An enhanced sensitivity methyl <Superscript>1</Superscript>H triple-quantum pulse scheme for measuring diffusion constants of macromolecules

We present a pulse scheme that exploits methyl ¹H triple-quantum (TQ) coherences for the measurement of diffusion rates of slowly diffusing molecules in solution. It is based on the well-known stimulated echo experiment, with encoding and decoding of TQ coherences. The size of quantifiable diffusion coefficients is thus lowered by an order of magnitude with respect to single-quantum (SQ) approaches. Notably, the sensitivity of the scheme is high, approximately ¾ that of the corresponding single quantum experiment, neglecting relaxation losses, and on the order of a factor of 4 more sensitive than a previously published sequence for AX₃ spin systems (Zheng et al. in JMR 198:271–274, 2009) for molecules that are only ¹³C labeled at the methyl carbon position. Diffusion coefficients measured from TQ- and SQ-based experiments recorded on a range of protein samples are in excellent agreement. We present an application of this technique to the study of phase-separated proteins where protein concentrations in the condensed phase can exceed 400 mg/mL, diffusion coefficients can be as low as ~10^?9 cm²s^?1 and traditional SQ experiments fail.     

Rapid characterization of protein molecular weights and hydrodynamic structures by quasielastic laser-light scattering

Two methods for the characterization of protein molecular weights from their diffusion coefficients are discussed. These measurements can be made quickly and reliably at low concentrations using quasielastic light-scattering techniques. First, an empirical calibration of the diffusion coefficient at infinite dilution of denatured random coils against molecular weight is reported. The second method combines the measurement of D₀ with the intrinsic viscosity [η]. This D₀–[η] relationship proves to be very insensitive to polymers structure or solvent type. The data indicate that the ratio of the hydrodynamic radius measured by viscosity to the hydrodynamic radius measured by diffusion is about 15% smaller than that predicted by theoretical models. The nature of the molecular-weight average obtained for polydisperse systems is defined for a Schulz distribution. These hydrodynamic methods have also been used to demonstrate the presence of chain branching in the glycoprotein ovomucoid. In addition, a method is proposed by which the effective segment length and an excluded volume parameter for random coils may be evaluated for diffusion measurements.     

Differential sensitivities of water diffusion in maize root cortex and stele to HgCl<Subscript>2</Subscript>-induced blockade of aquaporins

Spin-echo NMR comparative study of water diffusion in the cortex and stele of maize (Zea mays L.) roots was made with the aim to determine predominant pathways of radial water movement in the root. The root parts examined differed in terms of water diffusion coefficients and sensitivity to HgCl₂, the aquaporin blocker. These differences are discussed from the viewpoint of unequal contributions of separate transport pathways (apoplastic, symplastic, and transmembrane) to the overall water flow. Characteristics of water diffusion in roots with the endodermis damaged suggest an inconsiderable contribution of the endodermis into resistance to water movement.     

Hyaluronate diffusion in semidilute solutions

Analysis of the mutual diffusion coefficient of hyaluronate reveals that it rapidly increases with increasing concentration or decreasing ionic strength. The mutual diffusion coefficients analyzed by boundary relaxation in the analytical ultracentrifuge by either Raleigh interference optics or absorption optics (through the use of fluorescein-labeled hyaluronate) yielded similar values. The theoretical treatment of the mutual diffusion coefficient has been analyzed in terms of experimentally measured intradiffusion coefficients and thermodynamic virial coefficients. Only approximate agreement between theory and experiment was found. The concept of formation of transient statistical network structures in semidilute solutions of hyaluronate was applied to evaluate a critical concentration at which network formation occurs. This has been discussed in relation to the marked decrease in the intradiffusion coefficient of hyaluronate with concentration. The formation of network structures in hyaluronate was found not to preclude the hyaluronate undergoing extremely rapid rates of mutual diffusion (with diffusion coefficients ～30 × 10^?11 m² s¹) under conditions of relatively large initial chemical potential gradients. Measurements of the unidirectional flux of hyaluronate for nonzero gradients demonstrated their marked sensitivity to the magnitude of the concentration difference across the boundary. An experimental feature of the unidrectional diffusion coefficients of hyaluronate is that they may be analyzed purely in terms of mutual and intradiffusion processes. The backflux diffusion coefficient (describing the flux against the imposed concentration gradient) appeared identical with the intradiffusion coefficient. The analysis of the various sources of errors made in this study suggests that the magnitude of the diffusion coefficients measured may be regarded only as approximate.     

