Colloidal Mikado: Self-motion of a stiff slender rod in a maze of linelike obstacles
Final Report Abstract
The interior of a living cell comprises a dense packing of a plethora of proteins as well as a network of stiff biofilaments. For intracellular transport processes the natural question emerges how stiff biofilaments can move through such structures. Vividly spoken the problem of a needle in a haystack is addressed. We have developed a powerful and versatile computer code adapted to the infinite aspect ratio of needle systems. At the same time we elaborated and extended earlier analytic approaches to provide a complete characterization of the spatiotemporal dynamics of a single needle. As idealization of long stiff biopolymers we used infinitely thin needles that can move in a semidilute suspension of other needles. While the excluded volume vanishes and correspondingly the structural properties of such a suspension are trivial, the dynamics is strongly correlated since the needles are not allowed crossing each other. The strong topological constraints for the dynamics of a such a needle system has led Doi and Edwards to develop their celebrated tube model with a series of ramifications for the single-needle dynamics. While in the original approach a series of simplifying assumptions were made to tackle the problem in our work we could solve analytically for the complete dynamics of a phantom needle with strongly renormalized transport coefficients to take into account the constraints of the medium. We have validated the theoretical framework in extensive state-of-the-art computer simulations thereby entering for the first time the regime of high entanglement. The simulations covered our simplified model of a Lorentz needle system, where only a single needle moves in a quenched array of other needles, as well as the fully moving needle liquid where all constituents are treated on the same footing. We have corroborated our initial intuition that both model systems are captured by the tube model and provide solid simulational evidence that such a description becomes quantitative at high needle densities. What remains to be investigated further is the dynamics of a rodlike object of finite thickness. This is relevant to make connection to experiments on suspensions of biofilaments such as actin or microtubili or synthetic systems comprised of silver nanorods or carbon nanotubes. While conceptionally our computer code contains the main ingredients to address this problem, a series of modifications is needed to make the code efficient to make quantitative predictions also for finite aspect ratios. For biological samples the constituents are not infinitely stiff but display bending fluctuations in addition to the translational and orientational motion. Brute force simulations for such systems don’t reach the regime of high entanglement yet and no coherent theoretical picture has emerged yet. A quantitative theory for semidilute solutions of semiflexible polymers still needs to be elaborated. The methods that we developed in this project to derive an analytic solution for the intermediate scattering function of a phantom needle have been very fruitful also in related topics. The field of active particles is rapidly growing but even a complete characterization of spatiotemporal dynamics of a single active agents has been missing so far. We have solved for the first time for the intermediate scattering function of self-propelled particles possible with anisotropic diffusion and deterministic torques. Similarly the solution methods translate to the conformations of semiflexible polymers where we could provide the first analytic exact expressions for the force-extension relation as well as the susceptibilities. In total, we have advanced the field of suspensions of needles significantly and believe that we have made a lasting impact on the field. Additionally we have developed a new solution strategy with applications that reach far beyond the field of entangled dynamics.
Publications
- Intermediate scattering function of an anisotropic active Brownian particle, Scientific Reports 6, 36702 (2016)
C. Kurzthaler, S. Leitmann, and T. Franosch
(See online at https://doi.org/10.1038/srep36702) - Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time, Phys. Rev. Lett. 117, 097801 (2016)
S. Leitmann, F. Höfling, T. Franosch
(See online at https://doi.org/10.1103/PhysRevLett.117.097801) - Dynamically crowded solutions of infinitely thin Brownian needles, Phys. Rev. E 96, 012118 (2017)
S. Leitmann, F. Höfling, and T. Franosch
(See online at https://doi.org/10.1103/PhysRevE.96.012118) - Exact solution for the force-extension relation of a semiflexible polymer under compression, Phys. Rev. E 95, 052501 (2017)
C. Kurzthaler and T. Franosch
(See online at https://doi.org/10.1103/PhysRevE.95.052501) - Intermediate scattering function of an anisotropic Brownian circle swimmer, Soft Matter 13, 6396 (2017)
C. Kurzthaler and T. Franosch
(See online at https://doi.org/10.1039/c7sm00873b)
