and we show that this chaotic model or any model that treats the set of channel openings and closings as independent events is inadequate to describe the long-term correlation (memory) already described for the experimental data. (C) 2008 American Institute of Physics.

SZNAJD MODEL AND PROPORTIONAL ELECTIONS: THE ROLE OF THE TOPOLOGY OF THE NETWORK

The Sznajd model (SM) has been employed with success in the last years to describe opinion propagation in a community. In particular, it has been claimed that its transient is able to reproduce some scale properties observed in data of proportional elections, in different countries, if the community structure (the network) is scale-free. In this work, we investigate the properties of the transient of a particular version of the SM, introduced by Bernardes and co-authors in 2002. We studied the behavior of the model in networks of different topologies through the time evolution of an order parameter known as interface density, and concluded that regular lattices with high dimensionality also leads to a power-law distribution of the number of candidates with v votes. Also, we show that the particular absorbing state achieved in the stationary state (or else, the winner candidate), is related to a particular feature of the model, that may not be realistic in all situations.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Deterministic mathematical model for the prediction of the as-cast macrostructure

A multiphase deterministic mathematical model was implemented to predict the formation of the grain macrostructure during unidirectional solidification. The model consists of macroscopic equations of energy, mass, and species conservation coupled with dendritic growth models. A grain nucleation model based on a Gaussian distribution of nucleation undercoolings was also adopted. At some solidification conditions, the cooling curves calculated with the model showed oscillations (""wiggles""), which prevented the correct prediction of the average grain size along the structure. Numerous simulations were carried out at nucleation conditions where the oscillations are absent, enabling an assessment of the effect of the heat transfer coefficient on the average grain size and columnar-to-equiaxed transition.

Influence of a probiotic soy product on fecal microbiota and its association with cardiovascular risk factors in an animal model

Background: Previous work showed that daily ingestion of an aqueous soy extract fermented with Enterococcus faecium CRL 183 and Lactobacillus helveticus 416, supplemented or not with isoflavones, reduced the total cholesterol and non-HDL-cholesterol levels, increased the high-density lipoprotein (HDL) concentration and inhibited the raising of autoantibody against oxidized low-density lipoprotein (ox-LDL Ab) and the development of atherosclerotic lesions. Objective: The aim of this study was to characterize the fecal microbiota in order to investigate the possible correlation between fecal microbiota, serum lipid parameters and atherosclerotic lesion development in rabbits with induced hypercholesterolemia, that ingested the aqueous soy extract fermented with Enterococcus faecium CRL 183 and Lactobacillus helveticus 416. Methods: The rabbits were randomly allocated to five experimental groups (n = 6): control (C), hypercholesterolemic (H), hypercholesterolemic plus unfermented soy product (HUF), hypercholesterolemic plus fermented soy product (HF) and hypercholesterolemic plus isoflavone-supplemented fermented soy product (HIF). Lipid parameters and microbiota composition were analyzed on days 0 and 60 of the treatment and the atherosclerotic lesions were quantified at the end of the experiment. The fecal microbiota was characterized by enumerating the Lactobacillus spp., Bifidobacterium spp., Enterococcus spp., Enterobacteria and Clostridium spp. populations. Results: After 60 days of the experiment, intake of the probiotic soy product was correlated with significant increases (P < 0.05) on Lactobacillus spp., Bifidobacterium spp. and Enterococcus spp. and a decrease in the Enterobacteria population. A strong correlation was observed between microbiota composition and lipid profile. Populations of Enterococcus spp., Lactobacillus spp. and Bifidobacterium spp. were negatively correlated with total cholesterol, non-HDL-cholesterol, autoantibodies against oxidized LDL (ox-LDL Ab) and lesion size. HDL-C levels were positively correlated with Lactobacillus spp., Bifidobacterium spp., and Enterococcus spp. populations. Conclusion: In conclusion, daily ingestion of the probiotic soy product, supplemented or not with isoflavones, may contribute to a beneficial balance of the fecal microbiota and this modulation is associated with an improved cholesterol profile and inhibition of atherosclerotic lesion development.

