Pattern Formation and Synchronization in Nonlinear Systems: Application to Cellular Communication Models
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Nonlinear Dynamics, Pattern Formation, Systems Biology
Abstract
The emergence of complex, coordinated behavior from local interactions is a fundamental principle in biology, with pattern formation and synchronization being critical to processes like morphogenesis and intercellular signaling. Understanding the underlying nonlinear dynamics that govern this self-organization remains a central challenge in systems biology. This study aimed to develop a unified theoretical framework to investigate the conditions that drive pattern formation versus synchronization in generalized models of cellular communication. We employed a hybrid approach combining analytical methods with extensive numerical simulations of coupled reaction-diffusion and phase-oscillator models. The models incorporated key biological motifs such as activator-inhibitor signaling and time-delayed feedback loops. The results revealed that the interplay between the diffusion rate of signaling molecules and the time delay in the intracellular response is a critical bifurcation parameter. Slow diffusion and short delays favored robust Turing-like pattern formation, while rapid diffusion and longer delays promoted widespread phase synchronizationThis research concludes that cellular collectives can leverage fundamental principles of nonlinear dynamics, specifically the tuning of interaction range and response time, to select between distinct modes of self-organization.
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