Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.

Spatio-temporal patterns of tuberculosis incidence in Ribeirao Preto, State of Sao Paulo, southeast Brazil, and their relationship with social vulnerability: a Bayesian analysis

Introduction: The purpose of this ecological study was to evaluate the urban spatial and temporal distribution of tuberculosis (TB) in Ribeirao Preto, State of Sao Paulo, southeast Brazil, between 2006 and 2009 and to evaluate its relationship with factors of social vulnerability such as income and education level. Methods: We evaluated data from TBWeb, an electronic notification system for TB cases. Measures of social vulnerability were obtained from the SEADE Foundation, and information about the number of inhabitants, education and income of the households were obtained from Brazilian Institute of Geography and Statistics. Statistical analyses were conducted by a Bayesian regression model assuming a Poisson distribution for the observed new cases of TB in each area. A conditional autoregressive structure was used for the spatial covariance structure. Results: The Bayesian model confirmed the spatial heterogeneity of TB distribution in Ribeirao Preto, identifying areas with elevated risk and the effects of social vulnerability on the disease. We demonstrated that the rate of TB was correlated with the measures of income, education and social vulnerability. However, we observed areas with low vulnerability and high education and income, but with high estimated TB rates. Conclusions: The study identified areas with different risks for TB, given that the public health system deals with the characteristics of each region individually and prioritizes those that present a higher propensity to risk of TB. Complex relationships may exist between TB incidence and a wide range of environmental and intrinsic factors, which need to be studied in future research.

Spatio-temporal patterns of tuberculosis incidence in Ribeirão Preto, State of São Paulo, southeast Brazil, and their relationship with social vulnerability: a Bayesian analysis

INTRODUCTION: The purpose of this ecological study was to evaluate the urban spatial and temporal distribution of tuberculosis (TB) in Ribeirão Preto, State of São Paulo, southeast Brazil, between 2006 and 2009 and to evaluate its relationship with factors of social vulnerability such as income and education level. METHODS: We evaluated data from TBWeb, an electronic notification system for TB cases. Measures of social vulnerability were obtained from the SEADE Foundation, and information about the number of inhabitants, education and income of the households were obtained from Brazilian Institute of Geography and Statistics. Statistical analyses were conducted by a Bayesian regression model assuming a Poisson distribution for the observed new cases of TB in each area. A conditional autoregressive structure was used for the spatial covariance structure. RESULTS: The Bayesian model confirmed the spatial heterogeneity of TB distribution in Ribeirão Preto, identifying areas with elevated risk and the effects of social vulnerability on the disease. We demonstrated that the rate of TB was correlated with the measures of income, education and social vulnerability. However, we observed areas with low vulnerability and high education and income, but with high estimated TB rates. CONCLUSIONS: The study identified areas with different risks for TB, given that the public health system deals with the characteristics of each region individually and prioritizes those that present a higher propensity to risk of TB. Complex relationships may exist between TB incidence and a wide range of environmental and intrinsic factors, which need to be studied in future research.

Identifying regulational alterations in gene regulatory networks by state space representation of vector autoregressive models and variational annealing

Background: In the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded. Methods: We propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood. Results: For the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib. Conclusions: From the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib.

Infant mortality in Brazil, 1980-2000: A spatial panel data analysis

Background: Infant mortality is an important measure of human development, related to the level of welfare of a society. In order to inform public policy, various studies have tried to identify the factors that influence, at an aggregated level, infant mortality. The objective of this paper is to analyze the regional pattern of infant mortality in Brazil, evaluating the effect of infrastructure, socio-economic, and demographic variables to understand its distribution across the country. Methods: Regressions including socio-economic and living conditions variables are conducted in a structure of panel data. More specifically, a spatial panel data model with fixed effects and a spatial error autocorrelation structure is used to help to solve spatial dependence problems. The use of a spatial modeling approach takes into account the potential presence of spillovers between neighboring spatial units. The spatial units considered are Minimum Comparable Areas, defined to provide a consistent definition across Census years. Data are drawn from the 1980, 1991 and 2000 Census of Brazil, and from data collected by the Ministry of Health (DATASUS). In order to identify the influence of health care infrastructure, variables related to the number of public and private hospitals are included. Results: The results indicate that the panel model with spatial effects provides the best fit to the data. The analysis confirms that the provision of health care infrastructure and social policy measures (e. g. improving education attainment) are linked to reduced rates of infant mortality. An original finding concerns the role of spatial effects in the analysis of IMR. Spillover effects associated with health infrastructure and water and sanitation facilities imply that there are regional benefits beyond the unit of analysis. Conclusions: A spatial modeling approach is important to produce reliable estimates in the analysis of panel IMR data. Substantively, this paper contributes to our understanding of the physical and social factors that influence IMR in the case of a developing country.

