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Composites of flexible and rigid polymers are ubiquitous in biology and industry alike, yet the physical principles determining their mechanical properties are far from understood. Here, we couple force spectroscopy with large-scale Brownian dynamics simulations to elucidate the unique viscoelastic properties of custom-engineered blends of entangled flexible DNA molecules and semiflexible actin filaments. We show that composites exhibit enhanced stress stiffening and prolonged mechanomemory compared to systems of actin or DNA alone, and that these nonlinear features display a surprising nonmonotonic dependence on the fraction of actin in the composite. Simulations reveal that these counterintuitive results arise from synergistic microscale interactions between the two biopolymers. Namely, DNA entropically drives actin filaments to form bundles that stiffen the network but reduce the entanglement density, while a uniform well-connected actin network is required to reinforce the DNA network against yielding and flow. The competition between bundling and connectivity triggers an unexpected stress response that leads equal mass DNA-actin composites to exhibit the most pronounced stress stiffening and the most long-lived entanglements.

We track the deformation of discrete entangled actin segments while simultaneously measuring the resistive force the deformed filaments exert in response to an optically driven microsphere. We precisely map the network deformation field to show that local microscale stresses can induce filament deformations that propagate beyond mesoscopic length scales (60 μm, >3 persistence lengths lp). We show that the filament persistence length controls the critical length scale at which distinct entanglement deformations become driven by collective network mechanics. Mesoscale propagation beyond lp is coupled with nonlinear local stresses arising from steric entanglements mimicking cross-links.

Chain topology has a profound impact on the flow behavior of single macromolecules. For circular polymers, the absence of free ends results in a unique chain architecture compared to linear or branched chains, thereby generating distinct molecular dynamics. Here, we report the direct observation of circular DNA dynamics in transient and steady flows for molecular sizes spanning the range of 25.0–114.8 kilobase pairs (kbp). Our results show that the longest relaxation times of the rings follow a power-law scaling relation with molecular weight that differs from that of linear chains. Also, relative to their linear counterparts, circular DNA molecules show a shifted coil-to-stretch transition and less diverse “molecular individualism” behavior as evidenced by their conformational stretching pathways. These results show the impact of chain topology on dynamics and reveal commonalities in the steady state behavior of circular and linear DNA that extends beyond chain architecture.

Using single-molecule fluorescence microscopy and particle-tracking techniques, we elucidate the role DNA topology plays in the diffusion and conformational dynamics of crowded DNA molecules. We focus on large (115 kbp), double-stranded ring and linear DNA crowded by varying concentrations (0–40%) of dextran (10, 500 kDa) that mimic cellular conditions. By tracking the center-of-mass and measuring the lengths of the major and minor axes of single DNA molecules, we characterize both DNA mobility reduction as well as crowding-induced conformational changes (from random spherical coils). We reveal novel topology-dependent conformations, with single ring molecules undergoing compaction to ordered spherical configurations ∼20% smaller than dilute random coils, while linear DNA elongates by ∼2-fold. Surprisingly, these highly different conformations result in nearly identical exponential mobility reduction dependent solely on crowder volume fraction Φ, revealing a universal critical crowding concentration of Φc ≅ 2.3. Beyond Φc DNA exhibits topology-independent conformational relaxation dynamics despite highly distinct topology-driven conformations. Our collective results reveal that topology-dependent conformational changes, unique to crowded environments, enable DNA to overcome the classically expected mobility reduction that high-viscosity crowded environments impose. Such coupled universal dynamics suggest a mechanism for DNA to maintain sufficient mobility required for wide-ranging biological processes despite severe cellular crowding.

We use optical tweezers microrheology and fluorescence microscopy to apply nonlinear microscale strains to entangled and cross-linked actin networks, and measure the resulting stress and actin filament deformations. We couple nonlinear stress response and relaxation to the velocities and displacements of individual fluorescent-labeled actin segments, at varying times throughout the strain and varying distances from the strain path, to determine the underlying molecular dynamics that give rise to the debated nonlinear response and stress propagation of cross-linked and entangled actin networks at the microscale. We show that initial stress stiffening arises from acceleration of strained filaments due to molecular extension along the strain, while softening and yielding is coupled to filament deceleration, halting, and recoil. We also demonstrate a surprising nonmonotonic dependence of filament deformation on cross-linker concentration. Namely, networks with no cross-links or substantial cross-links both exhibit fast initial filament velocities and reduced molecular recoil while intermediate cross-linker concentrations display reduced velocities and increased recoil. We show that these collective results are due to a balance of network elasticity and force-induced cross-linker unbinding and rebinding. We further show that cross-links dominate entanglement dynamics when the length between cross-linkers becomes smaller than the length between entanglements. In accord with recent simulations, we demonstrate that post-strain stress can be long-lived in cross-linked networks by distributing stress to a small fraction of highly strained connected filaments that span the network and sustain the load, thereby allowing the rest of the network to recoil and relax.

