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Three-dimensional (3D) imaging and object tracking is critical for medical and biological research and can be achieved by multifocal imaging with diffractive optical elements (DOEs) converting depth (To precisely track microscopic fluorescent objects in biological systems in 3D with a simple low-cost DOE system.We designed a multiring spiral phase plate (SPP) generating a single-spot rotating point spread function (SS-RPSF) in a microscope. Our simple, analytically transparent design process uses Bessel beams to avoid rotational ambiguities and achieve a significant depth range. The SPP was inserted into the Nomarski prism slider of a standard microscope. Performance was evaluated using fluorescent beads and in live cells expressing a fluorescent chromatin marker.Bead localization precision wasPrecise 3D localization and tracking can be achieved with a SS-RPSF SPP in a standard microscope with minor modifications.

A recently developed variational Bayesian analysis using pattern recognition and machine learning of single viral ribonucleoprotein (RNP) particle tracks in the cytoplasm of living cells provides a quantitative molecular explanation for active diffusion, a concept previously “explained” largely by hypothetical models based on indirect analyses such as continuum microrheology. Machine learning shows that vesicular stomatitis virus (VSV) RNP particles are temporarily confined to dynamic traps or pores made up of cytoskeletal elements. Active diffusion occurs when the particles escape from one trap to a nearby trap. In this paper, we demonstrate that actin filament disruption increased RNP mobility by increasing trap size. Inhibition of nonmuscle myosin II ATPase decreased mobility by decreasing trap size. Trap sizes were observed to fluctuate with time, dependent on nonmuscle myosin II activity. This model for active diffusion is likely to account for the dominant motion of other viral and cellular elements. IMPORTANCE RNA virus ribonucleoproteins (RNPs) are too large to freely diffuse in the host cytoplasm, yet their dominant motions consist of movements in random directions that resemble diffusion. We show that vesicular stomatitis virus (VSV) RNPs overcome limitations on diffusion in the host cytoplasm by hopping between traps formed in part by actin filaments and that these traps expand and contract by nonmuscle myosin II ATPase activity. ATP-dependent random motion of cellular particles has been termed “active diffusion.” Thus, these mechanisms are applicable to active diffusion of other cellular and viral elements.

Chromatin motions depend on and may regulate genome functions, in particular the DNA damage response. In yeast, DNA double-strand breaks (DSBs) globally increase chromatin diffusion, whereas in higher eukaryotes the impact of DSBs on chromatin dynamics is more nuanced. We mapped the motions of chromatin microdomains in mammalian cells using diffractive optics and photoactivatable chromatin probes and found a high level of spatial heterogeneity. DNA damage reduces heterogeneity and imposes spatially defined shifts in motions: Distal to DNA breaks, chromatin motions are globally reduced, whereas chromatin retains higher mobility at break sites. These effects are driven by context-dependent changes in chromatin compaction. Photoactivated lattices of chromatin microdomains are ideal to quantify microscale coupling of chromatin motion. We measured correlation distances up to 2 µm in the cell nucleus, spanning chromosome territories, and speculate that this correlation distance between chromatin microdomains corresponds to the physical separation of A and B compartments identified in chromosome conformation capture experiments. After DNA damage, chromatin motions become less correlated, a phenomenon driven by phase separation at DSBs. Our data indicate tight spatial control of chromatin motions after genomic insults, which may facilitate repair at the break sites and prevent deleterious contacts of DSBs, thereby reducing the risk of genomic rearrangements.

Within 2–6 hours after infection by vesicular stomatitis virus (VSV), newly assembled VSV particles are released from the surface of infected cells. In that time, viral ribonucleoprotein (RNP) particles (nucleocapsids) travel from their initial sites of synthesis near the nucleus to the edge of the cell, a distance of 5–10 μm. The hydrodynamic radius of RNP particles (86 nm) precludes simple diffusion through the mesh of cytoskeletal fibers. To reveal the relative importance of different transport mechanisms, movement of GFP-labeled RNP particles in live A549 cells was recorded within 3 to 4 h postinfection at 100 frames/s by fluorescence video microscopy. Analysis of more than 200 RNP particle tracks by Bayesian pattern recognition software found that 3% of particles showed rapid, directional motion at about 1 μm/s, as previously reported. 97% of the RNP particles jiggled within a small, approximately circular area with Gaussian width σ = 0.06 μm. Motion within such “traps” was not directional. Particles stayed in traps for approximately 1 s, then hopped to adjacent traps whose centers were displaced by approximately 0.17 μm. Because hopping occurred much more frequently than directional motion, overall transport of RNP particles was dominated by hopping over the time interval of these experiments.

The distribution of vesicular stomatitis virus (VSV) nucleocapsids in the cytoplasm of infected cells was analyzed by scanning confocal fluorescence microscopy using a newly developed quantitative approach called the border-to-border distribution method. Nucleocapsids were located near the cell nucleus at early times postinfection (2 h) but were redistributed during infection toward the edges of the cell. This redistribution was inhibited by treatment with nocodazole, colcemid, or cytochalasin D, indicating it is dependent on both microtubules and actin filaments. The role of actin filaments in nucleocapsid mobility was also confirmed by live-cell imaging of fluorescent nucleocapsids of a virus containing P protein fused to enhanced green fluorescent protein. However, in contrast to the overall redistribution in the cytoplasm, the incorporation of nucleocapsids into virions as determined in pulse-chase experiments was dependent on the activity of actin filaments with little if any effect on inhibition of microtubule function. These results indicate that the mechanisms by which nucleocapsids are transported to the farthest reaches of the cell differ from those required for incorporation into virions. This is likely due to the ability of nucleocapsids to follow shorter paths to the plasma membrane mediated by actin filaments. IMPORTANCE Nucleocapsids of nonsegmented negative-strand viruses like VSV are assembled in the cytoplasm during genome RNA replication and must migrate to the plasma membrane for assembly into virions. Nucleocapsids are too large to diffuse in the cytoplasm in the time required for virus assembly and must be transported by cytoskeletal elements. Previous results suggested that microtubules were responsible for migration of VSV nucleocapsids to the plasma membrane for virus assembly. Data presented here show that both microtubules and actin filaments are responsible for mobility of nucleocapsids in the cytoplasm, but that actin filaments play a larger role than microtubules in incorporation of nucleocapsids into virions.

