Phase-field model for collective cell migration

We construct a phase-field model for collective cell migration based on a Ginzburg-Landau free-energy formulation. We model adhesion, surface tension, repulsion, coattraction, and polarization, enabling us to follow the cells' morphologies and the effect of their membranes fluctuations on collective motion. We were able to measure the tissue surface tension as a function of the individual cell cortical tension and adhesion and identify a density threshold for cell-sheet formation

Support for UNRWA's survival

The United Nations Relief and Works Agency for Palestine Refugees in the Near East (UNRWA) provides life-saving humanitarian aid for 5·4 million Palestine refugees now entering their eighth decade of statelessness and conflict. About a third of Palestine refugees still live in 58 recognised camps. UNRWA operates 702 schools and 144 health centres, some of which are affected by the ongoing humanitarian disasters in Syria and the Gaza Strip. It has dramatically reduced the prevalence of infectious diseases, mortality, and illiteracy. Its social services include rebuilding infrastructure and homes that have been destroyed by conflict and providing cash assistance and micro-finance loans for Palestinians whose rights are curtailed and who are denied the right of return to their homeland

Generalized model for chemotactic and chemotropic effects coupled to actin dynamics: a phase field approach

The ubiquity of free boundary problems in biology, with which we are mainly concerned, led us to adopt a mathematical technique to render them tractable and relatively easy to solve. The phase field method, used when dealing with dynamical systems with moving boundary condition, addresses arising difficulties involved with tracking those boundaries. In this work we model the motion of neutrophils, cells of the immune system, in response to chemical driving. Their morphology changes dynamically as they move to neutralize their target, a mechanism called chemotaxis. Additionally, we propose a model for neural cell growth, which is insti- gated by mediators, a process termed chemotropism. When coupled to an internal mechanism of actin polymerization, this induces the advancement of the axonal tip. Lastly, we used the method to build a generalized model from which both chemo- tactic and chemotropic models can be derived. These three problems were solved by the construction of free energy functionals F that captured the main features of the dynamics, in relation to the order parameters φ that distinguished the phases of the system as well as their interfaces. We considered the membrane of the cells, their inside and outside, as well as their leading edges. The governing partial dif- ferential equations were obtained by a variational differentiation of F with respect to the fields. Following this method, we were able to model cell morphodynamics in two and three dimensions. The major contribution of our work lies in the reduction of the complexity of those problems: we solve partial differential equations of fields coupled to the underlying dynamics at the molecular level, which are derived from a closed form generalized functional describing both the cell motion, deformation and growth.L'abondance des problèmes à interface libre dans la biologie auxquels nous sommes principallement interéssés, nous a conduits à adopter une technique qui les rend relativement faciles à resoudre. Phase Field Method, utilisée pour examiner des systèmes dynamiques possédants des conditions aux limites en mouvement, resoud la diffuculté provenant de suivre leur évolution. Dans ce travail, on modèle le mouvement des neutrophiles qui sonts des cellules du système immunitaire en réponse aux signaux chimiques. Leur morphologie change dynamiquement quand ils se deplancent pour neutraliser leur cible: ce mécanisme est appelé chimiotaxie. Egalement, on propose un modèle pour le développement des cellules nerveuses induit par des médiateurs. Ce processus est nommé chémotropisme. Ce dernier, quand il est lié au mécanisme interne responsable de la polymérisation de l'actine, induit l'avancement du bout de l'axone. Finalement, on a employé la méthode pour construire un modèle généralisé qui permet de dériver les deux modèles chimiotactique et chémotropique. Ces problèmes ont été resouds en construisant des fonctionelles d'énergie libre F , capturant les caractéristiques principaux de la dynamique en fonction d'un paramètre d'order φ qui permet de dinstinguer les différentes phases du système aussi bien que les interfaces qui les séparent. Les éequations aux dérivées partielles décrivant leur evolution sont déterminées en effectuant une différenciation variationelle de F par rapport au champs φ. En suivant cette méthode, on était capable de reproduire la dynamique des morphologies en deux et trois dimensions. La contribution majeure de notre travail réside dans la réduction de la complexité de ces problèmes en suivant les équations aux dérivées partielles. Ces dernières sont liées aux mécanismes internes au niveau moléculaire dérivés dune fonctionelle généralisée F qui décrit le mouvement de la cellule ainsi que sa déformation et sa croissance

A phase field model for neural cell chemotropism

Chemotropism is the action of targeting a part of the cell by means of chemical mediators and cues, and subsequently delimiting the pathway that it should undertake. In a neural cell, this initiates axonal elongation. Herein we model this growth, where chemotropic forcing leads the axon, by a phase field method utilizing two dynamical fields assigned respectively to the cell and to its leading edge. Additionally we quantify the condition for the retraction of the axon which takes place when the cell fails to form a synaptic connection

Debye–Hückel theory for refugees’ migration

Abstract In this paper, we follow the short-ranged Syrian refugees’ migration to Lebanon as documented by the UNHCR. We propose a model inspired by the Debye–Hückel theory and show that it properly predicts the refugees’ mobility while the gravity model fails. We claim that the interaction between origin cities attenuates and/or extenuates the flux to destinations, and consequently, in analogy with the effective charges of interacting particles in a plasma, these source cities are characterized by effective populations determined by their pairwise remoteness/closeness and defined by areas of control between the fighting parties

MOESM3 of Debye–Hückel theory for refugees’ migration

Syria–Syria-distance. The Syria-Syria-Distance.csv contains the pairwise distance matrix between Syrian cities retrieved through the google API. (CSV 2 kB