The force exerted by an optical trap on a dielectric bead in a fluid is often found by fitting a Lorentzian to the power spectrum of Brownian motion of the bead in the trap. We present explicit functions of the experimental power spectrum that give the values of the parameters fitted, including error bars and correlations, for the best such 2 fit in a given frequency range. We use these functions to determine the information content of various parts of the power spectrum, and find, at odds with lore, much information at relatively high frequencies. Applying the method to real data, we obtain perfect fits and calibrate tweezers with less than 1% error when the trapping force is not too strong. Relatively strong traps have power spectra that cannot be fitted properly with any Lorentzian, we find. This underscores the need for better understanding of the power spectrum than the Lorentzian provides. This is achieved using old and new theory for Brownian motion in an incompressible fluid, and new results for a popular photodetection system. The trap and photodetection system are then calibrated simultaneously in a manner that makes optical tweezers a tool of precision for force spectroscopy, local viscometry, and probably other applications.

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion. of larger molecules or tracers in living cells [3,[6][7][8][9][10][11][12][13][14][15][16]. While normal diffusion, by virtue of the central limit theorem, is characterized by the universal Gaussian probability density function and therefore uniquely determined by the first and second moments [17], anomalous diffusion of the form (1) is non-universal and may be caused by different stochastic mechanisms. These would give rise to vastly different behavior for diffusional mixing, diffusionlimited reactions, signaling, or regulatory processes. To better understand cellular dynamics, knowledge of the underlying stochastic mechanism is thus imperative.Here we report experimental evidence from extensive single trajectory time series of lipid granule motion in Schizosaccharomyces pombe (S. pombe) fission yeast cells obtained from tracking with optical tweezers (resolving 10 −6 sec to 1 sec) and video microscopy (10 −2 sec to 100 sec). Using complementary analysis tools we demonstrate that at short times the data are described best by continuous time random walk (CTRW) subdiffusion, revealing pronounced features of weak ergodicity breaking in the time averaged mean squared displacement. At longer times the stochastic mechanism is closest to subdiffusive fractional Brownian motion (FBM). The time scales over which this anomalous behavior persists is relevant for biological processes occurring in the cell. Anomalous diffusion may indeed be a good strategy for cellular signaling and reactions [7,8].CTRW and FBM both effect anomalous diffusion of the type (1) [18]. Subdiffusive CTRWs are random walks with finite variance δx 2 of jump lengths, while the waiting times between successive jumps are drawn from a density ψ(t) ≃ τ α /t 1+α with diverging characteristic time [4,17]. Such scale-free behavior results from multiple trapping events in, e.g., comb-like structures [19] or random energy landscapes [20]. Power-law waiting time distributions were also identified for tracer motion in reconstituted actin networks [21]. Subdiffusive FBM is a random process driven by Gaussian noise ξ with longrange correlations, ξ(0)ξ(t) ≃ α(α − 1)t α−2 [22], and it is related to fractional Langevin equations [23]. The finite characteristic time scales associated with FBM contrast the ageing property of the subdiffusive CTRW processes [Supplementary Material (SM)].Single particle tracking microscopy has become a standard tool to probe the motion of individual tracers, espe...

The viscoelastic properties of the cytoplasm of living yeast cells were investigated by studying the motion of lipid granules naturally occurring in the cytoplasm. A large frequency range of observation was obtained by a combination of video-based and laser-based tracking methods. At time scales from 10(-4) to 10(2) s, the granules typically perform subdiffusive motion with characteristics different from previous measurements in living cells. This subdiffusive behavior is thought to be due to the presence of polymer networks and membranous structures in the cytoplasm. Consistent with this hypothesis, we observe that the motion becomes less subdiffusive upon actin disruption.

The biomolecule is among the most important building blocks of biological systems, and a full understanding of its function forms the scaffold for describing the mechanisms of higher order structures as organelles and cells. Force is a fundamental regulatory mechanism of biomolecular interactions driving many cellular processes. The forces on a molecular scale are exactly in the range that can be manipulated and probed with single molecule force spectroscopy. The natural environment of a biomolecule is inside a living cell, hence, this is the most relevant environment for probing their function. In vivo studies are, however, challenged by the complexity of the cell. In this review, we start with presenting relevant theoretical tools for analyzing single molecule data obtained in intracellular environments followed by a description of state-of-the art visualization techniques. The most commonly used force spectroscopy techniques, namely optical tweezers, magnetic tweezers, and atomic force microscopy, are described in detail, and their strength and limitations related to in vivo experiments are discussed. Finally, recent exciting discoveries within the field of in vivo manipulation and dynamics of single molecule and organelles are reviewed.

We investigate theoretically the properties of a Bose-Einstein condensate located in a spatially periodic potential. The excitations of the condensate are obtained from linear equations involving the periodic potential and the periodic condensate density. The Bloch ansatz therefore applies and the excitation spectrum exhibits band structure. If the periodic potential is accelerated, the condensate may undergo Bloch oscillations in the accelerated frame, corresponding to an acceleration without spreading of the entire condensate.

Green plants are Earth's primary solar energy collectors. They harvest the energy of the Sun by converting light energy into chemical energy stored in the bonds of sugar molecules. A multitude of carefully orchestrated transport processes are needed to move water and minerals from the soil to sites of photosynthesis and to distribute energy-rich sugars throughout the plant body to support metabolism and growth. The long-distance transport happens in the plants' vascular system, where water and solutes are moved along the entire length of the plant. In this review, the current understanding of the mechanism and the quantitative description of these flows are discussed, connecting theory and experiments as far as possible. The article begins with an overview of low-Reynolds-number transport processes, followed by an introduction to the anatomy and physiology of vascular transport in the phloem and xylem. Next, sugar transport in the phloem is explored with attention given to experimental results as well as the fluid mechanics of osmotically driven flows. Then water transport in the xylem is discussed with a focus on embolism dynamics, conduit optimization, and couplings between water and sugar transport. Finally, remarks are given on some of the open questions of this research field.

Using optical tweezers and single particle tracking, we have revealed the motion of a single protein, the lambda-receptor, in the outer membrane of living Escherichia coli bacteria. We genetically modified the lambda-receptor placing a biotin on an extracellular site of the receptor in vivo. The efficiency of this in vivo biotinylation is very low, thus enabling the attachment of a streptavidin-coated bead binding specifically to a single biotinylated lambda-receptor. The bead was used as a handle for the optical tweezers and as a marker for the single particle tracking routine. We propose a model that allows extraction of the motion of the protein from measurements of the mobility of the bead-molecule complex; these results are equally applicable to analyze bead-protein complexes in other membrane systems. Within a domain of radius approximately 25 nm, the receptor diffuses with a diffusion constant of (1.5 +/- 1.0) x 10(-9) cm(2)/s and sits in a harmonic potential as if it were tethered by an elastic spring of spring constant of ~1.0 x 10(-2) pN/nm to the bacterial membrane. The purpose of the protein motion might be to facilitate transport of maltodextrins through the outer bacterial membrane.

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