Inferring diffusion in single live cells at the single-molecule level

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single-molecule and single-cell level can add significant insight into understanding molecular architectures of diffus- ing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell mem- brane under relatively physiological conditions compared with competing single-molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the mol- ecular level owing to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles; however, this generally requires more data points than is typical for single FP tracks owing to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes to dis-criminate multiple complex modes probabilistically. It is a computational approach that biologists can use to understand single-molecule features in live cells.

The Tarim picrite-basalt-rhyolite suite, a Permian flood basalt from Northwest China with contrasting rhyolites produced by fractional crystallization and anatexis

We report major and trace element composition, Sr–Nd isotopic and seismological data for a picrite–basalt–rhyolite suite from the northern Tarim uplift (NTU), northwest China. The samples were recovered from 13 boreholes at depths between 5,166 and 6,333 m. The picritic samples have high MgO (14.5–16.8 wt%, volatiles included) enriched in incompatible element and have high 87Sr/86Sr and low 143Nd/144Nd isotopic ratios (εNd (t) = −5.3; Sri = 0.707), resembling the Karoo high-Ti picrites. All the basaltic samples are enriched in TiO2 (2.1–3.2 wt%, volatiles free), have high FeOt abundances (11.27–15.75 wt%, volatiles free), are enriched in incompatible elements and have high Sr and low Nd isotopic ratios (Sri = 0.7049–0.7065; εNd (t) = −4.1 to −0.4). High Nb/La ratios (0.91–1.34) of basalts attest that they are mantle-derived magma with negligible crustal contamination. The rhyolite samples can be subdivided into two coeval groups with overlapping U–Pb zircon ages between 291 ± 4 and 272 ± 2 Ma. Group 1 rhyolites are enriched in Nb and Ta, have similar Nb/La, Nb/U, and Sr–Nd isotopic compositions to the associated basalts, implying that they are formed by fractional crystallization of the basalts. Group 2 rhyolites are depleted in Nb and Ta, have low Nb/La ratios, and have very high Sr and low Nd isotopic ratios, implying that crustal materials have been extensively, if not exclusively, involved in their source. The picrite–basalt–rhyolite suite from the NTU, together with Permian volcanic rocks from elsewhere Tarim basin, constitute a Large Igneous Province (LIP) that is characterized by large areal extent, rapid eruption, OIB-type chemical composition, and eruption of high temperature picritic magma. The Early Permian magmatism, which covered an area >300,000 km2, is therefore named the Tarim Flood Basalt.

Characterizing transport through a crowded environment with different obstacle sizes

Transport through crowded environments is often classified as anomalous, rather than classical, Fickian diffusion. Several studies have sought to describe such transport processes using either a continuous time random walk or fractional order differential equation. For both these models the transport is characterized by a parameter α, where α = 1 is associated with Fickian diffusion and α < 1 is associated with anomalous subdiffusion. Here, we simulate a single agent migrating through a crowded environment populated by impenetrable, immobile obstacles and estimate α from mean squared displacement data. We also simulate the transport of a population of such agents through a similar crowded environment and match averaged agent density profiles to the solution of a related fractional order differential equation to obtain an alternative estimate of α. We examine the relationship between our estimate of α and the properties of the obstacle field for both a single agent and a population of agents; we show that in both cases, α decreases as the obstacle density increases, and that the rate of decrease is greater for smaller obstacles. Our work suggests that it may be inappropriate to model transport through a crowded environment using widely reported approaches including power laws to describe the mean squared displacement and fractional order differential equations to represent the averaged agent density profiles.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Characterisation of the micro-architecture of direct writing melt electrospun tissue engineering scaffolds using diffusion tensor and computed tomography microimaging

