skip to main content


Title: The conformation of a semiflexible filament in a random potential
Motivated by the observation of the storage of excess elastic free energy -- prestress in cross linked semiflexible filament networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross linking to other filaments is assumed to have a finite correlation length and mean strength. We examine the statistical distribution of curvature in the limit that the filaments are much shorter than their thermal persistence length. We compare our theoretical predictions to finite element Brownian dynamics simulations. Lastly we comment on the validity of replica field techniques in addressing these questions.  more » « less
Award ID(s):
1709785
NSF-PAR ID:
10135522
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Physical review and Physical review letters index
Volume:
99
ISSN:
0094-0003
Page Range / eLocation ID:
042501
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Semiflexible slender filaments are ubiquitous in nature and cell biology, including in the cytoskeleton, where reorganization of actin filaments allows the cell to move and divide. Most methods for simulating semiflexible inextensible fibers/polymers are based on discrete (bead-link or blob-link) models, which become prohibitively expensive in the slender limit when hydrodynamics is accounted for. In this paper, we develop a novel coarse-grained approach for simulating fluctuating slender filaments with hydrodynamic interactions. Our approach is tailored to relatively stiff fibers whose persistence length is comparable to or larger than their length and is based on three major contributions. First, we discretize the filament centerline using a coarse non-uniform Chebyshev grid, on which we formulate a discrete constrained Gibbs–Boltzmann (GB) equilibrium distribution and overdamped Langevin equation for the evolution of unit-length tangent vectors. Second, we define the hydrodynamic mobility at each point on the filament as an integral of the Rotne–Prager–Yamakawa kernel along the centerline and apply a spectrally accurate “slender-body” quadrature to accurately resolve the hydrodynamics. Third, we propose a novel midpoint temporal integrator, which can correctly capture the Ito drift terms that arise in the overdamped Langevin equation. For two separate examples, we verify that the equilibrium distribution for the Chebyshev grid is a good approximation of the blob-link one and that our temporal integrator for overdamped Langevin dynamics samples the equilibrium GB distribution for sufficiently small time step sizes. We also study the dynamics of relaxation of an initially straight filament and find that as few as 12 Chebyshev nodes provide a good approximation to the dynamics while allowing a time step size two orders of magnitude larger than a resolved blob-link simulation. We conclude by applying our approach to a suspension of cross-linked semiflexible fibers (neglecting hydrodynamic interactions between fibers), where we study how semiflexible fluctuations affect bundling dynamics. We find that semiflexible filaments bundle faster than rigid filaments even when the persistence length is large, but show that semiflexible bending fluctuations only further accelerate agglomeration when the persistence length and fiber length are of the same order. 
    more » « less
  2. Merks, Roeland M.H. (Ed.)
    Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks. 
    more » « less
  3. The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed state to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find that the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show that the theory is highly sensitive to fluctuations in length in two dimensions and the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts. 
    more » « less
  4. Studying the Brownian motion of fibers and semi-flexible filaments in porous media is the key to understanding the transport and mechanical properties in a variety of systems. The motion of semi-flexible filaments in gel-like porous media including polymer networks and cell cytoskeleton has been studied theoretically and experimentally, whereas the motion of these materials in packed-colloid porous media, advanced foams, and rock-like systems has not been thoroughly studied. Here we use video microscopy to directly visualize the reptation and transport of intrinsically fluorescent, semiflexible, semiconducting single-walled carbon nanotubes (SWCNTs) in the sub-micron pores of packed colloids as fixed obstacles of packed-colloid porous media. By visualizing the filament motion and Brownian diffusion at different locations in the pore structures, we study how the properties of the environment, like the pore shape and pore structure of the porous media, affect SWCNT mobility. These results show that the porous media structure controls SWCNT reorientation during Brownian diffusion. In packed-colloid pores, SWCNTs diffuse along straight pores and bend across pores; conversely, in gel pores, SWCNTs consistently diffuse into curved pores, displaying a faster parallel motion. In both gel and packed-colloid porous media, SWCNT finite stiffness enhances SWCNT rotational diffusion and prevents jamming, allowing for inter-pore diffusion. 
    more » « less
  5. Abstract

    The nuclear lamina is widely recognized as the most crucial component in providing mechanical stability to the nucleus. However, it is still a significant challenge to model the mechanics of this multilayered protein network. We developed a constitutive model of the nuclear lamina network based on its microstructure, which accounts for the deformation phases at the dimer level, as well as the orientational arrangement and density of lamin filaments. Instead of relying on homology modeling in the previous studies, we conducted molecular simulations to predict the force‐extension response of a highly accurate lamin dimer structure obtained through X‐ray diffraction crystallography experimentation. Furthermore, we devised a semiflexible worm‐like chain extension‐force model of lamin dimer as a substitute, incorporating phases of initial stretching, uncoiling of the dimer coiled‐coil, and transition of secondary structures. Subsequently, we developed a 2D network continuum model for the nuclear lamina by using our extension‐force lamin dimer model and derived stress resultants. By comparing with experimentally measured lamina modulus, we found that the lamina network has sharp initial strain‐hardening behavior. This also enabled us to carry out finite element simulations of the entire nucleus with an accurate microstructure‐based nuclear lamina model. Finally, we conducted simulations of transendothelial transmigration of a nucleus and investigated the impact of varying network density and uncoiling constants on the critical force required for successful transmigration. The model allows us to incorporate the microstructure characteristics of the nuclear lamina into the nucleus model, thereby gaining insights into how laminopathies and mutations affect nuclear mechanics.

     
    more » « less