Many organelles and vesicles in live cells move in a start–stop manner when observed for ~10 s by optical microscopy. Changes in velocity and directional persistence of such particles are a potentially rich source of insight into the mechanisms leading to the start and stop states. Unbiased assessment of the most probable number of states, the properties of each state, and the most probable state for the particle at each moment can be accomplished by variational Bayesian methods combined with a hidden Markov model and a Gaussian mixture model. Our track analysis method, “vbTRACK”, applied this combination of methods to particle velocity v or changes in the direction of travel evaluated from simulated tracks and from tracks of peroxisomes in live cells. When tested with numerical data, vbTRACK reliably determined the number of states, the mean and variance of the velocity or the direction of travel for each state, and the most probable state during each frame. When applied to the tracks of peroxisomes in live cells, some tracks separated into two states, one with high velocity and directionality, the other approximately Brownian. Other tracks of particles in live cells separated into several diffusive states with distinct diffusion constants.

We describe a simple optical method that creates structured illumination of a photoactivatable probe and apply this method to characterize chromatin motions in nuclei of live cells. A laser beam coupled to a diffractive optical element at the back focal plane of an excitation objective generates an array of near diffraction-limited beamlets with FWHM of [Formula: see text] , which simultaneously photoactivate a [Formula: see text] matrix pattern of GFP-labeled histones, with spots [Formula: see text] apart. From the movements of the photoactivated spots, we map chromatin diffusion coefficients at multiple microdomains of the cell nucleus. The results show correlated motions of nearest chromatin microdomain neighbors, whereas chromatin movements are uncorrelated at the global scale of the nucleus. The method also reveals a DNA damage-dependent decrease in chromatin diffusion. The diffractive optical element instrumentation can be easily and cheaply implemented on commercial inverted fluorescence microscopes to analyze adherent cell culture models. A protocol to measure chromatin motions in nonadherent human hematopoietic stem and progenitor cells is also described. We anticipate that the method will contribute to the identification of the mechanisms regulating chromatin mobility, which influences most genomic processes and may underlie the biogenesis of genomic translocations associated with hematologic malignancies.

Although the velocity of single kinesin motors against an opposing force F of 0-10 pN is well known, the behavior of multiple kinesin motors working to overcome a larger load is still poorly understood. We have carried out gliding assays in which 3-7 Drosophila kinesin-1 motors moved a microtubule at 200-700 μm/s against a 0-31 pN load at saturating [ATP]. The load F was generated by applying a spatially uniform magnetic field gradient to a superparamagnetic bead attached to the (+) end of the microtubule. When F was scaled by the average number of motors [Symbol: see text]n[Symbol: see text], the force-velocity relationship for multiple motors was similar to the force-velocity relationship for a single motor, supporting a minimal load-sharing model. The velocity distribution at low load has a single mode consistent with rapid fluctuations of n. However, against a load of 2.5-4.7 pN/motor, additional modes appeared at lower velocity. These observations support the Klumpp-Lipowsky model of multimotor transport [Proc Natl Acad Sci USA 102. 17284-17289 (2005)].

Although the properties of single kinesin molecular motors are well understood, it is not clear whether multiple motors pulling a single vesicle in a cell cooperate or interfere with one another. To learn how small numbers of motors interact, microtubule gliding assays were carried out with full-length Drosophila kinesin in a novel motility medium containing xanthan, a stiff, water-soluble polysaccharide. At 2 mg/ml xanthan, the zero-shear viscosity of this medium is 1,000 times the viscosity of water, similar to cellular viscosity. To mimic the rheological drag force on the motors when attached to a vesicle in a cell, we attached a 2 microm bead to one end of the microtubule (MT). During gliding assays in our novel medium, the moving bead exerted a drag force of 4-15 pN on the kinesins pulling the MT. The velocity of MTs with an attached bead increased with MT length and with kinesin concentration. The increase with MT length arose because the number of motors is directly proportional to MT length. Our results show that small numbers of kinesins cooperate constructively when pulling against a viscoelastic drag. In the absence of a bead but still in the viscous medium, MT velocity was independent of MT length and kinesin concentration because the thin MT, like a snake moving through grass, was able to move between xanthan molecules with little resistance. A minimal shared-load model in which the number of motors is proportional to MT length fits the observed dependence of gliding velocity on MT length and kinesin concentration.

Determining in vivo force–velocity relationships of motor proteins is a critical step toward clarifying how they accomplish intracellular transport. We show that in vivo force–velocity curves corresponding to an estimated 1, 2, and 3 motors-per-vesicle can be constructed by tracking and sizing transported vesicles. The force range for these curves would normally be constrained by diffraction limited diameter measurements. However, we present a new method that uses the image intensity obtained with differential interference contrast microscopy as a proxy for vesicle diameters smaller than the diffraction limit. We calibrate this novel sizing method in vitro with polystyrene microsphere standards and apply it in vivo to vesicles. The resulting diameter vs. velocity data for large, small, and sub-diffraction limited vesicles is used to construct force–velocity curves that extend the force range of our previous curves. These extended 1-, 2-, and 3-motor in vivo curves qualitatively agree with a simple model of load sharing for motors that jointly transport a single vesicle.

