Gene Regulatory Network Reconstruction Using Dynamic Bayesian Networks

High-content technologies such as DNA microarrays can provide a system-scale overview of how genes interact with each other in a network context. Various mathematical methods and computational approaches have been proposed to reconstruct GRNs, including Boolean networks, information theory, differential equations and Bayesian networks. GRN reconstruction faces huge intrinsic challenges on both experimental and theoretical fronts, because the inputs and outputs of the molecular processes are unclear and the underlying principles are unknown or too complex. In this work, we focused on improving the accuracy and speed of GRN reconstruction with Dynamic Bayesian based method. A commonly used structure-learning algorithm is based on REVEAL (Reverse Engineering Algorithm). However, this method has some limitations when it is used for reconstructing GRNs. For instance, the two-stage temporal Bayes network (2TBN) cannot be well recovered by application of REVEAL; it has low accuracy and speed for high dimensionality networks that has above a hundred nodes; and it even cannot accomplish the task of reconstructing a network with 400 nodes. We implemented an algorithm for DBN structure learning with Friedman\u27s score function to replace REVEAL, and tested it on reconstruction of both synthetic networks and real yeast networks and compared it with REVEAL in the absence or presence of preprocessed network generated by Zou and Conzen\u27s algorithm. The new score metric improved the precision and recall of GRN reconstruction. Networks of gene interactions were reconstructed using a Dynamic Bayesian Network (DBN) approach and were analyzed to identify the mechanism of chemical-induced reversible neurotoxicity through reconstruction of gene regulatory networks in earthworms with tools curating relevant genes from non-model organism\u27s pathway to model organism pathway

Derivative-variable correlation reveals the structure of dynamical networks

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the network adjacency matrix. Our assumptions are the possession of time series describing the network dynamics, and the precise knowledge of the interaction functions. Our method involves a tunable parameter, allowing for the reconstruction precision to be optimized within the constraints of given dynamical data. The method is illustrated on a simple example, and the dependence of the reconstruction precision on the dynamical properties of time series is discussed. Our theory is in principle applicable to any weighted or directed network whose internal interaction functions are known.Comment: Submitted to EPJ

Inferring Network Topology from Complex Dynamics

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is not restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstruct both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of substantial external noise.Comment: 11 pages, 4 figure

Reconstructing propagation networks with natural diversity and identifying hidden sources

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.Comment: 20 pages and 5 figures. For Supplementary information, please see http://www.nature.com/ncomms/2014/140711/ncomms5323/full/ncomms5323.html#

Enhanced reconstruction of weighted networks from strengths and degrees

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naive approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths. This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns