An integrated parametric model for MT self-assembly formation analysis

Self-assembly is a ubiquitous, naturally occurring, robust process in many living organisms. Microtubule (MT), a self-organization system assemble itself into functional units by attaching to cellular structures. Modeling microtubule self-organization is of interest as microtubule forms a network of protein filaments that is critical to many processes in eukaryotic cells. In this paper, we propose an optimization framework that considers MT self-assembly starting from alpha (α) and beta (β) tubulins as basic building blocks in the self-organization of MT. Using this framework we present separate analysis of MT self-assembly strength by considering two aspects of MT self-assembly. First, the affinity factor distribution between neighboring tubulins of an MT is considered for the analysis. Second, this paper also present an analysis of structural stability considering geometric parameter distribution of tubulins within an MT. We present separate algorithms for the analysis in detail. The proposed models show convergence and robustness under random initialization and thus justify the effectiveness of the proposed convergence criteria for stability analysis of MT self-organization. The proposed algorithms show the ability to emulate MT self-assembly from random initial configurations.