Video-enhanced differential interference contrast microscopy with background subtraction has made visible many structures and processes in living cells. In video-enhanced differential interference contrast, the background image is stored manually by defocusing the microscope before images are acquired. We have updated and improved video-enhanced differential interference contrast by adding automatic generation of the background image as a rolling average of the incoming image stream. Subtraction of this continuously updated 12-bit background image from the incoming 12-bit image stream provides a flat background which allows the contrast of moving objects, such as vesicles, to be strongly enhanced while suppressing stationary features such as the overall cell shape. We call our method MEDIC, for motion-enhanced differential interference contrast. By carrying out background subtraction with 12-bit images, the number of grey levels in the moving vesicles can be maximized and a single look-up table can be applied to the entire image, enhancing the contrast of all vesicles simultaneously. Contrast is increased by as much as a factor of 13. The method is illustrated with raw, background and motion-enhanced differential interference contrast images of moving vesicles within a neurite of a live PC12 cell and a live chick motorneuron.

Gliding assays of motor proteins such as kinesin, dynein and myosin are commonly carried out with fluorescently labeled microtubules or filamentous actin. In this paper, we show that speckled microtubules (MTs), prepared by copolymerizing 98% unlabeled tubulin with 2% rhodamine-labeled tubulin, can be localized to +/-7.4 nm (24 measurements) in images acquired every 125 ms. If the speckled MTs move at about 800 nm s(-1), ten images are sufficient to determine their velocity to a precision of +/-6.8 nm s(-1) (6 microtubules, 24 measurements). This velocity precision is four-fold better than manual methods for measuring the gliding velocity of uniformly labeled MTs by end-point localization. The improved velocity precision will permit the determination of velocity-force curves when one, two and three kinesin motors pull a single load in vitro.

A cell’s mechanical properties are important in determining its adhesion, migration, and response to the mechanical properties of its microenvironment and may help explain behavioral differences between normal and cancerous cells. Using fluorescently labeled peroxisomes as microrheological probes, the interior mechanical properties of normal breast cells were compared to a metastatic breast cell line, MDA-MB-231. To estimate the mechanical properties of cell cytoplasms from the motions of their peroxisomes, it was necessary to reduce the contribution of active cytoskeletal motions to peroxisome motion. This was done by treating the cells with blebbistatin, to inhibit myosin II, or with sodium azide and 2-deoxy- $$\textsc {d}$$ -glucose, to reduce intracellular ATP. Using either treatment, the peroxisomes exhibited normal diffusion or subdiffusion, and their mean squared displacements (MSDs) showed that the MDA-MB-231 cells were significantly softer than normal cells. For these two cell types, peroxisome MSDs in treated and untreated cells converged at high frequencies, indicating that cytoskeletal structure was not altered by the drug treatment. The MSDs from ATP-depleted cells were analyzed by the generalized Stokes–Einstein relation to estimate the interior viscoelastic modulus $$G^{*}$$ and its components, the elastic shear modulus $$G^{\prime }$$ and viscous shear modulus $$G^{\prime \prime }$$ , at angular frequencies between 0.126 and 628 rad/s. These moduli are the material coefficients that enter into stress–strain relations and relaxation times in quantitative mechanical models such as the poroelastic model of the interior regions of cancerous and non-cancerous cells.

Many organelles and vesicles move in a start-stop manner in live cells when observed by optical microscopy at 10 to 100 frames/s. One explanation for start-stop behavior is that the vesicles switch between a driven state in which they are being actively pulled by motor proteins, and a Brownian state in which they obey the laws of diffusion in the cytoplasm. To test this idea, we have carried out a hidden Markov, variational Bayesian Expectation Maximization, Gaussian mixture model ("Bayes") analysis. Either vesicle velocity v(t) or the direction of travel theta(t) was used to "train" the model. When tested with simulated tracks, Bayes reliably determined the number of states K_best corresponding to the number of distinct physical processes required to describe the data. The mean and variance of the velocity or direction were also found reliably for each state in the simulated dataset. The assignment of individual frames to particular states showed few false positives or false negatives as long as the vesicle remained in each state for 6 or more adjacent frames. Once each frame was assigned to a state by Bayes, the mean-squared displacement (msd) for each state was computed, displaying the distinctive t-dependence of its physical origin, e.g. motor-driven, Brownian, etc. Individual tracks of fluorescently labeled peroxisomes in HME cells and unlabeled vesicles in PC12 cells were analyzed in the same manner to separate driven from Brownian bouts in an objective manner.This research is supported by the National Science Foundation under Grant CMMI-1106105. AMS is supported by NSF GRFP 0907738.

It is demonstrated experimentally, as well as analytically, that when the polarization of the light incident upon the first Nomarski–Wollaston prism in a differential interference contrast (DIC) light microscope is switched by 90°, image highlights are changed into shadows and vice versa. Using an inexpensive ferroelectric liquid-crystal modulator, which is easily installed in the microscope, this switching can be done at 30 frames s−1, synchronized to the camera. Subtraction of alternate digitized frames generates a stream of images in which contrast is doubled, compared with conventional video-enhanced DIC, while image defects and noise tend to cancel. Subtraction of alternate images is carried out efficiently by frame buffer operations and amounts to massively parallel synchronous detection. The new method eliminates the problems inherent in obtaining a separate background image, as required by current video-enhanced DIC practice, without loss of resolution.

