Monte Carlo Simulation of Wnt Propagation by a Novel Transport Mechanism Complementing a Joint Experimental Study

Abstract

Tissue development is a key process in living organisms. An essential component for these developmental processes - but also for tissue regeneration and stem cell regulation - is the communication of cells by paracrine signaling. Following the French flag model, these processes are responsive to concentration gradients of signal carrying molecules, so-called morphogens. The highly conserved family of Wnt proteins can act as morphogens and represents important regulators of all these processes. After secretion, specific transport mechanism must ensure proper distribution of the morphogen. Experimental studies in zebrafish embryos and human kidney cells have given first evidence for a novel short-range transport of Wnt morphogens from the Wnt active tissue towards receiving cells using cell protrusions, so-called filopodia, as mediating agent. These specialized filopodia transmit signaling proteins between communicating cells and allow a high degree of control of propagation speed, direction and concentration of the transmitted ligand. The crucial question is how this novel short-range mechanism can result in a long-range gradient of morphogen molecules covering the complete responsive tissue. In order to give an answer to this question and address the theoretical feasibility of the new model we have set up complementary Monte Carlo simulations. The simulation iteratively reproduces ligand production, cell migration, and a slight ligand decay in concordance with experimentally measured boundary conditions. In a filopodia mediated transport system the major parameters are not anymore diffusion rate, cell adhesion, and concentration of the ligand but length, angle distribution, and growth frequency of filopodia. During the simulation we were able to identify key parameters of the underlying mechanism and quantitatively reproduce our experimental data. These results provide evidence that a filopodia based short-range transport system for Wnt has long-range signalling function.