Graph analysis of cell clusters forming vascular networks

This manuscript describes the experimental observation of vasculogenesis in chick embryos by means of network analysis. The formation of the vascular network was observed in the area opaca of embryos from 40 to 55 h of development. In the area opaca endothelial cell clusters self-organize as a primitive and approximately regular network of capillaries. The process was observed by bright-field microscopy in control embryos and in embryos treated with Bevacizumab (Avastin^®), an antibody that inhibits the signalling of the vascular endothelial growth factor (VEGF). The sequence of images of the vascular growth were thresholded, and used to quantify the forming network in control and Avastin-treated embryos. This characterization is made by measuring vessels density, number of cell clusters and the largest cluster density. From the original images, the topology of the vascular network was extracted and characterized by means of the usual network metrics such as: the degree distribution, average clustering coefficient, average short path length and assortativity, among others. This analysis allows to monitor how the largest connected cluster of the vascular network evolves in time and provides with quantitative evidence of the disruptive effects that Avastin has on the tree structure of vascular networks.

Controlling Cooperativity in β-Cyclodextrin-DNA Binding Reactions

We have investigated the interaction between the native neutral β-cyclodextrin (CD) and the DNA molecule by performing single-molecule stretching experiments with optical tweezers. In particular, we have monitored the changes of the mechanical properties of the CD-DNA complexes as a function of the CD concentration in the sample. By using a quenched disorder statistical model, we were also capable to extract important physicochemical information (equilibrium binding constants, cooperativity degree) of such interaction from the mechanical data. In addition, we have found that the interaction occurs by two different mechanisms, first with the formation of relatively large CD clusters along the double helix, which thereafter can locally denature the DNA molecule by forming hydrogen bonds with the base pairs that eventually flip out. A prediction of our quenched disorder model was that cooperativity could be controlled by adjusting the surface charge of β-CD molecules. This prediction is confirmed in the present work.

Quantitative assessment of the interplay between DNA elasticity and cooperative binding of ligands

Binding of ligands to DNA can be studied by measuring the change of the persistence length of the complex formed, in single-molecule assays. We propose a methodology for persistence length data analysis based on a quenched disorder statistical model and describing the binding isotherm by a Hill-type equation. We obtain an expression for the effective persistence length as a function of the total ligand concentration, which we apply to our data of the DNA-cationic β-cyclodextrin and to the DNA-HU protein data available in the literature, determining the values of the local persistence lengths, the dissociation constant, and the degree of cooperativity for each set of data. In both cases the persistence length behaves nonmonotonically as a function of ligand concentration and based on the results obtained we discuss some physical aspects of the interplay between DNA elasticity and cooperative binding of ligands.

Transition on the entropic elasticity of DNA induced by intercalating molecules

We use optical tweezers to perform stretching experiments on DNA molecules when interacting with the drugs daunomycin and ethidium bromide, which intercalate the DNA molecule. Our results show that the persistence length of the DNA-drug complexes increases strongly as the drug concentration increases up to some critical value. Above this critical value, the persistence length decreases abruptly and remains approximately constant for larger drug concentrations, at least in the concentration range used in our experiments. Measured intercalators critical concentrations for the persistence length transition coincide with the reported values for the helix-coil transition of DNA-drug complexes obtained from sedimentation experiments. The contour length of the molecules increases monotonically and saturates as the drug concentration increases. The neighbor exclusion model fits to our results for the total drug concentration as a function of the relative increase of the contour length.

Towards absolute calibration of optical tweezers

Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of Mie-Debye-spherical aberration (MDSA) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass-water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius, and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points, and "hopping" effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.

DNA-psoralen interaction: a single molecule experiment

By attaching one end of a single lambda-DNA molecule to a microscope coverslip and the other end to a polystyrene microsphere trapped by an optical tweezers, we can study the entropic elasticity of the lambda-DNA by measuring force versus extension as we stretch the molecule. This powerful method permits single molecule studies. We are particularly interested in the effects of the photosensitive drug psoralen on the elasticity of the DNA molecule. We have illuminated the sample with different light sources, studying how the different wavelengths affect the psoralen-DNA linkage. To do this, we measure the persistence length of individual DNA-psoralen complexes.

