Incomplete penetrance: the role of stochasticity in developmental cell colonization

Available online: 3 June 2015Cell colonization during embryonic development involves cells migrating and proliferating over growing tissues. Unsuccessful colonization, resulting from genetic causes, can result in various birth defects. However not all individuals with the same mutation show the disease. This is termed incomplete penetrance, and it even extends to discordancy in monozygotic (identical) twins. A one-dimensional agent-based model of cell migration and proliferation within a growing tissue is presented, where the position of every cell is recorded at any time. We develop a new model that approximates this agent-based process – rather than requiring the precise configuration of cells within the tissue, the new model records the total number of cells, the position of the most advanced cell, and then invokes an approximation for how the cells are distributed. The probability mass function (PMF) for the most advanced cell is obtained for both the agent-based model and its approximation. The two PMFs compare extremely well, but using the approximation is computationally faster. Success or failure of colonization is probabilistic. For example for sufficiently high proliferation rate the colonization is assured. However, if the proliferation rate is sufficiently low, there will be a lower, say 50%, chance of success. These results provide insights into the puzzle of incomplete penetrance of a disease phenotype, especially in monozygotic twins. Indeed, stochastic cell behavior (amplified by disease-causing mutations) within the colonization process may play a key role in incomplete penetrance, rather than differences in genes, their expression or environmental conditions.Benjamin J. Binder, Kerry A. Landman, Donald F. Newgreen, Joshua V. Ros

Generalized Contour Dynamics: A Review

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow

Tumour dynamics and necrosis: surface tension and stability

A model is developed for the motion of cells within a multicell spherical tumour. The model allows either for the intercellular forces to be in compression and cells to be compacted to a fixed number density, or for the cell number density to fall and cells to become isolated from each other. The model develops necrotic regions naturally due to force balances rather than being directly attributable to a critical oxygen concentration. These necrotic regions may result in a gradual reduction in local cell density rather than jump to a completely dead region.Numerical and analytical analysis of the spherically symmetric model shows that the long time behaviour of the spheroid depends on any surface tension effects created by cells on the outer surface. For small surface tension the spheroid grows linearly in time developing a large necrotic region, while for larger surface tension the growth can be halted. The linear stability to spherically symmetric perturbations of all the possible resulting steady states is revealed

Modelling moisture uptake in a cereal grain

Recent experimental data have revealed the spatial and temporal structure of moisture content within a cereal grain immersed in boiling water. A simple model of the water's motion is presented, guided by the observed behaviour, which allows for nonlinear (exponential) diffusion within the grain and a constant mass-transfer coefficient to represent the pericarp on the outer surface. Numerical results are presented illustrating the close relationship of the predictions to the experimental results, with the mass-transfer coefficient as a fitting parameter. The model is studied using asymptotic analysis, in the limit of large activation energy in the diffusion coefficient and large mass transfer. The analysis gives insight into the three phases of the process, consisting of initial linear diffusion, linear motion of the moisture front into the grain, and slow filling of the grain in a relatively uniform manner. The problem is also studied using mean-action-time analysis to derive simple expressions for the time for the grain to saturate

Analytic solution for the non-linear drying problem

Recently, Landman, Pel and Kaasschieter proposed an analytic solution for a non-linear drying problem using a quasi-steady state solution. This analytic model for drying is explained here. An important consequence of this model is that the drying front has a constant speed when it is entering the material. This is also observed in experiments. On the basis of this constant drying front speed comparisons are made between the analytic model and numerical simulations. Finally comparisons are made between measured moisture profiles during drying and the analytic model