Nonconservative forcing and diffusion in refractive optical traps

Refractive optical trapping forces can be nonconservative in the vicinity of a stable equilibrium point even in the absence of radiation pressure. We discuss how nonconservative 3D force fields, in the vicinity of an equilibrium point, reduce to circular forcing in a plane; a simple model of such forcing is the refractive trapping of a sphere by a four rays. We discuss in general the diffusion of an anisotropically trapped, circularly forced particle and obtain its spectrum of motion. Equipartition of potential energy holds even though the nonconservative flow does not follow equipotentials of the trap. We find that the dissipated nonconservative power is proportional to temperature, providing a mechanism for a runaway heating instability in traps.Comment: To appear in the Journal of the Optical Society of America

Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations

We have developed a new technique to measure viscoelasticity in soft materials such as polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kHz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G'=0.11 +/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G(omega) as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateau moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of two with values obtained from conventional rheology. We also found evidence for scaling of G(omega) as \omega^(1/2), consistent with the predictions of the Rouse model for flexible polymers.Comment: 16 pages, with 15 PostScript figures (to be published in Macromolecules

Experimental study of the Fluctuation-Dissipation-Relation during an aging process

The validity of fluctuation dissipation relations in an aging system is studied in a colloidal glass during the transition from a fluid-like to a solid-like state. The evolution of the rheological and electrical properties is analyzed in the range $1Hz - 40Hz$. It is found that at the beginning of the transition the fluctuation dissipation relation is strongly violated in electrical measurements. The amplitude and the persistence time of this violation are decreasing functions of frequency. At the lowest frequencies of the measuring range it persists for times which are about 5% of the time needed to form the colloidal glass. This phenomenology is quite close to the recent theoretical predictions done for the violation of the fluctuation dissipation relation in glassy systems. In contrast in the rheological measurements no violation of the fluctuation dissipation relation is observed. The reasons of this large difference between the electrical and rheological measurements are discussed.Comment: to be published on physica

Elementary simulation of tethered Brownian motion

We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity in many experimental contexts, for instance in single molecule biophysics; and its simulation helps the student to appreciate the dynamical character of thermal equilibrium. We show that the simulation succeeds in capturing behavior seen in experimental data on tethered particle motion.Comment: Submitted to American Journal of Physic

Brownian motion in a Maxwell fluid.

The equilibrium dynamics of a spherical particle immersed in a complex Maxwell fluid is analyzed in terms of velocity autocorrelation function (VACF), mean-square displacement (MSD), and power spectral density (PSD). We elucidate the role of hydrodynamic memory and its interplay with medium viscoelasticity for a free and a harmonically confined particle. The elastic response at high frequencies introduces oscillations in the VACF, which are found to be strongly damped by the coupling to the fluid. We show that in all Maxwell fluids hydrodynamic memory eventually leads to a power-law decay in the VACF as is already known for Newtonian fluids. The MSD displays asymptotically an intermediate plateau reflecting the elastic restoring forces of the medium. In the frequency domain, the PSD exhibits at high frequencies a step due to the trapping, whereas the low-frequency decay reflects the viscoelastic relaxation. Our results suggest that high-frequency microrheology is well-suited to infer the elastic modulus, which is sensitive over a wide range of Maxwell times

Towards the molecular workshop: entropy-driven designer molecules, entropy activation, and nanomechanical devices

We introduce some basic concepts for designer molecules with functional units which are driven by entropic rather than energetic forces. This idea profits from the mechanically interlocked nature of topological molecules such as catenanes and rotaxanes, which allows for mobile elements whose accessible configuration space gives rise to entropic intramolecular forces. Such entropy-driven designer molecules open the possibility for externally controllable functional molecules and nanomechanical devices.Comment: 4 pages, 4 figure

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the Stokes-Einstein relation as a special case of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this non-equilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging. This is the clearest change in material properties of the system with aging.Comment: 5 pages,4 figure

Endothelial Progenitors Exist within the Kidney and Lung Mesenchyme

The renal endothelium has been debated as arising from resident hemangioblast precursors that transdifferentiate from the nephrogenic mesenchyme (vasculogenesis) and/or from invading vessels (angiogenesis). While the Foxd1-positive renal cortical stroma has been shown to differentiate into cells that support the vasculature in the kidney (including vascular smooth muscle and pericytes) it has not been considered as a source of endothelial cell progenitors. In addition, it is unclear if Foxd1-positive mesenchymal cells in other organs such as the lung have the potential to form endothelium. This study examines the potential for Foxd1-positive cells of the kidney and lung to give rise to endothelial progenitors. We utilized immunofluorescence (IF) and fluorescence-activated cell sorting (FACS) to co-label Foxd1-expressing cells (including permanently lineage-tagged cells) with endothelial markers in embryonic and postnatal mice. We also cultured FACsorted Foxd1-positive cells, performed in vitro endothelial cell tubulogenesis assays and examined for endocytosis of acetylated low-density lipoprotein (Ac-LDL), a functional assay for endothelial cells. Immunofluorescence and FACS revealed that a subset of Foxd1-positive cells from kidney and lung co-expressed endothelial cell markers throughout embryogenesis. In vitro, cultured embryonic Foxd1-positive cells were able to differentiate into tubular networks that expressed endothelial cell markers and were able to endocytose Ac-LDL. IF and FACS in both the kidney and lung revealed that lineage-tagged Foxd1-positive cells gave rise to a significant portion of the endothelium in postnatal mice. In the kidney, the stromal-derived cells gave rise to a portion of the peritubular capillary endothelium, but not of the glomerular or large vessel endothelium. These findings reveal the heterogeneity of endothelial cell lineages; moreover, Foxd1-positive mesenchymal cells of the developing kidney and lung are a source of endothelial progenitors that are likely critical to patterning the vasculature. © 2013 Sims-Lucas et al