Dynamic analysis of a diffusing particle in a trapping potential

Lindner, Moshe; Nir, Guy; Vivante, Anat; Young, Ian T.; Garini, Yuval

doi:10.1103/physreve.87.022716

Cited by 34 publications

(35 citation statements)

References 31 publications

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“…In addition, some progress has been made recently in extracting relevant physical parameters using data collected in the regime where both drift and diffusion effects are significant [24,30]. Accounting for drift effects will allow sampling rates that are slower relative to the diffusion time scales to still yield useful information.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of an optically confined nanoparticle diffusing normal to a surface

2016

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Here we measure the hindered diffusion of an optically confined nanoparticle in the direction normal to a surface, and we use this to determine the particle-surface interaction profile in terms of the absolute height. These studies are performed using the evanescent field of an optically excited single-mode silicon nitride waveguide, where the particle is confined in a height-dependent potential energy well generated from the balance of optical gradient and surface forces. Using a high-speed CMOS camera, we demonstrate the ability to capture the short time-scale diffusion dominated motion for 800-nm-diam polystyrene particles, with measurement times of only a few seconds per particle. Using established theory, we show how this information can be used to estimate the equilibrium separation of the particle from the surface. As this measurement can be made simultaneously with equilibrium statistical mechanical measurements of the particle-surface interaction energy landscape, we demonstrate the ability to determine these in terms of the absolute rather than relative separation height. This enables the comparison of potential energy landscapes of particle-surface interactions measured under different experimental conditions, enhancing the utility of this technique.

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Section: Discussionmentioning

confidence: 99%

Dynamics of an optically confined nanoparticle diffusing normal to a surface

2016

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S (t, t_{0}) = 1 - \exp true(- \frac{4 (t - t_{0})}{τ} true),

with time constant

τ = \frac{2 k_{B} T}{K D},

and D is the diffusion constant given by the Stokes-Einstein equation [30]

D = \frac{k_{B} T}{6 π η R} .

In the limit t → ∞ , the distribution decays to the steady-state …”

Section: Introductionmentioning

confidence: 99%

“…In the low-force regime, DNA has an effective spring constant of

K \approx \frac{3 k_{B} T}{2 L_{0} L_{p}}

[30]. For a 900 bp tether and a particle with radius R =160 nm Eq.…”

Section: Introductionmentioning

confidence: 99%

Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors

Kovari

Yan

Finzi

et al. 2017

Methods in Molecular Biology

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Tethered Particle Motion (TPM) is a versatile in vitro technique for monitoring the conformations a linear macro-molecule, such as DNA, can exhibit. The technique involves monitoring the diffusive motion of a tracker particle anchored to a fixed point via the macro-molecule of interest, which acts as a tether. In this chapter, we provide an overview of TPM, review the fundamental principles that determine the accuracy with which effective tether lengths can be used to distinguish different tether conformations, present software tools that assist in capturing and analyzing TPM data, and provide a protocol which uses TPM to characterize lac repressor induced DNA looping. Critical to any TPM assay is understanding the timescale over which the diffusive motion of the tracker particle must be observed to accurately distinguish tether conformations. Approximating the tether as a Hookean spring, we show how to estimate the diffusion timescale, and discuss how it relates to the confidence with which tether conformations can be differentiated. Applying those estimates to a lac repressor titration assay, we describe how to perform a TPM experiment. Additionally, we also provide graphically driven software which can be used to speed up data collection and analysis. Lastly, we detail how TPM data from the titration assay can be used to calculate relevant molecular descriptors such as the DNA looping J factor and lac repressor – operator dissociation constants. While the included protocol is geared toward studying DNA looping, the technique, fundamental principles, and analytical methods are more general and can be adapted to a wide variety of molecular systems.

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“…Along the y axis, this gradient force acts as a harmonic optical restoring force which is counterbalanced by Brownian fluctuations. The probability density function of the nanoparticle position over time is governed by the Smoluchowski equation for a harmonic biasing force [25]:

\frac{\partial}{\partial t} P false(y, t | y_{0}, t_{0} false) = D (\frac{\partial^{2}}{\partial y^{2}} + \frac{k_{trap}}{k_{B} T} \frac{\partial}{\partial y} y) P (y, t | y_{0}, t_{0}),

where D is the diffusion coefficient and k trap is the spring constant of the effective harmonic potential.…”

Section: D Nfm Theorymentioning

confidence: 99%

“…Following the results of Lindner et al for tethered Brownian motion [25], the solution to this partial differential equation is a Gaussian function with a variance that grows over time and depends on both k trap and D :

σ^{2} false(Δ t false) = \frac{k_{B} T}{k_{trap}} [1 - normalexp (- \frac{2 false(k_{trap} D false) Δ t}{k_{B} T})] .

…”

Section: D Nfm Theorymentioning

confidence: 99%

Simultaneous Characterization of Nanoparticle Size and Particle-Surface Interactions with Three-Dimensional Nanophotonic Force Microscopy

2016

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The behavior of a nanoparticle in solution depends strongly on the particle’s physical and chemical characteristics, most notably the particle size and the surface properties. Accurately characterizing these properties is critical for quality control in a wide variety of industries. To understand a complex and polydisperse nanoparticle suspension, however, ensemble averaging is not sufficient, and there is a great need for direct measurements of size and surface properties at the individual nanoparticle level. In this work, we present an analysis technique for simultaneous characterization of particle-surface interactions and size using near-field light scattering and verify it using Brownian-dynamics simulations. Using a nanophotonic waveguide, single particles can be stably held near the waveguide’s surface by strongly localized optical forces. By tracking the dynamic 3D motion of the particle under the influence of these forces using an optical microscope, it is possible to extract the particle-surface interaction forces, as well as to estimate the size and refractive index of the nanoparticle. Because of the strong light-scattering signal, this method is viable for high-throughput characterization of particles as small as 100 nm in only a few seconds each.

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Dynamic analysis of a diffusing particle in a trapping potential

Cited by 34 publications

References 31 publications

Dynamics of an optically confined nanoparticle diffusing normal to a surface

Dynamics of an optically confined nanoparticle diffusing normal to a surface

Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors

Simultaneous Characterization of Nanoparticle Size and Particle-Surface Interactions with Three-Dimensional Nanophotonic Force Microscopy

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