Motivation The inference of gene regulatory networks (GRNs) from DNA microarray measurements forms a core element of systems biology-based phenotyping. In the recent past, numerous computational methodologies have been formalized to enable the deduction of reliable and testable predictions in today’s biology. However, little focus has been aimed at quantifying how well existing state-of-the-art GRNs correspond to measured gene-expression profiles. Results Here, we present a computational framework that combines the formulation of probabilistic graphical modeling, standard statistical estimation, and integration of high-throughput biological data to explore the global behavior of biological systems and the global consistency between experimentally verified GRNs and corresponding large microarray compendium data. The model is represented as a probabilistic bipartite graph, which can handle highly complex network systems and accommodates partial measurements of diverse biological entities, e.g. messengerRNAs, proteins, metabolites and various stimulators participating in regulatory networks. This method was tested on microarray expression data from the M3D database, corresponding to sub-networks on one of the best researched model organisms, Escherichia coli. Results show a surprisingly high correlation between the observed states and the inferred system’s behavior under various experimental conditions. Availability and implementation Processed data and software implementation using Matlab are freely available at https://github.com/kotiang54/PgmGRNs. Full dataset available from the M3D database.

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In this paper, we derive new analytic expressions for the atmospheric-induced frequency spread of optical plane and spherical waves propagating in a horizontal path and experiencing anisotropic non-Kolmogorov turbulence. The anisotropic spectrum model is based on the assumption that circular symmetry is maintained in the orthogonal xy-plane throughout the path and that it includes the same degree of anisotropy along the direction of propagation for all the turbulence cell sizes. These expressions are developed in the weak fluctuation region using the Rytov approximation method and are independent of the knowledge of the temporal mutual coherence function for the optical waves. We perform our analysis based on a generalized von Karman power spectrum of the index of refraction. The spectrum considers the effect of finite inner and outer scales of turbulence, together with a non-Kolmogorov spectral power exponent α that varies between 3–4. The simulation results show that the anisotropic parameter impacts on the frequency spread by a factor . Moreover the frequency spread is most significant for α values around 3.1.

Accurate prediction of noise propagation in biological networks is key to understanding faithful signal propagation in gene networks as well as for designing noise-tolerant synthetic gene circuits. Knowledge on how biological fluctuations propagate up the development ladder of biological systems is currently lacking. Similarly, little research effort has been devoted to the analysis of error propagation in biological networks. To capture and characterize error evolution, this paper considers a Boolean network (BN) model representation of a biological network such that nodes on the graph represent diverse biological entities, e.g., proteins, genes, messenger-RNAs, etc. In addition, the network edges capture the interactions between nodes. By conducting a density evolution analysis on the graphical model based on node functionalities, a recursive closed-form expression for error propagation is derived. Subsequently, the recursive equation allows us to obtain a necessary condition to guarantee noise-error elimination in dynamic discrete gene networks. Our analytical formulations provide a step toward achieving optimal network parameters for resilience against variability or noise in biology.