Session V38: Mechanics of Biopolymers: Single Polymer Dynamics

Non-continuum correlated intermolecular dynamical displacements in entangled biopolymer solutions.

Understanding correlated intermolecular motion is important in biology and of fundamental interest in polymer physics. We performed real space measurements of the correlated dynamical displacements of a pair of biopolymers in entangled F-actin solutions over mesoscopic and continuum length scales, and on time scales beyond the entanglement crossover but much shorter than the reptation time. A microscopic theory is constructed based on generalizing a recent force-level statistical mechanical approach for predicting the separation-dependent, non-hydrodynamic relative friction of a pair of colloids in polymer melts [1] and in dense suspensions [2]. In the mesoscopic time regime, individual biopolymers move by reptation, and the dynamically-emergent intermolecular correlation hole is proposed as the mechanism for inducing non-hydrodynamic collective Fickian motion. Non-continuum cross correlations are predicted to dominate for inter-polymer separations up to the rod length ($\sim$15 microns), beyond which a crossover to hydrodynamic behavior occurs. The theoretical results agree well with our measurements at different observation times and physical mesh values. [1] Yamamoto, Schweizer, J.Chem.Phys.139,064907(2013); [2] Dell, Tsang, Jian, Granick, Schweizer, Phys.Rev.E, in press, 2015   

Force fluctuation in a semiflexible loop

DNA-binding proteins can regulate genetic expression by holding two sites in close proximity, forming a closed loop. Such complexes may require strong bending of DNA segments on the order of one persistence length or less. Both this elastic bending and the thermal fluctuations of the DNA molecule are necessary to describe the resulting behavior. To explore this problem, we consider a discrete model of a wormlike chain, kept in the fixed extension ensemble. By using a novel method to sample conformations in both position and momentum space, we can obtain a distribution of constraint forces as a function of chain length, extension, and flexibility. Our coarse-grained model allows us to explore the space of these parameters more efficiently than a detailed molecular dynamics approach. We find that increasing contour length decreases average force by relieving bending stress, but that the additional freedom allows fluctuations in the constraint force to increase. This implies that the probability of large forces may go up even as the mean goes down, impacting the lifetime of such bound states in a way unforeseen by purely equilibrium methods.   

Watching entangled circular DNA in real time with super-resolution

In this talk, we will show how we unraveled the conformational dynamics of entangled ring-shaped polymers in network, which is one of the most well-known problems in polymer physics, using deep imaging based on super-resolution fluorescence imaging, stimulated emission depletion (STED) microscopy. By using home-written software, we obtained the statistics of each of the hundreds of molecules, mapping out a large statistical distribution. Through inspection we not only found some aspects of the classic understanding of polymers, but some surprising aspects as well.   

Single Molecule Dynamics of Branched DNA Polymers

This work focuses on extending the field of single polymer dynamics to topologically complex polymers. Here, we report the direct observation of DNA-based branched polymers. Recently, we recently demonstrated a two-step synthesis method to generate star, H-shaped, and comb polymers for single molecule visualization. Following synthesis, we use single-color or dual-color single molecule fluorescence microscopy to directly visualize branched polymer dynamics in flow, in particular tracking side branches and backbones independently. In this way, our imaging method allows for characterization of molecular properties, including quantification of polymer contour length and branch distributions. Moving beyond characterization, we use molecular rheology and single molecule techniques to study the dynamics of single branched polymers in flow. Here, we utilize precision microfluidics to directly observe branched DNA polymer conformations during transient stretching, steady-state extension, and relaxation from high stretch. We specifically measure backbone end-to-end distance as a function of time. Experiments and Brownian dynamics simulations show that branched polymer relaxation is a strong function of the number of branches and position of branch points along the main chain backbone.   

