Andrés Córdoba

Elimination of inertia from a Generalized Langevin Equation: Applications to microbead rheology modeling and data analysis

SynopsisViscoelastic properties of condensed soft matter can be estimated by following the trajectory of an embedded micron-sized particle in a method called passive microbead rheology. Data analysis of passive microbead rheology is usually based on formulas that relate bead displacement statistics to the dynamic modulus of the material in the frequency-domain. Therefore, methods of analysis require conversion of the data to the frequency-domain using numerical Fourier transform routines. These methods are known to introduce errors associated with frequency discretization and finite window size. Time-domain data analysis methods based on a single bead trajectory were introduced by Fricks et al. [SIAM J. Appl. Math. 69, 1277–1308 (2009)] as an alternative to the frequency-domain formulas. We have expanded these ideas with the aim of performing Monte Carlo simulations on synthetic data to evaluate and compare analysis algorithms for systems in which particles are trapped in linear or nonlinear traps. Brownian dynamics simulations were used to generate trajectories of beads embedded in viscoelastic materials having a discrete relaxation spectrum, with multiple relaxation times. We show that by including a small purely dissipative element in the memory function of the generalized Langevin equation (GLE), we can eliminate inertia-related fast variables directly from the GLE to find an inertia-less GLE, avoiding the singularity reported by McKinley et al. [J. Rheol. 53, 1487–1506 (2009)]. Using the inertia-less GLE, the computational cost of the simulations is reduced by nearly 5 orders of magnitude. We also show that, in real systems, this purely dissipative element can arise from fluid inertia, since for the bead the Basset force acts dissipative at high frequencies.SynopsisViscoelastic properties of condensed soft matter can be estimated by following the trajectory of an embedded micron-sized particle in a method called passive microbead rheology. Data analysis of passive microbead rheology is usually based on formulas that relate bead displacement statistics to the dynamic modulus of the material in the frequency-domain. Therefore, methods of analysis require conversion of the data to the frequency-domain using numerical Fourier transform routines. These methods are known to introduce errors associated with frequency discretization and finite window size. Time-domain data analysis methods based on a single bead trajectory were introduced by Fricks et al. [SIAM J. Appl. Math. 69, 1277–1308 (2009)] as an alternative to the frequency-domain formulas. We have expanded these ideas with the aim of performing Monte Carlo simulations on synthetic data to evaluate and compare analysis algorithms for systems in which particles are trapped in linear or nonlinear traps. Browni...

The effects of hydrodynamic interaction and inertia in determining the high-frequency dynamic modulus of a viscoelastic fluid with two-point passive microrheology

In two-point passive microrheology, a modification of the original one-point technique, introduced by Crocker et al. [Phys. Rev. Lett. 85, 888 (2000)]10.1103/PhysRevLett.85.888, the cross-correlations of two micron-sized beads embedded in a viscoelastic fluid are used to estimate the dynamic modulus of a material. The two-point technique allows for the sampling of larger length scales, which means that it can be used in materials with a coarser microstructure. An optimal separation between the beads exists at which the desired length and time scales are sampled while keeping a desired signal-to-noise-ratio in the cross-correlations. A large separation can reduce the effect of higher order reflections, but will increase the effects of medium inertia and reduce the signal-to-noise-ratio. The modeling formalisms commonly used to relate two-bead cross-correlations to G*(ω) neglect inertia effects and underestimate the effect of reflections. A simple dimensional analysis for a model viscoelastic fluid suggests...

Tension-Dependent Free Energies of Nucleosome Unwrapping

Nucleosomes form the basic unit of compaction within eukaryotic genomes, and their locations represent an important, yet poorly understood, mechanism of genetic regulation. Quantifying the strength of interactions within the nucleosome is a central problem in biophysics and is critical to understanding how nucleosome positions influence gene expression. By comparing to single-molecule experiments, we demonstrate that a coarse-grained molecular model of the nucleosome can reproduce key aspects of nucleosome unwrapping. Using detailed simulations of DNA and histone proteins, we calculate the tension-dependent free energy surface corresponding to the unwrapping process. The model reproduces quantitatively the forces required to unwrap the nucleosome and reveals the role played by electrostatic interactions during this process. We then demonstrate that histone modifications and DNA sequence can have significant effects on the energies of nucleosome formation. Most notably, we show that histone tails contribute asymmetrically to the stability of the outer and inner turn of nucleosomal DNA and that depending on which histone tails are modified, the tension-dependent response is modulated differently.