A spatial stochastic model for rumor transmission

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate lambda. At rate alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

Stochastic lattice model describing a vector-borne disease

We employ the approach of stochastic dynamics to describe the dissemination of vector-borne diseases such as dengue, and we focus our attention on the characterization of the threshold of the epidemic. The coexistence space comprises two representative spatial structures for both human and mosquito populations. The human population has its evolution described by a process that is similar to the Susceptible-Infected-Recovered (SIR) dynamics. The population of mosquitoes follows a dynamic of the type of the Susceptible Infected-Susceptible (SIS) model. The coexistence space is a bipartite lattice constituted by two structures representing the human and mosquito populations. We develop a truncation scheme to solve the evolution equations for the densities and the two-site correlations from which we get the threshold of the disease and the reproductive ratio. We present a precise deØnition of the reproductive ratio which reveals the importance of the correlations developed in the early stage of the disease. According to our deØnition, the reproductive rate is directed related to the conditional probability of the occurrence of a susceptible human (mosquito) given the presence in the neighborhood of an infected mosquito (human). The threshold of the epidemic as well as the phase transition between the epidemic and the non-epidemic states are also obtained by performing Monte Carlo simulations. References: [1] David R. de Souza, T^ania Tom∂e, , Suani R. T. Pinho, Florisneide R. Barreto and M∂ario J. de Oliveira, Phys. Rev. E 87, 012709 (2013). [2] D. R. de Souza, T. Tom∂e and R. M. ZiÆ, J. Stat. Mech. P03006 (2011).

A Spatial Propensity Score Matching Evaluation of the Social Impacts of Sugarcane Growing on Municipalities in Brazil

The expansion of sugarcane growing in Brazil, spurred particularly by increased demand for ethanol, has triggered the need to evaluate the economic, social, and environmental impacts of this process, both on the country as a whole and on the growing regions. Even though the balance of costs and benefits is positive from an overall standpoint, this may not be so in specific producing regions, due to negative externalities. The objective of this paper is to estimate the effect of growing sugarcane on the human development index (HDI) and its sub-indices in cane producing regions. In the literature on matching effects, this is interpreted as the effect of the treatment on the treated. Location effects are controlled by spatial econometric techniques, giving rise to the spatial propensity score matching model. The authors analyze 424 minimum comparable areas (MCAs) in the treatment group, compared with 907 MCAs in the control group. The results suggest that the presence of sugarcane growing in these areas is not relevant to determine their social conditions, whether for better or worse. It is thus likely that public policies, especially those focused directly on improving education, health, and income generation/distribution, have much more noticeable effects on the municipal HDI.

Integration of spatial and temporal models to predict extreme water table depths

The objective of this work was to evaluate extreme water table depths in a watershed, using methods for geographical spatial data analysis. Groundwater spatio-temporal dynamics was evaluated in an outcrop of the Guarani Aquifer System. Water table depths were estimated from monitoring of water levels in 23 piezometers and time series modeling available from April 2004 to April 2011. For generation of spatial scenarios, geostatistical techniques were used, which incorporated into the prediction ancillary information related to the geomorphological patterns of the watershed, using a digital elevation model. This procedure improved estimates, due to the high correlation between water levels and elevation, and aggregated physical sense to predictions. The scenarios showed differences regarding the extreme levels - too deep or too shallow ones - and can subsidize water planning, efficient water use, and sustainable water management in the watershed.

Computational tools for comparing asymmetric GARCH models via Bayes factors

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the marginal likelihood, based on the MCMC output. From these approximations we compute Bayes factors and posterior model probabilities. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

A palaeobiogeographic model for biotic diversification within Amazonia over the past three million years

Many hypotheses have been proposed to explain high species diversity in Amazonia, but few generalizations have emerged. In part, this has arisen from the scarcity of rigorous tests for mechanisms promoting speciation, and from major uncertainties about palaeogeographic events and their spatial and temporal associations with diversification. Here, we investigate the environmental history of Amazonia using a phylogenetic and biogeographic analysis of trumpeters (Aves: Psophia), which are represented by species in each of the vertebrate areas of endemism. Their relationships reveal an unforeseen 'complete' time-slice of Amazonian diversification over the past 3.0 Myr. We employ this temporally calibrated phylogeny to test competing palaeogeographic hypotheses. Our results are consistent with the establishment of the current Amazonian drainage system at approximately 3.0-2.0 Ma and predict the temporal pattern of major river formation over Plio-Pleistocene times. We propose a palaeobiogeographic model for the last 3.0 Myr of Amazonian history that has implications for understanding patterns of endemism, the temporal history of Amazonian diversification and mechanisms promoting speciation. The history of Psophia, in combination with new geological evidence, provides the strongest direct evidence supporting a role for river dynamics in Amazonian diversification, and the absence of such a role for glacial climate cycles and refugia.

