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PubMed2000

Diffusion of molecules in brain extracellular space: theory and experiment.

Volume transmission depends on the migration of informational substances through brain extracellular space (ECS) and almost always involves diffusion; basic concepts of diffusion are outlined from both the microscopic viewpoint based on random walks and the macroscopic viewpoint based on the solution of equations embodying Fick's Laws. In a complex medium like the brain, diffusing molecules are constrained by the local volume fraction of the ECS and tortuosity, a measure of the hindrance imposed by cellular obstacles. Molecules can also experience varying degrees of uptake or clearance. Bulk flow and the extracellular matrix may also play a role. Examples of recent work on diffusion of tetramethylammonium (molecular weight, 74) in brain slices, using iontophoretic application and ion-selective microelectrodes, are reviewed. In slices, the volume fraction is about 20% and tortuosity about 1.6, both similar to values found in the intact brain. Using integrative optical imaging, results obtained with dextrans and albumins up to a molecular weight of 70,000 are summarized, for such large molecules the tortuosity is about 2.3. Experiments using synthetic long-chain PHPMA polymers up to 1,000,000 molecular weight show that these molecules also diffuse in the ECS but with a tortuosity of about 1.6. Studies with osmotic challenge show that volume fraction and tortuosity do not vary together as expected when the size of the ECS changes; a model is presented that explains the osmotic-challenge on the basis of changes in cell shape. Finally, new analytical insights are provided into the complex movement of potassium in the brain.

Animals↗
PubMed1996

Perception of direction of visual motion. I. Influence of angular body acceleration and tilt.

We investigated, psychophysically, the influence of body rotation on visual motion direction thresholds for both upright sitting and tilted observers. Four angular accelerations (0, 20, 40 and 60 degrees/s2) were combined with 3 concurrent backward-tilt positions (0, 45 and 90 degrees). This led to combined stimulation of the semicircular canals and otoliths. Vestibular stimulation was combined with a visual motion stimulus. Random-dot kinematograms in which varying percentages of pixels coherently moving to the left were presented upon a background of otherwise randomly moving pixels (random walk). The smallest percentage of coherently moving pixels leading to a clear perception of motion direction represented as the perceptual threshold. Angular accelerations about the longitudinal body axis significantly increased motion-direction thresholds. Concurrent backward tilt did not influence thresholds. These results differ from those of studies in which translational linear acceleration was employed. Our results support the view that it is necessary to distinguish between linear acceleration caused by gravitational forces and that caused by additional linear accelerations about the x-, y-, and z-axes.

Acceleration↗
PubMed1997

Conformation of thermally denatured RNase T1 with intact disulfide bonds: a study by small-angle X-ray scattering.

Small-angle X-ray scattering of RNase T1 with intact disulfide bonds was measured at 20 degrees and 60 degrees C in order to get insight into the structural changes of the protein caused by thermal denaturation. The radius of gyration increases from R(G)= 1.43 nm to R(G) = 2.21 nm. The conformations of the molecules at 60 degrees C are similar to those of ring-shaped random walk chains. However, the molecules are more compact than one would expect under theta conditions due to attractive interactions between the chain segments. The volume needed for free rotation of the thermally unfolded protein molecules about any axis in solution is five times greater than in the native state whereas the hydrodynamic effective volume is increasing only two times.

Disulfides↗
PubMed2003

Controlled release with coating layer of permeable particles.

An enhanced method was proposed for controlled release of core material using a coating layer of fine permeable particles dispersed in an impermeable wax prepared by dry-based process. A mathematical model was constructed to describe in detail the core material release by diffusion through the connected permeable particles inside the coating layer. The effective diffusivity was simulated by a random walk method taking into account the structure of the coating layer. The released characteristics were measured for the urea core particle coated with the layer of the starch permeable particles dispersed in the paraffin wax. The calculated results were in a good quantitative agreement with experimental data in all range of coating conditions. As a result, the low release rate was proven to be obtained with thicker coating layer of lower volume fraction of permeable particles. Moreover, the application of permeable particles instead of soluble ones [J. Chem. Eng. Jpn. 35 (2002) 40] resulted in significant decrease in release rate.

