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Algorithm for the Time-Propagation of the Radial Diffusion Equation Based on a Gaussian Quadrature.
PUBLISHED: 07-25-2015
The numerical integration of the time-dependent spherically-symmetric radial diffusion equation from a point source is considered. The flux through the source can vary in time, possibly stochastically based on the concentration produced by the source itself. Fick's one-dimensional diffusion equation is integrated over a time interval by considering a source term and a propagation term. The source term adds new particles during the time interval, while the propagation term diffuses the concentration profile of the previous time step. The integral in the propagation term is evaluated numerically using a combination of a new diffusion-specific Gaussian quadrature and interpolation on a diffusion-specific grid. This attempts to balance accuracy with the least number of points for both integration and interpolation. The theory can also be extended to include a simple reaction-diffusion equation in the limit of high buffer concentrations. The method is unconditionally stable. In fact, not only does it converge for any time step ?t, the method offers one advantage over other methods because ?t can be arbitrarily large; it is solely defined by the timescale on which the flux source turns on and off.
Authors: Laurence Daheron.
Published: 11-30-2006
22 Related JoVE Articles!
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Combining Single-molecule Manipulation and Imaging for the Study of Protein-DNA Interactions
Authors: Carina Monico, Gionata Belcastro, Francesco Vanzi, Francesco S. Pavone, Marco Capitanio.
Institutions: University of Florence, University of Oxford, University of Florence, University of Florence, National Institute of Optics-National Research Council, Italy, International Center of Computational Neurophotonics.
The paper describes the combination of optical tweezers and single molecule fluorescence detection for the study of protein-DNA interaction. The method offers the opportunity of investigating interactions occurring in solution (thus avoiding problems due to closeby surfaces as in other single molecule methods), controlling the DNA extension and tracking interaction dynamics as a function of both mechanical parameters and DNA sequence. The methods for establishing successful optical trapping and nanometer localization of single molecules are illustrated. We illustrate the experimental conditions allowing the study of interaction of lactose repressor (lacI), labeled with Atto532, with a DNA molecule containing specific target sequences (operators) for LacI binding. The method allows the observation of specific interactions at the operators, as well as one-dimensional diffusion of the protein during the process of target search. The method is broadly applicable to the study of protein-DNA interactions but also to molecular motors, where control of the tension applied to the partner track polymer (for example actin or microtubules) is desirable.
Bioengineering, Issue 90, Single molecule biophysics, Optical tweezers, fluorescence microscopy, DNA binding proteins, lactose repressor, microfluidics
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High-resolution Spatiotemporal Analysis of Receptor Dynamics by Single-molecule Fluorescence Microscopy
Authors: Titiwat Sungkaworn, Finn Rieken, Martin J. Lohse, Davide Calebiro.
Institutions: University of Würzburg, Germany.
Single-molecule microscopy is emerging as a powerful approach to analyze the behavior of signaling molecules, in particular concerning those aspect (e.g., kinetics, coexistence of different states and populations, transient interactions), which are typically hidden in ensemble measurements, such as those obtained with standard biochemical or microscopy methods. Thus, dynamic events, such as receptor-receptor interactions, can be followed in real time in a living cell with high spatiotemporal resolution. This protocol describes a method based on labeling with small and bright organic fluorophores and total internal reflection fluorescence (TIRF) microscopy to directly visualize single receptors on the surface of living cells. This approach allows one to precisely localize receptors, measure the size of receptor complexes, and capture dynamic events such as transient receptor-receptor interactions. The protocol provides a detailed description of how to perform a single-molecule experiment, including sample preparation, image acquisition and image analysis. As an example, the application of this method to analyze two G-protein-coupled receptors, i.e., β2-adrenergic and γ-aminobutyric acid type B (GABAB) receptor, is reported. The protocol can be adapted to other membrane proteins and different cell models, transfection methods and labeling strategies.
Bioengineering, Issue 89, pharmacology, microscopy, receptor, live-cell imaging, single-molecule, total internal reflection fluorescence, tracking, dimerization, protein-protein interactions
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An Inverse Analysis Approach to the Characterization of Chemical Transport in Paints
Authors: Matthew P. Willis, Shawn M. Stevenson, Thomas P. Pearl, Brent A. Mantooth.
Institutions: U.S. Army Edgewood Chemical Biological Center, OptiMetrics, Inc., a DCS Company.