Analytic slip-link expressions for universal dynamic modulus predictions of linear monodisperse polymer melts

The discrete slip-link model (DSM) is a robust mesoscopic theory that has great success predicting the rheology of flexible entangled polymer liquids and gels. In the most coarse-grained version of the DSM, we exploit heavily the universality observed in the shape of the relaxation modulus of linear monodisperse melts. For this type of polymer, we present here analytic expressions for the relaxation modulus. The high-frequency dynamics which are typically coarse-grained out from the DSM are added back into these expressions by using a Rouse chain with fixed ends to represent the fast motion of Kuhn steps between entanglements. We find consistency in the friction used for both fast and slow modes. We test these expressions against experimental data for three chemistries and molecular weights with good agreement. Using these analytic expressions, the polymer density, the molecular weight of a Kuhn step, MK, and the low-frequency cross-over between the storage and loss moduli, G′

The effects of compressibility, hydrodynamic interaction and inertia on two-point, passive microrheology of viscoelastic materials

G^{\prime }

Anisotropy and probe-medium interactions in the microrheology of nematic fluids

and G′′

A single-chain model for active gels I: active dumbbell model

G^{\prime \prime }

The Effects of the Interplay between Motor and Brownian Forces on the Rheology of Active Gels

, it is now straightforward to estimate model parameter values and obtain predictions over the experimentally accessible frequency range without performing expensive numerical calculations.

A Molecular View of the Dynamics of dsDNA Packing Inside Viral Capsids in the Presence of Ions

In two-point passive microrheology, a modification of the original one-point technique the cross-correlations of two micron-sized beads embedded in a viscoelastic material are used to estimate the dynamic modulus of a material. The two-point technique allows for sampling of larger length scales which means that it can be used in materials with a coarser microstructure. An optimal separation between the beads exists at which the desired length and time scales are sampled while keeping an acceptable signal-to-noise-ratio in the cross-correlations. A larger separation can reduce the effect of higher-order reflections, but will increase the effects of medium inertia and reduce the signal-to-noise-ratio. The modeling formalisms commonly used to relate two-bead cross-correlations to the dynamic modulus and the complex Poisson ratio neglect inertia effects and underestimate the effect of reflections. A simple dimensional analysis suggests that for a model viscoelastic solid there exists a very narrow window of bead separation and frequency range where these effects can be neglected. In a recent work [Phys. Fluids, 2012, 24, 073103] we proposed an analysis formalism that accounts for medium inertia and high-order hydrodynamic reflections and therefore significantly increases the versatility of the two-point microrheology technique. In this paper we extend our analysis to compressible viscoelastic solids. There has been a recent interest in using two-point microrheology to measure the complex Poisson ratio of biopolymers [Das and MacKintosh, Phys. Rev. Lett., 2010, 105, 138102] however a rigorous analysis of the sensitivity of the technique to the static and dynamic properties of the Poisson ratio is still lacking. There are two decoupled statistics that can be followed with such a technique: motion parallel and perpendicular to the line of centers of the probe beads. We show that the cross-correlation in the direction parallel to the line of centers is insensitive to compressibility, so may reliably be used to determine G* (dynamic modulus) alone. Although, the cross-correlation in the perpendicular direction may then be used to extract a constant Poisson ratio, it is relatively insensitive to its frequency dependence. We consider the example of a composite actin/microtubule network.

Mechanical Response of DNA–Nanoparticle Crystals to Controlled Deformation

A theoretical formalism is presented to analyze and interpret microrheology experiments in anisotropic fluids with nematic order. The predictions of that approach are examined in the context of a simple coarse-grained molecular model which is simulated using nonequilibrium molecular dynamics calculations. The proposed formalism is used to study the effect of confinement, the type of anchoring at the probe-particle surface, and the strength of the nematic field on the rheological response functions obtained from probe-particle active microrheology. As expected, a stronger nematic field leads to increased anisotropy in the rheological response of the material. It is also found that the defect structures that arise around the probe particle, which are determined by the type of anchoring and the particle size, have a significant effect on the rheological response observed in microrheology simulations. Independent estimates of the bulk dynamic modulus of the model nematic fluid considered here are obtained from small-amplitude oscillatory shear simulations with Lees–Edwards boundary conditions. The results of simulations indicate that the dynamic modulus extracted from particle-probe microrheology is different from that obtained in the absence of the particle, but that the differences decrease as the size of the defect also decreases. Importantly, the results of the nematic microrheology theory proposed here are in much closer agreement with simulations than those from earlier formalisms conceived for isotropic fluids. As such, it is anticipated that the theoretical framework advanced in this study could provide a useful tool for interpretation of microrheology experiments in systems such as liquid crystals and confined macromolecular solutions or gels.