Abstract
BackgroundRobust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. In fission yeast cells undergoing division, the mitotic spindle spontaneously emerges from the interaction of microtubules, motor proteins and the confining cell walls, and asters and vortices have been observed to self-assemble in quasi-two dimensional microtubule-kinesin assays. There is no clear microscopic picture of the role of the active motors driving this pattern formation, and the relevance of continuum modeling to filament-scale structures remains uncertain.ResultsHere we present results of numerical simulations of a discrete filament-motor protein model confined to a pressurised cylindrical box. Stable spindles, nematic configurations, asters and high-density semi-asters spontaneously emerge, the latter pair having also been observed in cytosol confined within emulsion droplets. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. We further highlight a parameter regime where vortices form exhibiting collective rotation of all filaments, but have a finite life-time before contracting to a semi-aster. Quantifying the distribution of life-times suggests this contraction is a Poisson process. Equivalent systems with fixed volume exhibit persistent vortices with stochastic switching in the direction of rotation, with switching times obeying similar statistics to contraction times in pressurised systems. Furthermore, we show that increasing the detachment rate of motors from filament plus-ends can both destroy vortices and turn some asters into vortices.ConclusionsWe have shown that discrete filament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phenomena occur on the length-scale of single filaments. Based on our findings, we argue the need for a deeper understanding of the microscopic activities underpinning macroscopic self-organization in active gels and urge further experiments to help bridge these lengths.
Highlights
Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life
1 Background Filamentous proteins are prevalent within eukaryotic cells and perform a variety of crucial tasks relating to cellular integrity, locomotion, transport and division [1,2]. Such tasks are often active in that they can only proceed in concert with energy-consuming mechanisms, including directed filament growth and motor proteingenerated tension, placing such processes outside the realm of equilibrium thermodynamics [3]
Motors are modeled as two-headed Hookean springs with a spring constant kBT/b2 and dynamics defined by four rates as shown in Figure 1(a): (i) The attachment rate kA for a motor to attach to two monomers within a predefined range, here taken to be the excluded volume radius 21/6s; (ii) the detachment rate kD of each head independently from its filament; (iii) the movement rate kM of each head independently towards the filament’s [+]-end, and (iv) the detachment rate kE for motor heads already at a [+] end
Summary
Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. Experiments on growing microtubules confined to spherical emulsion droplets revealed a droplet-size dependency on the observed structure [11]: Droplets larger than ≈ 29 μm in diameter contained asters with the polar microtubules pointing towards the centre, controlled by the motor protein dynein, whereas smaller droplets were found to contain semi-asters with the aster’s focus near the interface. These findings demonstrate that the degree of confinement can partly determine structure formation, but as motor density and speed were not control variables in these experiments their influence could not be assayed
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