Algorithms↗
PubMed2001

Analysis of field observations of tracer transport in a fractured till.

We analyze a set of observations from a recently published, field-scale tracer test in a fractured till. These observations demonstrate a dominant, underlying non-Fickian behavior, which cannot be quantified using traditional modeling approaches. We use a continuous time random walk (CTRW) approach which thoroughly accounts for the measurements, and which is based on a physical picture of contaminant motion that is consistent with the geometric and hydraulic characterization of the fractured formation. We also incorporate convolution techniques in the CTRW theory, to consider transport between different regions containing distinct heterogeneity patterns. These results enhance the possibility that limitations in predicting non-Fickian modes of contaminant migration can be overcome.

Chlorides↗
PubMed2001

Eulerian derivation of the fractional advection-dispersion equation.

A fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the second-order derivative is replaced with a fractional-order derivative. In contrast to the classical ADE, the fractional ADE has solutions that resemble the highly skewed and heavy-tailed breakthrough curves observed in field and laboratory studies. These solutions, known as alpha-stable distributions, are the result of a generalized central limit theorem which describes the behavior of sums of finite or infinite-variance random variables. We use this limit theorem in a model which sums the length of particle jumps during their random walk through a heterogeneous porous medium. If the length of solute particle jumps is not constrained to a representative elementary volume (REV), dispersive flux is proportional to a fractional derivative. The nature of fractional derivatives is readily visualized and their parameters are based on physical properties that are measurable. When a fractional Fick's law replaces the classical Fick's law in an Eulerian evaluation of solute transport in a porous medium, the result is a fractional ADE. Fractional ADEs are ergodic equations since they occur when a generalized central limit theorem is employed.

Computer Simulation↗
PubMed2001

Modelling chromosomal aberration induction by ionising radiation: the influence of interphase chromosome architecture.

Several advances have been achieved in the knowledge of nuclear architecture and functions during the last decade, thus allowing the identification of interphase chromosome territories and sub-chromosomal domains (e.g. arm and band domains). This is an important step in the study of radiation-induced chromosome aberrations; indeed, the coupling between track-structure simulations and reliable descriptions of the geometrical properties of the target is one of the main tasks in modelling aberration induction by radiation, since it allows one to clarify the role of the initial positioning of two DNA lesions in determining their interaction probability. In the present paper, the main recent findings on nuclear and chromosomal architecture are summarised. A few examples of models based on different descriptions of interphase chromosome organisation (random-walk models, domain models and static models) are presented, focussing on how the approach adopted in modelling the target nuclei and chromosomes can influence the simulation of chromosomal aberration yields. Each model is discussed by taking into account available experimental data on chromosome aberration induction and/or interphase chromatin organisation. Preliminary results from a mechanistic model based on a coupling between radiation track-structure features and explicitly-modelled, non-overlapping chromosome territories are presented.

Animals↗
PubMed1998

The relationship between biological activity and the electronic structure and transfer of the whole acidic PLA2 molecule in ab initio level.

The electronic structure of the whole molecule of acidic phospholipase A2 (PLA2) from the venom of Agkistrodon halys pallas (A. halys pallas) has been calculated using the extended negative factor counting (ENFC) method in which dimers were calculated at the ab initio level using a minimal basis set, with simulation of the aqueous environment. Hopping conductivities were determined by the use of random walk theory. The results show that the frontier orbitals are mainly localized to residues which are involved in the biological activity of acidic PLA2. The C-terminal region might play some important role in biological activity because of its active electrons. The aromatic patch on the surface of the enzyme, together with two neighbouring acidic residues, has very active electrons that may be responsible for the inhibition of platelet aggregation. Trp30, which is involved in the interfacial recognition region, may transfer its electrons to the aggregated substrate. It is also concluded that the conductivity of the protein is caused mainly by holes transported through the valence band rather than electrons transferred in the conductive band. The a.c. conductivity of acidic PLA2 confirms that proteins, if doped, are amorphous conductors. Moreover, the a.c. conductivities of acidic PLA2 are approximately one order of magnitude higher than those of some other proteins. This suggests that the toxicity of acidic PLA2 may be related to its high a.c. conductivity.