This article describes the first steps toward comprehensive characterization of molecular transport within scaffolds for tissue engineering. The scaffolds were fabricated using a novel melt electrospinning technique capable of constructing 3D lattices of layered polymer fibers with well - defined internal microarchitectures. The general morphology and structure order was then determined using T 2 - weighted magnetic resonance imaging and X - ray microcomputed tomography. Diffusion tensor microimaging was used to measure the time - dependent diffusivity and diffusion anisotropy within the scaffolds. The measured diffusion tensors were anisotropic and consistent with the cross - hatched geometry of the scaffolds: diffusion was least restricted in the direction perpendicular to the fiber layers. The results demonstrate that the cross - hatched scaffold structure preferentially promotes molecular transport vertically through the layers ( z - axis), with more restricted diffusion in the directions of the fiber layers ( x – y plane). Diffusivity in the x – y plane was observed to be invariant to the fiber thickness. The characteristic pore size of the fiber scaffolds can be probed by sampling the diffusion tensor at multiple diffusion times. Prospective application of diffusion tensor imaging for the real - time monitoring of tissue maturation and nutrient transport pathways within tissue engineering scaffolds is discussed.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Ion-assisted precursor dissociation and surface diffusion : enabling rapid, low-temperature growth of carbon nanofibers

Growth kinetics of carbon nanofibers in a hydrocarbon plasma is studied. In addition to gas-phase and surface processes common to chemical vapor deposition, the model includes (unique to plasma-exposed catalyst surfaces) ion-induced dissociation of hydrocarbons, interaction of adsorbed species with incoming hydrogen atoms, and dissociation of hydrocarbon ions. It is shown that at low, nanodevice-friendly process temperatures the nanofibers grow via surface diffusion of carbon adatoms produced on the catalyst particle via ion-induced dissociation of a hydrocarbon precursor. These results explain a lower activation energy of nanofiber growth in a plasma and can be used for the synthesis of other nanoassemblies. © 2007 American Institute of Physics.

Low-pressure diffusion equilibrium of electronegative complex plasmas

A model for electronegative plasmas containing charged dust or colloidal grains was used. Numerical solutions based on the model demonstrate how a low-pressure diffusion equilibrium of the complex electronegative plasma system is dynamically sustained through plasma particle sources.

Comparison of block and event-related experimental designs in diffusion-weighted functional MRI

PURPOSE To compare diffusion-weighted functional magnetic resonance imaging (DfMRI), a novel alternative to the blood oxygenation level-dependent (BOLD) contrast, in a functional MRI experiment. MATERIALS AND METHODS Nine participants viewed contrast reversing (7.5 Hz) black-and-white checkerboard stimuli using block and event-related paradigms. DfMRI (b = 1800 mm/s2 ) and BOLD sequences were acquired. Four parameters describing the observed signal were assessed: percent signal change, spatial extent of the activation, the Euclidean distance between peak voxel locations, and the time-to-peak of the best fitting impulse response for different paradigms and sequences. RESULTS The BOLD conditions showed a higher percent signal change relative to DfMRI; however, event-related DfMRI showed the strongest group activation (t = 21.23, P < 0.0005). Activation was more diffuse and spatially closer to the BOLD response for DfMRI when the block design was used. DfMRIevent showed the shortest TTP (4.4 +/- 0.88 sec). CONCLUSION The hemodynamic contribution to DfMRI may increase with the use of block designs.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Enterprise resource planning or enterprise resource plotting? Technological, organisational and inter-organisational aspects of enterprise resource planning package adoption and diffusion

Those in organisations tend to adopt new technologies as a way to improve their functions, reduce cost and attain best practices. Thus, technology promoters (or vendors) work along those lines in order to convince adopters to invest in those technologies and develop their own organisations profit in return. The possible resultant ‘conflicts of interest’ makes the study of reasons behind IT diffusion and adoption an interesting subject. In this paper we look at IT diffusion and adoption in terms of technology (system features), organisational aspects (firm level characteristics) and inter-organisational aspects (market dynamics) in order to see who might be the real beneficiaries of technology adoption. We use ERP packages as an example of an innovation that has been widely diffused and adopted for the last 10 years. We believe that our findings can be useful to those adopting ERP packages as it gives them a wider view of the situation.