The ability to directly characterize chemical transport and interactions that occur within a material (i.e., subsurface dynamics) is a vital component in understanding contaminant mass transport and the ability to decontaminate materials. If a material is contaminated, over time, the transport of highly toxic chemicals (such as chemical warfare agent species) out of the material can result in vapor exposure or transfer to the skin, which can result in percutaneous exposure to personnel who interact with the material. Due to the high toxicity of chemical warfare agents, the release of trace chemical quantities is of significant concern. Mapping subsurface concentration distribution and transport characteristics of absorbed agents enables exposure hazards to be assessed in untested conditions. Furthermore, these tools can be used to characterize subsurface reaction dynamics to ultimately design improved decontaminants or decontamination procedures. To achieve this goal, an inverse analysis mass transport modeling approach was developed that utilizes time-resolved mass spectroscopy measurements of vapor emission from contaminated paint coatings as the input parameter for calculation of subsurface concentration profiles. Details are provided on sample preparation, including contaminant and material handling, the application of mass spectrometry for the measurement of emitted contaminant vapor, and the implementation of inverse analysis using a physics-based diffusion model to determine transport properties of live chemical warfare agents including distilled mustard (HD) and the nerve agent VX.
Chemistry, Issue 90, Vacuum, vapor emission, chemical warfare agent, contamination, mass transport, inverse analysis, volatile organic compound, paint, coating
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From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
Authors: Carmine Di Rienzo, Enrico Gratton, Fabio Beltram, Francesco Cardarelli.
Institutions: Scuola Normale Superiore, Instituto Italiano di Tecnologia, University of California, Irvine.
It has become increasingly evident that the spatial distribution and the motion of membrane components like lipids and proteins are key factors in the regulation of many cellular functions. However, due to the fast dynamics and the tiny structures involved, a very high spatio-temporal resolution is required to catch the real behavior of molecules. Here we present the experimental protocol for studying the dynamics of fluorescently-labeled plasma-membrane proteins and lipids in live cells with high spatiotemporal resolution. Notably, this approach doesn’t need to track each molecule, but it calculates population behavior using all molecules in a given region of the membrane. The starting point is a fast imaging of a given region on the membrane. Afterwards, a complete spatio-temporal autocorrelation function is calculated correlating acquired images at increasing time delays, for example each 2, 3, n repetitions. It is possible to demonstrate that the width of the peak of the spatial autocorrelation function increases at increasing time delay as a function of particle movement due to diffusion. Therefore, fitting of the series of autocorrelation functions enables to extract the actual protein mean square displacement from imaging (iMSD), here presented in the form of apparent diffusivity vs average displacement. This yields a quantitative view of the average dynamics of single molecules with nanometer accuracy. By using a GFP-tagged variant of the Transferrin Receptor (TfR) and an ATTO488 labeled 1-palmitoyl-2-hydroxy-sn-glycero-3-phosphoethanolamine (PPE) it is possible to observe the spatiotemporal regulation of protein and lipid diffusion on µm-sized membrane regions in the micro-to-milli-second time range.
Bioengineering, Issue 92, fluorescence, protein dynamics, lipid dynamics, membrane heterogeneity, transient confinement, single molecule, GFP
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Tracking the Mammary Architectural Features and Detecting Breast Cancer with Magnetic Resonance Diffusion Tensor Imaging
Authors: Noam Nissan, Edna Furman-Haran, Myra Feinberg-Shapiro, Dov Grobgeld, Erez Eyal, Tania Zehavi, Hadassa Degani.
Institutions: Weizmann Institute of Science, Weizmann Institute of Science, Meir Medical Center, Meir Medical Center.
Breast cancer is the most common cause of cancer among women worldwide. Early detection of breast cancer has a critical role in improving the quality of life and survival of breast cancer patients. In this paper a new approach for the detection of breast cancer is described, based on tracking the mammary architectural elements using diffusion tensor imaging (DTI). The paper focuses on the scanning protocols and image processing algorithms and software that were designed to fit the diffusion properties of the mammary fibroglandular tissue and its changes during malignant transformation. The final output yields pixel by pixel vector maps that track the architecture of the entire mammary ductal glandular trees and parametric maps of the diffusion tensor coefficients and anisotropy indices. The efficiency of the method to detect breast cancer was tested by scanning women volunteers including 68 patients with breast cancer confirmed by histopathology findings. Regions with cancer cells exhibited a marked reduction in the diffusion coefficients and in the maximal anisotropy index as compared to the normal breast tissue, providing an intrinsic contrast for delineating the boundaries of malignant growth. Overall, the sensitivity of the DTI parameters to detect breast cancer was found to be high, particularly in dense breasts, and comparable to the current standard breast MRI method that requires injection of a contrast agent. Thus, this method offers a completely non-invasive, safe and sensitive tool for breast cancer detection.
Medicine, Issue 94, Magnetic Resonance Imaging, breast, breast cancer, diagnosis, water diffusion, diffusion tensor imaging
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Diffusion Imaging in the Rat Cervical Spinal Cord
Authors: Elizabeth Zakszewski, Brian Schmit, Shekar Kurpad, Matthew D. Budde.