Characterization of objective transmittance for optical tweezers

We have measured the overall transmittance of a laser beam through an oil immersion objective as a function of the transverse size of the laser beam, using the dual-objective method. Our results show that the objective transmittance is not uniform and that its dependence on the radial beam's position can be modeled by a Gaussian function. This property affects the intensity distribution pattern in the sample region and should be taken into account in theoretical descriptions of optical tweezers. Moreover, one must consider this position dependence to determine the local laser power delivered at the sample region by the dual-objective method, especially when the beam overfills the objective's back entrance. If the transmittance is assumed to be uniform, the local power is overestimated.

Defocusing microscopy

Transparent objects (phase objects) are not visible in a standard brightfield optical microscope. In order to see such objects the most used technique is phase-contrast microscopy. In phase-contrast microscopy the contrast observed is proportional to the optical path difference introduced by the object. If the index of refraction is uniform, phase-contrast microscopy then yields a measure of the thickness profile of phase objects. We show that by slightly defocusing an optical microscope operating in brightfield, phase objects become visible. We modeled such an effect and show that the image contrast of a phase object is proportional to the amount of defocusing and proportional to the two-dimensional Laplacian of the optical path difference introduced by the object. For uniform index of refraction, defocusing microscopy then yields a measure of the curvature profile of phase objects. We extended our previous model for thin objects to thick objects. To check our theoretical model, we use as phase objects polystyrene spherical caps and compare their curvature radii obtained by defocusing microscopy (DM) to those obtained with atomic force microscopy (AFM). We also show that for thick curved phase objects one can reconstruct their thickness profiles from DM images. We illustrate the utility of defocusing microscopy in biological systems to study cell motility. In particular, we visualize and quantitatively measure real-time cytoskeleton curvature fluctuations of macrophages (a cell of the innate immune system). The study of such fluctuations might be important for a better understanding of the engulfment process of pathogens during phagocytosis.

Measurements and modeling of water transport and osmoregulation in a single kidney cell using optical tweezers and videomicroscopy

With an optical tweezer installed in our optical microscope we grab a single Madin Darby Canine kidney cell and keep it suspended in the medium without touching the glass substrate or other cells. Since the optically trapped cell remains with a closely round shape, we can directly measure its volume by using videomicroscopy with digital image analysis. We submit this cell to a hyperosmotic shock (up-shock) and video record the process: the cell initially shrinks due to osmotic efflux of water and after a while, due to regulatory volume increase (RVI), an osmoregulation response, it inflates again (water influx) until it reaches a new volume (the regulatory volume VR). In addition to considering standard osmotic water transport, we model RVI using a simple phenomenological model. We obtain an expression for cell volume variation as a function of time that fits very well with our experimental data, where two characteristic times appear naturally: one related to water transport and the other related to RVI. From the fit we obtain water permeability, osmolyte influx rate for RVI, and regulatory volume. With the addition of the hormone vasopressin, water permeability increases while the regulatory volume decreases until inhibition of RVI. In summary, we present a technique to measure directly volume changes of a single isolated kidney cell under osmotic shock and a phenomenological analysis of water transport that takes into account osmoregulation.

