Complex Automata as a Novel Conceptual Framework for Modeling Biomedical Phenomena

We show that the complex automata (CxA) paradigm can serve as a robust general framework which can be applied for developing advanced models of biological systems. CxA integrates particle method (PM) and cellular automata (CA) computational techniques. Instead of developing complicated multi-scale models which consist of many submodels representing various scales coupled by a scales-bridging mechanism, we propose here a uniform, single scale, coarse grained computational framework for which information about finer scales is inscribed in CA rules and particle interactions. We demonstrate that our approach can be especially attractive for modeling biological systems, e.g., intrinsically complex phenomena of growth such as cancer proliferation fueled by the process of angiogenesis and Fusarium Graminearum wheat infection. We show that these systems can be discretized and represented by an ensemble of moving particles, which states are defined by a finite set of attributes. The particles may represent spherical cells and other non-spherical fragments of more sophisticated structures, such as, transportation system (vasculature, capillaries), pathogen individuals, neural network fragments etc. The particles interact with their closest neighbors via semi-harmonic central forces mimicking mechanical resistance of the cell walls. The particle motion is governed by both the Newtonian laws and cellular automata rules employing the attributes (states) of neighboring cells. CA rules may reflect e.g., cell life-cycle influenced by accompanying biological processes while the laws of particle dynamics and the character of collision operators simulate the mechanical properties of the system. The ability of mimicking mechanical interactions of tumor with the rest of tissue and penetration properties of Fusarium graminearum, confirms that our model can reproduce realistic 3-D dynamics of these complex biological systems.