Institutions: Medical College of Wisconsin, Marquette University.
Magnetic resonance imaging (MRI) is the state of the art approach for assessing the status of the spinal cord noninvasively, and can be used as a diagnostic and prognostic tool in cases of disease or injury. Diffusion weighted imaging (DWI), is sensitive to the thermal motion of water molecules and allows for inferences of tissue microstructure. This report describes a protocol to acquire and analyze DWI of the rat cervical spinal cord on a small-bore animal system. It demonstrates an imaging setup for the live anesthetized animal and recommends a DWI acquisition protocol for high-quality imaging, which includes stabilization of the cord and control of respiratory motion. Measurements with diffusion weighting along different directions and magnitudes (b-values) are used. Finally, several mathematical models of the resulting signal are used to derive maps of the diffusion processes within the spinal cord tissue that provide insight into the normal cord and can be used to monitor injury or disease processes noninvasively.
Neurobiology, Issue 98, spinal cord, magnetic resonance imaging, diffusion tensor imaging, respiratory gating, diffusion kurtosis imaging, rat, spine
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Electrochemically and Bioelectrochemically Induced Ammonium Recovery
Authors: Sylvia Gildemyn, Amanda K. Luther, Stephen J. Andersen, Joachim Desloover, Korneel Rabaey.
Institutions: Ghent University, Rutgers University.
Streams such as urine and manure can contain high levels of ammonium, which could be recovered for reuse in agriculture or chemistry. The extraction of ammonium from an ammonium-rich stream is demonstrated using an electrochemical and a bioelectrochemical system. Both systems are controlled by a potentiostat to either fix the current (for the electrochemical cell) or fix the potential of the working electrode (for the bioelectrochemical cell). In the bioelectrochemical cell, electroactive bacteria catalyze the anodic reaction, whereas in the electrochemical cell the potentiostat applies a higher voltage to produce a current. The current and consequent restoration of the charge balance across the cell allow the transport of cations, such as ammonium, across a cation exchange membrane from the anolyte to the catholyte. The high pH of the catholyte leads to formation of ammonia, which can be stripped from the medium and captured in an acid solution, thus enabling the recovery of a valuable nutrient. The flux of ammonium across the membrane is characterized at different anolyte ammonium concentrations and currents for both the abiotic and biotic reactor systems. Both systems are compared based on current and removal efficiencies for ammonium, as well as the energy input required to drive ammonium transfer across the cation exchange membrane. Finally, a comparative analysis considering key aspects such as reliability, electrode cost, and rate is made. This video article and protocol provide the necessary information to conduct electrochemical and bioelectrochemical ammonia recovery experiments. The reactor setup for the two cases is explained, as well as the reactor operation. We elaborate on data analysis for both reactor types and on the advantages and disadvantages of bioelectrochemical and electrochemical systems.
Chemistry, Issue 95, Electrochemical extraction, bioelectrochemical system, bioanode, ammonium recovery, microbial electrocatalysis, nutrient recovery, electrolysis cell
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Whole Vitreous Humor Dissection for Vitreodynamic Analysis
Authors: Karthik Murali, Amir H. Kashani, Mark S. Humayun.
Institutions: University of Southern California, University of Southern California.
The authors propose an effective technique to isolate whole, intact vitreous core and cortex from post mortem enucleated porcine eyes. While previous studies have shown the results of such dissections, the detailed steps have not been described, precluding researchers outside the field from replicating their methods. Other studies harvest vitreous either through aspiration, which does not maintain the vitreous structure anatomy, or through partial dissection, which only isolates the vitreous core. The proposed method isolates the whole vitreous body, with the vitreous core and cortex intact, while maintaining vitreous anatomy and structural integrity. In this method, a full thickness scleral flap in an enucleated porcine eye is first created and through this, the choroid tissue can be separated from the sclera. The scleral flap is then expanded and the choroid is completely separated from the sclera. Finally the choroid-retina tissue is peeled off the vitreous to leave an isolated intact vitreous body. The proposed vitreous dissection technique can be used to study physical properties of the vitreous humor. In particular, this method has significance for experimental studies involving drug delivery, vitreo-retinal oxygen transport, and intraocular convection.
Medicine, Issue 99, Vitreous Humor, Dissection, Vitreous core, Vitreous cortex, Medicine, Eye, vitreodynamics, drug delivery, diffusion
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Measurement of Extracellular Ion Fluxes Using the Ion-selective Self-referencing Microelectrode Technique
Authors: Guillaume Luxardi, Brian Reid, Fernando Ferreira, Pauline Maillard, Min Zhao.
Institutions: University of California, Davis, Universidade do Minho, University of California, Davis Imaging of Dementia and Aging Laboratory, University of California, Davis.
