Exact solving and sensitivity analysis of stochastic continuous time Boolean models.

BACKGROUND: Solutions to stochastic Boolean models are usually estimated by Monte Carlo simulations, but as the state space of these models can be enormous, there is an inherent uncertainty about the accuracy of Monte Carlo estimates and whether simulations have reached all attractors. Moreover, these models have timescale parameters (transition rates) that the probability values of stationary solutions depend on in complex ways, raising the necessity of parameter sensitivity analysis. We address these two issues by an exact calculation method for this class of models. RESULTS: We show that the stationary probability values of the attractors of stochastic (asynchronous) continuous time Boolean models can be exactly calculated. The calculation does not require Monte Carlo simulations, instead it uses graph theoretical and matrix calculation methods previously applied in the context of chemical kinetics. In this version of the asynchronous updating framework the states of a logical model define a continuous time Markov chain and for a given initial condition the stationary solution is fully defined by the right and left nullspace of the master equation's kinetic matrix. We use topological sorting of the state transition graph and the dependencies between the nullspaces and the kinetic matrix to derive the stationary solution without simulations. We apply this calculation to several published Boolean models to analyze the under-explored question of the effect of transition rates on the stationary solutions and show they can be sensitive to parameter changes. The analysis distinguishes processes robust or, alternatively, sensitive to parameter values, providing both methodological and biological insights. CONCLUSION: Up to an intermediate size (the biggest model analyzed is 23 nodes) stochastic Boolean models can be efficiently solved by an exact matrix method, without using Monte Carlo simulations. Sensitivity analysis with respect to the model's timescale parameters often reveals a small subset of all parameters that primarily determine the stationary probability of attractor states.

Collective intelligence defines biological functions in Wikipedia as communities in the hidden protein connection network.

English Wikipedia, containing more than five millions articles, has approximately eleven thousands web pages devoted to proteins or genes most of which were generated by the Gene Wiki project. These pages contain information about interactions between proteins and their functional relationships. At the same time, they are interconnected with other Wikipedia pages describing biological functions, diseases, drugs and other topics curated by independent, not coordinated collective efforts. Therefore, Wikipedia contains a directed network of protein functional relations or physical interactions embedded into the global network of the encyclopedia terms, which defines hidden (indirect) functional proximity between proteins. We applied the recently developed reduced Google Matrix (REGOMAX) algorithm in order to extract the network of hidden functional connections between proteins in Wikipedia. In this network we discovered tight communities which reflect areas of interest in molecular biology or medicine and can be considered as definitions of biological functions shaped by collective intelligence. Moreover, by comparing two snapshots of Wikipedia graph (from years 2013 and 2017), we studied the evolution of the network of direct and hidden protein connections. We concluded that the hidden connections are more dynamic compared to the direct ones and that the size of the hidden interaction communities grows with time. We recapitulate the results of Wikipedia protein community analysis and annotation in the form of an interactive online map, which can serve as a portal to the Gene Wiki project.

QuantumClone: clonal assessment of functional mutations in cancer based on a genotype-aware method for clonal reconstruction.

Motivation: In cancer, clonal evolution is assessed based on information coming from single nucleotide variants and copy number alterations. Nonetheless, existing methods often fail to accurately combine information from both sources to truthfully reconstruct clonal populations in a given tumor sample or in a set of tumor samples coming from the same patient. Moreover, previously published methods detect clones from a single set of variants. As a result, compromises have to be done between stringent variant filtering [reducing dispersion in variant allele frequency estimates (VAFs)] and using all biologically relevant variants. Results: We present a framework for defining cancer clones using most reliable variants of high depth of coverage and assigning functional mutations to the detected clones. The key element of our framework is QuantumClone, a method for variant clustering into clones based on VAFs, genotypes of corresponding regions and information about tumor purity. We validated QuantumClone and our framework on simulated data. We then applied our framework to whole genome sequencing data for 19 neuroblastoma trios each including constitutional, diagnosis and relapse samples. We confirmed an enrichment of damaging variants within such pathways as MAPK (mitogen-activated protein kinases), neuritogenesis, epithelial-mesenchymal transition, cell survival and DNA repair. Most pathways had more damaging variants in the expanding clones compared to shrinking ones, which can be explained by the increased total number of variants between these two populations. Functional mutational rate varied for ancestral clones and clones shrinking or expanding upon treatment, suggesting changes in clone selection mechanisms at different time points of tumor evolution. Availability and implementation: Source code and binaries of the QuantumClone R package are freely available for download at https://CRAN.R-project.org/package=QuantumClone. Contact: gudrun.schleiermacher@curie.fr or valentina.boeva@inserm.fr. Supplementary information: Supplementary data are available at Bioinformatics online.

HMCan: a method for detecting chromatin modifications in cancer samples using ChIP-seq data.

MOTIVATION: Cancer cells are often characterized by epigenetic changes, which include aberrant histone modifications. In particular, local or regional epigenetic silencing is a common mechanism in cancer for silencing expression of tumor suppressor genes. Though several tools have been created to enable detection of histone marks in ChIP-seq data from normal samples, it is unclear whether these tools can be efficiently applied to ChIP-seq data generated from cancer samples. Indeed, cancer genomes are often characterized by frequent copy number alterations: gains and losses of large regions of chromosomal material. Copy number alterations may create a substantial statistical bias in the evaluation of histone mark signal enrichment and result in underdetection of the signal in the regions of loss and overdetection of the signal in the regions of gain. RESULTS: We present HMCan (Histone modifications in cancer), a tool specially designed to analyze histone modification ChIP-seq data produced from cancer genomes. HMCan corrects for the GC-content and copy number bias and then applies Hidden Markov Models to detect the signal from the corrected data. On simulated data, HMCan outperformed several commonly used tools developed to analyze histone modification data produced from genomes without copy number alterations. HMCan also showed superior results on a ChIP-seq dataset generated for the repressive histone mark H3K27me3 in a bladder cancer cell line. HMCan predictions matched well with experimental data (qPCR validated regions) and included, for example, the previously detected H3K27me3 mark in the promoter of the DLEC1 gene, missed by other tools we tested.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

UNLABELLED: Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. BACKGROUND: There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. RESULTS: Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. CONCLUSIONS: Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

ITALICS: an algorithm for normalization and DNA copy number calling for Affymetrix SNP arrays.

MOTIVATION: Affymetrix SNP arrays can be used to determine the DNA copy number measurement of 11 000-500 000 SNPs along the genome. Their high density facilitates the precise localization of genomic alterations and makes them a powerful tool for studies of cancers and copy number polymorphism. Like other microarray technologies it is influenced by non-relevant sources of variation, requiring correction. Moreover, the amplitude of variation induced by non-relevant effects is similar or greater than the biologically relevant effect (i.e. true copy number), making it difficult to estimate non-relevant effects accurately without including the biologically relevant effect. RESULTS: We addressed this problem by developing ITALICS, a normalization method that estimates both biological and non-relevant effects in an alternate, iterative manner, accurately eliminating irrelevant effects. We compared our normalization method with other existing and available methods, and found that ITALICS outperformed these methods for several in-house datasets and one public dataset. These results were validated biologically by quantitative PCR. AVAILABILITY: The R package ITALICS (ITerative and Alternative normaLIzation and Copy number calling for affymetrix Snp arrays) has been submitted to Bioconductor.