Spatial information analysis of chemotactic trajectories

During bacterial chemotaxis, a cell acquires information about its environment by sampling changes in the local concentration of a chemoattractant, and then uses that information to bias its motion relative to the source of the chemoattractant. The trajectory of a chemotaxing bacteria is thus a spatial manifestation of the information gathered by the cell. Here we show that a recently developed approach for computing spatial information using Fourier coefficient probabilities, the k-space information (kSI), can be used to quantify the information in such trajectories. The kSI is shown to capture expected responses to gradients of a chemoattractant. We then extend the k-space approach by developing an experimental probability distribution (EPD) that is computed from chemotactic trajectories collected under a reference condition. The EPD accounts for connectivity and other constraints that the nature of the trajectories imposes on the k-space computation. The EPD is used to compute the spatial information from any trajectory of interest, relative to the reference condition. The EPD-based spatial information also captures the expected responses to gradients of a chemoattractant, although the results differ in significant ways from the original kSI computation. In addition, the entropy calculated from the EPD provides a useful measure of trajectory space. The methods developed are highly general, and can be applied to a wide range of other trajectory types as well as non-trajectory data.     

Spatial Fourier analysis of video photobleaching measurements. Principles and optimization.

The major use of the fluorescence recovery after photobleaching (FRAP) technique is to measure the translational motion of the molecular components in various condensed media. In a conventional laser spot photobleaching experiment, a photomultiplier is used to measure the total brightness levels of the bleached region in the sample, so no spatial information can be directly obtained. In video-FRAP, a series of images after photobleaching is acquired, allowing the spatial character of the recovery to be determined; this permits direct detection of both anisotropic diffusion and flow. To utilize all of the available image data to determine the transport coefficients, a two-dimensional spatial Fourier transform analysis of the images after photobleaching was employed. The change in the transform between two time points reflects the action of diffusion during the interim. An important advantage of this method, which involves taking the ratio of image transforms at different time points, is that it does not require a specific initial condition to be created by laser photobleaching. The ability of the analysis to extract transport coefficients from computer-simulated diffusional recovery is assessed in the presence of increasing amounts of noise. Experimental data analysis from the diffusion of proteins in viscous solutions and from the diffusion of protein receptors on cell surfaces demonstrate the feasibility of the Fourier analysis to obtain transport coefficients from the video FRAP measurement.     

Raster image correlation spectroscopy in live cells

Raster image correlation spectroscopy (RICS) is a noninvasive technique to detect and quantify events in a live cell, including concentration of molecules and diffusion coefficients of molecules; in addition, by measuring changes in diffusion coefficients, RICS can indirectly detect binding. Any specimen containing fluorophores that can be imaged with a laser scanning microscope can be analyzed using RICS. There are other techniques to measure diffusion coefficients and binding; however, RICS fills a unique niche. It provides spatial information and can be performed in live cells using a conventional confocal microscope. It can measure a range of diffusion coefficients that is not accessible with any other single optical correlation-based technique. In this article we describe a protocol to obtain raster scanned images with an Olympus FluoView FV1000 confocal laser scanning microscope using Olympus FluoView software to acquire data and SimFCS software to perform RICS analysis. Each RICS measurement takes several minutes. The entire procedure can be completed in ～2 h. This procedure includes focal volume calibration using a solution of fluorophores with a known diffusion coefficient and measurement of the diffusion coefficients of cytosolic enhanced green fluorescent protein (EGFP) and EGFP-paxillin.     

The spatial distribution of moving macromolecules undergoing isomerization

In this paper we use probabilistic arguments to derive and discuss the spatial distribution of molecules which are undergoing electrophoresis or centrifugation while at the same time they are switching back and forth between two configurational states. An exact solution is obtained for arbitrary values of the diffusion coefficients of the two isomerizing states. The traditional analytic method of solving this problem, namely, by use of “master equations,” is not completely satisfactory because one can find only the Fourier transform of the solution rather than the solution itself. Our treatment yields the answer one would get if it were feasible to perform the inversion of the Fourier transform.     

Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media.

