Vilda Purutçuoğlu

Clustering current climate regions of Turkey by using a multivariate statistical method

In this study, the hierarchical clustering technique, called Ward method, was applied for grouping common features of air temperature series, precipitation total and relative humidity series of 244 stations in Turkey. Results of clustering exhibited the impact of physical geographical features of Turkey, such as topography, orography, land–sea distribution and the high Anatolian peninsula on the geographical variability. Based on the monthly series of nine climatological observations recorded for the period of 1970–2010, 12 and 14 clusters of climate zones are determined. However, from the comparative analyses, it is decided that 14 clusters represent the climate of Turkey more realistically. These clusters are named as (1) Dry Summer Subtropical Semihumid Coastal Aegean Region; (2) Dry-Subhumid Mid-Western Anatolia Region; (3 and 4) Dry Summer Subtropical Humid Coastal Mediterranean region [(3) West coast Mediterranean and (4) Eastern Mediterranean sub-regions]; (5) Semihumid Eastern Marmara Transition Sub-region; (6) Dry Summer Subtropical Semihumid/Semiarid Continental Mediterranean region; (7) Semihumid Cold Continental Eastern Anatolia region; (8) Dry-subhumid/Semiarid Continental Central Anatolia Region; (9 and 10) Mid-latitude Humid Temperate Coastal Black Sea Region [(9) West Coast Black Sea and (10) East Coast Black Sea sub-regions]; (11) Semihumid Western Marmara Transition Sub-region; (12) Semihumid Continental Central to Eastern Anatolia Sub-region; (13) Rainy Summer Semihumid Cold Continental Northeastern Anatolia Sub-region; and (14) Semihumid Continental Mediterranean to Eastern Anatolia Transition Sub-region. We believe that this study can be considered as a reference for the other climate-related researches of Turkey, and can be useful for the detection of Turkish climate regions, which are obtained by a long-term time course dataset having many meteorological variables.

Bayesian inference for the MAPK/ERK pathway by considering the dependency of the kinetic parameters

The MAPK/ERK pathway is one of the major signal transduction systems which regulates the cellular growth control of all eukaryotes like the cell proliferation and the apoptosis. Because of its importance in cellular lifecycle, it has been studied intensively, resulting in a number of qualitative descriptions of this regulatory mechanism. In this study we describe the MAPK/ERK pathway as an explicit set of reactions by combining different sources. Our reaction set takes into account the localization and different binding sites of the molecules in the cell by implementing the multiple parametrization. Then we estimate the model parameters of the network in a Bayesian setting via MCMC and data augmentation schemes. In the estimation we apply the Euler approximation, which is the discretized version of the diffusion technique. Additionally in inference of such a realistic and complex system we consider all possible kinds of dependencies coming from distinct stages of updates. To test the inference method we use the simulated data generated by the Gillespie algorithm. From the analysis it is clear that the sampler mixes well and partially is able to identify the dynamics of the MAPK/ERK pathway.

MARS as an alternative approach of Gaussian graphical model for biochemical networks

ABSTRACT 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 systems 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.

Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks

In this study, some methodologies and a review of the recently obtained new results are presented for the problem of modeling, anticipation and forecasting of genetic regulatory systems, as complex systems. In this respect, such kind of complex systems are modeled in the dynamical sense into the two different ways, namely, by a system of ordinary differential equations (ODEs) and Gaussian graphical methods (GGM). An artificial time-course microarray dataset of a gene-network is modeled as an example by using both ODE method and GGM. In this analysis, since the actual interactions of the nodes, i.e., genes, are assumed to be unknown, the discrete time measurements are initially used for the inference of the system’s interactions, i.e., the edges between nodes, by the underlying two methods. Then, the results of inference from ordinary differential equation based model are applied to a class of previously developed new numerical schemes for the generation of further states of the system. In this simulation, we present the recent results of a set of explicit Runge-Kutta methods that are implemented.

Estimating Network Kinetics of the MAPK/ERK Pathway Using Biochemical Data

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.

Determining the Climate Zones of Turkey by Center-Based Clustering Methods

There is a growing evidence that the climate change has already had significant impacts on the world’s physical, biological, and human systems, and it is expected that these impacts will become more severe in the near future. Alterations in the weather patterns and the existence of extreme events can be considered as important indicators of this change. The validity of this reality can be judged by analyzing climate data thoroughly. In this study, for determining the climate zones of Turkey, temperature measures obtained from the Turkish State Meteorological Service stations in the period 1950–2006 are examined by using two center-based clustering methods, namely k-means and fuzzy k-means. The clusters obtained from these methods are compared using objective criteria. They are also evaluated subjectively by the domain experts.

