Identifying differentially expressed genes in cancer patients using a non-parameter Ising model

Inferring excitation-inhibition dynamics using a maximum entropy model unifying brain structure and function

Neural activity coordinated across different scales from neuronal circuits to large-scale brain networks gives rise to complex cognitive functions. Bridging the gap between micro- and macroscale processes, we present a novel framework based on the maximum entropy model to infer a hybrid resting-state structural connectome, representing functional interactions constrained by structural connectivity. We demonstrate that the structurally informed network outperforms the unconstrained model in simulating brain dynamics, wherein by constraining the inference model with the network structure we may improve the estimation of pairwise BOLD signal interactions. Further, we simulate brain network dynamics using Monte Carlo simulations with the new hybrid connectome to probe connectome-level differences in excitation-inhibition balance between apolipoprotein E (APOE)-ε4 carriers and noncarriers. Our results reveal sex differences among APOE-ε4 carriers in functional dynamics at criticality; specifically, female carriers appear to exhibit a lower tolerance to network disruptions resulting from increased excitatory interactions. In sum, the new multimodal network explored here enables analysis of brain dynamics through the integration of structure and function, providing insight into the complex interactions underlying neural activity such as the balance of excitation and inhibition.

A modified Ising model of Barabási-Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

Pathway-Based Genomics Prediction using Generalized Elastic Net

We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach.

Incorporating prior knowledge into Gene Network Study

MOTIVATION

A major goal in genomic research is to identify genes that may jointly influence a biological response. From many years of intensive biomedical research, a large body of biological knowledge, or pathway information, has accumulated in available databases. There is a strong interest in leveraging these pathways to improve the statistical power and interpretability in studying gene networks associated with complex phenotypes. This prior information is a valuable complement to large-scale genomic data such as gene expression data generated from microarrays. However, it is a non-trivial task to effectively integrate available biological knowledge into gene expression data when reconstructing gene networks.

RESULTS

In this article, we developed and applied a Lasso method from a Bayesian perspective, a method we call prior Lasso (pLasso), for the reconstruction of gene networks. In this method, we partition edges between genes into two subsets: one subset of edges is present in known pathways, whereas the other has no prior information associated. Our method assigns different prior distributions to each subset according to a modified Bayesian information criterion that incorporates prior knowledge on both the network structure and the pathway information. Simulation studies have indicated that the method is more effective in recovering the underlying network than a traditional Lasso method that does not use the prior information. We applied pLasso to microarray gene expression datasets, where we used information from the Pathway Commons (PC) and the Kyoto Encyclopedia of Genes and Genomes (KEGG) as prior information for the network reconstruction, and successfully identified network hub genes associated with clinical outcome in cancer patients.

AVAILABILITY

The source code is available at http://nba.uth.tmc.edu/homepage/liu/pLasso.