Figure 8

Synergistic-topological matrix model*. This model summarizes our findings that indicate that there is strong mutual interdependence between the pattern formation and the local boundary solution conditions, which is driven by ‘intrinsic synergistic-topological mechanism’ (see Figure 9). For example calcium, GTP-tubulin concentration, the vicinity of other microtubules etc. may affect the morphology of pattern formation and vice versa the pattern affects the local solution condition (e.g. by fiber microtubule dynamic instability and generating depletion). A. Synergistic-topological matrix* constituted by the pattern (fiber) of axially shifted (staggered) microtubules, and associated specific boundary solution conditions. B. Synergistic-topological matrix* constituted by the pattern (fiber) of non-shifted (non-staggered) microtubules, and associated specific boundary solution conditions. *Mutual interdependence of microtubule pattern and associated local specific solution conditions may be physico-mathematically modeled as synergistic-topological matrix that is formed through ‘intrinsic synergistic mechanism’ (see Figure 9). Associated local solution conditions include: local cross diffusion, local GTP-tubulin fluctuations (including GTP-tubulin depletion), and different molecular species (such as proteins, and ions). The matrix concept specifically related to microtubule mitotic spindle system can be found elsewhere (Lince-Faria, et al. [24] and Johansen, et al. [26]).