Direction-dependent turning leads to anisotropic diffusion and persistence

Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains

Roche-lobe filling factor of mass-transferring red giants - the PIONIER view

Using the PIONIER visitor instrument that combines the light of the four Auxiliary Telescopes of ESO's Very Large Telescope Interferometer, we measure precisely the diameters of several symbiotic and related stars: HD 352, HD 190658, V1261 Ori, ER Del, FG Ser, and AG Peg. These diameters - in the range of 0.6 to 2.3 milli-arcseconds - are used to assess the filling factor of the Roche lobe of the mass-losing giants and provide indications on the nature of the ongoing mass transfer. We also provide the first spectroscopic orbit of ER Del, based on CORAVEL and HERMES/Mercator observations. The system is found to have an eccentric orbit with a period of 5.7 years. In the case of the symbiotic star FG Ser, we find that the diameter is changing by 13% over the course of 41 days, while the observations of HD 352 are indicative of an elongation. Both these stars are found to have a Roche filling factor close to 1, as is most likely the case for HD 190658 as well, while the three other stars have factors below 0.5-0.6. Our observations reveal the power of interferometry for the study of interacting binary stars - the main limitation in our conclusions being the poorly known distances of the objects.Comment: A&A, in pres

Class of self-limiting growth models in the presence of nonlinear diffusion

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.Comment: RevTex, 13 pages, 5 figures. To appear in Physical Review

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion

How linear features alter predator movement and the functional response

In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic first passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines influence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator–prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were significantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them

Flow cytometric quantification of tumour endothelial cells; an objective alternative for microvessel density assessment

Assessment of microvessel density by immunohistochemical staining is subject to a considerable inter-observer variation, and this has led to variability in correlation between microvessel density and clinical outcome in different studies. In order to improve the method of microvessel density measurement in tumour biopsies, we have developed a rapid, objective and quantitative method using flow cytometry on frozen tissues. Frozen tissue sections of archival tumour material were enzymatically digested. The single-cell suspension was stained for CD31 and CD34 for flow cytometry. The number of endothelial cells was quantified using light scatter- and fluorescence-characteristics. Tumour endothelial cells were detectable in a single cell suspension, and the percentage of endothelial cells detected in 32 colon carcinomas correlated highly (r=0.84, P<0.001) with the immunohistochemical assessment of microvessel density. Flow cytometric endothelial cells quantification was found to be more sensitive especially at lower levels of immunohistochemical microvessel density measurement. The current method was found to be applicable for various tumour types and has the major advantage that it provides a retrospective and quantitative approach to the angiogenic potential of tumours

Hyperbolic traveling waves driven by growth

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ (\epsilon\textgreater{}0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter $\epsilon$: for small $\epsilon$ the behaviour is essentially the same as for the diffusive Fisher-KPP equation. However, for large $\epsilon$ the traveling front with minimal speed is discontinuous and travels at the maximal speed $\epsilon^{-1}$. The traveling fronts with minimal speed are linearly stable in weighted $L^2$ spaces. We also prove local nonlinear stability of the traveling front with minimal speed when $\epsilon$ is smaller than the transition parameter.Comment: 24 page

Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up

We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free energy written in Lagrangian coordinates. We focus on the description of the blow-up of the particle system, namely: the number of particles involved in the first aggregate, and the limiting profile of the rescaled system. We exhibit basins of stability for which the number of particles is critical, and we prove a weak rigidity result concerning the rescaled dynamics. This work is complemented with a detailed analysis of the case where only three particles interact

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog