Topological chaos in active nematics, Amanda J. Tan, Eric Roberts, Spencer Smith, Ulyses Alvarado, Jorge Arteaga, Sam Fortini, Kevin Mitchell, and Linda S. Hirst, Aug 5th, NATURE PHYSICS (2019) Link
Abstract: Active nematics are out-of-equilibrium fluids composed of rod-like subunits, which can generate large-scale, self-driven flows. We examine a microtubule-kinesin-based active nematic confined to two dimensions, exhibiting chaotic flows with moving topological defects. Applying tools from chaos theory, we investigate self-driven advection and mixing on different length scales. Local fluid stretching is quantified by the Lyapunov exponent. Global mixing is quantified by the topological entropy, calculated from both defect braiding and curve extension rates. We find excellent agreement between these independent mea-sures of chaos, demonstrating that the extensile stretching between microtubules directly translates into macroscopic braiding of positive defects. Remarkably, increasing extensile activity (through ATP concentration) does not increase the dimensionless topological entropy. This study represents an application of chaotic advection to the emerging field of active nematics and quantification of the collective motion of an ensemble of defects (through topological entropy) in a liquid crystal.
The Hirst Lab has been awarded a new three-year NSF grant along with collaborator UC Merced’s Kevin Mitchell.
The grant, combining experiment and theory is titled “Self-mixing Active Fluids”
Active matter is one of the most exciting frontiers in soft matter science. Unlike typical fluids, active fluids are not in equilibrium. Instead, they consume energy locally, translating this energy into internal flows and spontaneous mixing. In this project, mass transport and chaotic mixing in active fluids will be investigated using a fluid consisting of microtubules and kinesin, biological molecules found in the cell. Densely packed microtubules slide antiparallel to each other at a controlled rate due to coupled kinesin molecular motors. An exciting outcome of this work could be the development of a new class of self-mixing active solvents. Such a solvent could revolutionize our understanding of the kinetics of mass transport and chemical reactions. The present proposal concerns much larger length scales than that of standard solvents and will thus serve as an experimental model for these new ideas, helping to establish fundamental laws that govern the behavior of active matter. Since the contents of biological cells are highly complex active materials, far from equilibrium, this work is expected to yield new insights into the role of active materials in biology. A proposed Telluride workshop on transport in active fluids will help to bring together the relatively disparate fields of liquid crystals, biological fluids and nonlinear dynamics. This work will have a significant educational impact at UC Merced, a new university in one of California’s most socio-economically disadvantaged areas. This research will provide the basis for several undergraduate theses and the PIs will use insights from this work to introduce cutting edge materials to their graduate and undergraduate teaching.
This project focuses on transport and mixing in a biologically inspired extensile active nematic. Densely packed microtubules slide antiparallel to each other at a controlled rate due to kinesin molecular motors and the resulting chaotic advection will be measured on different length scales, using the experimental tools of particle tracking, particle image velocimetry, and fluorescence imaging of labeled tracers. Experimental data will be theoretically interpreted using the tools of nonlinear and topological dynamics, thereby merging the fields of chaotic advection and liquid crystals in a unique collaborative effort. Topological entropy will play a central, unifying role in this study. Topological entropy is well known in studies of chaotic advection, but has been thus far overlooked in studies of active nematics. Specific aims are to: 1) use bead tracking and velocity reconstruction, together with tools from nonlinear dynamics, to measure the topological entropy of active nematic mixing; 2) measure the effective diffusivity, enhanced by chaotic advection, of the active nematic on the macroscale; and 3) investigate correlations between molecular-scale dynamics, mesoscale mixing, and macroscale diffusion by varying system parameters.
Recently Prof Hirst authored a News and Views in Nature focussed on two exciting articles about the cell epithelium as active matter.
“Evidence has been found that a biological tissue might behave like a liquid crystal. Even more remarkably, topological defects in this liquid-crystal system seem to influence cell behaviour. A materials physicist and a biologist discuss what the findings mean for researchers in their fields”.