Microrheology has emerged as a powerful approach for elucidating mechanical properties of soft materials and complex fluids, especially biomaterials. In this technique, embedded microspheres are used to determine viscoelastic properties via generalized Stokes–Einstein relations, which assume the material behaves as a homogeneous continuum on the length scale of the probe. However, this condition can be violated if macromolecular systems form characteristic length scales that are larger than the probe size. Here we report observations of the onset of this effect in DNA solutions. We use microspheres driven with optical tweezers to determine the frequency dependence of the linear elastic and viscous moduli and their dependence on probe radius and DNA length. For well-entangled DNA, we find that the threshold probe radius yielding continuum behavior is ∼3× the reptation tube diameter, consistent with recent theoretical predictions. Notably, this threshold is significantly larger than the mesh size of the pol...

Using light-sheet microscopy combined with digital Fourier methods we probe the dynamics of colloidal samples and DNA molecules. This combination, referred to as selective-plane illumination differential dynamic microscopy (SPIDDM), has the benefit of optical sectioning to study, with minimal photobleaching, thick samples allowing us to measure the diffusivity of colloidal particles at high volume fractions. Further, SPIDDM exploits the inherent spatially-varying thickness of Gaussian light-sheets. Where the excitation sheet is most focused, we capture high spatial frequency dynamics as the signal-to-background is high. In thicker regions, we capture the slower dynamics as diffusion out of the sheet takes longer.

We characterize the lengthscale-dependent rheological properties of mucus from the ubiquitous Chaetopterus marine worm. We use optically trapped probes (2–10 μm) to induce microscopic strains and measure the stress response as a function of oscillation amplitude. Our results show that viscoelastic properties are highly dependent on strain scale (l), indicating three distinct lengthscale-dependent regimes at l1 ≤4 μm, l2≈4–10 μm, and l3≥10 μm. While mucus response is similar to water for l1, suggesting that probes rarely contact the mucus mesh, the response for l2 is distinctly more viscous and independent of probe size, indicative of continuum mechanics. Only for l3 does the response match the macroscopic elasticity, likely due to additional stiffer constraints that strongly resist probe displacement. Our results suggest that, rather than a single lengthscale governing crossover from viscous to elastic, mucus responds as a hierarchical network with a loose biopolymer mesh coupled to a larger scaffold responsible for macroscopic gel-like mechanics.

We drive optically trapped microspheres through entangled F-actin at constant speeds and distances well beyond the linear regime, and measure the microscale force response of the entangled filaments during and following strain. Our results reveal a unique crossover to appreciable nonlinearity at a strain rate of [small gamma, Greek, dot above]c ≈ 3 s(-1) which corresponds remarkably well with the theoretical rate of relaxation of entanglement length deformations 1/τent. Above [small gamma, Greek, dot above]c, we observe stress stiffening which occurs over very short time scales comparable to the predicted timescale over which mesh size deformations relax. Stress softening then takes over, yielding to an effectively viscous regime over a timescale comparable to the entanglement length relaxation time, τent. The viscous regime displays shear thinning but with a less pronounced viscosity scaling with strain rate compared to flexible polymers. The relaxation of induced force on filaments following strain shows that the relative relaxation proceeds more quickly for increasing strain rates; and for rates greater than [small gamma, Greek, dot above]c, the relaxation displays a complex power-law dependence on time. Our collective results reveal that molecular-level nonlinear viscoelasticity is driven by non-classical dynamics of individual entanglement segments that are unique to semiflexible polymers.

