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

Structure-dependent ferroelectricity of niobium clusters (NbN, N=2-52)

The ground-state structures and ferroelectric properties of NbN (N=2-52) have been investigated by a combination of density-functional theory (DFT) in the generalized gradient approximation (GGA) and an unbiased global search with the guided simulated annealing. It is found that the electric dipole moment (EDM) exists in the most of NbN and varies considerably with their sizes. And the larger NbN (N>=25) prefer the amorphous packing. Most importantly, our numerical EDM values of NbN (N>=38) exhibit an extraordinary even-odd oscillation, which is well consistent with the experimental observation, showing a close relationship with the geometrical structures of NbN. Finally, an inverse coordination number (ICN) function is proposed to account for the structural relation of the EDM values, especially their even-odd oscillations starting from Nb38.Comment: 11 pages and 4 figure

Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Preventing pain on injection of propofol: A comparison between lignocaine pre-treatment and lignocaine added to propofol

Publisher's copy made available with the permission of the publisherA randomized double-blind study compared two methods of preventing the pain from injection of propofol, lignocaine pre-treatment followed by propofol and lignocaine added to propofol. One hundred patients received a 4 ml solution intravenously with a venous tourniquet for 1 minute, followed by propofol mixed with 2 ml of solution. Patients were divided into two treatment groups of 50 patients each: 4 ml 1% lignocaine pre-treatment followed by propofol and 2 ml saline, or 4 ml saline followed by propofol and 2 ml 2% lignocaine. Pain was assessed with a 100 mm visual analogue scale after induction and in recovery. The incidence of injection pain was 8% in the propofol mixed with lignocaine group, and 28% in the lignocaine pre-treatment group. This difference is statistically significant (P=0.017). For those patients who had pain, the mean pain score was 26.5 on induction for the propofol with lignocaine group (n=4), while the mean score was 44.4 for the pre-treatment group (n=13). The difference was not statistically significant (P=0.25). None of the propofol mixed with lignocaine group recalled pain, while 13 of the pre-treatment group did so. Lignocaine pre-treatment does not improve the immediate or the recalled comfort of patients during propofol induction when compared to lignocaine added to propofol. It is recommended that lignocaine should be added to propofol for induction rather than given before induction.P. Lee, W. J. Russellhttp://www.aaic.net.au/Article.asp?D=200339

Nestling diet, secondary sexual traits and fitness in the zebra finch

We examined the effect of nestling diet quality on a suite of physiological, morphological and life-history traits in adult male zebra finches,Taeniopygia guttata. Compared with birds reared on a supplemented diet, nestlings reared on a seed-only diet showed a reduced rate of growth and reduced cell-mediated immune function as measured by an in vivo response to aT lymphocyte-dependent mitogen. There were no differences between birds reared on the two diets in any of the following adult traits: body size, primary sexual traits (testes mass, numbers of stored sperm, sperm function, velocity and morphology), secondary sexual traits (beak colour and song rate), serological traits or immunological traits. The only differences we detected were a lower body mass and a greater proportion of individuals with plumage abnormalities among those reared on a seed-only diet (this latter effect was transient). The fact that male zebra finches reared on a seed-only diet were, as adults, virtually indistinguishable from those reared on a supple- mented diet, despite having reduced growth and immune function as nestlings, demonstrates that they subsequently compensated through the di¡erential allocation of resources. Our results indicate that differ- ential allocation is costly in terms of fitness since birds reared on a seed-only diet experienced a significantly greater mortality rate than those reared on a supplemented diet. This in turn suggests the existence of a trade-of between the development of traits important for reproduction, such as primary and secondary sexual traits and longevity

Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory

The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of the Green's functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not only possible to apply the Source Galerkin method to higher dimensional field theories, but also leads to a new approach to perturbation theory calculations in scalar and fermionic field theories. This report summarizes the methodologies for solving quantum field theories with the Source Galerkin method and for performing perturbation theory calculations using Sinc approximations.Comment: Lattice2001(theorydevelop

A simplified protocol for detecting two systemic bait markers (Rhodamine B and iophenoxic acid) in small mammals

We developed a method of quantifying levels of fluorescence in the whiskers of wild stoats (Mustela erminea) using fluorescence microscopy and Axiovision 3.0.6.1 software. The method allows for discrimination between natural fluorescence present in or on a whisker, and the fluorescence resulting from the ingestion of the systemic marker Rhodamine B (RB), although some visual judgement is still required. We also developed a new high performance liquid chromatography (HPLC) protocol for detecting the systemic marker iophenoxic acid (IPA) in the blood of laboratory rats (Rattus norvegicus) and wild stoats. With this method, the blood of an animal that has consumed IPA can be tested for the presence of the foreign IPA compound itself. This is a more reliable test than the previous method, which measured the raised level of natural blood protein-bound iodine correlated with IPA absorption. The quantity of blood required from animal subjects is very small (10 μl), so the testing is less intrusive and the method can be extended to smaller species. The extraction technique uses methanol, rather than acids and heavy metal salts, thereby simplifying the procedure. Recovery of IPA is quantitative, giving a highly reliable reading. In experiments on captive rats the IPA method proved successful. Of 12 positively marked carcasses, two that had not been frozen for the 24 h before blood samples were taken showed relatively lower IPA levels. The same IPA detection method, as well as the whisker analysis for RB, was applied successfully to a population of wild stoats to which both Rhodamine B and IPA were made available at bait stations. The presence of both bait markers was detectable in rats for at least 21 days and in stoats for at least 27 days

Plasmonic Resonances and Electromagnetic Forces Between Coupled Silver Nanowires

We compute the electromagnetic response and corresponding forces between two silver nanowires. The wires are illuminated by a plane wave which has the electric field vector perpendicular to the axis of the wires, insuring that plasmonic resonances can be excited. We consider a nontrivial square cross section geometry that has dimensions on the order of $0.1 \lambda$, where $\lambda$ is the wavelength of the incident electromagnetic field. We find that due to the plasmonic resonance, there occurs great enhancement of the direct and mutual electromagnetic forces that are exerted on the nanowires. The Lippman-Schwinger volume integral equation is implemented to obtain solutions to Maxwell's equations for various $\lambda$ and separation distances between wires. The forces are computed using Maxwell's stress tensor and numerical results are shown for both on and off resonant conditions

A First Principle Approach to Rescale the Dynamics of Simulated Coarse-Grained Macromolecular Liquids

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the Generalized Langevin Equations (GLE) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse-graining: monomeric as a bead-and-spring model and molecular as a soft-colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse-graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse-graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples.Comment: 21 pages, 6 figures, 6 tables. Submitted to Phys. Rev.