Single polymer dynamics of linear and architecturally complex chains in semi-dilute solutions

The interplay between polymer topology and concentration gives rise to complex dynamics due to inter- and intramolecular interactions. We use a molecular level approach to study the threading behavior for linear and ring polymers near equilibrium and in non-linear flows. A semi-dilute solution of linear DNA chains is doped with fluorescently labeled ring polymers (circular DNA plasmids), and this material is used to study the dynamics of rings in semi-dilute solutions of linear chains. Single molecule fluorescence microscopy in combination with a custom-built microfluidic trapping system is used to study collective polymer dynamics at the molecular level, which allows us to precisely control flow rates and accumulated fluid strain applied to single polymer. We performed step-strain experiments on ring polymer in linear semi-dilute polymer solutions undergoing deformation in planar extensional flow. In comparison to our previous work on semi-dilute linear chains, ring polymers exhibit large fluctuations in fractional extension at steady state extension, indicating strong interactions with the background polymer solution. Transient stretching dynamics of ring polymer is inhibited in semi-dilute linear background, similar to our previous observation in linear systems. Our findings show that topology and concentration play a strong role on polymer chain dynamics in non-equilibrium flow.   

Study of mechanical properties of DNA in E. coli cells by fluorescence correlation spectroscopy

Mechanical quantities like the elasticity of cells are conventionally measured by directly probing them mechanically. Measurements of these quantities for subcellular structures in living cells are almost impossible this way. We use fluorescence correlation spectroscopy (FCS) to measure such mechanical quantities in chromosomal DNA in \textit{E. coli} cells. We present methods to address complexities of live-cell FCS such as photobleaching, and calculate the viscoelastic moduli from the FCS data. We compare the measured viscoelastic moduli of live cells with those that are ATP-depleted to stop all molecular motor action and find substantial differences. Active processes are stopped in ATP-depleted cells and hence the bacterial DNA appears to become stiffer and the surrounding intracellular medium more viscous. We also compare our results with the FCS data obtained from the lambda DNA solution in various concentrations to mimic the cellular environment.   

Single Polymer Dynamics under Large Amplitude Oscillatory Extensional (LAOE) Flow

Over the past two decades, advances in fluorescence imaging and particle manipulation have enabled the direct observation of single polymer dynamics in model flows such as shear flow and planar extensional flow. The vast majority of single polymer studies, however, has focused on chain dynamics using simple transient step forcing functions. In order to study single polymer dynamics in non-idealized model flows, there is a clear need to implement more complicated transient flow forcing functions. In bulk rheology, large amplitude oscillatory shear (LAOS) was widely used to study the linear and nonlinear viscoelasticity of materials, but not yet been applied to molecular rheology. In this work, we directly probe single polymer dynamics using oscillatory extensional flow in precisely controlled microfluidic devices. We are able to generate large and small amplitude sinusoidal oscillatory extensional flow in a cross-slot microfluidic device while imaging the conformational dynamics of a single polymer trapped at the stagnation point. In this flow, polymer chains are stretched, squeezed, and rotated between extensional/compressional axes in a highly dynamic and transient manner. Using this technique, we studied the dynamics and coil-stretch transition of a single $\lambda $-DNA as a function of the Weissenberg number (Wi) and Deborah number (De). Moreover, we use Brownian dynamics simulation to map a wide range of Pipkin space for polymers from linear steady-state conditions to non-linear unsteady-states. Our results reveal a critical Wi at the coil-stretch transition that is function of the De in LAOE flow.   

Large-scale structural transitions in supercoiled DNA revealed by coarse-grained simulations

Topological constraints, such as DNA supercoiling, play an integral role in genomic regulation and organization in living systems. However, physical understanding of the principles that underlie DNA structure and organization at biologically-relevant length-scales remains a formidable challenge. We develop a coarse-grained simulation approach for predicting equilibrium conformations of supercoiled DNA. With this approach, we study the conformational transitions that arise due to supercoiling across the full range of supercoiling densities that are commonly explored by living systems. Simulations of ring DNA molecules with lengths up to the scale of topological domains in the E. coli chromosome ($\sim$10 kilobases) reveal large-scale structural transitions elicited by supercoiling, resulting in 3 supercoiling conformational regimes: chiral coils, extended plectonemes, and branched hyper-supercoils. These results capture the non-monotonic relationship of size versus degree of supercoiling observed in experimental sedimentation studies of supercoiled DNA, and our results provide a physical explanation of the structural transitions underlying this behavior.   