A new method for the measurement of diffusion in thick samples is introduced, based upon the spatial Fourier analysis of Tsay and Jacobson (Biophys. J. 60: 360-368, 1991) for the video image analysis of fluorescence recovery after photobleaching (FRAP). In this approach, the diffusion coefficient is calculated from the decay of Fourier transform coefficients in successive fluorescence images. Previously, the application of FRAP in thick samples has been confounded by the optical effects of out-of-focus light and scattering and absorption by the sample. The theory of image formation is invoked to show that the decay rate is the same for both the observed fluorescence intensity and the true concentration distribution in the tissue. The method was tested in a series of macromolecular diffusion measurements in aqueous solution, in agarose gel, and in simulated tissue consisting of tumor cells (45% v/v) and blood cells (5% v/v) in an agarose gel. For a range of fluorescently labeled proteins (MW = 14 to 600 kD) and dextrans (MW = 4.4 to 147.8 kD), the diffusion coefficients in aqueous solution were comparable to previously published values. A comparison of the spatial Fourier analysis with a conventional direct photometric method revealed that even for the weakly scattering agarose sample, the conventional method gives a result that is inaccurate and dependent on sample thickness whereas the diffusion coefficient calculated by the spatial Fourier method agreed with published values and was independent of sample thickness. The diffusion coefficient of albumin in the simulated tissue samples, as determined by the spatial Fourier analysis, varied slightly with sample thickness.(ABSTRACT TRUNCATED AT 250 WORDS)     

An NMR study of the temperature dependence of the coefficient of water self-diffusion through lipid bilayer membranes

The temperature dependence of the coefficient of water self-diffusion through plane-parallel lipid multilayers of the phospholipid dioleoylphosphatidylcholine oriented on a glass support has been studied in the temperature range of 20-60 degrees C by the method of NMR with magnetic field pulse gradient. The values of the coefficients of transbilayer water diffusion are by four orders of magnitude less than for bulky water and ten times less than the coefficients of lateral diffusion of the lipid under the same conditions. The temperature dependence of the coefficient of water diffusion is described by the Arrhenius law with an apparent activation energy of about 41 kJ/mol, which far exceeds the activation energy for the diffusion of bulky water (18 kJ/mol). The experimental data were analyzed using a "dissolving-diffusion" model, by simulating the passage of water through membrane channels, and by analyzing the exchange of water molecules in states with different modes of translation mobility, including pore channels and bilayer "defects". Each of the approaches used made it possible to take the significance of bilayer permeability for the apparent energy of activation of water diffusion into account and estimate the energies of activation of water diffusion in the hydrophobic moiety of the bilayer, which were found to be close to the values for bulky water. The coefficients of water diffusion in the system under examination and the coefficients of permeation of water through the bilayer were estimated, and the effect of bilayer "defects" on the coefficients of water diffusion along and across bilayers was studied.     

Water state and diffusion through lipid bilayers: Effect of hydration degree

The dependences of adsorbed water state (obtained from the variations in ¹H NMR spectra with the angle between the bilayer normal and magnetic field direction) and water diffusion along the bilayer normal (measured using pulsed field gradient ¹H NMR) on hydration degree have been studied in macroscopically oriented bilayers of dioleoylphosphatidylcholine. The angle dependences of the shape of NMR spectrum are qualitatively different only for water concentrations higher and lower than that achieved by hydration from saturated vapors (χ_eq, about 23%). At concentrations lower than χ_eq, all water in the sample either makes the hydration shells of the lipid polar heads or is in fast exchange with the shell water, so the spin-echo signal from water is detected only within a narrow range of angles close to the magic angle, 54.7°. At concentration exceeding χ_eq, the spin-echo signal from water is retained at all orientations, suggesting that a portion of water between bilayers (quasi-free water) slowly exchanges with water bound to the polar heads. There is an inverse dependence of the coefficient of water self-diffusion through the bilayer system on the hydration degree, which is described in the Tanner model with account of water self-diffusion in the hydrophobic part of the bilayer. Bilayer permeability, distribution coefficient of molecules between aqueous and lipid phases, and water self-diffusion coefficient in the hydrophobic region of the bilayer are estimated.     

The size of the unstirred layer as a function of the solute diffusion coefficient.

By monitoring the concentration distribution of several solutes that are diffusing at the same time under given mixing conditions, it was established that the unstirred layer (USL) has no clearly defined boundary. For the cases of solute permeation and water movement across planar bilayer lipid membranes, respectively, experiments carried out with double-barreled microelectrodes have shown that the thickness of the USL depends on which species is diffusing. Small molecules with a larger diffusion coefficient encounter an apparently thicker USL than larger molecules with a smaller diffusion coefficient. The ratio of the USL thicknesses of two different substances is equal to the third root of the ratio of the respective diffusion coefficients. This experimental finding is in good agreement with theoretical predictions from the theory of physicochemical hydrodynamics.     

