Graphical models in inference of biological networks

Farnoudkia, Hajar
In recent years, particularly, on the studies about the complex system’s diseases, better understanding the biological systems and observing how the system’s behaviors, which are affected by the treatment or similar conditions, accelerate with the help of the explanation of these systems via the mathematical modeling. Gaussian Graphical Models (GGM) is a model that describes the relationship between the system’s elements via the regression and represents the states of the system via the multivariate Gaussian (normal) distribution. This distribution also explains the structure of biological systems by means of its "conditional independence" feature. Therefore, in the inverse of the covariance matrix of the multivariate normal distribution, the "zero" value implies no functional interaction, and the "non-zero" value stands for the interaction between the proteins in the estimate of the system’s structure. In this study, as the novelty, we use the Copula Gaussian Graphical Models (CGGM) in modeling the steady-state activation of the biological networks and make the inference of the model parameters under the Bayesian setting. We suggest the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to estimate the plausible interactions (conditional dependence) between the systems’ elements which are proteins or genes. Several data sets are used to illustrate the out-performance of the proposed RJMCMC in comparison with most of its alternatives. Also, we used some semi- Bayesian RJMCMC method to estimate the autoregressive coefficient matrix where GGM repeated through time. We improved the model by full-Bayesian approach and followingly, by a tuning parameter to increase the accuracy of the estimated matrices. Some simulated data sets are used to show the accuracy of the different proposed methods. Finally, we suggested a method to discover the relationships between variables through copula which is more flexible and it is more appropriate for the nonsymmetric or tail dependent cases. We applied the suggested ways in four real data set and we saw that copula can discover the joint density structure in addition to the available relationships in terms of the shape of the joint distribution to see whether it is symmetric or non-symmetric or even tail dependent or not.


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Cancer is a very common system’s disease with its structural and functional complexities caused by high dimension and serious correlation of genes as well as sparsity of gene interactions. Hereby, different mathematical models have been suggested in the literature to unravel these challenges. Among many alternates, in this study we use the Gaussian graphical model, Gaussian copula graphical model and loop-based multivariate adaptive regression splines with/without interaction models due to their advantages ...
Copula Gaussian graphical modeling of biological networks and Bayesian inference of model parameters
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A proper understanding of complex biological networks facilitates a better perception of those diseases that plague systems and efficient production of drug targets, which is one of the major research questions under the personalized medicine. However, the description of these complexities is challenging due to the associated continuous, high-dimensional, correlated and very sparse data. The Copula Gaussian Graphical Model (CGGM), which is based on the representation of the multivariate normal distribution ...
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The construction of biological networks via time-course datasets can be performed both deterministic models such as ordinary differential equations and stochastic models such as diffusion approximation. Between these two branches, the former has wider application since more data can be available. In this study, we particularly deal with the probabilistic approaches for the steady-state or deterministic description of the biological systems when the systems are observed though time. Hence, we consider time s...
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In this study, a theoretical model is developed to simulate the biophysical events in the intracellular spaces considering the biphasic, i.e., poroelastic, behavior of the cytoplasm. Most previous studies in the cryobiology literature have modeled the biophysical response of cells to freezing assuming the spatial homogeneity of all physical properties within the intracellular space without considering fluid-structure interaction in both the intracellular and extracellular spaces. However, a few recent studi...
Citation Formats
H. Farnoudkia, “Graphical models in inference of biological networks,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Statistics., Middle East Technical University, 2020.