Session T31: Biopolymers: Dynamics of Molecules Under Confinement, Networks, and Proteins

Tales told by tails: watching DNA driven through a random medium

DNA ligation is used to label separately the ends and centers of monodisperse DNA 16 $\mu $m in contour length, and 2-color fluorescence microscopy is used to follow with nm resolution how chains migrate through agarose networks driven by electric fields, at both whole chain and segment level. We observe that the leading segment is always a physical chain end which stretches and pulls out slack in the still-quiescent remainder of the chain until the other end is taken up. Heads and tails behave strikingly differently: the leading end of migrating chains migrates more smoothly, whereas motion of the trailing end shows intermittent pauses and jerky recoil. None of the mechanisms imagined classically for this situation - chain reptation, hooking or entropic trapping, appears to fully describe these data obtained from single-molecule visualization.   

A localized transition in the size variation of circular DNA in nanoslits

We observe a localized transition in the size variation of circular DNA between strong and moderate regimes of nanofluidic slitlike confinement. We applied a rigorous statistical analysis to our recent experimental measurements of DNA size for linear and circular topologies in nanoslits with depths around $\approx $2p, where p is the DNA persistence length [E. A. Strychalski, J. Geist, M. Gaitan, L. E. Locascio, S. M. Stavis. Macromolecules, 45, 1602-1611 (2012)]. Our empirical approach revealed a localized transition between confinement regimes for circular DNA at a nanoslit depth of $\approx $3p but detected no such transition for linear DNA with a similar contour length. These results provide the first indication of the localized influence of polymer topology on size variation across changing nanoslit depths. Improved understanding of differences in polymer behavior due to topology in this controversial system is of fundamental importance in polymer science and will inform new nanofluidic methods for biopolymer analysis.   

Analysis of conflicting experimental studies of DNA size in nanofluidic slits

Recent experimental studies have reported conflicting accounts of the size variation of DNA in nanofluidic slitlike confinement; [Bonthuis et al., Physical Review Letters 101, 10, 108303 (2008)], [Tang et al., Macromolecules 43, 17, 7368 (2010)], [Strychalski et al., Macromolecules 45, 3, 1602 (2012)], [Lin et al., Macromolecules 45, 6, 2920 (2012)], [Dai et al., Soft Matter 8, 10, 2972 (2012)]. In an effort to resolve this controversy, these studies are analyzed by a reductive as opposed to predictive approach. Minimum references for DNA size (baselines) are simulated by a Monte Carlo methodology and quantitatively compared to measured and inferred DNA sizes. The measurements of Tang et al., Strychalski et al., and Lin et al. are consistent with the related baselines and in semi-quantitative agreement with each other. The inferences of Tang et al. and Dai et al. are consistent with the related baseline and in qualitative agreement with the measurements of Tang et al., Strychalski et al., and Lin et al. The measurements of Bonthuis et al. are inconsistently larger than the related baseline and the other experimental measurements and inferences of DNA size around the transition from moderate to weak slitlike confinement. A variety of physical and chemical differences between the experimental systems are examined in detail to elucidate this inconsistency. Detailed analyses of the baseline distribution and variation clarify several core physical attributes of the system related to excluded volume effects and chain dimensionality.   

Universal Regimes of Semiflexible Polymers Confined in a Channel

The problem of a semiflexible polymer confined in a tube was considered solved almost 30 years ago, until a measurement of the extension of DNA in nanochannels challenged these classical results in polymer physics. Moreover, emerging genomics methods that take advantage of confined DNA have provided a strong motivation for reconciling theory and experiment in this field. As a result, there are a number of simulations and experiments aimed at examining the equilibrium extension of confined DNA as a function of the channel size. While these results have shed some light on the problem, a complete theoretical description for a confined semiflexible polymer still does not exist. We will present a combination of scaling theory and simulation results using an implementation of the Pruned-Enriched Rosenbluth method (PERM) that provides such a description in terms of both the confinement free energy and the extension of very long chains. In doing so, we provide clear evidence that a Gaussian-like regime emerges for stiff chains in between the classic Odijk and de Gennes regimes. The observation of this regime leads to our key conclusion that confined, semiflexible chains are best understood in the context of a rod-to-coil transition, which is directly analogous to its bulk counterpart.   