In situ reverse transcription-polymerase chain reaction. Applications for light and electron microscopy

Since its discovery in 1986 by Mullis, the polymerase chain reaction (PCR) has been extensively developed by morphologists in order to overcome the main limitation of in situ hybridization, the lack of sensitivity. In situ PCR combines the extreme sensitivity of PCR with the cell-localizing ability of in situ hybridization. The amplification of DNA (PCR) or a cDNA (RT-PCR) in cell or tissue sections has been developed at light and electron microscopic levels. A successful PCR experiment requires the careful optimization of several parameters depending on the tissue (or of cell types), and a compromise must be found between the fixation time, pretreatments and a good preservation of the morphology. Other crucial factors (primer design, concentration in MgCl₂, annealing and elongation temperatures during the amplification steps) and their influence on the specificity and sensitivity of in situ PCR or RT-PCR are discussed. The necessity to run appropriate controls, especially to assess the lack of diffusion of the amplified products, is stressed. Current applications and future trends are also presented.     

Theoretical Considerations when Estimating the Mesophyll Conductance to CO(2) Flux by Analysis of the Response of Photosynthesis to CO(2)

The conductance for CO₂ diffusion in the mesophyll of leaves can limit photosynthesis. We have studied two methods for determining the mesophyll conductance to CO₂ diffusion in leaves. We generated an ideal set of photosynthesis rates over a range of partial pressures of CO₂ in the stroma and studied the effect of altering the mesophyll diffusion conductance on the measured response of photosynthesis to intercellular CO₂ partial pressure. We used the ideal data set to test the sensitivity of the two methods to small errors in the parameters used to determine mesophyll conductance. The two methods were also used to determine mesophyll conductance of several leaves using measured rather than ideal data sets. It is concluded that both methods can be used to determine mesophyll conductance and each method has particular strengths. We believe both methods will prove useful in the future.     

Use of holographic laser interferometry to study the diffusion of polymers in gels

The aim of this study was to demonstrate the potential for holographic interferometry to be used for diffusion studies of large molecules in gels. The diffusion and partitioning of BSA (67,000 g/mol) and pullulans (5,900-112,000 g/mol) in agarose gel were investigated. The gel diffusion coefficients obtained for BSA were higher when distilled water was used as a solvent compared to those obtained with 0.1 M NaCl as the solvent. Furthermore, the gel diffusion coefficient increased with increasing BSA concentration. The same trend was found for liquid BSA diffusion coefficients obtained by DLS. BSA partition coefficients obtained at different agarose gel concentrations (2-6%, w/w) decreased slightly with increasing gel concentration. However, all BSA gel diffusion coefficients measured were significantly lower than those in pure solvent and they decreased with increasing agarose concentration. The gel diffusion coefficients obtained for pullulans decreased with increasing pullulan molecular weight. The same effect from increased molecular weight was seen in the liquid diffusion coefficients measured by DLS. The pullulan partition coefficients obtained decreased with increasing molecular weight. However, pullulans with a larger Stokes' radius than BSA had partition coefficients that were higher or approximately the same as BSA. This implied that the pullulan molecules were more flexible than the BSA molecules. The results obtained for BSA in this study agreed well with other experimental studies. In addition, the magnitude of the relative standard deviation was acceptable and in the same range as for many other methods. The results thereby obtained showed that holographic interferometry is a suitable method for studying diffusion of macromolecules in gels.     

Controlled in meso phase crystallization--a method for the structural investigation of membrane proteins

We investigated in meso crystallization of membrane proteins to develop a fast screening technology which combines features of the well established classical vapor diffusion experiment with the batch meso phase crystallization, but without premixing of protein and monoolein. It inherits the advantages of both methods, namely (i) the stabilization of membrane proteins in the meso phase, (ii) the control of hydration level and additive concentration by vapor diffusion. The new technology (iii) significantly simplifies in meso crystallization experiments and allows the use of standard liquid handling robots suitable for 96 well formats. CIMP crystallization furthermore allows (iv) direct monitoring of phase transformation and crystallization events. Bacteriorhodopsin (BR) crystals of high quality and diffraction up to 1.3 Å resolution have been obtained in this approach. CIMP and the developed consumables and protocols have been successfully applied to obtain crystals of sensory rhodopsin II (SRII) from Halobacterium salinarum for the first time.     