We report on our effort to characterize the mechanical changes in cells that undergo neoplastic transformation. The cells we are studying include normal human mammary epithelial cells, as well as immortalized and tumorigenic versions of the same cells. We are studying three different aspects of cell behavior using different tools. The measurements include determining the elastic moduli of the different cells (in both the nuclear and cytoplasmic regions) using an Atomic Force Microscope (AFM) with a 5.3 um diameter spherical probe; measuring the diffusion and binding of mismatch repair proteins in the different cells using a confocal microscope to perform Fluorescence Recovery After Photobleaching (FRAP) measurements as well as Raster Imaging Correlation Spectroscopy (RICS); and finally measuring the diffusion and transport of different natural organelles such as lysosomes and peroxisomes using particle tracking microscopy. In this presentation, we plan to provide a summary of results in all three areas to date, and to put our measurements in the context of related work published by others.This work is supported by NSF Materials and Surface Engineering grant CMMI-1152781.

Many organelles and vesicles move in an intermittent (start-stop) manner in live cells when observed by video microscopy. We propose that such vesicles travel in one of two states, a driven state in which they are being actively pulled along a cytoskeletal fiber by motor proteins, and a Brownian state in which they are detached from the fiber and obey the laws of diffusion in the cytoplasm. Using variational Bayesian analysis, we analyze the tracks of peroxisomes, lysosomes, and other organelles in PC12 and HME cells to reveal the probability that the vesicle is in the driven or the Brownian state at each time (frame). Instantaneous vesicle velocity and directional persistence are the input data for our hidden Markov, Gaussian mixture model Bayesian analysis. This analysis evaluates the most probable velocity as well the variance of the velocity of each state. It also determines the most probable times at which the state changes. Further analysis of the motions of the vesicles during the Brownian episodes may permit a cleaner assessment of the viscoelastic properties of cytoplasm. This research is supported by the National Science Foundation under Grant No. CMMI-1106105. AMS is supported by the NIGMS of the National Institutes of Health under award number T32GM095440.

The velocity v of bands of double-stranded, linear DNAs containing 48.5-5700 kbp was determined with 0.3 s resolution during field-inversion agarose gel electrophoresis (FIGE) for a broad range of the forward pulse period T+, keeping the duration of the backward pulse T- = T+/3. Within 0.6 s or less after the field changed sign from-to +, the velocity showed a sharp positive peak; a similar spike, but with negative velocity, occurred immediately after the field changed from + to -. For long pulses, the magnitude of this spike increased with M0.36, reaching ten times the steady-state velocity for M = 5.7 kbp. After this spike, the velocity dipped to 55-75% of its value in a steady field, then increased to a small secondary peak before reaching a steady-state plateau. The duration of the velocity trough, and the time of the small peak, increased as M1. For standard FIGE conditions (ratio of forward:reverse pulse duration, T+:T- = 3:1; equal forward and reverse field amplitudes, E+ = E-), the mobility mu = integral of vdt over a complete cycle was a minimum when E+ terminated at the end of the velocity trough. The minimum occurred because the velocity during E+ sampled primarily the trough, and because the backward velocity during E- was exceptionally large; the negative velocity spike was maximized when T+ terminated at the end of the velocity trough. Computer simulations of FIGE by Zimm (J. Chem. Phys. 1991, 94, 2187-2206) and by Duke and Viovy (J. Chem. Phys. 1992, 96, 8552-8563) generate real-time velocities that are in excellent agreement with our experimental data.

In pulsed-field gel electrophoresis, megabase DNAs are well separated if the angle theta between the two electric fields is 120 degrees but not if theta = 90 degrees. To elucidate the molecular basis for this observation, we measured the instantaneous position (x, y) and velocity (v(x), v(y)) of a band of G-DNA (670 kb) while the field switched direction, for 90 degrees less than or equal to theta less than or equal to 120 degrees. For theta = 120 degrees and long pulse period T, the band retraced the last segment of the preceding pulse before moving in the new field dir ec The retracing was done at a velocity much greater than the average forward velocity. For theta = 90 degrees rather than retrace itself the path during one pulse appeared to originate from a point beyond that reached in the previous pulse, and the velocity showed only a brief backward spike.A Monte Carlo simulation that included tube-length fluctuations and hernias was carried out for a model DNA chain moving through a three-dimensional network of interconnected pores, with parameters corresponding to the DNA size, agarose concentration, and field strength of the experiments. Both the xy paths and the instantaneous velocities of the simulation were in excellent agreement with experiment for 90 degrees less than or equal to theta less than or equal to 120 degrees. When the field changed direction in the simulation, hernias often advanced from both ends in the new field direction. In the 120 degrees case, those near the erstwhile trailing segments of the chain soon established superiority because chain tension and a component of the new field aided their growth. For theta = 90 degrees and long T, however, segments from the head end were more likely to continue to lead because there was often an excess of relaxed segments there, and no component of the field aided either end. (C) 1995 John Wiley & Sons, Inc.

The instantaneous position and velocity of bands of linear, double-stranded DNA were measured during 120° pulsed-field electrophoresis in 1% agarose gels, using a video micrometer capable of simultaneous measurements in two dimensions. When the direction of the field was switched, the band initially retraced the last portion of its path during the preceding pulse. The distance the band moved backward increased with DNA length: 48.5 kb (kilobase pair) DNA moved backward only 0.2 μm, but 1110 kb DNA moved backward 24 μm, before setting off in a positive direction. The velocity of the DNA band was particularly rapid during the backward movement: the magnitude of the velocity spike increased with M, reaching 2.4 μm/s for 1110 kb DNN, which was about 5 times the steady-state velocity. The velocity in the y direction, perpendicular to the mean drift direction, allowed an even larger transient spike, which also increased with M. Simulation of the dynamics of long DNA chins undergoing gel electrophoresis by a dynamic Monte Carlo method gave instantaneous xy position and velocity in excellent agreement with experiment. The simulation included extensional motions of the DNA within the tube of interconnected agarose pores as well as the possibility of loops (hernias) that escape laterally from the tube. © 1995 John Wiley & Sons, Inc.