Agkistrodon↗
PubMed2003

Response kinetics of tethered bacteria to stepwise changes in nutrient concentration.

We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial response and the adaptation to the sustained concentration of the chemical. This was carried out by tethering motile cells by their flagella to glass slides and following the rotational behaviour of their cell bodies in response to the nutrient change. Computerised motion analysis was used to analyse the behaviour. Distributions of run and stop times were obtained from rotation data for tethered cells. Exponential and Weibull fits for these distributions, and variability in individual responses are discussed. In terms of parameters derived from the run and stop time distributions, we compare the responses to stepwise changes in the nutrient concentration and the long-term behaviour of 84 cells under 12 propionate concentration levels from 1 nM to 25 mM. We discuss traditional assumptions for the random walk approximation to bacterial swimming and compare them with the observed R. sphaeroides motile behaviour.

Culture Media↗
PubMed1998

Information loss in the continuum limit and Schrödinger's equation in an electromagnetic field.

Since the time of Einstein's work on Brownian motion it has been known that random walks provide a microscopic model for the diffusion equation. Less well known is the fact that some instances of Schrödinger's equation occur naturally in the description of the statistics of these same walks and thus have classical contexts which are distinct from their usual association with quantum mechanics. An interesting feature of these models is the fact that the information which relates Schrödinger's equation to its classical context is not contained in the partial differential equation itself, but is lost in the continuum limit which gives rise to the equation. In this article we illustrate the above by showing that Schrödinger's equation for a particle in an electromagnetic field in 1 + 1 dimension occurs as a continuum limit of a description of a classical system of point particles on a lattice. The derivation shows that the information lost in the continuum limit is necessary to link the mathematics to the physical context of the equation.

Electromagnetic Fields↗
PubMedDate not supplied

Probing nanoscale surface enhanced Raman-scattering fluctuation dynamics using correlated AFM and confocal ultramicroscopy.

We have studied the laser-excitation-intensity-dependent and Ag-nanocluster interstitial-site-dependent SERS intensity fluctuations under low molecule surface coverage of rhodamine 6G and cytochrome c. A new two-channel photon time-stamping system coupled with atomic force microscopic (AFM), Raman spectroscopic, and imaging microscopy was developed and applied to record Raman intensity fluctuation trajectories at sub-microsecond resolution correlated with in situ characterization of the nanoparticle clusters. Our experimental results suggest that the nanoconfinement of the local electromagnetic-field enhancement and the interaction of the local field with the molecules, presumably under rotational motions, result in nano-Raman fluctuations. The SERS spectral fluctuation was pertinent to the nanoscale local enhancement and local interaction of the molecules with the surface when the surface coverage of the nanoparticles was less than a monolayer, and the nanoscale interstitial space controlled the finite number of molecules to contribute the microscopic Raman signal collected from a diffraction-limited focus spot. The fluctuation amplitude significantly decreased with the number of molecules confined at the nanolocal field. The nano-SERS fluctuation dynamics were both photo-induced and spontaneous for rhodamine 6G, but only the photo-induced component was observable for cytochrome c. The fluctuation dynamics were also found to be highly inhomogeneous at interstitial sites with heterogeneous geometries. To interpret the observed nano-SERS fluctuation dynamics, we used computer simulation of optical multiple scattering, based on multi-sphere scattering Mie theory, and rotational diffusion of molecules at an interstitial site, based on a random walk in orientation space.

Journal Article↗
PubMed2001

Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.

