Conformations, correlations, and instabilities of a flexible fiber in an active fluid

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Conformations, correlations, and instabilities of a flexible fiber in an active fluid

Scott Weady, David B. Stein, Alexandra Zidovska, and Michael J. Shelley

Phys. Rev. Fluids 9, 013102 – Published 18 January 2024

Abstract

Fluid-structure interactions between active and passive components are important for many biological systems to function. A particular example is chromatin in the cell nucleus, where ATP-powered processes drive coherent motions of the chromatin fiber over micron lengths. Motivated by this system, we develop a multiscale model of a long flexible polymer immersed in a suspension of active force dipoles as an analog to a chromatin fiber in an active fluid—the nucleoplasm. Linear analysis identifies an orientational instability driven by hydrodynamic and alignment interactions between the fiber and the suspension, and numerical simulations show activity can drive coherent motions and structured conformations. These results demonstrate how active and passive components, connected through fluid-structure interactions, can generate coherent structures and self-organize on large scales.

Received 21 September 2023
Accepted 6 December 2023

DOI:https://doi.org/10.1103/PhysRevFluids.9.013102

Physics Subject Headings (PhySH)

Biological fluid dynamics Fluid-particle interactions Polymer conformation & topology

Chromatin

Immersed boundary methods Multiscale modeling

Fluid DynamicsPhysics of Living SystemsPolymers & Soft Matter

Authors & Affiliations

Scott Weady ^1,*, David B. Stein ¹, Alexandra Zidovska ², and Michael J. Shelley ^1,3

¹Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
²Department of Physics, New York University, New York, New York 10003, USA
³Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA

^*sweady@flatironinstitute.org

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Issue

Vol. 9, Iss. 1 — January 2024

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Images

Figure 1
Linear theory of the coaligned configuration. (a) The bimodal equilibrium distribution, shown for several values of $ξ = 2 β / D_{R}$ . (b) Growth rate $Re (σ)$ for perturbations with $\hat{k} \cdot \hat{z} = 0$ . For fixed $D_{R}$ , increasing $β$ reduces the growth rate, causing such perturbations to decay when $β$ is sufficiently large. (c) Growth rate $Re (σ)$ for perturbations with $\hat{k} \cdot \hat{z} = 1$ . Increasing $β$ always has a destabilizing effect, triggering an instability even beyond the threshold of the isotropic state $D_{R} = 1 / 32$ for the fluid alone.
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Figure 2
Snapshots of fiber conformations from a simulation with alignment strength $β = 0.1$ . The fiber is initially disordered and undergoes persistent fluctuations, gradually condensing towards the center of the sphere. At late times the conformation is characterized by broad regions of high nematic alignment. An accompanying movie can be found as Supplemental Material [52].
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Figure 3
Large-scale correlations of fiber displacements. (a) The displacement of the fiber shows broad regions of directed motion with increasing time lag $Δ t$ . (b) The spatial autocorrelation function of the displacement map confirms this, showing increased correlations with $Δ t$ at all scales. At large distances, the autocorrelation function becomes strongly negative, indicating global rotation. (c) Displacement maps of tracer particles without an immersed fiber appear less ordered and remain relatively uniform in space. (d) The autocorrelation function shows correlations increase at intermediate scales with $Δ t$ , but have a slightly lower magnitude.
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Figure 4
Nematic order of the fiber configuration. Panels (a)–(c) show a cross section of the scalar nematic order field $s_{f} = (3 | | Q_{f} | | - 1) / 2$ with the director $m_{f}$ superimposed at a late time. (a) For the initial configuration, nematic order is relatively low. (b) Order increases only slightly for the case $β = 0$ . (c) Including alignment interactions, $β = 0.2$ , increases nematic order, with the fiber exhibiting a large degree of global alignment. (d) The long-time nematic order appears to increase monotonically with $β$ .
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Figure 5
Nematic order of the dipole suspension. Panels (a) and (b) show cross sections of the scalar nematic order parameter $s = (3 | | Q | | - 1) / 2$ for (a) $β = 0$ and (b) $β = 0.2$ at a late time. The latter exhibits substantially higher nematic order which is organized around the fiber. Panel (c) shows the time evolution of the scalar nematic order parameter for several values of $β$ , where we find the long-time mean increases with $β$ .
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Figure 6
Temporal evolution of the effective fiber persistence length, defined in Eq. (51). Following an initial decay, the persistence length grows over time, with a value that increases with the alignment interaction coefficient $β$ . For higher alignment strengths, the persistence length tends to show increased fluctuations.
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