Michael Hörnquist

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.

Comparison and validation of community structures in complex networks

The issue of partitioning a network into communities has attracted a great deal of attention recently. Most authors seem to equate this issue with the one of finding the maximum value of the modularity, as defined by Newman. Since the problem formulated this way is believed to be NP-hard, most effort has gone into the construction of search algorithms, and less to the question of other measures of community structures, similarities between various partitionings and the validation with respect to external information.

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.

Revisiting Salerno’s sine-Gordon model of DNA: active regions and robustness

Abstract We return to a simple model of DNA-transcription, first investigated by Salerno more than 10 years ago. One conjecture that time was that the promoter-regions were “dynamically active” in the sense that a stationary kink solution to the discrete sine-Gordon equation spontaneously starts to move when positioned in certain regions. Here we explore the whole genome of the bacteriophage T7, which is the same that was used in the first studies. We find that the regions in the promoters where the DNA-binding molecules attach have no special significance, while the start of the RNA-coding regions are dynamically active on a significant level. The results are checked to be robust by imposing an external disturbance in the form of a thermostat, simulating a constant temperature.

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.

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.

Genome-wide system analysis reveals stable yet flexible network dynamics in yeast

Recently, important insights into static network topology for biological systems have been obtained, but still global dynamical network properties determining stability and system responsiveness have not been accessible for analysis. Herein, we explore a genome-wide gene-to-gene regulatory network based on expression data from the cell cycle in Saccharomyces cerevisae (budding yeast). We recover static properties like hubs (genes having several out-going connections), network motifs and modules, which have previously been derived from multiple data sources such as whole-genome expression measurements, literature mining, protein-protein and transcription factor binding data. Further, our analysis uncovers some novel dynamical design principles; hubs are both repressed and repressors, and the intra-modular dynamics are either strongly activating or repressing whereas inter-modular couplings are weak. Finally, taking advantage of the inferred strength and direction of all interactions, we perform a global dynamical systems analysis of the network. Our inferred dynamics of hubs, motifs and modules produce a more stable network than what is expected given randomised versions. The main contribution of the repressed hubs is to increase system stability, while higher order dynamic effects (e.g. module dynamics) mainly increase system flexibility. Altogether, the presence of hubs, motifs and modules induce few flexible modes, to which the network is extra sensitive to an external signal. We believe that our approach, and the inferred biological mode of strong flexibility and stability, will also apply to other cellular networks and adaptive systems.

Solitary wave propagation in periodic and aperiodic diatomic Toda lattices

We investigate numerically how a solitary wave propagates in some one-dimensional diatomic periodic and aperiodic Toda lattices. It is found that a nearly stable wave of rather high amplitude can propagate in the periodic lattice. For several of the deterministic aperiodic sequences considered, the damping of the wave in the corresponding lattice is considerable less than for a random lattice. The short range correlation between the atoms in the aperiodic lattices seems to be of main importance for how much the wave is damped. We suggest therefore that the entropy according to Shannon might be a relevant measure for the properties of the lattices in this case. It is shown that this measure yields at least an approximative agreement with what is actually achieved by our numerical experiments. It is also shown that the earlier proposed idea of viewing the process as multiple scattering cannot be applied to other cases than random sequences with small mass-differences.

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.