Exercise improves cardiovascular control in a model of dislipidemia and menopause

The present study investigated the effects of exercise training on arterial pressure, baroreflex sensitivity, cardiovascular autonomic control and metabolic parameters on female LDL-receptor knockout ovariectomized mice. Mice were divided into two groups: sedentary and trained. Trained group was submitted to an exercise training protocol. Blood cholesterol was measured. Arterial pressure (AP) signals were directly recorded in conscious mice. Baroreflex sensitivity was evaluated by tachycardic and bradycardic responses to AP changes. Cardiovascular autonomic modulation was measured in frequency (FFT) and time domains. Maximal exercise capacity was increased in trained as compared to sedentary group. Blood cholesterol was diminished in trained mice (191 +/- 8 mg/dL) when compared to sedentary mice (250 +/- 9 mg/dL, p<0.05). Mean AP and HR were reduced in trained group (101 +/- 3 mmHg and 535 +/- 14 bpm, p<0.05) when compared with sedentary group (125 +/- 3 mmHg and 600 +/- 12 bpm). Exercise training induced improvement in bradycardic reflex response in trained animals (-4.24 +/- 0.62 bpm/mmHg) in relation to sedentary animals (-1.49 +/- 0.15 bpm/mmHg, p<0.01); tachycardic reflex responses were similar between studied groups. Exercise training increased the variance (34 +/- 8 vs. 6.6 +/- 1.5 ms(2) in sedentary, p<0.005) and the high-frequency band (HF) of the pulse interval (IP) (53 +/- 7% vs. 26 +/- 6% in sedentary, p<0.01). It is tempting to speculate that results of this experimental study might represent a rationale for this non-pharmacological intervention in the management of cardiovascular risk factors in dyslipidemic post-menopause women. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

Mortalidade cardiovascular por sexo e faixa etária em São Paulo, Brasil: 1996 a 1998 e 2003 a 2005

FUNDAMENTO: O conhecimento da evolução da mortalidade cardiovascular é importante para levantar hipóteses sobre a sua ocorrência e subsidiar medidas de prevenção e controle. OBJETIVOS: Comparar a mortalidade pelo conjunto das doenças cardiovasculares e seus principais subgrupos: doença isquêmica do coração e cerebrovasculares (DIC e DCBV), no município de São Paulo, por sexo e idade, de 1996 a 1998 e 2003 a 2005. MÉTODOS: Foram usados dados de óbitos do Programa de Aprimoramento das Informações de Mortalidade para o Município (PROAIM) e estimativas populacionais da Fundação Sistema Estadual de Análise de Dados (SEADE) do Estado de São Paulo. A magnitude na mortalidade e as mudanças entre os triênios foram medidas pela descrição de coeficientes e variação percentual relativa. O modelo de regressão de Poisson foi usado também para estimar a mudança na mortalidade entre os períodos. RESULTADOS: Observou-se redução importante da mortalidade cardiovascular. Os coeficientes aumentam com a idade em ambos os sexos. Também são mais elevados na população masculina, na faixa a partir dos 70 anos. Os coeficientes de mortalidade por DIC são maiores que aqueles por DCBV, tanto nos homens como nas mulheres de 50 anos ou mais. O declínio pelo conjunto das doenças cardiovasculares foi maior em mulheres de 20 a 29 anos (-30%) e em homens de 30 a 39 anos (-26%). CONCLUSÃO: A força da intensidade da mortalidade cardiovascular diminuiu entre 1996 e 1998, a 2003 e 2005. Ainda assim há diferenças entre os grupos. Essa redução pode significar, em parte, um maior acesso aos métodos diagnósticos e terapêuticos.

