Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

Cell organization in soft media due to active mechanosensing

Adhering cells actively probe the mechanical properties of their environment and use the resulting information to position and orient themselves. We show that a large body of experimental observations can be consistently explained from one unifying principle, namely that cells strengthen contacts and cytoskeleton in the direction of large effective stiffness. Using linear elasticity theory to model the extracellular environment, we calculate optimal cell organization for several situations of interest and find excellent agreement with experiments for fibroblasts, both on elastic substrates and in collagen gels: cells orient in the direction of external tensile strain, they orient parallel and normal to free and clamped surfaces, respectively, and they interact elastically to form strings. Our method can be applied for rational design of tissue equivalents. Moreover our results indicate that the concept of contact guidance has to be reevaluated. We also suggest that cell-matrix contacts are upregulated by large effective stiffness in the environment because in this way, build-up of force is more efficient.Comment: Revtex, 7 pages, 4 Postscript files include

Towards an integrated experimental-theoretical approach for assessing the mechanistic basis of hair and feather morphogenesis

In his seminal 1952 paper, ‘The Chemical Basis of Morphogenesis’, Alan Turing lays down a milestone in the application of theoretical approaches to understand complex biological processes. His deceptively simple demonstration that a system of reacting and diffusing chemicals could, under certain conditions, generate spatial patterning out of homogeneity provided an elegant solution to the problem of how one of nature's most intricate events occurs: the emergence of structure and form in the developing embryo. The molecular revolution that has taken place during the six decades following this landmark publication has now placed this generation of theoreticians and biologists in an excellent position to rigorously test the theory and, encouragingly, a number of systems have emerged that appear to conform to some of Turing's fundamental ideas. In this paper, we describe the history and more recent integration between experiment and theory in one of the key models for understanding pattern formation: the emergence of feathers and hair in the skins of birds and mammals

The subpulse modulation properties of pulsars at 92 cm and the frequency dependence of subpulse modulation

A large sample of pulsars has been observed to study their subpulse modulation at an observing wavelength (when achievable) of both 21 and 92 cm using the Westerbork Synthesis Radio Telescope. In this paper we present the 92-cm data and a comparison is made with the already published 21-cm results. We analysed 191 pulsars at 92 cm using fluctuation spectra. The sample of pulsars is as unbiased as possible towards any particular pulsar characteristics. For 15 pulsars drifting subpulses are discovered for the first time and 26 of the new drifters found in the 21-cm data are confirmed. We discovered nulling for 8 sources and 8 pulsars are found to intermittently emit single pulses that have pulse energies similar to giant pulses. It is estimated that at least half of the total population of pulsars have drifting subpulses when observations with a high enough signal-to-noise ratio would be available. It could well be that the drifting subpulse mechanism is an intrinsic property of the emission mechanism itself, although for some pulsars it is difficult or impossible to detect. Drifting subpulses are in general found at both frequencies, although the chance of detecting drifting subpulses is possibly slightly higher at 92 cm. It appears that the youngest pulsars have the most disordered subpulses and the subpulses become more and more organized into drifting subpulses as the pulsar ages. The correlations with the modulation indices are argued to be consistent with the picture in which the radio emission can be divided in a drifting subpulse signal plus a quasi-steady signal which becomes, on average, stronger at high observing frequencies. The measured values of P3 at the two frequencies are highly correlated, but there is no evidence for a correlation with other pulsar parameters.Comment: 30 pages, 10 figures, accepted for publication in A&A, astro-ph version is missing 191 figures due to file size restrictions. Please download the appendix from http://www.astron.nl/~stappers/wiki/doku.php?id=resources:publication

Elastic interactions of active cells with soft materials

Anchorage-dependent cells collect information on the mechanical properties of the environment through their contractile machineries and use this information to position and orient themselves. Since the probing process is anisotropic, cellular force patterns during active mechanosensing can be modelled as anisotropic force contraction dipoles. Their build-up depends on the mechanical properties of the environment, including elastic rigidity and prestrain. In a finite sized sample, it also depends on sample geometry and boundary conditions through image strain fields. We discuss the interactions of active cells with an elastic environment and compare it to the case of physical force dipoles. Despite marked differences, both cases can be described in the same theoretical framework. We exactly solve the elastic equations for anisotropic force contraction dipoles in different geometries (full space, halfspace and sphere) and with different boundary conditions. These results are then used to predict optimal position and orientation of mechanosensing cells in soft material.Comment: Revtex, 38 pages, 8 Postscript files included; revised version, accepted for publication in Phys. Rev.

