1,748 research outputs found
Inference of Sparse Networks with Unobserved Variables. Application to Gene Regulatory Networks
Networks are a unifying framework for modeling complex systems and network
inference problems are frequently encountered in many fields. Here, I develop
and apply a generative approach to network inference (RCweb) for the case when
the network is sparse and the latent (not observed) variables affect the
observed ones. From all possible factor analysis (FA) decompositions explaining
the variance in the data, RCweb selects the FA decomposition that is consistent
with a sparse underlying network. The sparsity constraint is imposed by a novel
method that significantly outperforms (in terms of accuracy, robustness to
noise, complexity scaling, and computational efficiency) Bayesian methods and
MLE methods using l1 norm relaxation such as K-SVD and l1--based sparse
principle component analysis (PCA). Results from simulated models demonstrate
that RCweb recovers exactly the model structures for sparsity as low (as
non-sparse) as 50% and with ratio of unobserved to observed variables as high
as 2. RCweb is robust to noise, with gradual decrease in the parameter ranges
as the noise level increases.Comment: 8 pages, 5 figure
Non-equilibrium phase transitions in biomolecular signal transduction
We study a mechanism for reliable switching in biomolecular
signal-transduction cascades. Steady bistable states are created by system-size
cooperative effects in populations of proteins, in spite of the fact that the
phosphorylation-state transitions of any molecule, by means of which the switch
is implemented, are highly stochastic. The emergence of switching is a
nonequilibrium phase transition in an energetically driven, dissipative system
described by a master equation. We use operator and functional integral methods
from reaction-diffusion theory to solve for the phase structure, noise
spectrum, and escape trajectories and first-passage times of a class of minimal
models of switches, showing how all critical properties for switch behavior can
be computed within a unified framework
An Introductory Guide to Aligning Networks Using SANA, the Simulated Annealing Network Aligner.
Sequence alignment has had an enormous impact on our understanding of biology, evolution, and disease. The alignment of biological networks holds similar promise. Biological networks generally model interactions between biomolecules such as proteins, genes, metabolites, or mRNAs. There is strong evidence that the network topology-the "structure" of the network-is correlated with the functions performed, so that network topology can be used to help predict or understand function. However, unlike sequence comparison and alignment-which is an essentially solved problem-network comparison and alignment is an NP-complete problem for which heuristic algorithms must be used.Here we introduce SANA, the Simulated Annealing Network Aligner. SANA is one of many algorithms proposed for the arena of biological network alignment. In the context of global network alignment, SANA stands out for its speed, memory efficiency, ease-of-use, and flexibility in the arena of producing alignments between two or more networks. SANA produces better alignments in minutes on a laptop than most other algorithms can produce in hours or days of CPU time on large server-class machines. We walk the user through how to use SANA for several types of biomolecular networks
Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle
Time-series of high throughput gene sequencing data intended for gene
regulatory network (GRN) inference are often short due to the high costs of
sampling cell systems. Moreover, experimentalists lack a set of quantitative
guidelines that prescribe the minimal number of samples required to infer a
reliable GRN model. We study the temporal resolution of data vs quality of GRN
inference in order to ultimately overcome this deficit. The evolution of a
Markovian jump process model for the Ras/cAMP/PKA pathway of proteins and
metabolites in the G1 phase of the Saccharomyces cerevisiae cell cycle is
sampled at a number of different rates. For each time-series we infer a linear
regression model of the GRN using the LASSO method. The inferred network
topology is evaluated in terms of the area under the precision-recall curve
AUPR. By plotting the AUPR against the number of samples, we show that the
trade-off has a, roughly speaking, sigmoid shape. An optimal number of samples
corresponds to values on the ridge of the sigmoid
Spectral Alignment of Networks
Network alignment refers to the problem of finding a bijective mapping across vertices of two or more graphs to maximize the number of overlapping edges and/or to minimize the number of mismatched interactions across networks. This paper introduces a network alignment algorithm inspired by eigenvector analysis which creates a simple relaxation for the underlying quadratic assignment problem. Our method relaxes binary assignment constraints along the leading eigenvector of an alignment matrix which captures the structure of matched and mismatched interactions across networks. Our proposed algorithm denoted by EigeAlign has two steps. First, it computes the Perron-Frobenius eigenvector of the alignment matrix. Second, it uses this eigenvector in a linear optimization framework of maximum weight bipartite matching to infer bijective mappings across vertices of two graphs. Unlike existing network alignment methods, EigenAlign considers both matched and mismatched interactions in its optimization and therefore, it is effective in aligning networks even with low similarity. We show that, when certain technical conditions hold, the relaxation given by EigenAlign is asymptotically exact over Erdos-Renyi graphs with high probability. Moreover, for modular network structures, we show that EigenAlign can be used to split the large quadratic assignment optimization into small subproblems, enabling the use of computationally expensive, but tight semidefinite relaxations over each subproblem. Through simulations, we show the effectiveness of the EigenAlign algorithm in aligning various network structures including Erdos-Renyi, power law, and stochastic block models, under different noise models. Finally, we apply EigenAlign to compare gene regulatory networks across human, fly and worm species which we infer by integrating genome-wide functional and physical genomics datasets from ENCODE and modENCODE consortia. EigenAlign infers conserved regulatory interactions across these species despite large evolutionary distances spanned. We find strong conservation of centrally-connected genes and some biological pathways, especially for human-fly comparisons
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