Jamming of Knots along a Tensioned Chain

In the limit of very long chains, coiled polymers almost always self-entangle and form knots. In this study, we characterize the motion of these knots along the chain contour when the chain is under very high tension. In this regime, we find that the knot exhibits glassy physics. For example, instead of moving continuously along the contour, the knot becomes kinetically trapped in long-lived, metastable states. This caging phenomenon follows Poisson statistics, and thus the long-time dynamics of the knot are diffusive. We quantify the long-time diffusivity of knots of various topologies, and we find that the diffusivity decays exponentially with increasing chain tension. The rate-of-decay of these transport properties is relatively insensitive to the knot's topology, which can be explained by examining the energy landscape of the self-reptation moves of the knot along the chain. Finally, we examine the role of bending and excluded volume interactions on this jamming phenomenon. Bending plays the biggest role in determining the onset of jamming, but the corrugation of the excluded volume interactions solely determines the rate-of-decay of the knot's transport properties.   

Activity induced phase separation in particles and (bio)polymers

It was recently shown that the non-equilibrium steady state of the mixture of two types of particles exposed to two different thermostats can phase separate (A.Y.Grosberg, J.-F.Joanny, PRE, v. \textbf{91}, 032118, 2015). similar result is valid also in the case when particles in question are monomers of two different polymer chains, or blocks of a co-polymer. We discuss the implications of these results for the physics of chromatin.   

Electrophoresis of semiflexible heteropolymers and the ``hydrodynamic Kuhn length''

Semiflexible polymers, such as DNA, are rodlike for short lengths and coil-like for long lengths. For purely geometric properties, such as the end-to-end distance, the crossover between these two behaviors occurs when the polymer length is on the order of the Kuhn length. On the other hand, for the hydrodynamic friction coefficient it is easy to see by comparing the expressions for a rod and a coil that the crossover should occur at the polymer length, termed by us the \textit{hydrodynamic Kuhn length} [1], which is larger than the ordinary Kuhn length by a logarithmic factor that can be quite significant. We show that for the problem of electrophoresis of a heteropolymer consisting of several blocks of (in general) different stiffnesses, both of these length scales can be important depending on the details of the problem. [1] M.~V.~Chubynsky and G.~W.~Slater, \textit{Macromolecules} 48 (2015) 5899.   

Viscoelastic dynamics in a system of two actin filaments under stress

The viscoelasticity of cytoskeleton networks is experimentally well-established but still lacks a consistent theoretical description. We present a novel minimal model that consists of two semi-flexible filaments coupled by cross-linkers, whose dynamics are described by Grand Canonical Monte Carlo. The mechanical properties are captured in the continuum and solved through an athermal finite-element approach. We discuss the phase diagram of the model and the emergence of viscoelastic behavior: the variation of the dynamic modulus as a function of loading frequency and density of cross-linkers, in thermodynamically and biologically realistic settings.   

How to Concentrate Genomic Length DNA in a Microfabricated Array

We demonstrate that a microfabricated bump array can concentrate genomic-length DNA molecules efficiently at continuous, high flow velocities, up to 40 ?m/s, if the single-molecule DNA globule has a sufficiently large shear modulus.. Increase in the shear modulus is accomplished by compacting the DNA molecules to minimal coil-size using polyethylene glycol (PEG) derived depletion forces. We map out the sweet spot where concentration occurs as a function of PEG con- centration, flow speed, and bump array parameters using a combination of theoretical analysis and experiment. Purification of DNA from enzymatic reactions for next-generation DNA-sequencing libraries will be an important application of this development.