A Mechanistic View of Collective Filament Motion in Active Nematic Networks

Moritz Striebel*, Isabella R. Graf*, Erwin Frey

Cells perform a variety of vital tasks ranging from cell division to motion and force generation. These abilities are intrinsically dynamic and rely on active network structures consisting of cytoskeletal filaments and crosslinking motor proteins. How does collective dynamics at the macroscopic level emerge from interactions of individual filaments and motor proteins? We address this open question through a conceptual model for motor-induced motion in networks of interconnected filaments. A prominent representative of this class of structures is the mitotic spindle where motor-driven filament flux is essential to maintain shape and functionality.

Our understanding of the mechanistic origin of filament dynamics in mixtures with motors is largely based on experimental studies of the interaction of purified components. A basic fact that has emerged from such studies is that two isolated antiparallel microtubules are pushed past one another by the action of sliding motors (kinesin-5 family), while parallel filaments remain static [1]. When this finding is applied to an ensemble of filaments crosslinked by motors, one would intuitively expect that the filament dynamics should strongly depend on the local number of antiparallel filaments. However, this intuition is clearly contradicted by experimental observations on the mitotic spindle [2,3] as well as in vitro structures consisting of filaments crosslinked by motors [4].

So how can motion emerge even in regions where there are no antiparallel filaments?

Employing a minimal but generic model for a nematic network where filament motion is driven by active motor proteins, we identify a mechanism which qualitatively accounts for those observations. Through theoretical and numerical analysis, we identify how the interplay between viscous drag on filaments and motor-induced forces governs force propagation through such interconnected filament networks. Motors do not only induce local motion but also translate this motion throughout the entire network. This motion propagation is however counteracted by viscous drag in the fluid. Together, these antagonistic forces define a length scale over which the filament movement generated at one position influences the movement of distant filaments. Intriguingly, for biologically realistic parameters, we find that this length scale is on the order of multiple filament lengths. Thereby we can explain the counterintuitive experimental observation that filament motion arises even in regions where there are no motion generating interactions.

On a broader perspective our work constitutes a step towards a more elaborated theory on active filament networks, which is essential to understand the functionality of the cytoskeleton.

[1] Kapitein, L. C., Peterman, E. J. G., Kwok, B. H., Kim, J. H., Kapoor, T. M., and Schmidt, C. F. (2005). The bipolar mitotic kinesin Eg5 moves on both microtubules that it crosslinks. Nature, 435(7038):114.

[2] Burbank, K. S., Mitchison, T. J., and Fisher, D. S. (2007). Slide-and-Cluster Models for Spindle Assembly. Current Biology, 17(16):1373–1383.

[3] Yang, G., Cameron, L. A., Maddox, P. S., Salmon, E. D., and Danuser, G. (2008). Regional variation of microtubule flux reveals microtubule organization in the metaphase meiotic spindle. Journal of Cell Biology, 182(4):631–639.

[4] Fürthauer, S., Lemma, B., Foster, P. J., Ems-McClung, S. C., Walczak, C. E., Dogic, Z., Needleman, D. J., and Shelley, M. J. (2018). Actively crosslinked microtubule networks: mechanics, dynamics and filament sliding. arXiv, arXiv:1812.01079