Flicker spectroscopy of thermal lipid bilayer domain boundary fluctuations

This contribution describes measurements of lipid bilayer domain line tension based on two-dimensional thermal undulations of membranes with liquid ordered/liquid disordered phase coexistence and near-critical composition at room temperature. Lateral inhomogeneity of lipid and protein composition is currently a subject of avid research aimed at determining both fundamental properties and biological relevance of membrane domains. Line tension at fluid lipid bilayer membrane domain boundaries controls the kinetics of domain growth and therefore regulates the size of compositional heterogeneities. High line tension promotes membrane domain budding and fission. Line tension could therefore be an important control parameter regulating functional aspects of biological membranes. Here the established method of fluid domain flicker spectroscopy is applied to examine thermal domain wall fluctuations of phase-separated bilayer membranes. We find a Gaussian probability distribution for the first few excited mode amplitudes, which permits an analysis by means of appropriately specialized capillary wave theory. Time autocorrelation functions are found to decay exponentially, and relaxation times are fitted by means of a hydrodynamic theory relating line tensions and excited mode relaxation kinetics. Line tensions below 1 pN are obtained, with these two approaches yielding similar results. We examine experimental artifacts that perturb the Fourier spectrum of domain traces and discuss ways to identify the number of modes that yield reliable line tension information.     

Spatial Uncertainty Modeling of Fuzzy Information in Images for Pattern Classification

The modeling of the spatial distribution of image properties is important for many pattern recognition problems in science and engineering. Mathematical methods are needed to quantify the variability of this spatial distribution based on which a decision of classification can be made in an optimal sense. However, image properties are often subject to uncertainty due to both incomplete and imprecise information. This paper presents an integrated approach for estimating the spatial uncertainty of vagueness in images using the theory of geostatistics and the calculus of probability measures of fuzzy events. Such a model for the quantification of spatial uncertainty is utilized as a new image feature extraction method, based on which classifiers can be trained to perform the task of pattern recognition. Applications of the proposed algorithm to the classification of various types of image data suggest the usefulness of the proposed uncertainty modeling technique for texture feature extraction.     

The influence of weak electromagnetic fields on the stability of a computer monitor image: Possible consequences for an operator

The influence of instability of an image presented by means of a monitor on the efficiency of reading and information retrieval was studied. Jitter was caused by the weak external magnetic field. Additionally, the influence of the image quality on the memory processes, spatial attention, and automatic processing of verbal information assessed by means of tests performed by the subjects after 1.5 h of work with an unstable image was studied. A significant deterioration in information retrieval under image instability conditions was shown. Work at the subthreshold level of image jitter is accompanied by a decelerated heart rate. No effect of work with an unstable image on long-term memory tests, spatial attention, and Strup’s test was found.     

Effect of cholesterol on the structure and dynamic properties of unsaturated phospholipid bilayers

Molecular dynamics (MD) computer simulations of five different hydrated unsaturated phosphatidylcholine lipid bilayers built up by 18:0/18:1(n-9)cis PC, 18:0/18:2(n-6)cis PC, 18:0/18:3(n-3)cis PC, 18:0/20:4(n-6)cis PC, and 18:0/22:6(n-3)cis PC molecules with 40 mol% cholesterol, and the same five pure phosphatidylcholine bilayers have been performed at 303 K. The simulation box of a lipid bilayer contained 96 phosphatidylcholines, 64 cholesterols, and 3840 water molecules (48 phosphatidylcholine molecules and 32 cholesterols per layer and 24 water molecules per phospholipid or cholesterol in each case). The lateral self-diffusion coefficients of the lipids in these systems and mass density profiles with respect to the bilayer normal have been analyzed. It has been found that the lateral diffusion coefficients of phosphatidylcholine molecules increase with increasing number of double bonds in one of the lipid chains, both in pure bilayers and in bilayers with cholesterol. It has been found as well that the lateral diffusion coefficient of phosphatidylcholine molecules of a lipid bilayer with 40 mol% cholesterol is smaller than that for the corresponding pure phosphatidylcholine bilayer.     