To investigate the basis of the fluctuating activity present in neocortical neurons in vivo, we have combined computational models with whole-cell recordings using the dynamic-clamp technique. A simplified 'point-conductance' model was used to represent the currents generated by thousands of stochastically releasing synapses. Synaptic activity was represented by two independent fast glutamatergic and GABAergic conductances described by stochastic random-walk processes. An advantage of this approach is that all the model parameters can be determined from voltage-clamp experiments. We show that the point-conductance model captures the amplitude and spectral characteristics of the synaptic conductances during background activity. To determine if it can recreate in vivo-like activity, we injected this point-conductance model into a single-compartment model, or in rat prefrontal cortical neurons in vitro using dynamic clamp. This procedure successfully recreated several properties of neurons intracellularly recorded in vivo, such as a depolarized membrane potential, the presence of high-amplitude membrane potential fluctuations, a low-input resistance and irregular spontaneous firing activity. In addition, the point-conductance model could simulate the enhancement of responsiveness due to background activity. We conclude that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and GABAergic conductances varying stochastically.

Action Potentials↗
PubMed2002

Adaptive sampling in research on risk-related behaviors.

This article introduces adaptive sampling designs to substance use researchers. Adaptive sampling is particularly useful when the population of interest is rare, unevenly distributed, hidden, or hard to reach. Examples of such populations are injection drug users, individuals at high risk for HIV/AIDS, and young adolescents who are nicotine dependent. In conventional sampling, the sampling design is based entirely on a priori information, and is fixed before the study begins. By contrast, in adaptive sampling, the sampling design adapts based on observations made during the survey; for example, drug users may be asked to refer other drug users to the researcher. In the present article several adaptive sampling designs are discussed. Link-tracing designs such as snowball sampling, random walk methods, and network sampling are described, along with adaptive allocation and adaptive cluster sampling. It is stressed that special estimation procedures taking the sampling design into account are needed when adaptive sampling has been used. These procedures yield estimates that are considerably better than conventional estimates. For rare and clustered populations adaptive designs can give substantial gains in efficiency over conventional designs, and for hidden populations link-tracing and other adaptive procedures may provide the only practical way to obtain a sample large enough for the study objectives.

Adolescent↗
PubMedDate not supplied

Diffusion in thin films on the surface of a porous solid.

A water-wet mono-dispersed glass bead system is saturated with two phases, a wetting phase of water and a non-wetting phase of tetrachloroethylene (no 1H signal). Pulsed field gradient NMR measurements of the one-dimensional probability density distribution P(Delta) (X) for the diffusive displacements of water molecules in times, Delta, are presented for the whole accessible water saturation range. At lower water contents the distributions show a distinctive shape, which is attributed to the distribution of the aqueous phase in thin surface wetting films connecting pendular rings where the beads are in contact. The data are reproduced well by a computer simulation of a random walk model based on diffusion of molecules within such a structure, allowing determination of the surface film thickness.

Diffusion↗
PubMed1996

Self-diffusion in periodic porous media: a comparison of numerical simulation and eigenvalue methods.

Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.

Algorithms↗
PubMed2000

Detection and a possible mechanism of magnetic field effect on the crystal growth of sedimentary calcium carbonate.

Sedimentary calcium carbonate was grown at a physiological pH6.8 from a mixture of equivolume of 70 mM Ca(NO(3))(2) and 70 mM NaHCO(3) aqueous solution. The kinetics of the crystal growth was monitored by means of turbidity measurement. The apparent absorption is gradually increased with the elapsed time after the mixing and reaches its maximum at t(max). The average t(max) is significantly decreased from =467 s (for n=13 runs) to 408 s (n=13) by application of the static magnetic field (SMF) of H=400 mT to the precipitating solution. The application of SMF at 120 s later the mixing shows the same =396 s (n=9) as that of 408 s. It has been thus detected that the application of SMF is ineffective in the stage of the nucleation or the earlier stage of the crystal growth but effective in the Ostwald ripening stage of the growth nucleus or the later stage of the crystal growth where large numbers of the growing crystalline particles seem greater than a few hundred nanometers. A possible mechanism for the SMF effect is as follows. An ion escaping from the growing crystal surface with a certain 'migration velocity' due to a random walk process has significant probability to drift onto the identical surface or at least the identical crystal by means of Lorentz force, because the translational displacement of the crystal during a cycle of the cyclotron motion of the ion is smaller than the size of the growing crystal. This type of drift results in the suppression of re-dissolution of the ions on the growing surface and in the acceleration of the growth in the later stage of the crystal growth. The undetected SMF effect in the earlier stage of the crystal growth can be partly attributed to the re-dissolution due to the thermodynamic instability of the small nuclei which predominates over the presumable SMF effect. This can be partly ascribed to the large translational displacement of the small particle. The application of this mechanism to an oscillating magnetic field will predict the presence of a window for the frequency of the oscillating magnetic field.

