Towards an exact reconstruction of a time-invariant model from time series data

Dynamic processes in biological systems may be profiled by measuring system properties over time. One way of representing such time series data is through weighted interaction networks, where the nodes in the network represent the measurables and the weighted edges represent interactions between any pair of nodes. Construction of these network models from time series data may involve seeking a robust data-consistent and time-invariant model to approximate and describe system dynamics. Many problems in mathematics, systems biology and physics can be recast into this form and may require finding the most consistent solution to a set of first order differential equations. This is especially challenging in cases where the number of data points is less than or equal to the number of measurables. We present a novel computational method for network reconstruction with limited time series data. To test our method, we use artificial time series data generated from known network models. We then attempt to reconstruct the original network from the time series data alone. We find good agreement between the original and predicted networks

A Method to Identify and Analyze Biological Programs through Automated Reasoning.

Predictive biology is elusive because rigorous, data-constrained, mechanistic models of complex biological systems are difficult to derive and validate. Current approaches tend to construct and examine static interaction network models, which are descriptively rich but often lack explanatory and predictive power, or dynamic models that can be simulated to reproduce known behavior. However, in such approaches implicit assumptions are introduced as typically only one mechanism is considered, and exhaustively investigating all scenarios is impractical using simulation. To address these limitations, we present a methodology based on automated formal reasoning, which permits the synthesis and analysis of the complete set of logical models consistent with experimental observations. We test hypotheses against all candidate models, and remove the need for simulation by characterizing and simultaneously analyzing all mechanistic explanations of observed behavior. Our methodology transforms knowledge of complex biological processes from sets of possible interactions and experimental observations to precise, predictive biological programs governing cell function

Combining Bayesian Approaches and Evolutionary Techniques for the Inference of Breast Cancer Networks

Gene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental data through computational analysis. However, this task is typically complicated by the enormously large scale of the unknowns in a rather small sample size. Furthermore, when the goal is to study causal relationships within the network, tools capable of overcoming the limitations of correlation networks are required. In this work, we make use of Bayesian Graphical Models to attach this problem and, specifically, we perform a comparative study of different state-of-the-art heuristics, analyzing their performance in inferring the structure of the Bayesian Network from breast cancer data

Time-delayed models of gene regulatory networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems