Modeling signaling and migration of the Posterior Lateral Line primordium with agent based models Cells communicate with each other to determine the self-organization of cell communities within developing organs. Understanding the role individual signaling pathways play in these interactions has helped define simple rules by which cells interact with their environment and their neighbors to influence cell behavior, proliferation and differentiation. Agent-based computational models allow us to visualize how characteristic behaviors and patterns of differentiation emerge when large numbers of cells interact following simple rules that we can define based on genetic, molecular and cell biological analysis of cell-cell interactions in the embryo. We have been examining collective migration of cells in posterior lateral line primordium with time-lapse imaging in live zebrafish embryos and have built agent based models of this system based on what we have learnt from our observations. The computational models allow us to determine if our current understanding is adequate to account various behaviors of the cells in the lateral line primordium. While recapitulation of complex emergent behaviors in computer simulations provides support to our current hypotheses, failure of the computational models to recapitulate specific behaviors helps to identify missing pieces in our understanding. Formation of the Posterior Lateral Line (PLL) is spearheaded by the PLL primordium (PLLp), a collection of about 100 cells that migrates from the ear to the tip of the tail periodically depositing sensory organs called neuromasts from its trailing end. During this journey it follows a path defined by the expression of the chemokine CXCL12a or Sdf1a expressed by cells of the horizontal myoseptum. While the differential expression of this chemokine is what typically determines chemotactic migration of a variety of cells, the unidirectional migration of the PLLP along the horizontal is not determined by the inherent differences in CXCL12a expression along its path. Instead it is the polarized expression of two distinct chemokine receptors, CXCR4b in leading cells and CXCR7b in trailing cells, that allows the PLLp to migrate effectively along a relatively uniform stripe of chemokine expression. While leading CXCR4b receptor-expressing cells are capable of responding to the CXCL12a ligand with protrusive activity, trailing CXCR7b receptor expressing cells are not. However, interaction of CXCL12 with both receptors is followed by internalization of the bound ligandreceptor complex from the cells surface, which is expected to deplete CXCL12a from the immediate environment of the PLLp. This ensures that leading CXCR4b cells always encounter the higher levels of CXCL12a ahead of the migrating PLLp, in which direction leading cells continue to move. On the other hand, expression of the non-responsive CXCR7b receptor at the trailing end ensures the PLLp does not move in the opposite direction. We have constructed an agent-based model usig the Netlogo modeling environment to visualize how these functional differences in these chemokine receptors coupled with local depletion of CXCL12a contributes to polarized migration of the PLLp. This programming environment consists of individual, mobile agents called turtles, where multiple breeds of turtles can be defined that behave according to distinct sets of defined rules. In addition there are links that form visco-elastic connections between defined sets of turtles and individual non-motile agents called patches, which define the environment in which the motile agents operate. In our models patches are used to represent the substrate upon which the PLLp migrates and define the source of CXCL12a. The PLLp is made of two breeds of turtles;a leading compartment of CXCR4-turtles and a trailing compartment of CXCR7b-turtles. Links connect adjacent turtles and model adhesive interactions between cells of the PLLp. Movement of the PLLp is determined by the movement of CXCR4b-expressing turtles at the edge of the PLLp. This indirectly determines movement of trailing cells by virtue of the visco-elastic links connecting neighboring turtles. The model recapitulates polarized migration of the PLLp and allows us to explore how change in the relative size of CXCR4b and CXCR7b domains affects PLLp migratory behavior. When the migrating PLLp is cut with a laser so as to release a leading un-polarized fragment with only CXCR4b expressing cells and a remaining still-polarized trailing fragment with both CXCR4b and CXCR7b cells the two fragments acquire distinct and characteristic behaviors. To challenge our computational model we asked if it can recapitulate these behaviors following a similar simulated cut of the PLLp. The simulations were able to recapitulate bilateral stretching behavior of the leading fragment. However, they could not recapitulate the polarized protrusions of the trailing fragment toward the remaining leading fragment. This suggested that some behaviors of the PLLp cells could not be accounted for by assumptions of our chemokine signaling-based model and might be related to migratory behavior determined by other signaling pathways . The possibility that a mechanism independent of chemokine signaling was was responsible for trailing cell behavior in this context was confirmed by the observation that when the laser cut experiment was repeated in the embryo in the presence of chemokine signaling inhibitor, the polarized protrusions of the trailing toward the leading fragment persisted, even though bilateral stetching of the leading fragment was lost. This failure of our computational model prompted us to investigate the potential role of FGF signaling in determining behavior of the trailing cells toward the leading cells. Our experiments eventually demonstrated that leading cells, which not only express CXCR4b and help steer the PLLp along a path defined by CXCL12a expression, are the source of FGFs. These FGFs serve as a chemotactic cue for trailing cells that play follow leader as they follow leading cells that secrete FGFs. These lessons learnt from the extremely accessible and easy to image PLLp system will eventually contribute to our understanding of much less accessible and difficult to study metastatic cancer cells whose collective migrations appears to directed by principles and signaling mechanisms that have striking parallels with those we are investigating in the zebrafish lateral line system.

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Knutsdottir, Hildur; Zmurchok, Cole; Bhaskar, Dhananjay et al. (2017) Polarization and migration in the zebrafish posterior lateral line system. PLoS Comput Biol 13:e1005451
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