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The biological organism is a complex structure regulated by interactions of genes and proteins. Various linear and nonlinear models can define activations of these interactions. In this study, we have aimed to improve the Gaussian graphical model (GGM), which is one of the well-known probabilistic and parametric models describing steady-state activations of biological systems, and its inference based on the graphical lasso, shortly Glasso, method. Because, GGM with Glasso can have low accuracy when the system has many genes and data are far from the normal distribution. Hereby, we construct the model like GGM, but, suggest the long-tailed symmetric distribution (LTS), rather than the normality, and use the modified maximum likelihood (MML) estimator, rather than Glasso, in inference. From the assessment of simulated and real data analyses, it is seen that LTS with MML has higher accuracy and less computational demand with explicit expressions than results of GGM with Glasso. [ABSTRACT FROM AUTHOR]

The multivariate adaptive regression splines (MARS) model is one of the well-known, additive non-parametric models that can deal with highly correlated and nonlinear datasets successfully. From our previous analyses, we have seen that lasso-type MARS (LMARS) can be a strong alternative of the Gaussian graphical model (GGM) which is a well-known probabilistic method to describe the steady-state behaviour of the complex biological systems via the lasso regression. In this study, we extend our original LMARS model by taking into account the second-order interaction effects of genes as the representative of the feed-forward loop in biological networks. By this way, we can describe both linear and nonlinear activations of the genes in the same model. We evaluate the performance of our new model under different dimensional simulated and real systems, and then compare the accuracy of the estimates with GGM and LMARS outputs. The results show the advantage of this new model over its close alternatives. [ABSTRACT FROM AUTHOR]

Objective: Outlier detection is a crucial problem in many fields. Although there are too many outlier detection methods in the literature, only a few methods suitable for dependent, sparse and high dimensional data structure. In this study, we perform various univariate and multivariate outlier detection methods as a pre-processing step before modeling the protein-protein interaction networks in order to investigate whether the outlier detection can improve the accuracy of the model. Material and Methods: Within the univariate approaches, we implement the z-score and Box-plot methods which are the most well-known outlier detection approaches. Besides them, we also apply the multivariate outlier detection methods, called PCOut and Sign which are based on the robust principal component analysis and the BACON method which is a distance-based approach. These methods are applicable for the data type such that the number of variables are bigger than the observation. In the analysis, we use several synthetic and real benchmark biological datasets. Then, we infer the networks with 3 network models, namely, GGM, MARS and CMARS and finally, we check the validity of models via F-measure and the accuracy measures. Conclusion: From the results, it has been seen that the use of outlier detection methods before the modeling cannot contribute to the performance of the models in our datasets. Results: Based on the results obtained from different datasets, we suggest that the estimations of protein-protein interaction networks can be made with GGM, MARS and CMARS methods without the need for an outlier detection process. [ABSTRACT FROM AUTHOR]

The aim of this study is to explore the effects of heat stresses on global gene expression profiles and to identify the candidate genes for the heat stress response in commercial baker’s yeast (Saccharomyces cerevisiae) by using microarray technology and comparative statistical data analyses. The data from all hybridizations and array normalization were analyzed using the GeneSpringGX 12.1 (Agilent) and the R 2.15.2 program language. In the analysis, all required statistical methods were performed comparatively. For the normalization step, among alternatives, the RMA (Robust Microarray Analysis) results were used. To determine differentially expressed genes under heat stress treatments, the fold-change and the hypothesis testing approaches were executed under various cut-off values via different multiple testing procedures then the up/down regulated probes were functionally categorized via the PAMSAM clustering. The results of the analysis concluded that the transcriptome changes under the heat shock. Moreover, the temperature-shift stress treatments show that the number of differentially up-regulated genes among the heat shock proteins and transcription factors changed significantly. Finally, the change in temperature is one of the important environmental conditions affecting propagation and industrial application of baker’s yeast. This study statistically analyzes this affect via one-channel microarray data. [ABSTRACT FROM AUTHOR]

Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous, and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact that stochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples. [ABSTRACT FROM AUTHOR]