A novel correlation for protein diffusion coefficients based on molecular weight and radius of gyration

A new correlation is proposed for the prediction of protein diffusion coefficients in free solution. Molecular weight and radius of gyration of proteins are employed as correlation parameters in this method. Both parameters can be easily found in the literature. The correlation works well for diverse proteins with different shapes and extensive molecular weight. Furthermore, this method does not require a preassumption regarding the protein shape while it offers a rapid and convenient calculation with a high accuracy. Also, the proposed correlation can elucidate the estimation deviation of previous correlation methods in the literature.     

Studies on Transformations of Hemophilus influenzae : II. The molecular weight of transforming DNA by sedimentation and diffusion measurements

The sedimentation and diffusion coefficients have been determined for Hemophilus influenzae transforming activity and DNA using P³²-labeled DNA. The methods employed the Spinco fixed boundary separation cell for measurements of the sedimentation coefficient and the Northrop-Anson diffusion cell to determine the diffusion coefficient. There was a very close correlation between the amount of DNA and transforming activity sedimented or diffused. The sedimentation coefficient (s_20°), for both biological activity and DNA was 27 and the diffusion coefficient (D_20°) 1 x 10^-8 cm²/sec. The molecular weight calculated from these coefficients gave a value of 16 million. There was no difference in the sedimentation coefficients for the two unlinked markers, streptomycin and erythromycin resistance, and the diffusion coefficients for single markers or the linked markers, streptomycin and cathomycin, were the same.     

Measuring principles of frictional coefficients in cartilaginous tissues and its substitutes

The frictional properties of cartilaginous tissues, such as the hydraulic permeability, the electro-osmotic permeability, the diffusion coefficients of various ions and solutes, and the electrical conductance, are vital data to characterise the extracellular environment in which chondrocytes reside. This paper analyses one-dimensional measurement principles of these coefficients. Particular attention is given to the deformation dependence of them and the highly deformable nature of the tissues. A suggested strategy is the combination of a diffusion experiment using radiotracer methods, an electro-osmotic flow experiment and an electro-osmotic pressure experiment at low electric current.     

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer’s disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.     

Adsorption and diffusion of CO2 and CH4 in covalent organic frameworks: an MC/MD simulation study

Covalent organic frameworks (COFs) are a promising gas separation material which have been developed recently. In this work, we have used grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations to investigate the adsorption and diffusion properties of CO₂ and CH₄ in five recent synthesised COF materials. We have also considered the properties of amino-modified COFs by adding –NH₂ group to the five COFs. The adsorption isotherm, adsorption/diffusion selectivity, self/transport diffusion coefficients have been examined and discussed. All of the five COFs exhibit promising adsorption selectivity which is higher than common nanoporous materials. An S-shaped adsorption isotherm can be found for CO₂ instead of CH₄ adsorption. The introduction of –NH₂ group is effective at low pressure region (<200?kPa). The diffusion coefficients are similar for TS-COFs but increase with the pore size for PI-COFs, and the diffusion coefficients seem less dependent on the –NH₂ groups.     

Tracking the Mammary Architectural Features and Detecting Breast Cancer with Magnetic Resonance Diffusion Tensor Imaging

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.     

Analysis of Microscopic Parameters of Single-Particle Trajectories in Neurons

We performed a comparative study of the statistical uncertainties that arise when calculating the velocity and diffusion coefficients from single-particle trajectories. We show that a method where particle mean displacement is used to calculate velocity and mean square fluctuation is used to calculate diffusion coefficient offers greater accuracy than analysis of time-dependent mean square displacement. Our assessment of the performance of the two analysis strategies is conducted in two ways. First, we apply each of the methods to simulated trajectories where each parameter term is known. Second, we analyze the motion of previously uncharacterized EphB2 receptors in the membrane of hippocampal neurons. We find that EphB2 receptors display different types of motion mode and transition between these modes. We present our data as a distribution of microscopic diffusion coefficients for each particle trajectory, which we refer to as partial distributions. Partial distributions are summed to form a cumulative distribution of diffusion coefficients for EphB2 receptors in hippocampal neurons. The structure and interpretation of the EphB2 cumulative distribution are discussed.     

