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.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

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.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.