Controllability analysis of networks.

The concept of controllability of linear systems from control theory is applied to networks inspired by biology. A node is in this context controllable if an external signal can be applied which can adjust the level (e.g., protein concentration) of the node in a finite time to an arbitrary value, regardless of the levels of the other nodes. The property of being downstream of the node to which the input is applied turns out to be a necessary but not a sufficient condition for being controllable. An interpretation of the controllability matrix, when applied to networks, is also given. Finally, two case studies are provided in order to better explain the concepts, as well as some results for a gene regulatory network of fission yeast.

Reverse engineering galactose regulation in yeast through model selection.

We examine the application of statistical model selection methods to reverse-engineering the control of galactose utilization in yeast from DNA microarray experiment data. In these experiments, relationships among gene expression values are revealed through modifications of galactose sugar level and genetic perturbations through knockouts. For each gene variable, we select predictors using a variety of methods, taking into account the variance in each measurement. These methods include maximization of log-likelihood with Cp, AIC, and BIC penalties, bootstrap and cross-validation error estimation, and coefficient shrinkage via the Lasso.

Lowered Expression of Tumor Suppressor Candidate MYO1C Stimulates Cell Proliferation, Suppresses Cell Adhesion and Activates AKT.

Myosin-1C (MYO1C) is a tumor suppressor candidate located in a region of recurrent losses distal to TP53. Myo1c can tightly and specifically bind to PIP2, the substrate of Phosphoinositide 3-kinase (PI3K), and to Rictor, suggesting a role for MYO1C in the PI3K pathway. This study was designed to examine MYO1C expression status in a panel of well-stratified endometrial carcinomas as well as to assess the biological significance of MYO1C as a tumor suppressor in vitro. We found a significant correlation between the tumor stage and lowered expression of MYO1C in endometrial carcinoma samples. In cell transfection experiments, we found a negative correlation between MYO1C expression and cell proliferation, and MYO1C silencing resulted in diminished cell migration and adhesion. Cells expressing excess of MYO1C had low basal level of phosphorylated protein kinase B (PKB, a.k.a. AKT) and cells with knocked down MYO1C expression showed a quicker phosphorylated AKT (pAKT) response in reaction to serum stimulation. Taken together the present study gives further evidence for tumor suppressor activity of MYO1C and suggests MYO1C mediates its tumor suppressor function through inhibition of PI3K pathway and its involvement in loss of contact inhibition.

Constructing and analyzing a large-scale gene-to-gene regulatory network--lasso-constrained inference and biological validation.

We construct a gene-to-gene regulatory network from time-series data of expression levels for the whole genome of the yeast Saccharomyces cerevisae, in a case where the number of measurements is much smaller than the number of genes in the network. This network is analyzed with respect to present biological knowledge of all genes (according to the Gene Ontology database), and we find some of its large-scale properties to be in accordance with known facts about the organism. The linear modeling employed here has been explored several times, but due to lack of any validation beyond investigating individual genes, it has been seriously questioned with respect to its applicability to biological systems. Our results show the adequacy of the approach and make further investigations of the model meaningful.

Visualization of large-scale correlations in gene expressions.

Large-scale expression data are today measured for several thousands of genes simultaneously. Furthermore, most genes are being categorized according to their properties. This development has been followed by an exploration of theoretical tools to integrate these diverse data types. A key problem is the large noise-level in the data. Here, we investigate ways to extract the remaining signals within these noisy data sets. We find large-scale correlations within data from Saccharomyces cerevisiae with respect to properties of the encoded proteins. These correlations are visualized in a way that is robust to the underlying noise in the measurement of the individual gene expressions. In particular, for S. cerevisiae we observe that the proteins corresponding to the 400 highest expressed genes typically are localized to the cytoplasm. These most expressed genes are not essential for cell survival.

Scale-free growing networks imply linear preferential attachment.