Cell-specific chemotyping and multivariate imaging by combined FT-IR microspectroscopy and orthogonal projections to latent structures (OPLS) analysis reveals the chemical landscape of secondary xylem

Fourier‐transform infrared (FT‐IR) spectroscopy combined with microscopy enables chemical information to be acquired from native plant cell walls with high spatial resolution. Combined with a 64 × 64 focal plane array (FPA) detector, 4096 spectra can be simultaneously obtained from a 0.3 × 0.3 mm image; each spectrum represents a compositional and structural ‘fingerprint’ of all cell wall components. For optimal use and analysis of such a large amount of information, multivariate approaches are preferred. Here, FT‐IR microspectroscopy with FPA detection is combined with orthogonal projections to latent structures discriminant analysis (OPLS‐DA). This allows for: (i) the extraction of spectra from single cell types, (ii) identification and characterization of different chemotypes using the full spectral information, and (iii) further visualization of the pattern of identified chemotypes by multivariate imaging. As proof of concept, the chemotypes of Populus tremula xylem cell types are described. The approach revealed unknown features about chemical plasticity and patterns of lignin composition in wood fibers that would have remained hidden in the dataset with traditional data analysis. The applicability of the method to Arabidopsis xylem and its usefulness in mutant chemotyping is also demonstrated. The methodological approach is not limited to xylem tissues but can be applied to any plant organ/tissue also using other techniques such as Raman and UV microspectroscopy.     

Electrochemical measurement of lateral diffusion coefficients of ubiquinones and plastoquinones of various isoprenoid chain lengths incorporated in model bilayers.

The long-range diffusion coefficients of isoprenoid quinones in a model of lipid bilayer were determined by a method avoiding fluorescent probe labeling of the molecules. The quinone electron carriers were incorporated in supported dimyristoylphosphatidylcholine layers at physiological molar fractions (<3 mol%). The elaborate bilayer template contained a built-in gold electrode at which the redox molecules solubilized in the bilayer were reduced or oxidized. The lateral diffusion coefficient of a natural quinone like UQ10 or PQ9 was 2.0 +/- 0.4 x 10(-8) cm2 s(-1) at 30 degrees C, two to three times smaller than the diffusion coefficient of a lipid analog in the same artificial bilayer. The lateral mobilities of the oxidized or reduced forms could be determined separately and were found to be identical in the 4-13 pH range. For a series of isoprenoid quinones, UQ2 or PQ2 to UQ10, the diffusion coefficient exhibited a marked dependence on the length of the isoprenoid chain. The data fit very well the quantitative behavior predicted by a continuum fluid model in which the isoprenoid chains are taken as rigid particles moving in the less viscous part of the bilayer and rubbing against the more viscous layers of lipid heads. The present study supports the concept of a homogeneous pool of quinone located in the less viscous region of the bilayer.     

Mean-field calculations of chain packing and conformational statistics in lipid bilayers: comparison with experiments and molecular dynamics studies.

A molecular, mean-field theory of chain packing statistics in aggregates of amphiphilic molecules is applied to calculate the conformational properties of the lipid chains comprising the hydrophobic cores of dipalmitoyl-phosphatidylcholine (DPPC), dioleoyl-phosphatidylcholine (DOPC), and palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayers in their fluid state. The central quantity in this theory, the probability distribution of chain conformations, is evaluated by minimizing the free energy of the bilayer assuming only that the segment density within the hydrophobic region is uniform (liquidlike). Using this distribution we calculate chain conformational properties such as bond orientational order parameters and spatial distributions of the various chain segments. The lipid chains, both the saturated palmitoyl (-(CH2)14-CH3) and the unsaturated oleoyl (-(CH2)7-CH = CH-(CH2)7-CH3) chains are modeled using rotational isomeric state schemes. All possible chain conformations are enumerated and their statistical weights are determined by the self-consistency equations expressing the condition of uniform density. The hydrophobic core of the DPPC bilayer is treated as composed of single (palmitoyl) chain amphiphiles, i.e., the interactions between chains originating from the same lipid headgroup are assumed to be the same as those between chains belonging to different molecules. Similarly, the DOPC system is treated as a bilayer of oleoyl chains. The POPC bilayer is modeled as an equimolar mixture of palmitoyl and oleoyl chains. Bond orientational order parameter profiles, and segment spatial distributions are calculated for the three systems above, for several values of the bilayer thickness (or, equivalently, average area/headgroup) chosen, where possible, so as to allow for comparisons with available experimental data and/or molecular dynamics simulations. In most cases the agreement between the mean-field calculations, which are relatively easy to perform, and the experimental and simulation data is very good, supporting their use as an efficient tool for analyzing a variety of systems subject to varying conditions (e.g., bilayers of different compositions or thicknesses at different temperatures).     