The position and velocity of a band of double-stranded, linear DNA from bacteriophage G were measured during 120 degrees pulsed-field gel electrophoresis, using a video micrometer. Both the x and y coordinates were determined simultaneously in the plane of a 1% agarose gel; x is the mean drift direction. For pulse durations T greater than the tube renewal time T*, the path traced by the band of 670 kb DNA in the xy plane was in remarkably good accord with that predicted by Southern's ratchet model. However, the measured instantaneous velocity vx showed a sharp backward spike each time the field changed direction, with amplitude about twice the mean drift velocity. This spike is not consistent with models which assume a constant curvilinear velocity of DNA in a tube, nor with the biased reptation model without fluctuations. The corresponding measurements of vy showed a sharp positive spike with amplitude more than 3 times the plateau velocity in the y direction; neither model predicted this. The sharp velocity spikes are consistent with the idea that, for T > T*, a large fraction of the DNA chains are stretched into U-shaped or herniated configurations. When the field changes direction, the arms of the U's and the hernias recoil rapidly in response to intramolecular DNA chain tension. Because the base of a U or hernia is fixed by gel fibers, the center of mass of the chain recoils backward every time the field changes direction.

The molecular motor gliding assay, in which a microtubule or other filament moves across a surface coated with motors, has provided much insight into how molecular motors work. The kinesin-microtubule system is also a strong candidate for the job of nanoparticle transporter in nanotechnology devices. In most cases, several motors transport each filament. Each motor serves both to bind the microtubule to a stationary surface and to propel the microtubule along the surface. By applying a uniform transverse force of 4--19 pN to a superparamagnetic bead attached to the trailing end of the microtubule, we have measured the distance $d$ between binding points (motors). The average value of $d$ was determined as a function of motor surface density $\mathbit{\ensuremath{\sigma}}$. The measurements agree well with the scaling model of Duke, Holy, and Liebler, which predicts that $\ensuremath{\langle}d\ensuremath{\rangle}~{\mathbit{\ensuremath{\sigma}}}^{\ensuremath{-}2/5}$ if $0.05\ensuremath{\leqslant}\mathbit{\ensuremath{\sigma}}\ensuremath{\leqslant}20 \ensuremath{\mu}{\mathrm{m}}^{\ensuremath{-}2}$ [Phys. Rev. Lett. 74, 330 (1995)]. The distribution of $d$ fits an extension of the model. The radius of curvature of a microtubule bent at a binding point by the force of the magnetic bead was \ensuremath{\approx}1 \ensuremath{\mu}m, 5000-fold smaller than the radius of curvature of microtubules subjected only to thermal forces. This is evidence that at these points of high bending stress, generated by the force on the magnetic bead, the microtubule is in the more flexible state of a two-state model of microtubule bending proposed by Heussinger, Sch\"uller, and Frey [Phys. Rev. E 81, 021904 (2010)].

Here we report construction of a simple electromagnet with novel polepieces which apply a spatially uniform force to superparamagnetic beads in an optical microscope. The wedge-shaped gap was designed to keep partial differential B(x)/ partial differential y constant and B large enough to saturate the bead. We achieved fields of 300-600 mT and constant gradients of 67 T/m over a sample space of 0.5x4 mm(2) in the focal plane of the microscope and 0.05 mm along the microscope optic axis. Within this space the maximum force on a 2.8 microm diameter Dynabead was 12 pN with a spatial variation of approximately 10%. Use of the magnet in a biophysical experiment is illustrated by showing that gliding microtubules propelled by the molecular motor kinesin can be stopped by the force of an attached magnetic bead.

A liquid-crystal variable retarder inserted into a differential-interference contrast video microscope switches image highlights into shadows and vice versa in alternate frames. Synchronous computation and display of the difference between alternate frames yield a stream of images with doubled contrast and reduced fixed-position noise because of the automatic background subtraction. The measured signal-to-noise ratio (SNR) peaks when the modulation +/- Gamma of the retarder equals the phase shift delta of the sample. A Jones calculus model of the central ray in the polarization-modulated differential-interference contrast microscope yields SNR = (sin Gamma sin delta)/((1 - cos Gamma cos delta)N), where N is the rms time-dependent photon noise. This expression fits the experiments closely for 1.8 degrees < or = Gamma < or = 115 degrees.

Vesicle transport in cultured chick motoneurons was studied over a period of 3 days using motion-enhanced differential interference contrast (MEDIC) microscopy, an improved version of video-enhanced DIC. After 3 days in vitro (DIV), the average vesicle velocity was about 30% less than after 1 DIV. In observations at 1, 2 and 3 DIV, larger vesicles moved more slowly than small vesicles, and retrograde vesicles were larger than anterograde vesicles. The number of retrograde vesicles increased relative to anterograde vesicles after 3 DIV, but this fact alone could not explain the decrease in velocity, since the slowing of vesicle transport in maturing motoneurons was observed independently for both anterograde and retrograde vesicles. In order to better understand the slowing trend, the distance vs. time trajectories of individual vesicles were examined at a frame rate of 8.3/s. Qualitatively, these trajectories consisted of short (1-2 s) segments of constant velocity, and the changes in velocity between segments were abrupt (0.2 s). The trajectories were therefore fit to a series of connected straight lines. Surprisingly, the slopes of theses lines, i.e. the vesicle velocities, were often found to be multiples of ~0.6 mum/s. The velocity histogram showed multiple peaks, which, when fit with Gaussians using a least squares minimization, yielded an average spacing of 0.57 mum/s (taken as the slope of a fit to peak position vs. peak number, R(2)=0.994). We propose that the abrupt velocity changes occur when 1 or 2 motors suddenly begin or cease actively participating in vesicle transport. Under this hypothesis, the decrease in average vesicle velocity observed for maturing motoneurons is due to a decrease in the average number of active motors per vesicle.

