The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.
- Naama Barkai, Weizmann Institute of Science, Israel
© 2016, Marcon et al.
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Diabetes is caused by the inability of electrically coupled, functionally heterogeneous -cells within the pancreatic islet to provide adequate insulin secretion. Functional networks have been used to represent synchronized oscillatory [Ca2+] dynamics and to study -cell subpopulations, which play an important role in driving islet function. The mechanism by which highly synchronized -cell subpopulations drive islet function is unclear. We used experimental and computational techniques to investigate the relationship between functional networks, structural (gap-junction) networks, and intrinsic -cell dynamics in slow and fast oscillating islets. Highly synchronized subpopulations in the functional network were differentiated by intrinsic dynamics, including metabolic activity and KATP channel conductance, more than structural coupling. Consistent with this, intrinsic dynamics were more predictive of high synchronization in the islet functional network as compared to high levels of structural coupling. Finally, dysfunction of gap junctions, which can occur in diabetes, caused decreases in the efficiency and clustering of the functional network. These results indicate that intrinsic dynamics rather than structure drive connections in the functional network and highly synchronized subpopulations, but gap junctions are still essential for overall network efficiency. These findings deepen our interpretation of functional networks and the formation of functional sub-populations in dynamic tissues such as the islet.
T cells are required to clear infection, and T cell motion plays a role in how quickly a T cell finds its target, from initial naive T cell activation by a dendritic cell to interaction with target cells in infected tissue. To better understand how different tissue environments affect T cell motility, we compared multiple features of T cell motion including speed, persistence, turning angle, directionality, and confinement of T cells moving in multiple murine tissues using microscopy. We quantitatively analyzed naive T cell motility within the lymph node and compared motility parameters with activated CD8 T cells moving within the villi of small intestine and lung under different activation conditions. Our motility analysis found that while the speeds and the overall displacement of T cells vary within all tissues analyzed, T cells in all tissues tended to persist at the same speed. Interestingly, we found that T cells in the lung show a marked population of T cells turning at close to 180o, while T cells in lymph nodes and villi do not exhibit this “reversing” movement. T cells in the lung also showed significantly decreased meandering ratios and increased confinement compared to T cells in lymph nodes and villi. These differences in motility patterns led to a decrease in the total volume scanned by T cells in lung compared to T cells in lymph node and villi. These results suggest that the tissue environment in which T cells move can impact the type of motility and ultimately, the efficiency of T cell search for target cells within specialized tissues such as the lung.