Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process

Breakage-Fusion-Bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. The process has parallels with paper folding sequences that arise when a piece of paper is folded several times and then unfolded. Here we adapt such methods to study the breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are 2^(n(n-1)/2) qualitatively distinct evolutions involving n breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the fold positions, to determine evolution likelihoods, and also describe how amplicons become localised. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples

Daily reduction of oral malodor with the use of a sonic tongue brush combined with an antibacterial tongue spray in a randomized cross-over clinical investigation

Abstract The objective of this clinical investigation was to test the effectiveness on breath odor of a newly designed sonic tongue brush (TongueCare+, TC). It consists of a soft silicone brush optimally designed based on the tongue's anatomy to remove bacterial biofilm from the tongue's complex surface, and it is coupled with a sonic power toothbrush handle. TC was used in combination with an antibacterial tongue spray (BreathRx, BRx) containing 0.09% cetylpyridinium chloride and 0.7% zinc gluconate. A total of 21 participants with oral malodor exceeding the threshold for recognition took part in this cross-over clinical investigation, which consisted of a single use of four treatment arms with one week washout period in between. The treatments consisted of: (1) TC  +  BRx, (2) TC  +  water, (3) BRx and (4) water. Malodor levels and bacterial density were monitored up to 6 h by organoleptic scoring and selective plating, respectively. The organoleptic score and bacterial density were significantly lower after using TC  +  BRx compared to all alternative treatments at all time points. A significant decrease in both parameters was detected after a single use of TC  +  BRx, from levels characteristic of high oral malodor, to barely noticeable levels after treatment and this was maintained up to 6 h. Moreover, we identified a significant positive correlation between bacterial density and organoleptic score, confirming that bacterial tongue biofilm is the root cause of oral malodor in these subjects. The results of this clinical investigation demonstrated that the combined treatment of a sonic tongue brush with the antibacterial tongue spray is able to deliver more than 6 h of fresh breath following a single use. The clinical investigation was registered at the ISRCTN registry under study identification number ISRCTN38199132

Spectral statistics for quantized skew translations on the torus

We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level--spacing distribution and other common spectral statistics, like the number variance, do not exist in the semiclassical limit.Comment: 7 pages. One figure, include

Quantization of multidimensional cat maps

In this work we study cat maps with many degrees of freedom. Classical cat maps are classified using the Cayley parametrization of symplectic matrices and the closely associated center and chord generating functions. Particular attention is dedicated to loxodromic behavior, which is a new feature of two-dimensional maps. The maps are then quantized using a recently developed Weyl representation on the torus and the general condition on the Floquet angles is derived for a particular map to be quantizable. The semiclassical approximation is exact, regardless of the dimensionality or of the nature of the fixed points.Comment: 33 pages, latex, 6 figures, Submitted to Nonlinearit

Effects of Noise on Ecological Invasion Processes: Bacteriophage-mediated Competition in Bacteria

Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in nature. Using an experimental system of bacteriophage-mediated competition in bacterial populations and a deterministic model, we have shown in [Joo et al 2005] that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of the initial phage concentration and other phage and host parameters such as the infection-causing contact rate, the spontaneous and infection-induced lysis rates, and the phage burst size. Here we investigate the effects of stochastic fluctuations on bacterial invasion facilitated by bacteriophage, and examine the validity of the deterministic approach. We use both numerical and analytical methods of stochastic processes to identify the source of noise and assess its magnitude. We show that the conclusions obtained from the deterministic model are robust against stochastic fluctuations, yet deviations become prominently large when the phage are more pathological to the invading bacterial strain.Comment: 39 pages, 7 figure

Exact, time-independent estimation of clone size distributions in normal and mutated cells

Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size distributions in vivo are complicated by multiple cell types, and overlapping birth and death processes. This has led to the increased need for mathematically informed models to understand their biological significance. Standard approaches usually require knowledge of clonal age. We show that modelling on clone size independent of time is an alternative method that offers certain analytical advantages; it can help parameterize these models, and obtain distributions for counts of mutated or proliferating cells, for example. When applied to a general birth-death process common in epithelial progenitors this takes the form of a gamblers ruin problem, the solution of which relates to counting Motzkin lattice paths. Applying this approach to mutational processes, an alternative, exact, formulation of the classic Luria Delbruck problem emerges. This approach can be extended beyond neutral models of mutant clonal evolution, and also describe some distributions relating to sub-clones within a tumour. The approaches above are generally applicable to any Markovian branching process where the dynamics of different "coloured" daughter branches are of interest

Ab-Initio Calculation of Molecular Aggregation Effects: a Coumarin-343 Case Study

We present time-dependent density functional theory (TDDFT) calculations for single and dimerized Coumarin-343 molecules in order to investigate the quantum mechanical effects of chromophore aggregation in extended systems designed to function as a new generation of sensors and light-harvesting devices. Using the single-chromophore results, we describe the construction of effective Hamiltonians to predict the excitonic properties of aggregate systems. We compare the electronic coupling properties predicted by such effective Hamiltonians to those obtained from TDDFT calculations of dimers, and to the coupling predicted by the transition density cube (TDC) method. We determine the accuracy of the dipole-dipole approximation and TDC with respect to the separation distance and orientation of the dimers. In particular, we investigate the effects of including Coulomb coupling terms ignored in the typical tight-binding effective Hamiltonian. We also examine effects of orbital relaxation which cannot be captured by either of these models

Computational Cancer Biology: An Evolutionary Perspective

ISSN:1553-734XISSN:1553-735

A Path Integral Approach to Age Dependent Branching Processes

Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division