The Gaussian graphical model (GGM) is one of the well-known modelling approaches to describe biological networks under the steady-state condition via the precision matrix of data. In literature there are different methods to infer model parameters based on GGM. The neighbourhood selection with the lasso regression and the graphical lasso method are the most common techniques among these alternative estimation methods. But they can be computationally demanding when the system's dimension increases. Here, we suggest a non-parametric statistical approach, called the multivariate adaptive regression splines (MARS) as an alternative of GGM. To compare the performance of both models, we evaluate the findings of normal and non-normal data via the specificity, precision, F-measures and their computational costs. From the outputs, we see that MARS performs well, resulting in, a plausible alternative approach with respect to GGM in the construction of complex biological systems. [ABSTRACT FROM AUTHOR]

The Gaussian graphical model (GGM) is a powerful tool to describe the relationship between the nodes via the inverse of the covariance matrix in a complex biological system. But the inference of this matrix is problematic because of its high dimension and sparsity. From previous analyses, it has been shown that the Bernstein and Szasz polynomials can improve the accuracy of the estimate if they are used in advance of the inference as a processing step of the data. Hereby in this study, we consider whether any type of the Bernstein operators such as the Bleiman Butzer Hahn, Meyer-König, and Zeller operators can be performed for the improvement of the accuracy or only the Bernstein and the Szasz polynomials can satisfy this condition. From the findings of the Monte Carlo runs, we detect that the highest accuracies in GGM can be obtained under the Bernstein and Szasz polynomials, rather than all other types of the Bernstein polynomials, from small to high-dimensional biological networks. [ABSTRACT FROM AUTHOR]

The MAPK/ERK pathway is a major signal transduction system which regulates many fundamental cellular processes including the growth control and the cell death. As a result of these roles, it has a crucial importance in cancer as well as normal developmental processes. Therefore, it has been intensively studied resulting in a wealth of knowledge about its activation. It is also well documented that the activation kinetics of the pathway is crucial to determine the nature of the biological response. However, while individual biochemical steps are well characterized, it is still difficult to predict or even understand how the activation kinetics works. The aim of this paper is to estimate the stochastic rate constants of the MAPK/ERK network dynamics. Accordingly, taking a Bayesian approach, we combined underlying qualitative biological knowledge in several competing dynamic models via sets of quasireactions and estimated the stochastic rate constants of these reactions. Comparing the resulting estimates via the BIC and DIC criteria, we chose a biological model which includes EGFR degradation--Raf-MEK-ERK cascade without the involvement of RKIPs. [ABSTRACT FROM AUTHOR]

The frequentist gene expression index (FGX) was recently developed to measure expression on Affymetrix oligonucleotide DNA arrays. In this study, we extend FGX to cover nonnormal log expressions, specifically long-tailed symmetric densities and call our new index as robust gene expression index (RGX). In estimation, we implement the modified maximum likelihood method to unravel the elusive solutions of likelihood equations and utilize the Fisher information matrix for covariance terms. From the analysis via the bench-mark datasets and simulated data, it is shown that RGX has promising results and mostly outperforms FGX in terms of relative efficiency of the estimated signals, in particular, when the data are nonnormal. [ABSTRACT FROM AUTHOR]

The aim of this study is to explore the effects of heat stresses on global gene expression profiles and to identify the candidate genes for the heat stress response in commercial baker's yeast (Saccharomyces cerevisiae) by using microarray technology and comparative statistical data analyses. The data from all hybridizations and array normalization were analyzed using the GeneSpringGX 12.1 (Agilent) and the R 2.15.2 program language. In the analysis, all required statistical methods were performed comparatively. For the normalization step, among alternatives, the RMA (Robust Microarray Analysis) results were used. To determine differentially expressed genes under heat stress treatments, the fold-change and the hypothesis testing approaches were executed under various cut-off values via different multiple testing procedures then the up/down regulated probes were functionally categorized via the PAMSAM clustering. The results of the analysis concluded that the transcriptome changes under the heat shock. Moreover, the temperature-shift stress treatments show that the number of differentially up-regulated genes among the heat shock proteins and transcription factors changed significantly. Finally, the change in temperature is one of the important environmental conditions affecting propagation and industrial application of baker's yeast. This study statistically analyzes this affect via one-channel microarray data.