Pattern formation of reaction-diffusion system having self-determined flow in the amoeboid organism of Physarum plasmodium

The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critical wave number squared. Contrary to this, wave number isn't explicitly effective with lack of flow or constant flow. Thus, spatial size of pattern is especially important for regulating pattern formation in the plasmodium. On the other hand, the flow term is negligible in the vicinity of bifurcation at infinitely small wave number, and therefore the pattern formation by simple reaction-diffusion will also hold. A physiological role of pattern formation as above is discussed.Comment: REVTeX, one column, 7 pages, no figur

Observations of Non-radial Pulsations in Radio Pulsars

We introduce a model for pulsars in which non-radial oscillations of high spherical degree (l) aligned to the magnetic axis of a spinning neutron star reproduce the morphological features of pulsar beams. In our model, rotation of the pulsar carries a pattern of pulsation nodes underneath our sightline, reproducing the longitude stationary structure seen in average pulse profiles, while the associated time-like oscillations reproduce "drifting subpulses"--features that change their longitude between successive pulsar spins. We will show that the presence of nodal lines can account for observed 180 degree phase jumps in drifting subpulses and their otherwise poor phase stability, even if the time-like oscillations are strictly periodic. Our model can also account for the "mode changes" and "nulls" observed in some pulsars as quasiperiodic changes between pulsation modes of different l or radial overtone n, analogous to pulsation mode changes observed in oscillating white dwarf stars. We will discuss other definitive and testable requirements of our model and show that they are qualitatively supported by existing data. While reserving judgment until the completion of quantitative tests, we are inspired enough by the existing observational support for our model to speculate about the excitation mechanism of the non-radial pulsations, the physics we can learn from them, and their relationship to the period evolution of pulsars.Comment: 28 pages, 9 figures (as separate png files), Astrophysical Journal, in pres

The potential of trading activity income to fund third sector organisations operating in deprived areas

In the United Kingdom, as in other countries, Third Sector Organisations (TSOs) have been drawn towards income sources associated with trading activities (Teasdale, 2010), but many remain reliant on grant funding to support such activities (Chell, 2007). Using a multivariate analysis approach and data from the National Survey of Charities and Social Enterprises (NSCSE), it is found that trading activities are used relatively commonly in deprived areas. These organisations are also more likely to attempt to access public sector funds. This suggests policy-makers need to consider the impact of funding cuts on TSOs in the most deprived areas as TSOs are unlikely achieve their objectives without continuing support

An Empirical Model for the Radio Emission from Pulsars

A model for slow radio pulsars is proposed which involves the entire magnetosphere in the production of the observed radio emission. It is argued that observations of pulsar profiles suggest that a feedback mechanism exists between the star surface and the null charge surface, requiring particle flow in both directions. In their flow to and from the surface the particles execute an azimuthal drift around the magnetic pole, thereby creating a ring of discrete `emission nodes' close to the surface. Motion of the nodes is observed as the well-known subpulse `drift', but is interpreted here as a small residual component of the real particle drift. The nodes can therefore move in either direction, or even remain stationary. A precise fit is found for the pulsar PSR0943+10. Azimuthal interactions between different regions of the magnetosphere depend on the angle between the magnetic and rotation axes and influence the conal type, as observed. The requirement of intermittent weak pair-production in an outergap suggests a natural evolutionary link between radio and gamma-ray pulsars.Comment: 17 pages 8 figure