Cells from animals, plants and single cells are enclosed by a barrier called the cell membrane that separates the cytoplasm from the outside. Cell layers such as epithelia also form a barrier that separates the inside from the outside or different compartments of multicellular organisms. A key feature of these barriers is the differential distribution of ions across cell membranes or cell layers. Two properties allow this distribution: 1) membranes and epithelia display selective permeability to specific ions; 2) ions are transported through pumps across cell membranes and cell layers. These properties play crucial roles in maintaining tissue physiology and act as signaling cues after damage, during repair, or under pathological condition. The ion-selective self-referencing microelectrode allows measurements of specific fluxes of ions such as calcium, potassium or sodium at single cell and tissue levels. The microelectrode contains an ionophore cocktail which is selectively permeable to a specific ion. The internal filling solution contains a set concentration of the ion of interest. The electric potential of the microelectrode is determined by the outside concentration of the ion. As the ion concentration varies, the potential of the microelectrode changes as a function of the log of the ion activity. When moved back and forth near a source or sink of the ion (i.e. in a concentration gradient due to ion flux) the microelectrode potential fluctuates at an amplitude proportional to the ion flux/gradient. The amplifier amplifies the microelectrode signal and the output is recorded on computer. The ion flux can then be calculated by Fick’s law of diffusion using the electrode potential fluctuation, the excursion of microelectrode, and other parameters such as the specific ion mobility. In this paper, we describe in detail the methodology to measure extracellular ion fluxes using the ion-selective self-referencing microelectrode and present some representative results.
Cellular Biology, Issue 99, ion-selective, self-referencing, microelectrode, extracellular ion fluxes, in vivo measurements
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Authors: Olivier Morin, Jianli Liu, Kun Huang, Felippe Barbosa, Claude Fabre, Julien Laurat.
Institutions: Université Pierre et Marie Curie, Ecole Normale Supérieure, CNRS, East China Normal University, Universidade de São Paulo.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear χ2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong χ3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
Physics, Issue 87, Optics, Quantum optics, Quantum state engineering, Optical parametric oscillator, Squeezed vacuum, Single photon, Coherent state superposition, Homodyne detection
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Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
Authors: Johannes Felix Buyel, Rainer Fischer.
Institutions: RWTH Aachen University, Fraunhofer Gesellschaft.
Plants provide multiple benefits for the production of biopharmaceuticals including low costs, scalability, and safety. Transient expression offers the additional advantage of short development and production times, but expression levels can vary significantly between batches thus giving rise to regulatory concerns in the context of good manufacturing practice. We used a design of experiments (DoE) approach to determine the impact of major factors such as regulatory elements in the expression construct, plant growth and development parameters, and the incubation conditions during expression, on the variability of expression between batches. We tested plants expressing a model anti-HIV monoclonal antibody (2G12) and a fluorescent marker protein (DsRed). We discuss the rationale for selecting certain properties of the model and identify its potential limitations. The general approach can easily be transferred to other problems because the principles of the model are broadly applicable: knowledge-based parameter selection, complexity reduction by splitting the initial problem into smaller modules, software-guided setup of optimal experiment combinations and step-wise design augmentation. Therefore, the methodology is not only useful for characterizing protein expression in plants but also for the investigation of other complex systems lacking a mechanistic description. The predictive equations describing the interconnectivity between parameters can be used to establish mechanistic models for other complex systems.
Bioengineering, Issue 83, design of experiments (DoE), transient protein expression, plant-derived biopharmaceuticals, promoter, 5'UTR, fluorescent reporter protein, model building, incubation conditions, monoclonal antibody
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Visualizing Protein-DNA Interactions in Live Bacterial Cells Using Photoactivated Single-molecule Tracking
Authors: Stephan Uphoff, David J. Sherratt, Achillefs N. Kapanidis.
Institutions: University of Oxford, University of Oxford.
Protein-DNA interactions are at the heart of many fundamental cellular processes. For example, DNA replication, transcription, repair, and chromosome organization are governed by DNA-binding proteins that recognize specific DNA structures or sequences. In vitro experiments have helped to generate detailed models for the function of many types of DNA-binding proteins, yet, the exact mechanisms of these processes and their organization in the complex environment of the living cell remain far less understood. We recently introduced a method for quantifying DNA-repair activities in live Escherichia coli cells using Photoactivated Localization Microscopy (PALM) combined with single-molecule tracking. Our general approach identifies individual DNA-binding events by the change in the mobility of a single protein upon association with the chromosome. The fraction of bound molecules provides a direct quantitative measure for the protein activity and abundance of substrates or binding sites at the single-cell level. Here, we describe the concept of the method and demonstrate sample preparation, data acquisition, and data analysis procedures.
