Computational Mesoscale Framework for Biological Clustering and Fractal Aggregation

Complex hierarchical clustering mediated by diffusion and reaction is ubiquitous to many naturally occurring phenomena. The aggregates typically exhibit a fractal behavior or non-integer size scaling compared to their intrinsic dimensionality (2 - 3 dimensions). Such fractal aggregates have attracted attention in studying biological (i.e. bronchi and nervous system morphogenesis, blood clotting) and synthetic (i.e. colloids, polymers, catalysts, nano-dendrites, multicellular organisms) systems. In general, biological clustering can occur on a wide range of spatial/temporal scales, and depending on the type of interactions, multiple mechanisms (or stages) can be involved. As a consequence, the modeling of biological clustering is typically a challenging task, requiring the use of a variety of methods to capture the characteristic behavior of specific biological systems. Herein, we proposed a generalized-mesoscale-clustering (GMC) framework that incorporates hydrodynamic interactions, bonding, and surface tension effects. This framework allows for studying both static and dynamic states of cluster development. We showcase the framework using a variety of biological clustering mechanisms, and further illustrate its versatility to model different scales, focusing on blood-related clustering ranging from fibrin network formation to platelet aggregation. Besides the introduction of the mesoscale clustering framework, we show that a single biomarker (such as fractal dimension) is insufficient to fully characterize and distinguish different cluster structures (morphologies). To overcome this limitation, we propose a comprehensive characterization that relates the structural properties of the cluster using four key parameters, namely the fractal dimension, pore-scale diffusion, as well as the characteristic times for initiation and consolidation of the cluster. Additionally, we show that the GMC framework allows tracking of bond density providing another biomarker for cluster temporal evolution and final steady-state. Furthermore, this feature and built-in hydrodynamics interactions offer the potential to investigate cluster mechanical properties in a variety of biological systems.