The displacement per pulse of lambda, T4, and G DNA during pulsed-field agarose gel electrophoresis has been measured for a fine mesh of pulse durations T between 0.02 and 120 s. The slopes of these curves show that the DNA moves by two distinct processes, designated 1 and 2, depending upon the pulse duration T. Process 1 operates at short T and causes dx/dT to decrease gradually with increasing T. This process is independent of molecular weight M. Process 2 is effective at longer T and causes dx/dT to rise sharply in sigmoidal fashion at a value of T which increases as M1.2, finally reaching a plateau of 1.4 microns/s for E = 4 V/cm. The shape of the dx/dT curve and its dependence on M lead directly to 4 zones of separation in plots of mobility vs M for different T. The alignment of the 3 DNAs during PFGE was measured by fluorescence-detected linear dichroism for E between 4 and 10 V/cm. These results are used in developing a molecular understanding of the mobility data.

Cancerous cells display altered cytoskeletal structures from their normal counterparts, and their ability to invade other tissues demands mechanical properties that are conducive to deformation. Unlike proteins, water, and small molecules, the motions of large endogenous particles and organelles are sensitive to the mesh sizes and mechanics of the cytoskeletal network. By tracking peroxisomes, lysosomes, and other large vesicles, we measure the cytoplasmic viscoelastic properties of cells. To compare the viscoelastic properties of normal human mammary epithelial (HME) cells to those of tumorigenic, transformed HME cell lines, organelles undergoing Brownian motion within each cell type were tracked at 100 fps. The viscoelastic moduli were calculated from the mean square displacements and radii of these organelles using Mason's generalized Stokes-Einstein equation (GSE). In both normal and tumorigenic cell types, the curve for η∗ shows a low frequency viscosity of approximately 10−1 Pa s and exhibits shear-thinning. Similarly for both types, the viscous component of the modulus contributes predominately at low frequencies, and the elastic component predominates at higher frequencies.This research is supported by the National Science Foundation under Grant No. CMMI-1106105 and by the National Institute of General Medical Science of the National Institutes of Health under award number T32GM095440.

Variations in the lateral dimensions of capillaries and ultrathin gels along their length could lead to a distortion of the sample zone because charged particles traveling near the wall must travel a longer distance under a smaller field than particles traveling along the centerline. The size of the effect is computed by solving Laplace's equation for the potential everywhere in a conducting slab with a discontinuity in the lateral discontinuity in the lateral dimensions and integrating the travel time along different streamlines.

Although the mechanical behavior of single-motor protein molecules such as kinesin has been carefully studied in buffer, the mechanical behavior of motor-driven vesicles in cells is much less understood. We have tracked single vesicles in neurites of PC12 cells with a spatial precision of +/-30 nm and a time resolution of 120 ms. Because the neurites are thin, long, straight, and attached to the surface of planar cover glasses, the velocity of individual vesicles could be measured for times as long as 15 s and distances as long as 15 mum. The velocity of anterograde vesicles was in most cases constant for periods of 1-2 s, then changed in a step-like fashion to a new constant velocity. The viscoelastic modulus felt by the vesicles within live PC12 cells was determined from the Brownian motion, using Mason's generalization of the Stokes-Einstein equation. From Stokes' law, the drag force at the smallest sustained velocity was 4.2+/-0.6 pN for vesicles of radius 0.30-0.40 mum, about half the maximum force which conventional kinesin can develop during bead assays in buffer. We interpret the observed velocity steps as changes of +/-1 or occasionally +/-2 in the number of active motor proteins dragging that vesicle along a microtubule. Assuming that the motor is conventional kinesin, which hydrolyzes one ATP per 8 nm step along the microtubule, the motor protein efficiency in PC12 neurites is approximately 35%.

The purpose of this paper is to deduce whether the maximum force, steplike movement, and rate of ATP consumption of kinesin, as measured in buffer, are sufficient for the task of fast transport of vesicles in cells. Our results show that moving a 200-nm vesicle in viscoelastic COS7 cytoplasm, with the same steps as observed for kinesin-driven beads in buffer, required a maximum force of 16 pN and work per step of 1 +/- 0.7 ATP, if the drag force was assumed to decrease to zero between steps. In buffer, kinesin can develop a force of 6-7 pN while consuming 1 ATP/step, comparable to the required values. As an alternative to assuming that the force vanishes between steps, the measured COS7 viscoelasticity was extrapolated to zero frequency by a numerical fit. The force required to move the bead then exceeded 75 pN at all times and peaked briefly to 92 pN, well beyond the measured capabilities of a single kinesin in buffer. The work per step increased to 7 +/- 5 ATP, greatly exceeding the energy available to a single motor.

We tested the hypothesis that breast cancer cells have lower viscoelastic moduli than their normal counterparts. The moduli were evaluated by tracking peroxisomes within three human mammary epithelial cell types: normal, tumorigenic, and metastatic. Peroxisomes in these cells were labeled with GFP, and then imaged at 100 fps. From the resulting movies of peroxisome motion, mean squared displacements (MSDs) of the peroxisomes were evaluated. To assess the contribution of motor-driven ‘hum’ of the actomyosin network to the measured MSDs, peroxisome motion was also determined in the three cell types after they were treated with blebbistatin or sodium azide and 2-deoxy-D-glucose. Blebbistatin is a myosin II inhibitor, and sodium azide and 2-deoxy-D-glucose deplete cellular production of ATP. Our results indicate that peroxisome MSDs are larger in the presence of ATP and active myosin motors than when driven solely by thermal energy.By inserting these MSDs into the generalized Stokes-Einstein equation, apparent viscoelastic moduli were obtained for the cytoplasms of normal, tumorigenic, and metastatic breast cells with and without the motor-driven 'hum'. The generalized Stokes-Einstein equation assumes that the only energy that drives motion of the tracked peroxisomes in the cytoplasm is thermal. Peroxisomes in all three cell types report lowered apparent cytoplasmic viscoelastic moduli in the presence of uninhibited myosin II motors than when driven solely by thermal energy. The viscoelastic moduli determined from metastatic and tumorigenic cells without hum are significantly lower than those from their normal counterparts.This research is supported by the National Science Foundation under Grant CMMI-1106105. AMS has been supported by NIH/NIGMS T32 GM095440 and NSF GRFP 0907738.

