Measuring Cohesion between Macromolecular Filaments One Pair at a Time: Depletion-Induced Microtubule Bundling

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Measuring Cohesion between Macromolecular Filaments One Pair at a Time: Depletion-Induced Microtubule Bundling

Feodor Hilitski, Andrew R. Ward, Luis Cajamarca, Michael F. Hagan, Gregory M. Grason, and Zvonimir Dogic

Phys. Rev. Lett. 114, 138102 – Published 2 April 2015

Abstract

In the presence of nonadsorbing polymers, colloidal particles experience ubiquitous attractive interactions induced by depletion forces. Here, we measure the depletion interaction between a pair of microtubule filaments using a method that combines single filament imaging with optical trapping. By quantifying the dependence of filament cohesion on both polymer concentration and solution ionic strength, we demonstrate that the minimal model of depletion, based on the Asakura-Oosawa theory, fails to quantitatively describe the experimental data. By measuring the cohesion strength in two- and three- filament bundles, we verify pairwise additivity of depletion interactions for the specific experimental conditions. The described experimental technique can be used to measure pairwise interactions between various biological or synthetic filaments and complements information extracted from bulk osmotic stress experiments.

Received 18 August 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.138102

Authors & Affiliations

Feodor Hilitski¹, Andrew R. Ward¹, Luis Cajamarca², Michael F. Hagan¹, Gregory M. Grason³, and Zvonimir Dogic^1,*

¹Department of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
²Department of Physics, University of Massachusetts at Amherst, Amherst, Massachusetts 01003, USA
³Department of Polymer Science and Engineering, University of Massachusetts at Amherst, Amherst, Massachusetts 01003, USA

^*zdogic@brandeis.edu

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Vol. 114, Iss. 13 — 3 April 2015

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Images

Figure 1
Formation of a microtubule (MT) bundle in quasi-2D chamber. (a) Schematic depiction of the PEG-induced MT bundle, showing depleting polymer, excluded volume shells inaccessible to depleting coils, and disordered poly-aminoacid $c$ -terminus tails of tubulin monomers. Inset: Relevant length scales of the bristle-stabilized model: $R_{h}$ , effective radius of the polymer coils; $h$ , bristle height; $D$ , surface-to-surface MT separation. (b) Sequence of darkfield microscopy images showing evolution of a bundle (yellow arrows) formed by two filaments (MT1 and MT2). Short ( $\sim 1 μ m$ ) fragment bound to MT1 exhibits 1D diffusion along the filament.
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Figure 2
Experimental setup used to measure MT cohesion strength. (a) Left: two unbundled optically trapped bead-MT complexes. Right: upon bundle formation the depletion force pulls beads closer together, away from the trap centers. (b) Composite fluorescence image of the MT filaments showing biotin-free elongated segments (red) and biotin labeled seeds (green). Beads attached to seeds are not visible. Optical traps are indicated by the dashed lines. (c) Composite fluorescence image showing MTs from panel (b) forming a bundle, visible as the bright red region. Bundle overlap region and trap locations are indicated by the yellow and blue dashed lines, respectively. (d) Bundle overlap length (yellow arrows) is controlled by the independent movement of two optical traps (blue dashed lines).
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Figure 3
Analysis of the experimental data. (a) Fluctuations in the separation of two beads ( $R$ ) with and without bundled MTs (blue line). MT bundle formation is accompanied by a rapid reduction of $R$ (red line). (b) Probability distributions $P_{bundle} (R)$ and $P_{calibration} (R)$ are obtained by sampling statistically independent configurations of the two beads. (c) The bundle free energy, $G$ , scales linearly with the bead separation. Slope of the weighted linear fit gives the value of the cohesion strength, $λ$ . (d) $λ$ is independent of the bundle overlap, $L$ . Dashed lines correspond to the mean cohesion strength. Error bars for the individual measurements represent 95% confidence intervals.
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Figure 4
Dependence of $λ$ on the counterion concentration [ $K^{+}$ ] for several PEG concentrations. Inset: Dependence of $λ$ on [ $K^{+}$ ] for 2.0% dextran and 1.5% PEG. Each point is an average of $N = 5 - 60$ independent measurements. Error bars represent standard deviation.
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Figure 5
Comparisons of theoretical models of the cohesion strength. (a) Effective interactions between two parallel MTs (solid black curve) as a function of filament surface separation, $D$ . The effective potential is composed of the depletion attraction (dash-dotted blue curve) and repulsive potential due to charged hollow cylinders (red dashed curve) and charged bristles (dotted light brown curve). Inset: The predicted bristle height $h$ vs salt concentration. (b) Theoretical predictions of the cohesion strength for the primitive model (dashed curve), the bristle-stabilized model (solid curve), and experimental results (squares) for PEG 1.0%.
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Figure 6
Pairwise additivity of the depletion interaction. (a) Schematic representation and (b) fluorescence image of a three-filament bundle. The third MT is not attached to the beads. Scale bar, $5 μ m$ . (c) For a wide range of experimental conditions, $λ$ for three-MT bundles is double the value for the two-MT bundles. Error bars represent standard deviation.
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