Comparison of two inference approaches in Gaussian graphical models

Abstract Introduction: The Gaussian Graphical Model (GGM) is one of the well-known probabilistic models which is based on the conditional independency of nodes in the biological system. Here, we compare the estimates of the GGM parameters by the graphical lasso (glasso) method and the threshold gradient descent (TGD) algorithm. Methods: We evaluate the performance of both techniques via certain measures such as specificity, F-measure and AUC (area under the curve). The analyses are conducted by Monte Carlo runs under different dimensional systems. Results: The results indicate that the TGD algorithm is more accurate than the glasso method in all selected criteria, whereas, it is more computationally demanding than this method too. Discussion and conclusion: Therefore, in high dimensional systems, we recommend glasso for its computational efficiency in spite of its loss in accuracy and we believe than the computational cost of the TGD algorithm can be improved by suggesting alternative steps in inference of the network.

Transformations of Data in Deterministic Modelling of Biological Networks

The Gaussian graphical model (GGM) is a probabilistic modelling approach used in the system biology to represent the relationship between genes with an undirected graph. In graphical models, the genes and their interactions are denoted by nodes and the edges between nodes. Hereby, in this model, it is assumed that the structure of the system can be described by the inverse of the covariance matrix, \(\varTheta \), which is also called as the precision, when the observations are formulated via a lasso regression under the multivariate normality assumption of states. There are several approaches to estimate \(\varTheta \) in GGM. The most well-known ones are the neighborhood selection algorithm and the graphical lasso (glasso) approach. On the other hand, the multivariate adaptive regression splines (MARS) is a non-parametric regression technique to model nonlinear and highly dependent data successfully. From previous simulation studies, it has been found that MARS can be a strong alternative of GGM if the model is constructed similar to a lasso model and the interaction terms in the optimal model are ignored to get comparable results with respect to the GGM findings. Moreover, it has been detected that the major challenge in both modelling approaches is the high sparsity of \(\varTheta \) due to the possible non-linear interactions between genes, in particular, when the dimensions of the networks are realistically large. In this study, as the novelty, we suggest the Bernstein operators, namely, Bernstein and Szasz polynomials, in the raw data before any lasso type of modelling and associated inference approaches. Because from the findings via GGM with small and moderately large systems, we have observed that the Bernstein polynomials can increase the accuracy of the estimates. Hence, in this work, we perform these operators firstly into the most well-known inference approaches used in GGM under realistically large networks. Then, we investigate the assessment of these transformations for the MARS modelling as the alternative of GGM again under the same large complexity. By this way, we aim to propose these transformation techniques for all sorts of modellings under the steady-state condition of the protein-protein interaction networks in order to get more accurate estimates without any computational cost. In the evaluation of the results, we compare the precision and F-measures of the simulated datasets.

Different types of Bernstein operators in inference of Gaussian graphical model

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.

Empirical Copula in the Detection of Batch Effects

The activation of the complex biological systems is presented by different mathematical expressions, called models, under various assumptions. One of the common modeling types in this description is the steady-state approach. In this description, we assume that the stochastic behavior of the system may not be observed under the constant volume and the temperature, and the mean change in the states of the system’s components is bigger than the variation of the states. Since this sort of the system’s representation needs less information about the actual biological activation, and majority of the collected data is more suitable for this approach with respect to its stochastic alternates, it is the most common modeling type in the presentation of the biological networks. In this study, we particularly deal with the steady-state type of model and suggest a preprocessing step for the raw data that is based on the transformation via the empirical copula. Here, we use the empirical copula, also called the normal copula, for eliminating the batch effects in the measurements so that the new data can fit the multivariate normal distribution. Then, we implement both parametric and nonparametric models in order to describe the final transformed measurements. In the description of the systems, we choose the Gaussian graphical model as the parametric modeling approach and select the probabilistic Boolean as well as the lasso-based MARS model as its correspondence under the nonparametric representation. Finally, in the analyses, we evaluate the performance of all suggested models and the effect of the empirical copula based on various accuracy measures via Monte Carlo studies.