Fluctuations, structural transitions, and escape of confined biopolymers

Conformation, dynamics, and escape of semi-flexible biopolymers confined in narrow-slits are studied using Langevin dynamics simulation in two dimensions (2D). Along with chain the length and the slit width, we vary the chain stiffness and study how internal modes of the individual chain segments are affected by chain stiffness. In addition to the usual measurements of gyration radii, end to end distance, persistence length, {\em etc.}, we plan to report a detailed analysis of the sub-chain conformations and relaxation of the confined biopolymers both in de Gennes and Odjik limit We also study escape of confined semi-flexible biopolymers through narrow slits.   

Complex effects of molecular topology on diffusion in entangled biopolymer blends

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.   

Direct imaging of entangled actin solutions

It is well known that the traditional tube theory of entangled polymer cannot provide a full picture of microscopic heterogeneity. However, problems on modern topics such as nanocomposites and cell motility require us to understand microscopic details of such systems. In order to study their dynamics, direct imaging of entangled biopolymer, F-actin, was carried out. With our experimental technique it was possible to achieve sub-diffraction resolution on sparse points of a polymer, and simultaneously to observe the geometry of the contour. This enabled quantification without assumption about structure factor or the specific type of dynamical model. Preliminary results show that diffusion along the chain contour shows distinct variations according to spatial position even at constant polymer length. This may imply that, on a single polymer level, effects from heterogeneities could override mean field descriptions.   

Casimir interactions between crosslinkers in semiflexible networks

The equilibrium phase behavior of solutions of semiflexible filaments such as F-actin and cross-linking proteins is complex. As a function of both crosslinker density and the preferred filament crossing angle imposed by the cross-linker, one may observe a plethora of complex ordered phases in addition to bundles. Simulations report both the formation lamellar network structures and the aggregation of cross-linkers in thermal equilibrium. These complex phases result from an effective interaction between cross-linkers mediated by the filaments to which they are bound. In this talk, we explore interactions between labile cross-linking proteins bound to semiflexible filaments mediated by the effect of crosslinking on the thermal fluctuation spectrum the filaments involved. Such fluctuation induced interactions are of the Casimir type, which we study using a path integral formulation of the partition function of the crosslinked filaments. We also make predictions for the spatial organization of crosslinkers along semiflexible filaments and in complex semiflexible networks based on this Casimir interaction.   

Rheology of rigid rod -- flexible chain composite networks

Living cells are governed by active cellular processes such as cell division, adhesion and migration that depend on the cytoskeleton. The cytoskeleton is a composite cross-linked polymer network of cytoskeletal filaments ranging from rod-like microtubules and actin bundles to semi-flexible actin filaments and softer intermediate filaments. Single-component \textit{in vitro} networks have been studied, but well defined composites are more difficult to construct and are not yet well understood. Here, we have generated heterogeneous networks \textit{in vitro} by cross-linking microtubules and ds DNA via a heterobifunctional cross-linker (sulpho SMCC). DNA as a cross-linker has the unique advantage of having a well-defined length, which we vary in our experiments. We have measured the shear-elastic response in these networks by macrorheology experiments at varying strains and frequencies. The nonlinear response was also characterized using differential stiffness measurements in a macrorheometer. Simultaneously, we compare the experimental data to numerical simulations that we have developed for networks of stiff slender rods connected by semi-flexible linkers (see talk by Knut Heidemann).   

Cooperativity and redundancy in the mechanics of compositely crosslinked branched anisotropic cytoskeletal networks

At the leading edge of a crawling cell, the actin cytoskeleton extends itself in a particular direction via a branched crosslinked network of actin filaments with some overall alignment. This network is known as the lamellipodium. Branching via the complex Arp2/3 occurs at a reasonably well-defined angle of 70 degrees from the plus end of the mother filament such that Arp2/3 can be modeled as an angle-constraining crosslinker. Freely-rotating crosslinkers, such as alpha-actinin, are also present in lamellipodia. Therefore, we study the interplay between these two types of crosslinkers, angle-constraining and free-rotating, both analytically and numerically, to begin to quantify the mechanics of lamellipodia. We also investigate how the orientational ordering of the filaments affects this interplay. Finally, while role of Arp2/3 as a nucleator for filaments along the leading edge of a crawling cell has been studied intensely, much less is known about its mechanical contribution. Our work seeks to fill in this important gap in modeling the mechanics of lamellipodia.   