Polymers of intrinsic microporosity for gas permeation: a molecular simulation study

We report a molecular simulation study for gas permeation in two membranes constructed from polymers of intrinsic microporosity (PIM-1 and PIM-7). With rigid ladder polymer chains, the membranes posses approximately 47.7 and 46.6% fractional free volumes (FFVs) in PIM-1 and PIM-7, respectively. The voids in the membranes have a diameter up to 9 Å and are largely interconnected. The sorption and diffusion of four gases (H₂, O₂, CH₄ and CO₂) were calculated by Monte Carlo and molecular dynamics simulations. The solubility coefficients increase in the order of H₂ < O₂ < CH₄ < CO₂, while the diffusion coefficients increase in the following order: CH₄ < CO₂ < O₂ < H₂. The simulation results agree well with experimental data, particularly for the solubility coefficients. The solubility and diffusion coefficients correlate well separately with the critical temperatures and effective diameters of gases. These molecular-based correlations can be used in the prediction for other gases. As attributed to the microporous structure, PIM-1 and PIM-7 outperform most glassy polymeric membranes in sorption and diffusion. PIM-1 has larger solubility and diffusion coefficients than PIM-7 because the cyano groups in PIM-1 lead to a stronger affinity and a larger FFV. The simulated solubility, diffusivity and permeation selectivities of CO₂/H₂, CO₂/O₂ and CO₂/CH₄ are consistent with experimental data. The quantitative microscopic understanding of gas permeation in the PIM membranes is useful for the new development of high-performance membranes.     

Fluorescence correlation spectroscopy. II. An experimental realization

This paper describes the first experimental application of fluorescence correlation spectroscopy, a new method for determining chemical kinetic constants and diffusion coefficients. These quantities are measured by observing the time behaviour of the tiny concentration fluctuations which occur spontaneously in the reaction system even when it is in equilibrium. The equilibrium of the system is not disturbed during the experiment. The diffusion coefficients and chemical rate constants which determine the average time behaviour of these spontaneous fluctuations are the same as those sought by more conventional methods including temperature-jump or other perturbation techniques. The experiment consists essentially in measuring the variation with time of the number of molecules of specified reactants in a defined open volume of solution. The concentration of a reactant is measured by its fluorescence; the sample volume is defined by a focused laser beam which excites the fluorescence. The fluorescent emission fluctuates in proportion with the changes in the number of fluorescent molecules as they diffuse into and out of the sample volume and as they are created or eliminated by the chemical reactions. The number of these reactant molecules must be small to permit detection of the concentration fluctuations. Hence the sample volume is small (10^?8 ml) and the concentration of the solutes is low (～ 10^?9 M). We have applied this technique to the study of two prototype systems: the simple example of pure diffusion of a single fluorescent species, rhodamine 6G, and the more interesting but more challenging example of the reaction of macromolecular DNA with the drug ethidium bromide to form a fluorescent complex. The increase of the fluorescence of the ethidium bromide upon formation of the complex permits the observation of the decay of concentration fluctuations via the chemical reaction and consequently the determination of chemical rate constants.     

Application of the Poisson-Nernst-Planck theory with space-dependent diffusion coefficients to KcsA

The Poisson-Nernst-Planck electrodiffusion theory serves to compute charge fluxes and is here applied to the ion current through a protein channel. KcsA was selected as an example because of the abundance of experimental and theoretical data. The potassium channels MthK and KvAP were used as templates to define two open channel models for KcsA. Channel boundary surfaces and protein charge distributions were defined according to atomic radii and partial atomic charges. To establish the sensitivity of the results to these parameters, two different sets were used. Assigning the potassium diffusion coefficients equal to the value for free-diffusion in water (1.96 x 10(-9) m(2)/s), the computed currents overestimated the experimental data. Ion distributions inside the channel suggest that the overestimate is not due to an excess of charge shielding. A good agreement with the experimental data was achieved by reducing the potassium diffusion coefficient inside the channel to 1.96 x 10(-10) m(2)/s, a value of substantial motility but nonetheless in accord with the intuitive notion that the channel has a high affinity for the ions and therefore slows them down. These results are independent of the open channel model and the parameterization adopted for atomic radii and partial atomic charges. The method offers a reliable estimate of the channel current with low computational effort.     

Diffusion-controlled transport of methane from soil to atmosphere as mediated by rice plants

Methane emission from rice grown in flooded soil was measured in pot experiments using headspaces with different gas composition. The emission rates varied with the atmospheric composition. Based on the kinetic theory of gases the binary diffusion coefficients for methane in various gases were calculated. The ratios of the measured emissions under a certain atmosphere relative to that in air were similar to the ratios of the binary diffusion coefficients showing that plant-mediated CH₄ transport is driven by diffusion. Small deviations from the theoretical ratios of emissions support the hypothesis that mass flow of gas to the submerged parts of the rice plant may depress the upward diffusive CH₄ flux. The results in combination with data from the literature suggest that the rate limiting step in plant-mediated methane transport is diffusion of CH₄ across the root/shoot junction.