We characterize the lengthscale-dependent rheological properties of mucus from the ubiquitous Chaetopterus marine worm. We use optically trapped probes (2-10 μm) to induce microscopic strains and measure the stress response as a function of oscillation amplitude. Our results show that viscoelastic properties are highly dependent on strain scale (l), indicating three distinct lengthscale-dependent regimes at l1 ≤4 μm, l2≈4-10 μm, and l3≥10 μm. While mucus response is similar to water for l1, suggesting that probes rarely contact the mucus mesh, the response for l2 is distinctly more viscous and independent of probe size, indicative of continuum mechanics. Only for l3 does the response match the macroscopic elasticity, likely due to additional stiffer constraints that strongly resist probe displacement. Our results suggest that, rather than a single lengthscale governing crossover from viscous to elastic, mucus responds as a hierarchical network with a loose biopolymer mesh coupled to a larger scaffold responsible for macroscopic gel-like mechanics.

Despite the ubiquity of molecular crowding in living cells, the effects of crowding on the dynamics of genome-sized DNA are poorly understood. Here, we track single, fluorescent-labeled large DNA molecules (11, 115 kbp) diffusing in dextran solutions that mimic intracellular crowding conditions (0–40%), and determine the effects of crowding on both DNA mobility and conformation. Both DNAs exhibit ergodic Brownian motion and comparable mobility reduction in all conditions; however, crowder size (10 vs. 500 kDa) plays a critical role in the underlying diffusive mechanisms and dependence on crowder concentration. Surprisingly, in 10-kDa dextran, crowder influence saturates at ∼20% with an ∼5× drop in DNA diffusion, in stark contrast to exponentially retarded mobility, coupled to weak anomalous subdiffusion, with increasing concentration of 500-kDa dextran. Both DNAs elongate into lower-entropy states (compared to random coil conformations) when crowded, with elongation states that are gamma distributed and fluctuate in time. However, the broadness of the distribution of states and the time-dependence and length scale of elongation length fluctuations depend on both DNA and crowder size with concentration having surprisingly little impact. Results collectively show that mobility reduction and coil elongation of large crowded DNAs are due to a complex interplay between entropic effects and crowder mobility. Although elongation and initial mobility retardation are driven by depletion interactions, subdiffusive dynamics, and the drastic exponential slowing of DNA, up to ∼300×, arise from the reduced mobility of larger crowders. Our results elucidate the highly important and widely debated effects of cellular crowding on genome-sized DNA.

We optically drive a trapped microscale probe through entangled DNA at rates up to $100\ifmmode\times\else\texttimes\fi{}$ the disentanglement rate ($\mathrm{Wi}\ensuremath{\approx}100$), then remove the trap and track subsequent probe recoil motion. We identify a unique crossover to the nonlinear regime at $\mathrm{Wi}\ensuremath{\approx}20$. Recoil dynamics display rate-dependent dilation and complex power-law healing of the reptation tube. The force response during strain exhibits key nonlinear features such as shear thinning and yielding with power-law rate dependence. Our results, distinctly nonclassical and in accord with recent theoretical predictions, reveal molecular dynamics governed by individual stress-dependent entanglements rather than chain stretching.

To execute their diverse range of biological functions, RNA molecules must fold into specific tertiary structures and/or associate with one or more proteins to form ribonucleoprotein (RNP) complexes. Single-molecule fluorescence spectroscopy is a powerful tool for the study of RNA folding and RNP assembly processes, directly revealing different conformational subpopulations that are hidden in conventional ensemble measurements. Moreover, kinetic processes can be observed without the need to synchronize a population of molecules. In this chapter, we describe the fluorescence spectroscopic methods used for single-molecule measurements of freely diffusing or immobilized RNA molecules or RNA-protein complexes. We also provide practical protocols to prepare the fluorescently labeled RNA and protein molecules required for such studies. Finally, we provide two examples of how these various preparative and spectroscopic methods are employed in the study of RNA folding and RNP assembly processes.

Actin plays a major role in cell structure, cell motility, vesicle and organelle transport, and muscle contraction. Actin's ability to play these major roles is a direct consequence of the intricate relationship between stress and strain in a variety of filamentous actin (F-actin) networks. A thorough understanding of the unique stress-strain relationships in complex F-actin networks at the molecular-level is currently lacking despite the importance of such networks to fields such as biomimetic material engineering and cell biology. Here we develop novel single-molecule instrumentation that combines dual-trap force-measuring optical tweezers with fluorescence microscopy to enable simultaneous characterization of intermolecular forces and molecular dynamics within F-actin networks. This instrumentation is combined with a novel technique in which single F-actin “probes” are used to apply molecular-level strains and measure induced stress within entangled F-actin systems while the deformations and dynamics of surrounding fluorescent-labeled filaments are simultaneously imaged. Specifically, the dual-trap optical tweezers trap fluorescent-labeled, microsphere-conjugated probes and measure the force induced on the probe as it is moved through a network of selectively-labeled entangled F-actin by using a nanoprecison piezoelectric stage to move the sample chamber relative to the traps. Fluorescence microscopy is used simultaneously to image the dynamics of the moving probe as well as the surrounding labeled molecules subject to the applied strain. Specific bioconjugation of the fluorescent polystyrene microspheres to the ends of labeled F-actin is achieved by carbodiimide attachment of gelsolin to microspheres and combining gelsolin-coated microspheres with fluorescent phalloidin labeled actin. This powerful single-molecule technique allows simultaneous measurement of intermolecular forces and dynamics and deformations of single molecules, providing the much needed link between stress and strain at the molecular level in complex F-actin networks.

