An Evaluation of Methods for Inferring Boolean Networks from Time-Series Data

Regulatory networks play a central role in cellular behavior and decision making. Learning these regulatory networks is a major task in biology, and devising computational methods and mathematical models for this task is a major endeavor in bioinformatics. Boolean networks have been used extensively for modeling regulatory networks. In this model, the state of each gene can be either ‘on’ or ‘off’ and that next-state of a gene is updated, synchronously or asynchronously, according to a Boolean rule that is applied to the current-state of the entire system. Inferring a Boolean network from a set of experimental data entails two main steps: first, the experimental time-series data are discretized into Boolean trajectories, and then, a Boolean network is learned from these Boolean trajectories. In this paper, we consider three methods for data discretization, including a new one we propose, and three methods for learning Boolean networks, and study the performance of all possible nine combinations on four regulatory systems of varying dynamics complexities. We find that employing the right combination of methods for data discretization and network learning results in Boolean networks that capture the dynamics well and provide predictive power. Our findings are in contrast to a recent survey that placed Boolean networks on the low end of the ‘‘faithfulness to biological reality’’ and ‘‘ability to model dynamics’’ spectra. Further, contrary to the common argument in favor of Boolean networks, we find that a relatively large number of time points in the timeseries data is required to learn good Boolean networks for certain data sets. Last but not least, while methods have been proposed for inferring Boolean networks, as discussed above, missing still are publicly available implementations thereof. Here, we make our implementation of the methods available publicly in open source at http://bioinfo.cs.rice.edu/

Towards integrated computational models of cellular networks

The whole-cell behavior arises from the interplay among signaling, metabolic, and regulatory processes, which differ not only in their mechanisms, but also in the time scale of their execution. Proper modeling of the overall function of the cell requires development of a new modeling approach that accurately integrates these three types of processes, using the representation that best captures each one of them, and the interconnections between them. Traditionally, signaling networks have been modeled with ordinary differential equations (ODEs), regulation with Boolean networks, and metabolic pathways with Petri nets – these approaches are widely accepted and extensively used. Nonetheless, each of these methods, while being effective, have had limitations pointed out to them. Particularly, ODEs generally require very thorough parameterization, which is difficult to acquire, Boolean networks have been argued to be not capable of capturing complex systems dynamics, and the effectiveness of Petri nets when comparing to other, steady-state methods, have been debated. The main goal of this dissertation is to devise an integrated model that capture the whole-cell behavior and accurately combines these three components in the interplay between them. I provide a systematic study on using particle swarm optimization (PSO) as an effective approach for parameterizing ODEs. I survey different inference method for Boolean networks on the sets of complex dynamic data and demonstrate that they are, in fact, capable of capturing a variety of different systems. I review the existing use of Petri nets in modeling of biochemical system to show their effectiveness and, particularly, the ease for their integration with other methods. Finally, I propose an integrated hybrid model (IHM) that uses Petri nets to represent metabolic and signaling components, and Boolean networks to model regulation. The interconnections between these models allow to overcome the time scale differences of the processes by adding appropriate delay mechanisms. I validate IHM on two data sets. The significant advantage of IHM over other models is that it is able to capture the dynamics of all three components and can potentially identify novel and important cross-talk within the cell

Homogeneous Spaces with Intrinsic Metric

Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

On the Modeling of Signaling Networks with Petri Nets

The whole-cell behavior arises from the interplay among signaling, metabolic, and regulatory processes. Proper modeling of the overall function requires accurate interpretations of each component. The highly concurrent nature of the inner-cell interactions motivates the use of Petri nets as a framework for the whole-cell modeling. Petri nets have been successfully used in modeling of metabolic pathways, as it allows for a straightforward mapping from its stoichiometric matrix to the Petri net structure. The Boolean interpretation and modeling of transcription regulation networks also lends itself easily to Petri net modeling. However, Petri net modeling of signal transduction networks has been largely lacking, with the exception of simple ad hoc applications to specific signaling pathways. In this thesis, I investigate the applicability of Petri nets to modeling of signaling networks, by systematically analyzing initial token assignments, firing strategies, and robustness to errors and abstractions in the estimates of molecule concentrations and reaction rates

Iterative <i>k-means</i> clustering with (direct binarization) vs. .

<p>More refined binarization is achieved with higher values of .</p

Dynamics of Boolean networks learned from 16 time-points of the toy network.

<p>(a) Time points correspond to 0 min, 5 min, 15 min, 30 min, 45 min, 1 hr, 2hr, 3hr, 6hr, 8 hr, 10 hr, 12 hr, 15 hr, 18 hr, 21 hr, 24 hr. (b) Time points are manually selected to capture the oscillatory patterns of the original system. Left panels show the time points selected, and right panels show the binary data obtained by applying KM3 to the measurements at the selected time points in the left panels. Binarized data are shifted vertically for readability. Blue, green, red, and cyan curves correspond to species A, B, C, and D, respectively.</p

Algorithm 1 From Time-series to Boolean Networks.

<p>Algorithm 1 From Time-series to Boolean Networks.</p