Spatial distribution of arboviral mosquito vectors (Diptera, Culicidae) in Vale do Ribeira in the South-eastern Brazilian Atlantic Forest

Mosquitoes are vectors of arboviruses that can cause encephalitis and hemorrhagic fevers in humans. Aedes serratus (Theobald), Aedes scapularis (Rondani) and Psorophora ferox (Von Humboldt) are potential vectors of arboviruses and are abundant in Vale do Ribeira, located in the Atlantic Forest in the southeast of the State of Sao Paulo, Brazil. The objective of this study was to predict the spatial distribution of these mosquitoes and estimate the risk of human exposure to mosquito bites. Results of the analyses show that humans are highly exposed to bites in the municipalities of Cananeia, Iguape and Ilha Comprida. In these localities the incidence of Rocio encephalitis was 2% in the 1970s. Furthermore, Ae. serratus, a recently implicated vector of yellow fever virus in the State of Rio Grande do Sul, should be a target for the entomological surveillance in the southeastern Atlantic Forest. Considering the continental dimensions of Brazil and the inherent difficulties in sampling its vast area, the habitat suitability method used in the study can be an important tool for predicting the distribution of vectors of pathogens.

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies' growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.

A model of road effect using line integrals and a test of the performance of two new road indices using the distribution of small mammals in an Atlantic Forest landscape

Effects of roads on wildlife and its habitat have been measured using metrics, such as the nearest road distance, road density, and effective mesh size. In this work we introduce two new indices: (1) Integral Road Effect (IRE), which measured the sum effects of points in a road at a fixed point in the forest; and (2) Average Value of the Infinitesimal Road Effect (AVIRE), which measured the average of the effects of roads at this point. IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads. Combining tools of ArcGIS software with a numerical algorithm, we calculated these and other road and habitat cover indices in a sample of points in a human-modified landscape in the Brazilian Atlantic Forest, where data on the abundance of two groups of small mammals (forest specialists and habitat generalists) were collected in the field. We then compared through the Akaike Information Criterion (AIC) a set of candidate regression models to explain the variation in small mammal abundance, including models with our two new road indices (AVIRE and IRE) or models with other road effect indices (nearest road distance, mesh size, and road density), and reference models (containing only habitat indices, or only the intercept without the effect of any variable). Compared to other road effect indices, AVIRE showed the best performance to explain abundance of forest specialist species, whereas the nearest road distance obtained the best performance to generalist species. AVIRE and habitat together were included in the best model for both small mammal groups, that is, higher abundance of specialist and generalist small mammals occurred where there is lower average road effect (less AVIRE) and more habitat. Moreover, AVIRE was not significantly correlated with habitat cover of specialists and generalists differing from the other road effect indices, except mesh size, which allows for separating the effect of roads from the effect of habitat on small mammal communities. We suggest that the proposed indices and GIS procedures could also be useful to describe other spatial ecological phenomena, such as edge effect in habitat fragments. (C) 2012 Elsevier B.V. All rights reserved.

A biophysical model of Sugarcane growth

Scientists predict that global agricultural lands will expand over the next few decades due to increasing demands for food production and an exponential increase in crop-based biofuel production. These changes in land use will greatly impact biogeochemical and biogeophysical cycles across the globe. It is therefore important to develop models that can accurately simulate the interactions between the atmosphere and important crops. In this study, we develop and validate a new process-based sugarcane model (included as a module within the Agro-IBIS dynamic agro-ecosystem model) which can be applied at multiple spatial scales. At site level, the model systematically under/overestimated the daily sensible/latent heat flux (by -10.5% and 14.8%, H and E, respectively) when compared against the micrometeorological observations from southeast Brazil. The model underestimated ET (relative bias between -10.1% and 12.5%) when compared against an agro-meteorological field experiment from northeast Australia. At the regional level, the model accurately simulated average yield for the four largest mesoregions (clusters of municipalities) in the state of Sao Paulo, Brazil, over a period of 16 years, with a yield relative bias of -0.68% to 1.08%. Finally, the simulated annual average sugarcane yield over 31 years for the state of Louisiana (US) had a low relative bias (-2.67%), but exhibited a lower interannual variability than the observed yields.