Immunology, Issue 85, Super-resolution microscopy, single-particle tracking, Live-cell imaging, DNA-binding proteins, DNA repair, molecular diffusion
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Measuring Diffusion Coefficients via Two-photon Fluorescence Recovery After Photobleaching
Authors: Kelley D. Sullivan, Edward B. Brown.
Institutions: University of Rochester, University of Rochester.
Multi-fluorescence recovery after photobleaching is a microscopy technique used to measure the diffusion coefficient (or analogous transport parameters) of macromolecules, and can be applied to both in vitro and in vivo biological systems. Multi-fluorescence recovery after photobleaching is performed by photobleaching a region of interest within a fluorescent sample using an intense laser flash, then attenuating the beam and monitoring the fluorescence as still-fluorescent molecules from outside the region of interest diffuse in to replace the photobleached molecules. We will begin our demonstration by aligning the laser beam through the Pockels Cell (laser modulator) and along the optical path through the laser scan box and objective lens to the sample. For simplicity, we will use a sample of aqueous fluorescent dye. We will then determine the proper experimental parameters for our sample including, monitor and bleaching powers, bleach duration, bin widths (for photon counting), and fluorescence recovery time. Next, we will describe the procedure for taking recovery curves, a process that can be largely automated via LabVIEW (National Instruments, Austin, TX) for enhanced throughput. Finally, the diffusion coefficient is determined by fitting the recovery data to the appropriate mathematical model using a least-squares fitting algorithm, readily programmable using software such as MATLAB (The Mathworks, Natick, MA).
Cellular Biology, Issue 36, Diffusion, fluorescence recovery after photobleaching, MP-FRAP, FPR, multi-photon
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Fabrication and Operation of an Oxygen Insert for Adherent Cellular Cultures
Authors: Shawn Oppegard, Elly Sinkala, David Eddington.
Institutions: University of Illinois.
Oxygen is a key modulator of many cellular pathways, but current devices permitting in vitro oxygen modulation fail to meet the needs of biomedical research. The hypoxic chamber offers a simple system to control oxygenation in standard culture vessels, but lacks precise temporal and spatial control over the oxygen concentration at the cell surface, preventing its application in studying a variety of physiological phenomena. Other systems have improved upon the hypoxic chamber, but require specialized knowledge and equipment for their operation, making them intimidating for the average researcher. A microfabricated insert for multiwell plates has been developed to more effectively control the temporal and spatial oxygen concentration to better model physiological phenomena found in vivo. The platform consists of a polydimethylsiloxane insert that nests into a standard multiwell plate and serves as a passive microfluidic gas network with a gas-permeable membrane aimed to modulate oxygen delivery to adherent cells. The device is simple to use and is connected to gas cylinders that provide the pressure to introduce the desired oxygen concentration into the platform. Fabrication involves a combination of standard SU-8 photolithography, replica molding, and defined PDMS spinning on a silicon wafer. The components of the device are bonded after surface treatment using a hand-held plasma system. Validation is accomplished with a planar fluorescent oxygen sensor. Equilibration time is on the order of minutes and a wide variety of oxygen profiles can be attained based on the device design, such as the cyclic profile achieved in this study, and even oxygen gradients to mimic those found in vivo. The device can be sterilized for cell culture using common methods without loss of function. The device's applicability to studying the in vitro wound healing response will be demonstrated.
Cellular Biology, Issue 35, hypoxia, cell, culture, control, wound, healing, oxygen, microfluidic device, bioengineering
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Determination of Lipid Raft Partitioning of Fluorescently-tagged Probes in Living Cells by Fluorescence Correlation Spectroscopy (FCS)
Authors: Catherine Marquer, Sandrine Lévêque-Fort, Marie-Claude Potier.
Institutions: Hôpital de la Pitié-Salpêtrière, Université Paris-Sud, Université Paris-Sud.