Cell surface fluctuations studied with defocusing microscopy

Phase objects can become visible by slightly defocusing an optical microscope, a technique seldom used as a useful tool. We revisited the theory of defocusing and apply it to our optical microscope with optics corrected at infinity. In our approximation, we obtain that the image contrast is proportional to the two-dimensional (2D) Laplacian of the phase difference introduced by the phase object. If the index of refraction of the phase object is uniform the image obtained from defocusing microscopy is the image of curvature (Laplacian of the local thickness) of the phase object, while standard phase-contrast microscopy gives information about the thickness of the object. We made artificial phase objects and measured image contrasts with defocusing microscopy. Measured contrasts are in excellent agreement with our theoretical model. We use defocusing microscopy to study curvature fluctuations (ruffles) on the surface of macrophages (cell of the innate immune system), and try to correlate mechanical properties of macrophage surface and phagocytosis. We observe large coherent propagating structures: Their shape, speed, density are measured and curvature energy estimated. Inhomogeneities of cytoskeleton refractive index, curvature modulations due to thermal fluctuations and/or periodic changes in cytoskeleton-membrane interactions cause random fluctuations in image contrast. From the temporal and spatial contrast correlation functions, we obtain the decay time and correlation length of such fluctuations that are related to their size and the viscoelastic properties of the cytoskeleton. In order to associate the dynamics of cytoskeleton with the process of phagocytosis, we use an optical tweezers to grab a zymosan particle and put it into contact with the macrophage. We then measure the time for a single phagocytosis event. We add the drug cytochalasin D that depolymerizes the cytoskeleton F-actin network: It inhibits the large propagating coherent fluctuations on the cell surface, increases the relaxation time of cytoskeleton fluctuations, and increases the phagocytosis time. Our results suggest that the methods developed in this work can be of utility to assess the importance of cytoskeleton motility in the dynamics of cellular processes such as phagocytosis exhibited by macrophages.

Dynamic light scattering from an optically trapped microsphere

Using a single microscope objective lens to optically trap, illuminate, and collect backscattered light of a dielectric microsphere, we measure the temporal-intensity-autocorrelation functions (ACFs), and intensity profiles to obtain the trap stiffness and friction coefficient of the bead. This is an interesting study of an harmonically bound Brownian particle, with nanometer resolution. We extend the work of Bar-Ziv et al. [Phys. Rev. Lett. 78, 154 (1997)] to more general situations allowing for the use of our simpler geometry in other applications. As examples, we present measurements of the parallel Stokes friction coefficient on the trapped bead as a function of its distance from a surface and the entropic force of a single lambda-DNA molecule.

Anomalous capillary length in cellular nematic-isotropic interfaces

The long-standing puzzle of why capillary lengths measured in cellular nematic-isotropic interfaces are much longer than the value of 0.05 A predicted by Mullins-Sekerka theory has been solved. The resolution of the paradox is that in confined systems the substrate-nematic anchoring energy contributes to the capillary length which is greatly increased by selective adsorption of ions on the substrate.

Experimental test of the Warren-Langer model in nematic-isotropic planar interfaces

In a directional solidification apparatus, the recoil of the nonsteady planar nematic-isotropic interface of the liquid crystal 8CB doped with hexachloroethane was measured, for different pulling velocities. Results agree very well with the predictions of our two-sided extension of Warren and Langer's one-sided model [Phys. Rev. E 47, 2702 (1993)], therefore supporting the validity of their ansatz about the evolution of the dopant concentration field. From the comparison between experiment and theory we obtain values for the segregation and diffusion coefficients of hexachloroethane in 8CB comparable to those found in the literature and measured by other methods. Using the same procedure, we measured the value of the segregation coefficient of 8CB doped with water as a function of applied sinusoidal electric field perpendicular to the sample, along the homeotropic direction. The segregation coefficient increases with electric field. In addition, preliminary results on the cellular instability in this system show that the capillary length of the pattern also increases with electric field. To our knowledge, this is the first binary system with continuously tunable segregation coefficient and capillary length.

Gramicidin channel kinetics under tension

We have measured the effect of tension on dimerization kinetics of the channel-forming peptide gramicidin A. By aspirating large unilamellar vesicles into a micropipette electrode, we are able to simultaneously monitor membrane tension and electrical activity. We find that the dimer formation rate increases by a factor of 5 as tension ranges from 0 to 4 dyn/cm. The dimer lifetime also increases with tension. This behavior is well described by a phenomenological model of membrane elasticity in which tension modulates the mismatch in thickness between the gramicidin dimer and membrane.