Monte carlo simulation of the solvent structure in crystals of a hydrated cyclic peptide

The Monte Carlo simulation of the structure of the 16 ordered and disordered waters in the unit cell of crystals of the cyclic peptide cyclo(-L -Ala-L -Pro-D -Phe)₂ is reported. The water structure has been characterized in terms of the statistically averaged positions of the individual molecules, their root-mean-square movements about these positions, the probability of finding a water in a given spatial position in the crystal (probability maps), and examination of individual configurations of the system. In this way a picture is obtained of the water structure, including water orientations (hydrogen positions), the hydrogen-bonding network, and fluctuations in these structural features, to a degree hitherto unavailable either from experimental or theoretical studies. In addition, the variation in water structure in various peptide environments was studied and correlated with the energetics of the individual water molecules. Variations in the crystalline environment of different water molecules lead to energy differences of as much as 4–5 kcal/mol in their average energies. Similarly, differences are observed in the water–peptide and water–water components of the energy. Two different water potentials were tested. The results were compared with experimental data in terms of mean positions, root-mean-square movements, and the Fourier transform of the simulated water structure. The agreement factor (R factor) calculated from the theoretical water probability distribution was 18.8% compared to the x-ray value of 14.5%, and the value of 28% when the water is omitted.     

Temperature dependence of water self-diffusion through lipid bilayers assessed by NMR

The temperature dependence of the coefficient of water self-diffusion across plane-parallel multib-ilayers of dioleoylphosphatidylcholine oriented on a glass support was studied in the 20–60°C range by pulsed field gradient NMR. The coefficient for transbilayer diffusion of water proved almost four orders of magnitude smaller than for bulk water, and 10 times smaller than that for lateral diffusion of lipid under the same conditions. The temperature dependence obeyed the Arrhenius law with apparent activation energy of 41 kJ/mol, much higher than that for bulk water (18 kJ/mol). The experimental data were analyzed using the “dissolution-diffusion” model, by simulating water passage through membrane channels, and by examining water exchange in states with different modes of translational mobility, including pore channels and bilayer defects. Each approach could take into account the role of bilayer permeability and assess the apparent activation energy for water diffusion in the hydrophobic part of the bilayer, which proved close to the value for bulk water. Estimates were obtained for water diffusion coefficients in the system, coefficients of bilayer permeability for water, and the influence of bilayer defects on the lateral and transverse diffusion coefficients.     

Non-electrolyte permeability as a tool for studying membrane fluidity

1. The reflection coefficient for the permeation of thiourea through bilayers of phosphatidylcholine is a function of the fatty-acid composition of the lipid molecules. By means of these reflection coefficients an index for membrane fluidity has been given to each of those lipids, relative to that of egg phosphatidylcholine. 2. The maximum number of water molecules that can copermeate with each molecule of solute by means of solute-solvent interaction is a function of the packing of the lipid molecules in the bilayer. This parameter has been used in this paper for characterizing the fluidity of cholesterol-containing membranes and for membranes with their lipids in the gel state.     

Gap junction structures. VIII. Membrane cross-sections.

Profiles of negatively stained gap junctions have been measured by grid sectioning. After normal levels of electron irradiation, the membrane thickness shrinks to about half that of unirradiated controls, but no shrinkage occurs in the hexagonal lattice plane. Even under low irradiation conditions, there is significant thinning of the membranes. Edge views, in which rows of connexons are aligned parallel to the beam, were obtained from grid sections, folds in normal negatively stained specimens, and sections of a positively stained specimen. Averaging these micrographs with the translational and mirror symmetry of the projected lattice image displays conserved and variable features in the stain distribution of different specimens. Variations in the relative amount of negative stain in the gap at the surfaces and in the channel are uncorrelated with the irradiation but appear to depend on the local staining conditions and the integrity of the connexons. The dimensions measured from previously unirradiated grid sections, folds, and positively stained sections are in accord with x-ray diffraction measurements. Radiation-induced shrinkage can be accounted for by mass loss principally from the membrane bilayer. Disordering of the surface structure appears to be correlated with the radiation sensitivity of the bilayer; in contrast, the gap structure is well preserved under a variety of conditions.