Chai Lor1, Joseph D. Lopes2, Michelle K. Mattson-Hoss3, Jing Xu2* and Linda S. Hirst2*
1Biological Engineering and Small-scale Technologies Graduate Program, School of Engineering, University of California Merced, Merced, CA, USA
2Physics Department, School of Natural Science, University of California Merced, Merced, CA, USA
3Developmental and Cell Biology, School of Biological Sciences, University of California Irvine, Irvine, CA, USA
The presence of membrane tubules in living cells is essential to many biological processes. In cells, one mechanism to form nanosized lipid tubules is via molecular motor induced bilayer extraction. In this paper, we describe a simple experimental model to investigate the forces required for lipid tube formation using kinesin motors anchored to 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) vesicles. Previous related studies have used molecular motors actively pulling on the membrane to extract a nanotube. Here, we invert the system geometry; molecular motors are used as static anchors linking DOPC vesicles to a two-dimensional microtubule network and an external flow is introduced to generate nanotubes facilitated by the drag force. We found that a drag force of ≈7 pN was sufficient for tubule extraction for vesicles ranging from 1 to 2 μm in radius. By our method, we found that the force generated by a single molecular motor was sufficient for membrane tubule extraction from a spherical lipid vesicle.
Dr Chai Lor successfully defended his PhD thesis in the BEST (Bioengineering and small scale technologies) program on October 26th. Chai was a bioengineering undergraduate at UC Merced and a member of the first graduating class.
“Phase Behavior and Nanotube Formation in Lipid Membranes”
Biological cells are protected by a complex barrier called the lipid membrane. The lipid membrane is a soft material structure consisting of many lipid molecules held together by hydrophobic forces in an aqueous solution. Two simple experimental models were employed to investigate the role of specific lipid molecules in biological membranes. The first model investigated the phase behavior of the binary lipid mixture, 1-dipalmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphoethanolamine (DHA-PE) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), using small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS). Our results shows that DHA-PE induces phase separation into a DHA rich liquid crystalline (Lα) phase and a DHA poor gel (Lβ’) phase at overall DHA-PE concentrations as low as 0.1mol%. In addition, we find that the structure of the Lβ’ phase, from which the DHA-PE molecules are largely excluded, is modified in the phase-separated state at low DHA-PE concentrations, with a decrease in bilayer thickness of 1.34nm for 0.1mol% at room temperature compared to pure DPPC bilayers. The second model investigated the formation of lipid nanotubes using an anchor system consisting of lipids, kinesin molecular motors, and microtubules in a flow cell. Lipid tubulation was conducted on two different membranes, 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and DPPC. Lipid nanotubes were pulled from anchored giant unilamellar vesicles (GUVs) by drag force generated from the flow inside the channel. The results showed that DPPC membranes cannot generate lipid nanotubes while DOPC can, which was expected. We find that a drag force of approximately ≈7.9 pN is sufficient for tubule extraction and that it only requires 1-2 kinesin motor proteins for anchoring the GUV.
“Low concentrations of docosahexanoic acid significantly modify membrane structure and phase behavior” C. Lor and L.S. Hirst, MEMBRANES, 5(4), 857-874 Link (2015)
A dual-beam optical trap is used to trap and manipulate dielectric particles. When the refractive index of these particles is comparable to that of the surrounding medium, equilibrium trapping locations within the system shift from stable to unstable depending on fiber separation and particle size. This is due to to the relationship between gradient and scattering forces. We experimentally and computationally study the transitions between stable and unstable trapping of poly(methyl methacrylate) beads for a range of parameters relevant to experimental setups involving giant unilamellar vesicles. We present stability maps for various fiber separations and particle sizes, and find that careful attention to particle size and configuration is necessary to obtain reproducible quantitative results for soft matter stretching experiments.