In the past fifteen years the notion that cell membranes are not homogenous and rely on microdomains to exert their functions has become widely accepted. Lipid rafts are membrane microdomains enriched in cholesterol and sphingolipids. They play a role in cellular physiological processes such as signalling, and trafficking1,2 but are also thought to be key players in several diseases including viral or bacterial infections and neurodegenerative diseases3. Yet their existence is still a matter of controversy4,5. Indeed, lipid raft size has been estimated to be around 20 nm6, far under the resolution limit of conventional microscopy (around 200 nm), thus precluding their direct imaging. Up to now, the main techniques used to assess the partition of proteins of interest inside lipid rafts were Detergent Resistant Membranes (DRMs) isolation and co-patching with antibodies. Though widely used because of their rather easy implementation, these techniques were prone to artefacts and thus criticized7,8. Technical improvements were therefore necessary to overcome these artefacts and to be able to probe lipid rafts partition in living cells. Here we present a method for the sensitive analysis of lipid rafts partition of fluorescently-tagged proteins or lipids in the plasma membrane of living cells. This method, termed Fluorescence Correlation Spectroscopy (FCS), relies on the disparity in diffusion times of fluorescent probes located inside or outside of lipid rafts. In fact, as evidenced in both artificial membranes and cell cultures, probes would diffuse much faster outside than inside dense lipid rafts9,10. To determine diffusion times, minute fluorescence fluctuations are measured as a function of time in a focal volume (approximately 1 femtoliter), located at the plasma membrane of cells with a confocal microscope (Fig. 1). The auto-correlation curves can then be drawn from these fluctuations and fitted with appropriate mathematical diffusion models11. FCS can be used to determine the lipid raft partitioning of various probes, as long as they are fluorescently tagged. Fluorescent tagging can be achieved by expression of fluorescent fusion proteins or by binding of fluorescent ligands. Moreover, FCS can be used not only in artificial membranes and cell lines but also in primary cultures, as described recently12. It can also be used to follow the dynamics of lipid raft partitioning after drug addition or membrane lipid composition change12.
Cellular Biology, Issue 62, Lipid rafts, plasma membrane, diffusion times, confocal microscopy, fluorescence correlation spectroscopy (FCS)
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Controlling the Size, Shape and Stability of Supramolecular Polymers in Water
Authors: Pol Besenius, Isja de Feijter, Nico A.J.M. Sommerdijk, Paul H.H. Bomans, Anja R. A. Palmans.
Institutions: Westfälische Wilhelms-Universität Münster, Eindhoven University of Technology, Eindhoven University of Technology.
For aqueous based supramolecular polymers, the simultaneous control over shape, size and stability is very difficult1. At the same time, the ability to do so is highly important in view of a number of applications in functional soft matter including electronics, biomedical engineering, and sensors. In the past, successful strategies to control the size and shape of supramolecular polymers typically focused on the use of templates2,3, end cappers4 or selective solvent techniques5. Here we disclose a strategy based on self-assembling discotic amphiphiles that leads to the control over stack length and shape of ordered, chiral columnar aggregates. By balancing electrostatic repulsive interactions on the hydrophilic rim and attractive non-covalent forces within the hydrophobic core of the polymerizing building block, we manage to create small and discrete spherical objects6,7. Increasing the salt concentration to screen the charges induces a sphere-to-rod transition. Intriguingly, this transition is expressed in an increase of cooperativity in the temperature-dependent self-assembly mechanism, and more stable aggregates are obtained. For our study we select a benzene-1,3,5-tricarboxamide (BTA) core connected to a hydrophilic metal chelate via a hydrophobic, fluorinated L-phenylalanine based spacer (Scheme 1). The metal chelate selected is a Gd(III)-DTPA complex that contains two overall remaining charges per complex and necessarily two counter ions. The one-dimensional growth of the aggregate is directed by π-π stacking and intermolecular hydrogen bonding. However, the electrostatic, repulsive forces that arise from the charges on the Gd(III)-DTPA complex start limiting the one-dimensional growth of the BTA-based discotic once a certain size is reached. At millimolar concentrations the formed aggregate has a spherical shape and a diameter of around 5 nm as inferred from 1H-NMR spectroscopy, small angle X-ray scattering, and cryogenic transmission electron microscopy (cryo-TEM). The strength of the electrostatic repulsive interactions between molecules can be reduced by increasing the salt concentration of the buffered solutions. This screening of the charges induces a transition from spherical aggregates into elongated rods with a length > 25 nm. Cryo-TEM allows to visualise the changes in shape and size. In addition, CD spectroscopy permits to derive the mechanistic details of the self-assembly processes before and after the addition of salt. Importantly, the cooperativity -a key feature that dictates the physical properties of the produced supramolecular polymers- increases dramatically upon screening the electrostatic interactions. This increase in cooperativity results in a significant increase in the molecular weight of the formed supramolecular polymers in water.
Chemical Engineering, Issue 66, Chemistry, Physics, Self-assembly, cryogenic transmission electron microscopy, circular dichroism, controlled architecture, discotic amphiphile
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Authors: Rangaraj M. Rangayyan, Shantanu Banik, J.E. Leo Desautels.
Institutions: University of Calgary , University of Calgary .
