Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification

The Complexity of Admissibility in Omega-Regular Games

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this paper, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies

Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable

Duality Violation and the K --> pi pi Electroweak Penguin Operator Matrix Elements from Hadronic Tau Decays

We discuss a preliminary study of the impact of duality violations on extractions from tau decay data of the D=6 VEVs which determine chiral limit Standard Model K-->pi pi matrix elements of the electroweak penguin operators.Comment: 4 pages, 5 figures, prepared for the Proceedings of the 11th Particle and Nuclear Intersections Conference (PANIC 2011), Boston, USA, July 24-29, 201

Solute transport within porous biofilms: diffusion or dispersion?

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behaviour by controllling nutrient supply, evacuation of waste products and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilmscale. We show that solute transport may be described via two coupled partial differential equations for the averaged concentrations, or telegrapher’s equations. These models are particularly relevant for chemical species, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterised by a second-order tensor whose components depend on: (1) the topology of the channels’ network; (2) the solute’s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion-dominated, this analysis shows that dispersion effects may significantly contribute to transport

The interplay between tissue growth and scaffold degradation in engineered tissue constructs

In vitro tissue engineering is emerging as a potential tool to meet the high demand for replacement tissue, caused by the increased incidence of tissue degeneration and damage. A key challenge in this field is ensuring that the mechanical properties of the engineered tissue are appropriate for the in vivo environment. Achieving this goal will require detailed understanding of the interplay between cell proliferation, extracellular matrix (ECM) deposition and scaffold degradation.\ud \ud In this paper, we use a mathematical model (based upon a multiphase continuum framework) to investigate the interplay between tissue growth and scaffold degradation during tissue construct evolution in vitro. Our model accommodates a cell population and culture medium, modelled as viscous fluids, together with a porous scaffold and ECM deposited by the cells, represented as rigid porous materials. We focus on tissue growth within a perfusion bioreactor system, and investigate how the predicted tissue composition is altered under the influence of (i) differential interactions between cells and the supporting scaffold and their associated ECM, (ii) scaffold degradation, and (iii) mechanotransduction-regulated cell proliferation and ECM deposition.\ud \ud Numerical simulation of the model equations reveals that scaffold heterogeneity typical of that obtained from μCT scans of tissue engineering scaffolds can lead to significant variation in the flow-induced mechanical stimuli experienced by cells seeded in the scaffold. This leads to strong heterogeneity in the deposition of ECM. Furthermore, preferential adherence of cells to the ECM in favour of the artificial scaffold appears to have no significant influence on the eventual construct composition; adherence of cells to these supporting structures does, however, lead to cell and ECM distributions which mimic and exaggerate the heterogeneity of the underlying scaffold. Such phenomena have important ramifications for the mechanical integrity of engineered tissue constructs and their suitability for implantation in vivo

A temperate river estuary is a sink for methanotrophs adapted to extremes of pH, temperature and salinity

River Tyne (UK) estuarine sediments harbour a genetically and functionally diverse community of methane-oxidizing bacteria (methanotrophs), the composition and activity of which were directly influenced by imposed environmental conditions (pH, salinity, temperature) that extended far beyond those found in situ. In aerobic sediment slurries methane oxidation rates were monitored together with the diversity of a functional gene marker for methanotrophs (pmoA). Under near in situ conditions (4-30°C, pH 6-8, 1-15gl-1 NaCl), communities were enriched by sequences affiliated with Methylobacter and Methylomonas spp. and specifically a Methylobacter psychrophilus-related species at 4-21°C. More extreme conditions, namely high temperatures ≥40°C, high ≥9 and low ≤5 pH, and high salinities ≥35gl-1 selected for putative thermophiles (Methylocaldum), acidophiles (Methylosoma) and haloalkaliphiles (Methylomicrobium). The presence of these extreme methanotrophs (unlikely to be part of the active community in situ) indicates passive dispersal from surrounding environments into the estuary

Preparation of Inner Ear Sensory Hair Bundles for High Resolution Scanning Electron Microscopy

Chemical fixation techniques for preservation of sensory hair bundles in the mammalian inner ear for scanning electron microscopy (SEM) are reviewed. Fixatives employed were glutaraldehyde, glutaraldehyde-picrate, glutaraldehyde-tannic acid, glutaraldehyde-formaldehyde, glutaraldehyde followed by postfixation with osmium tetroxide and the osmium thiocarbohydrazide (OTOTO) method. Dehydration was routinely accomplished with ascending grades of acetone followed by critical point drying with liquid CO2 or fluorocarbon sublimation. Specimens other than those prepared by the OTOTO method were metal coated with gold, gold-palladium or platinum. Material was viewed at high resolution (2-3 nm) in a transmission electron microscope (TEM) fitted with a scanning system and an LaB6 filament. A few specimens, which were either coated with platinum, carbon or uncoated, were examined in a field emission SEM. We have concluded that glutaraldehyde fixation followed by critical point drying with CO2 and coating with platinum gives the best general preservation of stereocilia and their cross-links for routine high resolution SEM, but that carbon-coated or uncoated specimens offer potentially better results free from metal coating artifacts when viewed with field emission SEM. These methods have enabled us to make novel observations upon the surface detail and cross-links of stereocilia which have helped considerably in understanding the mechanical properties of hair bundles particularly in relation to sensory transduction. We have found that stereocilial surface detail and cross-links are sensitive to fixation regimes. In particular they are degraded by exposure to osmium tetroxide; they are also highly labile since deleterious changes in their appearance can be detected as early as 15 minutes following death

Computing eigenvalues of ordinary differential equations

Discretisations of differential eigenvalue problems have a sensitivity to perturbations which is asymptotically least as h ? 0 when the differential equation is in first order system form. Both second and fourth order accurate discretisations of the first order system are straightforward to derive and lead to generalised eigenvalue problems of the form ?? where both A and B are narrow-banded, block bidiagonal (hence unsymmetric) matrices, and typically B is singular. Solutions of the differential equation associated with eigenvalues of small magnitude are best determined by the discretisations. Thus Krylov subspace methods (for example) require A to be invertible and seek large solutions of ?? This already requires rational methods in principle. It follows that rapidly convergent methods based on inverse iteration applied to the original formulation as a nonstandard generalised eigenvalue problem prove attractive for the narrow-banded systems considered here. Also they have the advantage that they are applicable under the weaker condition A ? ?B ? =? . We have had extensive experience with a method combining aspects of Newton's method and inverse iteration and having a convergence rate of 3.56 . Our implementation combines this basic algorithm with a limiting form of Weilandt deflation to find a sequence of eigenvalues. It has proved extremely satisfactory in a range of applications. This formulation has the further advantage that it is easy to insert the eigenvalue calculation inside an outer loop to satisfy a constraint on an auxiliary parameter. Examples to illustrate both the robustness of the deflation and the flexibility of the approach are provided