Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Signatures of motor susceptibility to forces in the dynamics of a tracer particle in an active gel

Nitzan Razin, Raphael Voituriez, and Nir S. Gov
Phys. Rev. E 99, 022419 – Published 25 February 2019
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • MODEL DEFINITION
  • QUALITATIVE BEHAVIOR OF THE VAN HOVE…
  • VAN HOVE DISTRIBUTION PEAK RATIO
  • SUSCEPTIBLE MOTORS
  • DISCUSSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We study a model for the motion of a tracer particle inside an active gel, exposing the properties of the van Hove distribution of the particle displacements. Active events of a typical force magnitude can give rise to non-Gaussian distributions having exponential tails or side peaks. The side peaks are predicted to appear when the local bulk elasticity of the gel is large enough and few active sources are dominant. We explain the regimes of the different distributions and study the structure of the side peaks for active sources that are susceptible to the elastic stress that they cause inside the gel. We show how the van Hove distribution is altered by both the duty cycle of the active sources and their susceptibility, and suggest it as a sensitive probe to analyze microrheology data in active systems with restoring elastic forces.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    3 More
    • Received 22 June 2018
    • Revised 5 January 2019

    DOI:https://doi.org/10.1103/PhysRevE.99.022419

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Physical Systems
    ActinActive gelsCytoskeletal motor proteins
    1. Techniques
    Langevin equationMolecular dynamics
    Physics of Living SystemsPolymers & Soft Matter

    Authors & Affiliations

    Nitzan Razin1, Raphael Voituriez2, and Nir S. Gov1

    • 1Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
    • 2Laboratoire Jean Perrin and Laboratoire de Physique Théorique de la Matière Condensée, CNRS / Sorbonne Universite, 75005 Paris, France

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 99, Iss. 2 — February 2019

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      Exponential tails in the weak confinement k/γ≪koff,kon and small pon limits. The van Hove distribution is plotted for varying lag times Δt, for k=10, γ=50, kon=1, koff=10: (a) N=1 and (b) N=10.

      Reuse & Permissions
    • Figure 2
      Figure 2

      (a) Sketch of the steady-state position distribution of the particle for N=1 motor with the peak notations marked. (b) Sketch of the matching long-time VHD of particle displacements (P[Δx(Δt→∞)]). Notation for the distribution peaks and consecutive peak differences is marked. (c) The steady-state particle position distribution for N=1 adamant motor (kon=0.43, koff=1, k=1000, F0=1, γ=50). (d) The VHD for the same system as in (c). Different colors represent different lag times Δt. Detected peaks are marked by black x's and shoulders by black circles.

      Reuse & Permissions
    • Figure 3
      Figure 3

      r0 in simulations with N=1 adamant motor, koff=1, and varying kon (k=1000, F0=1, γ=50): (a) r0 vs pon. Different colors represent different lag times Δt. The black line is the approximate theoretical result for the fast particle limit at long lag times. (b) r0 vs Δt. Colors represent different pon values. For pon≲0.6, r0<1 at all lag times.

      Reuse & Permissions
    • Figure 4
      Figure 4

      (a)–(d) Long-time VHD for several simulations used to make Fig. 3, for varying kon values at constant koff. As pon increases, the i=2 peaks increase until passing the i=1 peaks.

      Reuse & Permissions
    • Figure 5
      Figure 5

      Comparison of systems of N=1 susceptible motor with susceptibility in the on or off rate. The VHD for various F1 values is plotted for (a), (b) kon±=e∓kx/F1, koff=10, for lag times of Δt=0.1 (a) and Δt=10 (b). For Δt=0.1, increasing the susceptibility (decreasing F1) increases the height of the shoulder P̃2 and therefore increases r0. (c), (d) kon=1, koff=10e−Mkx/F1, for lag times of Δt=0.1 (c) and Δt=10 (d). Increasing the susceptibility causes peaks to become shoulders and move to smaller |x|. It does not increase P̃2 or r0. (k=1000, F0=1, γ=50.)

      Reuse & Permissions
    • Figure 6
      Figure 6

      The effect of susceptibility on r0. For kon±=e∓kx/F1, koff=10, N=1: (a) r0 as a function of F1 for various lag times Δt. Inset: The average duty cycle 〈pon〉 as a function of F1. (b) r0 as a function of the average duty cycle 〈pon〉(F1) for various lag times Δt. For a small enough Δt, r0>1 for much smaller pon than in the adamant motor system. (c), (d) Same as (a) and (b) for kon=1, koff=10e−Mkx/F1 (k=1000, F0=1, γ=50).

      Reuse & Permissions
    • Figure 7
      Figure 7

      Comparison of systems of N=2 susceptible motor with susceptibility in the on or off rate. The van Hove distribution for various F1 values is plotted for (a), (b) kon±=kon0e∓kx/F1, koff=10, for lag times of Δt=0.1 (a) and Δt=10 (b). Visibly, for the short lag time Δt=0.1, increasing the susceptibility (decreasing F1) increases the height of the shoulder P̃2 and therefore increases r0. (c), (d) kon=1, koff=10e−Mkx/F1, for lag times of Δt=0.1 (c) and Δt=10 (d). Increasing the susceptibility causes peaks to become shoulders and move to smaller |x|. It does not increase P̃2 or r0. (k=1000, F0=1, γ=50.)

      Reuse & Permissions
    • Figure 8
      Figure 8

      The effect of susceptibility of the active event occurrence rate kon. For the model with kon±=e∓kx/F1, koff=10, N=2: (a) r0 as a function of F1 for various lag times Δt. Inset: The average time ratio in which the motor was on 〈pon〉 as a function of F1. (b) r0 as a function of the average duty cycle 〈pon〉(F1) for various lag times Δt. Note that for a small enough Δt, r0>1 for much smaller pon than in the adamant motor system. (c), (d) Same as (a) and (b) for kon=1, koff=10e−Mkx/F1. (k=1000, F0=1, γ=50.)

      Reuse & Permissions
    • Figure 9
      Figure 9

      (a)–(d) The results of the theoretical calculation of the long-time VHD peak ratio ri for i=0–3 in the fast particle limit [given by Eq. (C5) used in the definition of ri]. Plots are for motor number N=1–10, where the line color denotes the motor number and varies between dark blue (N=1) and red (N=10). Note ri→1 as pon→0, and ri<1 for pon≲0.6 for all shown parameters.

      Reuse & Permissions
    • Figure 10
      Figure 10

      (a)–(d) The results of the theoretical calculation of the long-time VHD peak difference Δi for i=0–3 in the fast particle limit. Plots are for motor number N=1–10 where the line color denotes the motor number and varies between dark blue (N=1) and red (N=10). Note that all the Δi are continuous and for even i positive, while for odd i cross zero.

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review E

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×