Journal Article↗
PubMed2001

Multiple regimes of constrained chromosome motion are regulated in the interphase Drosophila nucleus.

BACKGROUND: Increasing evidence indicates specific changes in the three-dimensional organization of chromosomes in the cell nucleus during the cell cycle and development. These changes may be linked to changes in both the coordinated regulation of gene transcription and the timing of chromosome replication. While there is cytological evidence for short-range diffusive motion of chromosomes during interphase, the mechanisms for large-scale chromosome remodeling inside the nucleus remain unknown. RESULTS: Chromosome motion was tracked in Drosophila spermatocyte nuclei by 3D fluorescence microscopy. The Lac repressor/lac operator system was used to label specific chromosomal sites in live tissues, allowing extended observation of chromatin motion in different cell cycle stages. Our results reveal a highly dynamic chromosome organization governed by two types of motion: a fast, short-range component over a 1-2 s time scale and a slower component related to long-range chromosome motion within the nucleus. The motion patterns are consistent with a random walk. In early G2, short-range motion occurs within a small, approximately 0.5 microm radius domain, while long-range motion is confined to a much larger, chromosome-sized domain. Progression through G2 as cells approach meiotic prophase is accompanied by a complete arrest of long-range chromosome motion. CONCLUSIONS: Our analysis provides direct evidence for cell cycle-regulated changes in interphase chromatin motion. These changes are consistent with changes in local and long-range constraints on chromosome motility. We propose that dynamic interactions between chromosomes and internal nuclear structures modulate the range and rate of interphase chromatin diffusion and thereby regulate large-scale nuclear chromosome organization.

Animals↗
PubMed2000

An improved technique for the extraction of stochastic parameters from stabilograms.

An improved characterization of the dynamics of postural sway can provide a better understanding about the functional organization of the postural control system as well as a more robust tool for postural pattern recognition. To this aim, a novel parameterization was applied to the stabilogram diffusion analysis formerly proposed by Collins and De Luca [Collins JJ, De Luca CJ. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp Brain Res 1993;95:308-18] that considered the act of maintaining posture as a stochastic process. The main purpose of the present technique was to overcome some drawbacks of the model presented by Collins and De Luca that may restrain its potential application in clinical practice. The approach uses a unique non-linear model to describe the center of pressure (COP) dynamics that reduces the number of parameters and decreases their intra-subject variability; consequently, fewer trials are required to perform reliable estimates of stochastic parameters and this is of particular importance for subjects that cannot afford many repeated measurements because of age or pathology. Four new statistical mechanics parameters (NSMP) were computed on the log-log stabilogram diffusion plots and their estimates were compared in terms of reliability and sensitivity to the visual conditions with: (1) a minimal set of four summary statistic scores (SSS); and (2) the six statistical mechanics parameters (SMP) proposed by Collins and De Luca. All four NSMP showed at least a fair-to-good reliability (intraclass correlation coefficient, ICC>0.49) while SMP (ICC>0.20) showed some poor reliability. A better overall reliability was also observed with respect to SSS. Moreover, only NSMP had a similar score for eyes open and eyes closed conditions. Three out of four NSMP were also significantly sensitive to eyes open or closed conditions (P<0.001) while only three out of six SMP were sensitive to operating conditions (P<0.01).

Humans↗