Session S38: Mechanics of Biopolymers: Networks and Assemblies

Rheology and nonlinear mechanics of transiently cross linked semiflexible networks: Bundling, ripping, healing, and mechnomemory

Transiently cross linked networks of semiflexible filaments make up the principal structural component of the cell — the cytoskeleton. This intracellular network, along with molecular motors, forms the basis for cellular control of morphology and force generation. In this talk, I report on investigations of the effect of transiently bound cross linkers on the structure and mechanics of semiflexible networks. Specifically, I address the role of Casimir or fluctuation-induced interactions between cross linkers in the formation of filament bundles. I report on the linear viscoelasticity of transiently cross-linked networks of bundles. Finally, I discuss the nonlinear mechanical response of such networks, where applied stress induces a persistent structural rearrangement of the network that can dramatically alter its nonlinear response to stresses subsequently applied.   

A coarse-grained model of microtubule self-assembly

Microtubules play critical roles in cell structures and functions. They also serve as a model system to stimulate the next-generation smart, dynamic materials. A deep understanding of their self-assembly process and biomechanical properties will not only help elucidate how microtubules perform biological functions, but also lead to exciting insight on how microtubule dynamics can be altered or even controlled for specific purposes such as suppressing the division of cancer cells. Combining all-atom molecular dynamics (MD) simulations and the essential dynamics coarse-graining method, we construct a coarse-grained (CG) model of the tubulin protein, which is the building block of microtubules. In the CG model a tubulin dimer is represented as an elastic network of CG sites, the locations of which are determined by examining the protein dynamics of the tubulin and identifying the essential dynamic domains. Atomistic MD modeling is employed to directly compute the tubulin bond energies in the surface lattice of a microtubule, which are used to parameterize the interactions between CG building blocks. The CG model is then used to study the self-assembly pathways, kinetics, dynamics, and nanomechanics of microtubules.   

Molecular Simulations of Actomyosin Network Self-Assembly and Remodeling

Actomyosin networks are an integral part of the cytoskeleton of eukaryotic cells and play an essential role in determining cellular shape and movement. Actomyosin network growth and remodeling in vivo is based on a large number of chemical and mechanical processes, which are mutually coupled and spatially and temporally resolved. To investigate the fundamental principles behind the self-organization of these networks, we have developed a detailed mechanochemical, stochastic model of actin filament growth dynamics, at a single-molecule resolution, where the nonlinear mechanical rigidity of filaments and their corresponding deformations under internally and externally generated forces are taken into account. Our work sheds light on the interplay between the chemical and mechanical processes governing the cytoskeletal dynamics, and also highlights the importance of diffusional and active transport phenomena. Our simulations reveal how different actomyosin micro-architectures emerge in response to varying the network composition.   

Active mechanics in living oocytes reveal molecular-scale force kinetics

Unlike traditional materials, living cells actively generate forces at the molecular scale that change their structure and mechanical properties. This nonequilibrium activity is essential for cellular function, and drives processes such as cell division. Single molecule studies have uncovered the detailed force kinetics of isolated motor proteins in-vitro, however their behavior in-vivo has been elusive due to the complex environment inside the cell. Here, we quantify active forces and intracellular mechanics in living oocytes using in-vivo optical trapping and laser interferometry of endogenous vesicles. We integrate an experimental and theoretical framework to connect mesoscopic measurements of nonequilibrium properties to the underlying molecular- scale force kinetics. Our results show that force generation by myosin-V drives the cytoplasmic-skeleton out-of-equilibrium (at frequencies below 300 Hz) and actively softens the environment. In vivo myosin-V activity generates a force of $F \sim0.4$ pN, with a power-stroke of length $\Delta x \sim 20$ nm and duration $\tau \sim300$ $\mu$s, that drives vesicle motion at $v_{\mathrm{v}}\sim320$ nm/s. This framework is widely applicable to characterize living cells and other soft active materials.   

Biopolymer mechanics across the force regimes

The elastic response of a single polymer can explain certain material properties, including the thickness of polymer brushes and the mechanics of gels; in turn, these material properties have a variety of biological applications, such as to the brush-like pericellular matrix surrounding certain cells. More fundamentally, the force-extension relation of a polymer can be predicted theoretically, making it possible to probe the structure of a polymer by measuring its elastic response. This works in a manner similar to scattering: just as scattering at a wave vector q gives information on structure at a length scale 1/q, the elastic response under applied tension f gives information on structure at a length scale of kT/f. Thus, in exact analogy to low-angle scattering, low-force elastic measurements are needed to probe the interesting long-range structure of polymers. I will discuss the basic physics of low-force elasticity, and present our experiments on various polymers, including nucleic acids and polysaccharides, that validate the power of low-force elastic measurements..   

Investigating collagen self-assembly with optical tweezers microrheology

Collagen is the fundamental structural protein in vertebrates. Assembled from individual triple-helical proteins to make strong fibres, collagen is a beautiful example of a hierarchical self-assembling system. Using optical tweezers to perform microrheology measurements, we explore the dynamics of interactions between collagens responsible for their self-assembly and examine the development of heterogeneous mechanics during assembly into fibrillar gels. Telopeptides, short non-helical regions that flank the triple helix, have long been known to facilitate fibril self-assembly. We find that their removal not only slows down fibril nucleation but also results in a significant frequency-dependent reduction in the elastic modulus of collagens in solution. We interpret these results in terms of a model in which telopeptides facilitate transient intermolecular interactions, which enhance network connectivity in solution and lead to more rapid assembly in fibril-forming conditions.   