Sacrificial bonds and hidden length in biomaterials -- a kinetic description of strength and toughness in bone

Sacrificial bonds and hidden length in structural molecules account for the greatly increased fracture toughness of biological materials compared to synthetic materials without such structural features, by providing a molecular-scale mechanism of energy dissipation. One example of occurrence of sacrificial bonds and hidden length is in the polymeric glue connection between collagen fibrils in animal bone. In this talk, we propose a simple kinetic model that describes the breakage of sacrificial bonds and the revelation of hidden length, based on Bell's theory. We postulate a master equation governing the rates of bond breakage and formation, at the mean-field level, allowing for the number of bonds and hidden lengths to take up non-integer values between successive, discrete bond-breakage events. This enables us to predict the mechanical behavior of a quasi-one-dimensional ensemble of polymers at different stretching rates. We find that both the rupture peak heights and maximum stretching distance increase with the stretching rate. In addition, our theory naturally permits the possibility of self-healing in such biological structures.   

Selectively Structural Determination of Cellulose and Hemicellulose in Plant Cell Wall

Primary plant cell walls support the plant body, and regulate cell size, and plant growth. It contains several biopolymers that can be categorized into three groups: cellulose, hemicellulose and pectin. To determine the structure of plant cell wall, we use small angle neutron scattering in combination with selective deuteration and contrast matching method. We compare the structure between wild Arabidopsis thaliana and its xyloglucan-deficient mutant. Hemicellulose in both samples forms coil with similar radii of gyration, and weak scattering from the mutant suggests a limited amount of hemicellulose in the xyloglucan-deficient mutant. We observe good amount of hemicellulose coating on cellulose microfibrils only in wild Arabidopsis. The absence of coating in its xyloglucan-deficient mutation suggests the other polysaccharides do not have comparable interaction with cellulose. This highlights the importance of xyloglucan in plant cell wall. At larger scale, the average distance between cellulose fibril is found smaller than reported value, which directly reflects on their smaller matured plant size.   

Glass micro-wire tracks for guiding kinesin-powered gliding motion of microtubules

Kinesin, an enzyme molecule found in eukaryotic cells, walks on specific paths, namely microtubules. These microtubules, self-assembled \textit{in-vitro}, cooperate with kinesin molecules by playing the role of either a track for the molecular motors or a lengthy cargo lorry driven by the motor molecules. One of major challenges in utilization of the latter case, which is particularly advantageous for practical applications because of the longer cruising range and the higher carrying capacity of the bio-transporter, is herding the gliding microtubules. A general approach to achieve this goal is aligning motor molecules along a track. In previous attempts such tracks were physically and/or chemically patterned on a glass surface. We use a kinesin-coated glass wire to demonstrate kinesin-powered gliding movement of microtubules confined by the wire-like structure. This new approach distinguishes itself in that the glass wire track is an independent entity, being separable from a two-dimensional surface in principle. We will also discuss quantitative analysis of the guided motility and potential applications.   

Nanotransport Using The Kinesin Motor Protein

The kinesin motor protein is one of the major contributors in cell division and intracellular transportation of cargo. Kinesin converts chemical energy into mechanical work with a yield greater than 50{\%} and it can transport large size cargo along several micrometers, moving on a biopolymer track called microtubule. The kinesin-microtubule system has been studied \textit{in vitro}. Two main configurations exist. In the first one, the gliding mode, microtubules are propelled by kinesin proteins bound to a substrate. In the second one, the kinesin molecules ``walk'' on the microtubule. Kinesin can be engineered in order to allow binding of specific cargo. In this study, we are using biotinated kinesin which allows strong non-covalent binding with streptavidin, which can cover any nano object. Using fluorescence microscopy, transport of quantum dots has been studied. Velocities have been analyzed and the results are in good agreement with data from the literature. New approaches using multiwall carbon nanotube tracks, aligned by dielectrophoresis, have also been investigated.   

On the assembly of kinesin-based nanotransport systems

The ongoing pursuit to construct an artificial functional nanorobot has been preceded by biological equivalent long ago. Many proteins act at the nano-scale as biological motors for rotation or translation, being responsible for many fundamental processes. Among these proteins, kinesin is considered a promising tool in the development of synthetic nano-machines. The kinesin protein is a well known naturally occurring molecular machine capable of cargo transport upon interaction with cytoplasmic systems of fibers, known as microtubules. Conversion of chemical energy into mechanical work, harnessed by the hydrolysis of ATP, propels kinesin along microtubules. Even though recent efforts were made to engineer tailor-made artificial nanotransport systems using kinesin, no systematic study investigated how these systems can be built from the bottom up. Relying on the Surface Plasmon Resonance technique, we will show for the first time that it is possible to quantitatively evaluate how each component of such nanoscopic machines is sequentially assembled by monitoring the individual association of its components, specifically, the kinesin association to microtubule as well as the cargo-kinesin association.