Reaction–Diffusion Finite Element Model of Lateral Line Primordium Migration to Explore Cell Leadership

Differential cell motion: A mathematical model of anterior posterior sorting

Here, we investigate how a subpopulation of cells can move through an aggregate of cells. Using a stochastic force-based model of Dictyostelium discoideum when the population is forming a slug, we simulate different strategies for prestalk cells to reliably move to the front of the slug while omitting interaction with the substrate thus ignoring the overall motion of the slug. Of the mechanisms that we simulated, prestalk cells being more directed is the best strategy followed by increased asymmetric motive forces for prestalk cells. The lifetime of the cell adhesion molecules, while not enough to produce differential motion, did modulate the results of the strategies employed. Finally, understanding and simulating the appropriate boundary conditions are essential to correctly predict the motion.

A hybrid integro-differential model for the early development of the zebrafish posterior lateral line

The aim of this work is to provide a mathematical model to describe the early stages of the embryonic development of zebrafish posterior lateral line (PLL). In particular, we focus on evolution of PLL proto-organ (said primordium), from its formation to the beginning of the cyclical behavior that amounts in the assembly of immature proto-neuromasts towards its caudal edge accompanied by the deposition of mature proto-neuromasts at its rostral region. Our approach has an hybrid integro-differential nature, since it integrates a microscopic/discrete particle-based description for cell dynamics and a continuous description for the evolution of the spatial distribution of chemical substances (i.e., the stromal-derived factor SDF1a and the fibroblast growth factor FGF10). Boolean variables instead implement the expression of molecular receptors (i.e., Cxcr4/Cxcr7 and fgfr1). Cell phenotypic transitions and proliferation are included as well. The resulting numerical simulations show that the model is able to qualitatively and quantitatively capture the evolution of the wild-type (i.e., normal) embryos as well as the effect of known experimental manipulations. In particular, it is shown that cell proliferation, intercellular adhesion, FGF10-driven dynamics, and a polarized expression of SDF1a receptors are all fundamental for the correct development of the zebrafish posterior lateral line.

Collective migration and patterning during early development of zebrafish posterior lateral line

The morphogenesis of zebrafish posterior lateral line (PLL) is a good predictive model largely used in biology to study cell coordinated reorganization and collective migration regulating pathologies and human embryonic processes. PLL development involves the formation of a placode formed by epithelial cells with mesenchymal characteristics which migrates within the animal myoseptum while cyclically assembling and depositing rosette-like clusters (progenitors of neuromast structures). The overall process mainly relies on the activity of specific diffusive chemicals, which trigger collective directional migration and patterning. Cell proliferation and cascade of phenotypic transitions play a fundamental role as well. The investigation on the mechanisms regulating such a complex morphogenesis has become a research topic, in the last decades, also for the mathematical community. In this respect, we present a multiscale hybrid model integrating a discrete approach for the cellular level and a continuous description for the molecular scale. The resulting numerical simulations are then able to reproduce both the evolution of wild-type (i.e. normal) embryos and the pathological behaviour resulting form experimental manipulations involving laser ablation. A qualitative analysis of the dependence of these model outcomes from cell-cell mutual interactions, cell chemical sensitivity and internalization rates is included. The aim is first to validate the model, as well as the estimated parameter values, and then to predict what happens in situations not tested yet experimentally. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium

Interactions between primordium cells and their environment determines the self-organization of the zebrafish posterior Lateral Line primordium as it migrates under the skin from the ear to the tip of the tail forming and depositing neuromasts to spearhead formation of the posterior Lateral Line sensory system. In this review we describe how the NetLogo agent-based programming environment has been used in our lab to visualize and explore how self-generated chemokine gradients determine collective migration, how the dynamics of Wnt signaling can be used to predict patterns of neuromast deposition, and how previously defined interactions between Wnt and Fgf signaling systems have the potential to determine the periodic formation of center-biased Fgf signaling centers in the wake of a shrinking Wnt system. We also describe how NetLogo was used as a database for storing and visualizing the results of in toto lineage analysis of all cells in the migrating primordium. Together, the models illustrate how this programming environment can be used in diverse ways to integrate what has been learnt from biological experiments about the nature of interactions between cells and their environment, and explore how these interactions could potentially determine emergent patterns of cell fate specification, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.

Polarization and migration in the zebrafish posterior lateral line system

Collective cell migration plays an important role in development. Here, we study the posterior lateral line primordium (PLLP) a group of about 100 cells, destined to form sensory structures, that migrates from head to tail in the zebrafish embryo. We model mutually inhibitory FGF-Wnt signalling network in the PLLP and link tissue subdivision (Wnt receptor and FGF receptor activity domains) to receptor-ligand parameters. We then use a 3D cell-based simulation with realistic cell-cell adhesion, interaction forces, and chemotaxis. Our model is able to reproduce experimentally observed motility with leading cells migrating up a gradient of CXCL12a, and trailing (FGF receptor active) cells moving actively by chemotaxis towards FGF ligand secreted by the leading cells. The 3D simulation framework, combined with experiments, allows an investigation of the role of cell division, chemotaxis, adhesion, and other parameters on the shape and speed of the PLLP. The 3D model demonstrates reasonable behaviour of control as well as mutant phenotypes.