Nonlinear microrheology and molecular imaging to map microscale deformations of entangled DNA networks

We use active microrheology coupled to single-molecule fluorescence imaging to elucidate the microscale dynamics of entangled DNA. DNA naturally exists in a wide range of lengths and topologies, and is often confined in cell nucleui, forming highly concentrated and entangled biopolymer networks. Thus, DNA is the model polymer for understanding entangled polymer dynamics as well as the crowded environment of cells. These networks display complex viscoelastic properties that are not well understood, especially at the molecular-level and in response to nonlinear perturbations. Specifically, how microscopic stresses and strains propagate through entangled networks, and what molecular deformations lead to the network stress responses are unknown. To answer these important questions, we optically drive a microsphere through entangled DNA, perturbing the system far from equilibrium, while measuring the resistive force the DNA exerts on the bead during and after bead motion. We simultaneously image single fluorescent-labeled DNA molecules throughout the network to directly link the microscale stress response to molecular deformations. We characterize the deformation of the network from the molecular-level to the mesoscale, and map the stress propagation throughout the network. We further study the impact of DNA length (11 -- 115 kbp) and topology (linear vs ring DNA) on deformation and propagation dynamics, exploring key nonlinear features such as tube dilation and power-law relaxation.   

Dual-feedback microrheology in cytoskeletal networks

Cytoskeletons are critical for understanding cell behaviors since they generate forces together with molecular motors and supply mechanical integrity to cells. Since response of cytoskeletons to motor-generated forces is highly nonlinear, cell behaviors intricately depend on activities and mechanics of cytoskeletons. Investigating local response of cytoskeletons to forces generated by molecular motors, which optical trap can imitatively reproduce, is therefore essential. Here, we performed this by developing a novel optical-trap-based microrheology implemented with dual-feedback control. With the slow feedback of piezo-stage, probes under drift, caused by the traction force applied by the optical trap, were stably tracked. By the rapid feedback of trapping laser, artifacts in probes motion, that had been caused by strong optical trap potential, were completely removed. We observed that fluctuations of probes embedded in various cytoskeletons were significantly reduced when subjected to forces. Under the assumption that the fluctuation-dissipation theorem is satisfied, our results indicate the stress stiffening of cytoskeletons, that became now possible to be studied in micro-scales and in a frequency range appropriate for cell behaviors.   

Coupled actin-lamin biopolymer networks and protecting DNA

The mechanical properties of cells are largely determined by networks of semiflexible biopolymers forming the cytoskeleton. Similarly, the mechanical properties of cell {\it nuclei} are also largely determined by networks of semiflexible biopolymers forming the {\it nuclear} cytoskeleton. In particular, a network of filamentous lamin sits just inside the inner nuclear membrane to presumably protect the heart of the cell nucleus---the DNA. It has been demonstrated over the past decade that the actin cytoskeletal biopolymer network and the lamin biopolymer network are coupled via a sequence of proteins bridging the outer and inner nuclear membranes, known as the LINC complex. We, therefore, probe the consequences of such a coupling in a model biopolymer network system via numerical simulations to understand the resulting deformations in the lamin network in response to perturbations in the actin cytoskeletal network. We find, for example, that the force transmission across the coupled system can depend sensitively on the concentration of LINC complexes. Such study could have implications for mechanical mechanisms of the regulation of transcription since DNA couples to lamin via lamin-binding domains so that deformations in the lamin network may result in deformations in the DNA.   

The Effect of Crosslinking on the Microscale Stress Response and Molecular Deformations in Actin Networks

Actin, the most abundant protein in eukaryotic cells, is a semi-flexible biopolymer in the cytoskeleton that plays a crucial structural and mechanical role in cell stability, motion and replication, as well as muscle contraction. Most of these mechanically driven structural changes in cells stem from the complex viscoelastic nature of entangled actin networks and the presence of a myriad of proteins that cross-link actin filaments. Despite their importance, the mechanical response of actin networks is not yet well understood, particularly at the molecular level. Here, we use optical trapping - coupled with fluorescence microscopy - to characterize the microscale stress response and induced filament deformations in entangled and cross-linked actin networks subject to localized mechanical perturbations. In particular, we actively drive a microsphere 10 microns through an entangled or cross- linked actin network at a constant speed and measure the resistive force that the deformed actin filaments exert on the bead during and following strain. We simultaneously visualize and track individual sparsely-labeled actin filaments to directly link force response to molecular deformations, and map the propagation of the initially localized perturbation field throughout the rest of the network (\textasciitilde 100 um). By varying the concentration of actin and cross-linkers we directly determine the role of crosslinking and entanglements on the length and time scales of stress propagation, molecular deformation and relaxation mechanisms in actin networks.   

Mechanically tunable actin networks using programmable DNA based cross-linkers

Cells employ multiple cross-linkers with very different properties. Studies of the entire phase space, however, were infeasible since they were restricted to naturally occurring cross-linkers. These components cannot be controllably varied and differ in many parameters. We resolve this limitation by forming artificial actin cross-linkers, which can be controllably varied. The basic building block is DNA enabling a well-defined length variation. DNA can be attached to actin binding peptides with known binding affinities. We used bulk rheology to investigate mechanical properties of these networks. We were able to reproduce mechanical features of actin networks cross-linked by fascin by using a short version of our artificial complex with a high binding affinity. Additionally, we were able to resemble findings for the cross-linker alpha-actinin by employing a long cross-linker with a low binding affinity. Between these natural limits we investigated three different cross-linker lengths each with two different binding affinities. With these controlled variations we are able to precisely screen the phase space of cross-linked actin networks by changing only one specific parameter and not the entire set of properties as in the case of naturally occurring cross-linking complexes.