In a classic paper, Howard, Hudspeth, and Vale[1] showed that the number of kinesin motors does not affect the velocity of gliding microtubules during motility assays. However, evidence is accumulating from our lab and others that the velocity of vesicle transport in vivo increases substantially if 2, 3, or 4 motors pull a single load. How can that be? To resolve this conflict, we performed upside-down kinesin motility assays with full-length Drosophila kinesin heavy chains working against viscous drag comparable to that experienced by moving vesicles in live cells. To do this, the viscosity of the medium was increased to approximately 1 Pa·s by adding 2 mg/mL of a stiff, high-MW polysaccharide here dubbed “PolymerX”[2]. Also, a single polystyrene bead (d = 2 μm) was attached to the +end of the microtubule. In PolymerX, with a bead attached, 3 μm MTs moved at 150 nm/s, 10 μm MTs moved at 400 nm/s, and greater than 30 μm MTs moved at 700 nm/s, the control velocity. However, without a bead, the velocity of all MTs in PolymerX increased to 700 nm/s. Apparently, a bead-free MT can easily slither end-on through the mesh of PolymerX fibers, but the attached bead cannot. The observed increase in velocity with MT length most likely arises because the number of attached motors is directly proportional to MT length in gliding assays.Support from the NIH NS053493 and the Dreyfus Foundation is gratefully acknowledged.[1] Howard, Hudspeth, and Vale, Nature 342, 154–158 (1989).[2] The Brownian motion of 2 μm beads in dilute PolymerX solutions and of 0.2–2 μm unattached vesicles in live cells, when analyzed by the Generalized Stokes-Einstein method, show similar G′ and G″ in the two environments.

The relationship between the velocity of one kinesin motor as it works against an increasing opposing load has been well studied. The relationship between the velocity of a cargo being moved against an opposing load by multiple kinesin motors is not well established experimentally. A major difficulty in determining the multiple motors relationship is measuring the number of motors acting against the load.We have developed a method for measuring the number of kinesins moving a microtubule during a gliding assay. When a 4 pN transverse force is applied to the trailing end of a gliding microtubule, the microtubule detaches one-by-one from its anchor points. Using video microscopy, we can determine the distance, d, between the anchor points. We measured d for several values of the kinesin surface density σ. We find that d scales as σ⊥(-2/5), as predicted by the theory of Duke, Holy, and Liebler (1995). From d, we can estimate the number of motors N on a microtubule of length L: N=L/d.In separate experiments, we measured the average velocity of a microtubule gliding anti-parallel to a magnetic force applied to its trailing end. We find that the average velocity, when scaled by the average number of motors, decreases linearly with the force. This suggests that the motors may correlate their stepping during gliding assays.

Determination of the number of active motors pulling a single MT or bead during motility assays has proven difficult. Traditional protein concentration assays, such as Bradford, cannot distinguish between active and inactive motors. We attach a superparamagnetic bead to the (+) end of a microtubule. When placed in a magnet with uniform magnetic field gradient, the bead pulls on the MT with a controllable 0-10 pN force. If the force is perpendicular to the gliding direction of the MT, a short section of the MT “pops off” the surface every 2 to 5 s, as shown in the diagram. This detachment is characterized by rapid motion of the superparamagnetic bead in the direction of higher magnetic field gradient followed by normal microtubule gliding velocity when the MT is pulled taut. The length of the short section between “popoffs” is the distance between active kinesins along a microtubule.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Can molecular motors pulling on the same load interact with each other to move faster than any one motor could? While the force generated by a single kinesin motor on a cargo in vitro has been studied extensively, the force generated by multiple kinesin motors in vitro has not been characterized as well. Using a novel Uniform Magnetic Force (UMF) apparatus, we are able to apply constant, computer controlled, uniform force over a large sample area, as opposed to a force dependent on distance from the magnetic pole. The UMF can be turned on and off rapidly, and acts upon a superparamagnetic bead bound to a microtubule through a biotin-streptavidin linkage, causing a force on the microtubule. Using Invitrogen M270 beads this force can be as high as 9pN. We employ our apparatus to investigate the velocities of microtubules being pulled by kinesin motors against a magnetic force. With a force on the order of the stall force for one kinesin we are able to see changes in the velocity of a microtubule-bead complex being pulled by kinesin motor proteins. The relative amount of velocity change is not constant for each microtubule-bead complex. This may show a dependence of velocity decrease due to the number of motors moving the microtubule.

Differential interference contrast (DIC) light microscopy, particularly when coupled with digital image processing, is a powerful tool for the high-resolution microscopy of unstained, transparent biological specimens and can equally well be applied to semiconductor measurements. We show analytically, and with images of diatoms, plant cells and protoplasts, that switching the polarization of the incident light by 90 degrees, changes the image highlights found in conventional DIC images into shadows and vice versa (1). Using a ferroelectric liquid-crystal modulator, this switching can be done at frame rates, synchronized to the camera. By subtracting alternate frames, a stream of difference DIC images is created. We call this technique Pol Mod DIC. Subtraction of alternate images is carried out efficiently by frame buffer operations and amounts to massively parallel synchronous detection. A similar method has been applied to confocal microscopy (2).