Oligomeric assembly of Rev on the Rev response element (RRE) is essential for the nuclear export of unspliced and singly spliced human immunodeficiency virus type 1 viral mRNA transcripts. Several host factors, including the human DEAD box protein DDX1, are also known to be required for efficient Rev function. In this study, spontaneous assembly and dissociation of individual Rev–RRE complexes in the presence or absence of DDX1 were observed in real time via single-molecule total internal reflection fluorescence microscopy. Binding of up to eight fluorescently labeled Rev monomers to a single RRE molecule was visualized, and the event frequencies and corresponding binding and dissociation rates for the different Rev–RRE stoichiometries were determined. The presence of DDX1 eliminated a second kinetic phase present during the initial Rev binding step, attributed to nonproductive nucleation events, resulting in increased occurrence of higher-order Rev–RRE stoichiometries. This effect was further enhanced upon the addition of a non-hydrolyzable ATP analog (adenylyl-imidophosphate), whereas ADP had no effect beyond that of DDX1 alone. Notably, the first three Rev monomer binding events were accelerated in the presence of DDX1 and adenylyl-imidophosphate, while the dissociation rates remained unchanged. Measurements performed across a range of DDX1 concentrations suggest that DDX1 targets Rev rather than the RRE to promote oligomeric assembly. Moreover, DDX1 is able to restore the oligomerization activity of a Rev mutant that is otherwise unable to assemble on the RRE beyond a monomeric complex. Taken together, these results suggest that DDX1 acts as a cellular cofactor by promoting oligomerization of Rev on the RRE.

By combining single-molecule tracking with bond-fluctuation model simulations, we show that diffusion is intricately linked to molecular topology in blends of entangled linear and ring biopolymers, namely DNA. Most notably, we find a previously unreported non-monotonic dependence of the self-diffusion coefficient for linear DNA on the fraction of linear DNA comprising the ring-linear blend, which we argue arises from a second-order effect of ring DNA molecules being threaded by varying numbers of linear DNA molecules. Results address several debated issues regarding molecular dynamics in biopolymer blends, which can be used to develop novel tunable biomaterials.

Rev, a key regulatory protein of HIV-1, activates nuclear export of unspliced and partially spliced viral mRNAs, which encode the viral genome and the genes encoding viral structural proteins, respectively. Initially, a single Rev monomer binds to a highly conserved region, stem IIB located on the Rev Response Element (RRE) of viral mRNA. Following this nucleation step, additional Rev monomers are recruited to the RRE through a combination of RNA-protein and protein-protein interactions, resulting in the formation of a functional nuclear export complex. In addition, several cellular proteins, such as the DEAD box helicases DDX1 and DDX3 are known to be required for efficient Rev function in vivo, although their precise role is unknown. In this study, single-molecule total internal reflection fluorescence (smTIRF) microscopy was used to visualize oligomeric assembly of Rev on the RRE with single monomer resolution. Binding of up to eight fluorescently labeled Rev monomers to a single immobilized RRE molecule was observed in real-time as discrete jumps in fluorescence intensity, and the event frequencies and corresponding binding and dissociation rates for the different Rev-RRE stoichiometries were determined. The smTIRF assay was used to study Rev-RRE assembly in the presence of DDX1, DDX3 and other cellular proteins. The presence of DDX1 promotes oligomeric assembly by accelerating the first few Rev monomer binding steps, suggesting that DDX1 acts as a chaperone of Rev. The smTIRF measurements are being extended to a multi-color format, in order to directly visualize the colocalization of Rev and selected cellular proteins on the same immobilized RRE molecules. These measurements are revealing the precise timing of various protein binding events during ribonucleoprotein assembly. Supported by NIH grant P50 GM082545.