It has been recognized for some time that a network grown by the addition of nodes with linear preferential attachment will possess a scale-free distribution of connectivities. Here we prove by some analytical arguments that the linearity is a necessary component to obtain this kind of distribution. However, the preferential linking rate does not necessarily apply to single nodes, but to groups of nodes of the same connectivity. We also point out that for a time-varying mean connectivity the linking rate will deviate from a linear expression by an extra asymptotically logarithmic term.

Effective dimensionality for principal component analysis of time series expression data.

Large-scale expression data are today measured for thousands of genes simultaneously. This development has been followed by an exploration of theoretical tools to get as much information out of these data as possible. Several groups have used principal component analysis (PCA) for this task. However, since this approach is data-driven, care must be taken in order not to analyze the noise instead of the data. As a strong warning towards uncritical use of the output from a PCA, we employ a newly developed procedure to judge the effective dimensionality of a specific data set. Although this data set is obtained during the development of rat central nervous system, our finding is a general property of noisy time series data. Based on knowledge of the noise-level for the data, we find that the effective number of dimensions that are meaningful to use in a PCA is much lower than what could be expected from the number of measurements. We attribute this fact both to effects of noise and the lack of independence of the expression levels. Finally, we explore the possibility to increase the dimensionality by performing more measurements within one time series, and conclude that this is not a fruitful approach.

Effective dimensionality of large-scale expression data using principal component analysis.

Large-scale expression data are today measured for thousands of genes simultaneously. This development is followed by an exploration of theoretical tools to get as much information out of these data as possible. One line is to try to extract the underlying regulatory network. The models used thus far, however, contain many parameters, and a careful investigation is necessary in order not to over-fit the models. We employ principal component analysis to show how, in the context of linear additive models, one can get a rough estimate of the effective dimensionality (the number of information-carrying dimensions) of large-scale gene expression datasets. We treat both the lack of independence of different measurements in a time series and the fact that that measurements are subject to some level of noise, both of which reduce the effective dimensionality and thereby constrain the complexity of models which can be built from the data.

Gene expression prediction by soft integration and the elastic net-best performance of the DREAM3 gene expression challenge.

BACKGROUND: To predict gene expressions is an important endeavour within computational systems biology. It can both be a way to explore how drugs affect the system, as well as providing a framework for finding which genes are interrelated in a certain process. A practical problem, however, is how to assess and discriminate among the various algorithms which have been developed for this purpose. Therefore, the DREAM project invited the year 2008 to a challenge for predicting gene expression values, and here we present the algorithm with best performance. METHODOLOGY/PRINCIPAL FINDINGS: We develop an algorithm by exploring various regression schemes with different model selection procedures. It turns out that the most effective scheme is based on least squares, with a penalty term of a recently developed form called the "elastic net". Key components in the algorithm are the integration of expression data from other experimental conditions than those presented for the challenge and the utilization of transcription factor binding data for guiding the inference process towards known interactions. Of importance is also a cross-validation procedure where each form of external data is used only to the extent it increases the expected performance. CONCLUSIONS/SIGNIFICANCE: Our algorithm proves both the possibility to extract information from large-scale expression data concerning prediction of gene levels, as well as the benefits of integrating different data sources for improving the inference. We believe the former is an important message to those still hesitating on the possibilities for computational approaches, while the latter is part of an important way forward for the future development of the field of computational systems biology.

Reverse engineering of gene networks with LASSO and nonlinear basis functions.

The quest to determine cause from effect is often referred to as reverse engineering in the context of cellular networks. Here we propose and evaluate an algorithm for reverse engineering a gene regulatory network from time-series and steady-state data. Our algorithmic pipeline, which is rather standard in its parts but not in its integrative composition, combines ordinary differential equations, parameter estimations by least angle regression, and cross-validation procedures for determining the in-degrees and selection of nonlinear transfer functions. The result of the algorithm is a complete directed network, in which each edge has been assigned a score from a bootstrap procedure. To evaluate the performance, we submitted the outcome of the algorithm to the reverse engineering assessment competition DREAM2, where we used the data corresponding to the InSilico1 and InSilico2 networks as input. Our algorithm outperformed all other algorithms when inferring one of the directed gene-to-gene networks.