The transient orientation of lambda DNA and lambda-DNA oligomers has been measured during pulsed field gel electrophoresis. The DNA becomes substantially aligned parallel to the electric field E. In response to a single rectangular pulse, orientation shows an overshoot with a peak at 1 second, then a small undershoot, and finally a plateau. When the field is turned off, the orientation dissipates in two distinct exponential phases. Field inversion leads to periods of orientation with intervening periods of reduced orientation as the chains reverse direction. Field inversion pulses applied to linear oligomers of lambda-DNA show that orientation responses slow down but increase in amplitude as molecular weight increases, for a given field. Because DNA stretching and alignment parallel to E are expected to correlate with DNA velocity, the velocity in response to a pulsed field is also expected to exhibit an overshoot.

The velocity of the center of mass of individual T4 DNA molecules during agarose gel electrophoresis, computed from digitized video-microscopic images, fluctuated between 0 and 4.5 mum/s after a field E = 5 V/cm was applied; the amplitude of the velocity peaks was twice the averaged steady-state velocity. The velocity fluctuations correlated with changes in molecular configuration. The mean velocity (10 molecules) showed a sharp rise in less than 0.2 s, followed by a shallow minimum and a broad peak, before reaching a plateau. The much smaller amplitude of these oscillatory features demonstrated that the velocity fluctuations of individual molecules were largely, but not entirely, uncorrelated with the onset of the field. The components of the shape tensor S of individual chains, which are a measure of the extension of the chains, were also determined for each image sequence. Only the principal component in the direction of E,S(xx), increased.

The velocity and alignment of T4 and \ensuremath{\lambda} DNA have been measured during field-inversion gel electrophoresis (FIGE) at field strengths E between 6 and 14 V/cm. Immediately after E changed sign, the velocity exhibited an oscillatory behavior before reaching a steady value. The times at which these oscillations occurred were shorter for \ensuremath{\lambda} DNA (48.5 kilo-base-pairs) and longer for smaller E. However, the distance each DNA had traveled, when scaled by its contour length L, was about 0.1 for the first velocity peak and 0.15--0.3 for the undershoot for both molecular weights and all values of E studied, provided that E was on for at least 12 s prior to the field inversion. If the field was on for only a short time before inversion, the first sharp peak in velocity was progressively reduced in magnitude and duration. The alignment function f=(3〈${\mathrm{cos}}^{2}$\ensuremath{\theta}〉-1)/2, where \ensuremath{\theta} is the angle between the helix axis and E, was measured for the same DNA's, field strengths, and pulse times. The alignment was at all times parallel to E but decreased sharply immediately after field inversion to a minimum, followed by an overshoot and then a plateau. The time after field inversion at which the minimum in f occurred was approximately the same as that of the velocity maximum. The anticorrelation between the velocity and f, as well as the invariance of x/L for the velocity overshoot, support the idea, first suggested by computer simulations, that DNA undergoing gel electrophoresis spends much time hooked over gel fibers in ssU-shaped chain configurations. The measured velocity curves of T4 DNA were integrated to compute the net displacement after a series of positive and negative field inversions. The average velocity computed from this displacement showed a pronounced ``antiresonance'' or minimum at the same pulse period as observed in practical FIGE separations.

The velocity and orientation of T4 and lambda DNA have been measured for the first 20 s during pulsed-field gel electrophoresis in order to clarify the DNA motions that occur. For a square pulse with field strength E = 10 V/cm, the velocity of lambda DNA increases gradually to 10.5 microns/s in 1.0 s, declines to 8.6 microns/s, and then rises to a plateau value of 9.3 microns/s after 4 s. T4 DNA behaves similarly, but more slowly. Parallel measurements of fluorescence-detected linear dichroism show that the DNA becomes substantially aligned with its chain axis parallel to the electrophoretic field E after the pulse is applied. The alignment also shows an overshoot, an undershoot, and a plateau comparable to those seen for velocity. When the field strength increases, both the velocity and the alignment reach their peaks more quickly. For all field strengths and both molecular weights, the velocity peak occurs when the molecular center of mass has moved 0.3 to 0.5 L, where L is the chain contour length. A qualitative model is provided.

The mobility of linear DNA during field-inversion gel electrophoresis was measured as a function of molecular weight Mr, pulse time t, and field strength E. Values of Mr between 48.5 and 194 kilobase pairs (kb), E from 5 to 14 V/cm and pulse times of 0.3 to 12 s were used. The data are presented as three-dimensional surfaces of mobility: E:t for fixed Mr or graphs of mobility: Mr:t for fixed E. The surfaces are not smoothly increasing functions of E, Mr, or t but instead show a valley with minimum mobility and a steep rise in mobility as t increases. For a field of 10 V/cm, 1% agarose gels, and 3:1 ratio of forward:back pulse time, the forward switching time t* at which the mobility changes most rapidly is given by t* = (0.034 +/- 0.003) Mr for Mr in kb and t* in seconds. The data and equations delineate the best conditions to achieve a particular separation.

The ultraviolet absorption, linear dichroism, circular dichroism, and oriented circular dichroism of collagen are reported and the spectra are resolved into a self-consistent set of bands in accord with exciton theory. The parallel band at 200 nm has 40% of the π π* intensity; the perpendicular band is placed at 189 nm yielding a splitting of 2700 cm−1. The circular dichroism is resolved into two Gaussians at λ∥ and λτ (rotational strengths +14 × 10−40 and −32 × 10−40 esu2. cm2) plus a large non-Gaussian (“helix”) band with ampplitude −25,000° at 201 nm. These data appear to be in reasonably good accord with recent calculations. Measurements of the absorption, linear dichroism and circular dichroism of polyproline I and II are also reported and are resolved into their component bands. Polyproline I is in good accord with exciton theory, whereas polyproline II remains unsatisfactory.