A fuzzy reed-frost model for epidemic spreading

In this paper, we present a fuzzy approach to the Reed-Frost model for epidemic spreading taking into account uncertainties in the diagnostic of the infection. The heterogeneities in the infected group is based on the clinical signals of the individuals (symptoms, laboratorial exams, medical findings, etc.), which are incorporated into the dynamic of the epidemic. The infectivity level is time-varying and the classification of the individuals is performed through fuzzy relations. Simulations considering a real problem with data of the viral epidemic in a children daycare are performed and the results are compared with a stochastic Reed-Frost generalization

Multistable behavior above synchronization in a locally coupled Kuramoto model

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that the solutions possess different characteristics, depending on the section of the boundary of the SR where they appear. We study the birth of these solutions and how they evolve when the coupling strength increases, and determine the diagram of solutions in phase space.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Parametric model for the analysis of concrete expansion due to alkali-aggregate reaction

The alkali-aggregate reaction (AAR) is a chemical reaction that provokes a heterogeneous expansion of concrete and reduces important properties such as Young's modulus, leading to a reduction in the structure's useful life. In this study, a parametric model is employed to determine the spatial distribution of the concrete expansion, combining normalized factors that influence the reaction through an AAR expansion law. Optimization techniques were employed to adjust the numerical results and observations in a real structure. A three-dimensional version of the model has been implemented in a finite element commercial package (ANSYS(C)) and verified in the analysis of an accelerated mortar test. Comparisons were made between two AAR mathematical descriptions for the mechanical phenomenon, using the same methodology, and an expansion curve obtained from experiment. Some parametric studies are also presented. The numerical results compared very well with the experimental data validating the proposed method.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

Evaluating gene by sex and age interactions on cardiovascular risk factors in Brazilian families

Background: In family studies, it is important to evaluate the impact of genes and environmental factors on traits of interest. In particular, the relative influences of both genes and the environment may vary in different strata of the population of interest, such as young and old individuals, or males and females. Methods: In this paper, extensions of the variance components model are used to evaluate heterogeneity in the genetic and environmental variance components due to the effects of sex and age (the cutoff between young and old was 43 yrs). The data analyzed were from 81 Brazilian families (1,675 individuals) of the Baependi Family Heart Study. Results: The models allowing for heterogeneity of variance components by sex suggest that genetic and environmental variances are not different in males and females for diastolic blood pressure, LDL-cholesterol, and HDL-cholesterol, independent of the covariates included in the models. However, for systolic blood pressure, fasting glucose and triglycerides, the evidence for heterogeneity was dependent on the covariates in the model. For instance, in the presence of sex and age covariates, heterogeneity in the genetic variance component was suggested for fasting glucose. But, for systolic blood pressure, there was no evidence of heterogeneity in any of the two variance components. Except for the LDL-cholesterol, models allowing for heterogeneity by age provide evidence of heterogeneity in genetic variance for triglycerides and systolic and diastolic blood pressure. There was evidence of heterogeneity in environmental variance in fasting glucose and HDL-cholesterol. Conclusions: Our results suggest that heterogeneity in trait variances should not be ignored in the design and analyses of gene-finding studies involving these traits, as it may generate additional information about gene effects, and allow the investigation of more sophisticated models such as the model including sex-specific oligogenic variance components.

A New Mouse Model for Marfan Syndrome Presents Phenotypic Variability Associated with the Genetic Background and Overall Levels of Fbn1 Expression

Marfan syndrome is an autosomal dominant disease of connective tissue caused by mutations in the fibrillin-1 encoding gene FBN1. Patients present cardiovascular, ocular and skeletal manifestations, and although being fully penetrant, MFS is characterized by a wide clinical variability both within and between families. Here we describe a new mouse model of MFS that recapitulates the clinical heterogeneity of the syndrome in humans. Heterozygotes for the mutant Fbn1 allele mg Delta(loxPneo), carrying the same internal deletion of exons 19-24 as the mg Delta mouse model, present defective microfibrillar deposition, emphysema, deterioration of aortic wall and kyphosis. However, the onset of a clinical phenotypes is earlier in the 129/Sv than in C57BL/6 background, indicating the existence of genetic modifiers of MFS between these two mouse strains. In addition, we characterized a wide clinical variability within the 129/Sv congenic heterozygotes, suggesting involvement of epigenetic factors in disease severity. Finally, we show a strong negative correlation between overall levels of Fbn1 expression and the severity of the phenotypes, corroborating the suggested protective role of normal fibrillin-1 in MFS pathogenesis, and supporting the development of therapies based on increasing Fbn1 expression.