Exact solution of a two-type branching process: Clone size distribution in cell division kinetics

We study a two-type branching process which provides excellent description of experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The model involves only a single type of progenitor cell, and does not require support from a self-renewed population of stem cells. The progenitor cells divide and may differentiate into post-mitotic cells. We derive an exact solution of this model in terms of generating functions for the total number of cells, and for the number of cells of different types. We also deduce large time asymptotic behaviors drawing on our exact results, and on an independent diffusion approximation.Comment: 16 page

Digital MDA for enumeration of total nucleic acid contamination

Multiple displacement amplification (MDA) is an isothermal, sequence-independent method for the amplification of high molecular weight DNA that is driven by ϕ29 DNA polymerase (DNAP). Here we report digital MDA (dMDA), an ultrasensitive method for quantifying nucleic acid fragments of unknown sequence. We use the new assay to show that our custom ϕ29 DNAP preparation is free of contamination at the limit of detection of the dMDA assay (1 contaminating molecule per assay microliter). Contamination in commercially available preparations is also investigated. The results of the dMDA assay provide strong evidence that the so-called ‘template-independent’ MDA background can be attributed to high-molecular weight contaminants and is not primer-derived in the commercial kits tested. dMDA is orders of magnitude more sensitive than PCR-based techniques for detection of microbial genomic DNA fragments and opens up new possibilities for the ultrasensitive quantification of DNA fragments in a wide variety of application areas using MDA chemistry and off-the-shelf hardware developed for digital PCR

Mapping the spatiotemporal dynamics of calcium signaling in cellular neural networks using optical flow

An optical flow gradient algorithm was applied to spontaneously forming net- works of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution. Optical flow estimates the direction and speed of motion of objects in an image between subsequent frames in a recorded digital sequence of images (i.e. a movie). Computed vector field outputs by the algorithm were able to track the spatiotemporal dynamics of calcium signaling pat- terns. We begin by briefly reviewing the mathematics of the optical flow algorithm, and then describe how to solve for the displacement vectors and how to measure their reliability. We then compare computed flow vectors with manually estimated vectors for the progression of a calcium signal recorded from representative astrocyte cultures. Finally, we applied the algorithm to preparations of primary astrocytes and hippocampal neurons and to the rMC-1 Muller glial cell line in order to illustrate the capability of the algorithm for capturing different types of spatiotemporal calcium activity. We discuss the imaging requirements, parameter selection and threshold selection for reliable measurements, and offer perspectives on uses of the vector data.Comment: 23 pages, 5 figures. Peer reviewed accepted version in press in Annals of Biomedical Engineerin

Network centrality: an introduction

Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the node centrality in networks. Here, we review the main centrality measures and discuss their main features and limitations. The influence of network centrality on epidemic spreading and synchronization is also pointed out in this chapter. Moreover, we present the application of centrality measures to understand the function of complex systems, including biological and cortical networks. Finally, we discuss some perspectives and challenges to generalize centrality measures for multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A Mathematical modeling approach" by Springe

Nonlinear analysis of biomagnetic signals recorded from uterine myomas

OBJECTIVE: To determine if there is any non-linearity in the biomagnetic recordings of uterine myomas and to find any differences that may be present in the mechanisms underlying their signal dynamics. METHODS: Twenty-four women were included in the study. Sixteen of them were characterised with large myomas and 8 with small ones. Uterine artery waveform measurements were evaluated by use of Pulsatility Index (PI) (normal value PI<1.45). RESULTS: Applying nonlinear analysis to the biomagnetic signals of the uterine myomas, we observed a clear saturation value for the group of large ones (mean = 11.35 ± 1.49) and no saturation for the small ones. CONCLUSION: The comparison of the saturation values in the biomagnetic recordings of large and small myomas may be a valuable tool in the evaluation of functional changes in their dynamic behavior

Combinatorial CRISPR-Cas9 screens for de novo mapping of genetic interactions.

We developed a systematic approach to map human genetic networks by combinatorial CRISPR-Cas9 perturbations coupled to robust analysis of growth kinetics. We targeted all pairs of 73 cancer genes with dual guide RNAs in three cell lines, comprising 141,912 tests of interaction. Numerous therapeutically relevant interactions were identified, and these patterns replicated with combinatorial drugs at 75% precision. From these results, we anticipate that cellular context will be critical to synthetic-lethal therapies

Deriving a mutation index of carcinogenicity using protein structure and protein interfaces

With the advent of Next Generation Sequencing the identification of mutations in the genomes of healthy and diseased tissues has become commonplace. While much progress has been made to elucidate the aetiology of disease processes in cancer, the contributions to disease that many individual mutations make remain to be characterised and their downstream consequences on cancer phenotypes remain to be understood. Missense mutations commonly occur in cancers and their consequences remain challenging to predict. However, this knowledge is becoming more vital, for both assessing disease progression and for stratifying drug treatment regimes. Coupled with structural data, comprehensive genomic databases of mutations such as the 1000 Genomes project and COSMIC give an opportunity to investigate general principles of how cancer mutations disrupt proteins and their interactions at the molecular and network level. We describe a comprehensive comparison of cancer and neutral missense mutations; by combining features derived from structural and interface properties we have developed a carcinogenicity predictor, InCa (Index of Carcinogenicity). Upon comparison with other methods, we observe that InCa can predict mutations that might not be detected by other methods. We also discuss general limitations shared by all predictors that attempt to predict driver mutations and discuss how this could impact high-throughput predictions. A web interface to a server implementation is publicly available at http://inca.icr.ac.uk/

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic

DNA methylation analysis by digital bisulfite genomic sequencing and digital MethyLight

Alterations in cytosine-5 DNA methylation are frequently observed in most types of human cancer. Although assays utilizing PCR amplification of bisulfite-converted DNA are widely employed to analyze these DNA methylation alterations, they are generally limited in throughput capacity, detection sensitivity, and or resolution. Digital PCR, in which a DNA sample is analyzed in distributive fashion over multiple reaction chambers, allows for enumeration of discrete template DNA molecules, as well as sequestration of non-specific primer annealing templates into negative chambers, thereby increasing the signal-to-noise ratio in positive chambers. Here, we have applied digital PCR technology to bisulfite-converted DNA for single-molecule high-resolution DNA methylation analysis and for increased sensitivity DNA methylation detection. We developed digital bisulfite genomic DNA sequencing to efficiently determine single-basepair DNA methylation patterns on single-molecule DNA templates without an interim cloning step. We also developed digital MethyLight, which surpasses traditional MethyLight in detection sensitivity and quantitative accuracy for low quantities of DNA. Using digital MethyLight, we identified single-molecule, cancer-specific DNA hypermethylation events in the CpG islands of RUNX3, CLDN5 and FOXE1 present in plasma samples from breast cancer patients