We demonstrate methods for the detection of architectural distortion in prior mammograms of interval-cancer cases based on analysis of the orientation of breast tissue patterns in mammograms. We hypothesize that architectural distortion modifies the normal orientation of breast tissue patterns in mammographic images before the formation of masses or tumors. In the initial steps of our methods, the oriented structures in a given mammogram are analyzed using Gabor filters and phase portraits to detect node-like sites of radiating or intersecting tissue patterns. Each detected site is then characterized using the node value, fractal dimension, and a measure of angular dispersion specifically designed to represent spiculating patterns associated with architectural distortion. Our methods were tested with a database of 106 prior mammograms of 56 interval-cancer cases and 52 mammograms of 13 normal cases using the features developed for the characterization of architectural distortion, pattern classification via quadratic discriminant analysis, and validation with the leave-one-patient out procedure. According to the results of free-response receiver operating characteristic analysis, our methods have demonstrated the capability to detect architectural distortion in prior mammograms, taken 15 months (on the average) before clinical diagnosis of breast cancer, with a sensitivity of 80% at about five false positives per patient.
Medicine, Issue 78, Anatomy, Physiology, Cancer Biology, angular spread, architectural distortion, breast cancer, Computer-Assisted Diagnosis, computer-aided diagnosis (CAD), entropy, fractional Brownian motion, fractal dimension, Gabor filters, Image Processing, Medical Informatics, node map, oriented texture, Pattern Recognition, phase portraits, prior mammograms, spectral analysis
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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
Authors: Hans-Peter Müller, Jan Kassubek.
Institutions: University of Ulm.
Diffusion tensor imaging (DTI) techniques provide information on the microstructural processes of the cerebral white matter (WM) in vivo. The present applications are designed to investigate differences of WM involvement patterns in different brain diseases, especially neurodegenerative disorders, by use of different DTI analyses in comparison with matched controls. DTI data analysis is performed in a variate fashion, i.e. voxelwise comparison of regional diffusion direction-based metrics such as fractional anisotropy (FA), together with fiber tracking (FT) accompanied by tractwise fractional anisotropy statistics (TFAS) at the group level in order to identify differences in FA along WM structures, aiming at the definition of regional patterns of WM alterations at the group level. Transformation into a stereotaxic standard space is a prerequisite for group studies and requires thorough data processing to preserve directional inter-dependencies. The present applications show optimized technical approaches for this preservation of quantitative and directional information during spatial normalization in data analyses at the group level. On this basis, FT techniques can be applied to group averaged data in order to quantify metrics information as defined by FT. Additionally, application of DTI methods, i.e. differences in FA-maps after stereotaxic alignment, in a longitudinal analysis at an individual subject basis reveal information about the progression of neurological disorders. Further quality improvement of DTI based results can be obtained during preprocessing by application of a controlled elimination of gradient directions with high noise levels. In summary, DTI is used to define a distinct WM pathoanatomy of different brain diseases by the combination of whole brain-based and tract-based DTI analysis.
Medicine, Issue 77, Neuroscience, Neurobiology, Molecular Biology, Biomedical Engineering, Anatomy, Physiology, Neurodegenerative Diseases, nuclear magnetic resonance, NMR, MR, MRI, diffusion tensor imaging, fiber tracking, group level comparison, neurodegenerative diseases, brain, imaging, clinical techniques
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Simultaneous Multicolor Imaging of Biological Structures with Fluorescence Photoactivation Localization Microscopy
Authors: Nikki M. Curthoys, Michael J. Mlodzianoski, Dahan Kim, Samuel T. Hess.
Institutions: University of Maine.
Localization-based super resolution microscopy can be applied to obtain a spatial map (image) of the distribution of individual fluorescently labeled single molecules within a sample with a spatial resolution of tens of nanometers. Using either photoactivatable (PAFP) or photoswitchable (PSFP) fluorescent proteins fused to proteins of interest, or organic dyes conjugated to antibodies or other molecules of interest, fluorescence photoactivation localization microscopy (FPALM) can simultaneously image multiple species of molecules within single cells. By using the following approach, populations of large numbers (thousands to hundreds of thousands) of individual molecules are imaged in single cells and localized with a precision of ~10-30 nm. Data obtained can be applied to understanding the nanoscale spatial distributions of multiple protein types within a cell. One primary advantage of this technique is the dramatic increase in spatial resolution: while diffraction limits resolution to ~200-250 nm in conventional light microscopy, FPALM can image length scales more than an order of magnitude smaller. As many biological hypotheses concern the spatial relationships among different biomolecules, the improved resolution of FPALM can provide insight into questions of cellular organization which have previously been inaccessible to conventional fluorescence microscopy. In addition to detailing the methods for sample preparation and data acquisition, we here describe the optical setup for FPALM. One additional consideration for researchers wishing to do super-resolution microscopy is cost: in-house setups are significantly cheaper than most commercially available imaging machines. Limitations of this technique include the need for optimizing the labeling of molecules of interest within cell samples, and the need for post-processing software to visualize results. We here describe the use of PAFP and PSFP expression to image two protein species in fixed cells. Extension of the technique to living cells is also described.
