Estimating sample-specific regulatory networks

Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large numbers of samples with measured gene expression profiles to infer connections between genes (or gene products). The result is an aggregate network model representing a single estimate for the likelihood of each interaction, or "edge," in the network. While informative, aggregate models fail to capture the heterogeneity that is represented in any population. Here we propose a method to reverse engineer sample-specific networks from aggregate network models. We demonstrate the accuracy and applicability of our approach in several data sets, including simulated data, microarray expression data from synchronized yeast cells, and RNA-seq data collected from human lymphoblastoid cell lines. We show that these sample-specific networks can be used to study changes in network topology across time and to characterize shifts in gene regulation that may not be apparent in expression data. We believe the ability to generate sample-specific networks will greatly facilitate the application of network methods to the increasingly large, complex, and heterogeneous multi-omic data sets that are currently being generated, and ultimately support the emerging field of precision network medicine

Broadly heterogeneous activation of the master regulator for sporulation in Bacillus subtilis

A model system for investigating how developmental regulatory networks determine cell fate is spore formation in Bacillus subtilis. The master regulator for sporulation is Spo0A, which is activated by phosphorylation via a phosphorelay that is subject to three positive feedback loops. The ultimate decision to sporulate is, however, stochastic in that only a portion of the population sporulates even under optimal conditions. It was previously assumed that activation of Spo0A and hence entry into sporulation is subject to a bistable switch mediated by one or more feedback loops. Here we reinvestigate the basis for bimodality in sporulation. We show that none of the feedback loops is rate limiting for the synthesis and phosphorylation of Spo0A. Instead, the loops ensure a just-in-time supply of relay components for rising levels of phosphorylated Spo0A, with phosphate flux through the relay being limiting for Spo0A activation and sporulation. In addition, genes under Spo0A control did not exhibit a bimodal pattern of expression as expected for a bistable switch. In contrast, we observed a highly heterogeneous pattern of Spo0A activation that increased in a nonlinear manner with time. We present a computational model for the nonlinear increase and propose that the phosphorelay is a noise generator and that only cells that attain a threshold level of phosphorylated Spo0A sporulate.Statistic

Keynote Talk (Cortex seq-FISH study)

Dr Guocheng Yuan (Dana-Farber Cancer Institute, Harvard TH Chan School of Public Health) Lab Website: http://bcb.dfci.harvard.edu/~gcyuan GC will present the SeqFish hackathon studyNon UBCUnreviewedAuthor affiliation: Dana-Farber Cancer InstituteResearche

Optimal Orbits of Hyperbolic Systems

Given a dynamical system and a function f from the state space to the real numbers, an optimal orbit for f is an orbit over which the average of f is maximal. In this paper we discuss some basic mathematical aspects of optimal orbits: existence, sensitivity to perturbations of f , and approximability by periodic orbits with low period. For hyperbolic systems, we conjecture that 1) for (topologically) generic smooth functions, there exists an optimal periodic orbit, and 2) the optimal average can be approximated exponentially well by averages over certain periodic orbits with increasing period. We prove several results Corresponding author. Email: [email protected]. Phone: (301) 405-5090. to support these conjectures. In particular, we show that optimal periodic orbits are insensitive to small C 1 perturbations of f , while the optimality of a non-periodic orbit can be destroyed by arbitrarily small C 1 perturbations. 1 Introduction Recently the following optimization problem..

Collapsing of Chaos in One Dimensional Maps

In their numerical investigation of the family of one dimensional maps f ` (x) = 1 \Gamma 2jxj ` , where ` ? 2, Diamond et al. have observed the surprising numerical phenomenon that a large fraction of initial conditions chosen at random eventually wind up at \Gamma1, a repelling fixed point. This is a numerical artifact because the continuous maps are chaotic and almost every (true) trajectory can be shown to be dense in [\Gamma1; 1]. The goal of this paper is to extend and resolve this obvious contradiction. We model the numerical simulation with a Corresponding author. Email: [email protected]. Phone: (301) 405-4875. randomly selected map. While they used 27 bit precision in computing f ` , we prove for our model that this numerical artifact persists for arbitrary high numerical precision. The fraction of initial points eventually winding up at \Gamma1 remains bounded away from 0 for every numerical precision. PACS: 05.45.+b Keywords: collapsing, natural measure, Schwarzian..

Thermodynamics and Agglomeration Behavior on Spinel Inclusion in Al-Deoxidized Steel Coupling with Mg Treatment

There are many types of non-metallic MgAl2O4 inclusions observed in Al-deoxidized steel coupling with Mg treatment, including single-particle MgAl2O4, agglomerated MgAl2O4, and MgAl2O4-MnS. Thermodynamic calculation shows that MgAl2O4 precipitates in the liquid phase. The phase transformation follows liquid + Al2O3 + MgAl2O4 → liquid + MgAl2O4 → liquid + MgO + MgAl2O4 → liquid + MgO with the Mg content increasing when the Al content is a constant in molten steel, and it is in agreement with the experimental results for the formation of MgAl2O4 in molten steel. The calculation results of various attractive forces between two particles show that the cavity bridge force plays a dominant role in the agglomeration process and results in the agglomerated MgAl2O4. The lattice mismatch calculation result shows that MgAl2O4 can provide effective sites for MnS nucleating in steel