Basic Protocol, Issue 82, Microscopy, Super-resolution imaging, Multicolor, single molecule, FPALM, Localization microscopy, fluorescent proteins
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Deriving the Time Course of Glutamate Clearance with a Deconvolution Analysis of Astrocytic Transporter Currents
Authors: Annalisa Scimemi, Jeffrey S. Diamond.
Institutions: National Institutes of Health.
The highest density of glutamate transporters in the brain is found in astrocytes. Glutamate transporters couple the movement of glutamate across the membrane with the co-transport of 3 Na+ and 1 H+ and the counter-transport of 1 K+. The stoichiometric current generated by the transport process can be monitored with whole-cell patch-clamp recordings from astrocytes. The time course of the recorded current is shaped by the time course of the glutamate concentration profile to which astrocytes are exposed, the kinetics of glutamate transporters, and the passive electrotonic properties of astrocytic membranes. Here we describe the experimental and analytical methods that can be used to record glutamate transporter currents in astrocytes and isolate the time course of glutamate clearance from all other factors that shape the waveform of astrocytic transporter currents. The methods described here can be used to estimate the lifetime of flash-uncaged and synaptically-released glutamate at astrocytic membranes in any region of the central nervous system during health and disease.
Neurobiology, Issue 78, Neuroscience, Biochemistry, Molecular Biology, Cellular Biology, Anatomy, Physiology, Biophysics, Astrocytes, Synapses, Glutamic Acid, Membrane Transport Proteins, Astrocytes, glutamate transporters, uptake, clearance, hippocampus, stratum radiatum, CA1, gene, brain, slice, animal model
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Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction
Authors: C. R. Gallistel, Fuat Balci, David Freestone, Aaron Kheifets, Adam King.
Institutions: Rutgers University, Koç University, New York University, Fairfield University.
We describe a high-throughput, high-volume, fully automated, live-in 24/7 behavioral testing system for assessing the effects of genetic and pharmacological manipulations on basic mechanisms of cognition and learning in mice. A standard polypropylene mouse housing tub is connected through an acrylic tube to a standard commercial mouse test box. The test box has 3 hoppers, 2 of which are connected to pellet feeders. All are internally illuminable with an LED and monitored for head entries by infrared (IR) beams. Mice live in the environment, which eliminates handling during screening. They obtain their food during two or more daily feeding periods by performing in operant (instrumental) and Pavlovian (classical) protocols, for which we have written protocol-control software and quasi-real-time data analysis and graphing software. The data analysis and graphing routines are written in a MATLAB-based language created to simplify greatly the analysis of large time-stamped behavioral and physiological event records and to preserve a full data trail from raw data through all intermediate analyses to the published graphs and statistics within a single data structure. The data-analysis code harvests the data several times a day and subjects it to statistical and graphical analyses, which are automatically stored in the "cloud" and on in-lab computers. Thus, the progress of individual mice is visualized and quantified daily. The data-analysis code talks to the protocol-control code, permitting the automated advance from protocol to protocol of individual subjects. The behavioral protocols implemented are matching, autoshaping, timed hopper-switching, risk assessment in timed hopper-switching, impulsivity measurement, and the circadian anticipation of food availability. Open-source protocol-control and data-analysis code makes the addition of new protocols simple. Eight test environments fit in a 48 in x 24 in x 78 in cabinet; two such cabinets (16 environments) may be controlled by one computer.
Behavior, Issue 84, genetics, cognitive mechanisms, behavioral screening, learning, memory, timing
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Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix
Authors: David A. Stout, Jennet Toyjanova, Christian Franck.
Institutions: California State University, Long Beach, Ximedica, Brown University.
The importance of cell migration can be seen through the development of human life. When cells migrate, they generate forces and transfer these forces to their surrounding area, leading to cell movement and migration. In order to understand the mechanisms that can alter and/or affect cell migration, one can study these forces. In theory, understanding the fundamental mechanisms and forces underlying cell migration holds the promise of effective approaches for treating diseases and promoting cellular transplantation. Unfortunately, modern chemotaxis chambers that have been developed are usually restricted to two dimensions (2D) and have complex diffusion gradients that make the experiment difficult to interpret. To this end, we have developed, and describe in this paper, a direct-viewing chamber for chemotaxis studies, which allows one to overcome modern chemotaxis chamber obstacles able to measure cell forces and specific concentration within the chamber in a 3D environment to study cell 3D migration. More compelling, this approach allows one to successfully model diffusion through 3D collagen matrices and calculate the coefficient of diffusion of a chemoattractant through multiple different concentrations of collagen, while keeping the system simple and user friendly for traction force microscopy (TFM) and digital volume correlation (DVC) analysis.
Bioengineering, Issue 100, Chemotaxis, 3D cell migration, diffusion, traction force microscopy, gradient, live-cell imaging
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