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PubMed2003

DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection.

Several approaches have been used to trace axonal trajectories from diffusion MRI data. If such techniques were first developed in a deterministic framework reducing the diffusion information to one single main direction, more recent approaches emerged that were statistical in nature and that took into account the whole diffusion information. Based on diffusion tensor MRI data coming from normal brains, this paper presents how brain connectivity could be modelled globally by means of a random walk algorithm. The mass of connections thus generated was then virtually dissected to uncover different tracts. Corticospinal, corticobulbar, and corticothalamic tracts, the corpus callosum, the limbic system, several cortical association bundles, the cerebellar peduncles, and the medial lemniscus were all investigated. The results were then displayed in the form of an in vivo brain connectivity atlas. The connectivity pattern and the individual fibre tracts were then compared to known anatomical data; a good matching was found.

Algorithms↗
PubMedDate not supplied

Residual eye-movements in macaque and their effects on visual responses of neurons.

We recorded continuously, with high precision, the positions of the eyes in anesthetized macaque monkeys prepared for physiological recording. Most recordings were made after the infusion of muscle relaxant to immobilize the eyes; in some cases we also were able to record eye position for periods before the eyes were immobilized. In all monkeys, the eyes moved continuously by as much as 0.5 deg over a 10-min sampling period. The average distance moved was proportional to the square root of the sampling period, as would be expected from a random walk. The movements had three distinct components: slow drifts, and two rhythms driven by the pulse and respiration. The rhythmic movements occurred only under paralysis: they were not discernible in measurements made before the infusion of muscle relaxant. The movements of the eye in the paralyzed animal can have substantial effects on the measured physiological characteristics of neurons. For excursions in the midrange of those we observed, a neuron's sensitivity to a spatial frequency of 10 cycle/deg might be underestimated by as much as a factor of three, depending on the method by which responses were averaged. We show how the effects of eye-movements can be mitigated by appropriate data analysis.

Animals↗
PubMed2002

Fundamentals of capillary electrochromatography: migration behavior of ionized sample components.

The mechanism of separating charged species by capillary electrochromatography (CEC) was modeled with the conditions of ideal/linear chromatography by using a simple random walk. The most novel aspect of the work rests with the assumption that in sufficiently high electric field ionized sample components can also migrate in the adsorbed state on the ionized surface of the stationary phase. This feature of CEC leads to the introduction of three dimensionless parameters: alpha, reduced mobility of a sample component with the electrosmotic mobility as the reference; beta, the CEC retention factor; and gamma, the ratio of the electrophoretic migration velocity and the velocity of surface electrodiffusion. Since the interplay of retentive and electrophoretic forces determines the overall migration velocity, the separation mechanism in CEC is governed by the relative importance of the above parameters. The model predicts conditions under which the features of the CEC system engender migration behavior that manifests itself in a relatively narrow elution window and in a gradient like elution pattern in the separation of peptides and proteins by using pro forma isocratic CEC. It is believed that such elution patterns, which resemble those obtained by the use of external gradient of the eluent, are brought about by the formation of an internal gradient in the CEC system that gave rise to concomitant peak compression. The peculiarities of CEC are discussed in the three operational modalities of the technique: co-current, countercurrent, and co-counter CEC. The results suggest that CEC, which is often called "liquid chromatography on electrophoretic platform" is an analytical tool with great potential in the separation of peptides and proteins.

Algorithms↗
PubMed2003

Single-molecule fluorescence trajectories for investigating molecular transport in thin silica sol-gel films.

Single-molecule fluorescence tracking has been used to examine diffusion of small molecules in sol-gel films in order to identify spatial heterogeneity in the structure and molecular diffusivities for different regions of the film. Fluorescence intensity profiles from single molecules are fit to a two-dimensional Gaussian function to determine their x,y positions with subpixel resolution. Scatter plots and histograms of molecular step sizes indicate that the trajectories conform to the predictions of a two-dimensional random walk. The mean-square step size is shown to be an unbiased estimate of the variance of the step-size probability distribution and a valid statistic for determining the diffusion coefficient from a molecular trajectory. The diffusion coefficients measured for different molecules are subjected to an F test, which showed that the sol-gel film exhibits spatial variation in the diffusion coefficient on a micrometer-length scale. The spatial variation in diffusivities is a measure of structural heterogeneity of these films.

Journal Article↗
PubMed2006

Liquid chromatography at critical conditions: comprehensive approach to sequence-dependent retention time prediction.

An approach to sequence-dependent retention time prediction of peptides based on the concept of liquid chromatography at critical conditions (LCCC) is presented. Within the LCCC approach applied to biopolymers (BioLCCC), the specific retention time corresponds to a particular sequence. In combination with mass spectrometry, this approach provides an efficient tool to solve problems wherein the protein sequencing is essential. In this work, we present a theoretical background of the BioLCCC concept and demonstrate experimentally its feasibility for sequence-dependent LC retention time prediction for peptides. BioLCCC model is based on three notions: (a) a random walk model for a macromolecule chain; (b) an entropy and energy compensation for the macromolecules within the adsorbent pore; and (c) a set of phenomenological parameters for the effective interaction energies of interactions between the amino acid residues and the adsorbent surface. In this work, the phenomenological parameters have been obtained for C18 reversed-phase HPLC. Note, that contrary to alternative additive models for retention time prediction based on summation of the so-called "retention coefficients", the BioLCCC approach takes into account the location of amino acids within the primary structure of a peptide and, thus, allows the identification of the peptides having the same composition of amino acids but differing by their arrangement. As a result, this new approach allows prediction of retention time for any possible amino acid sequence in particular HPLC experiments. In addition, the BioLCCC model lacks of main drawbacks of additive approaches that predict retention time for sequences of limited chain lengths and provide information about amino acid composition only. The proposed BioLCCC approach was characterized experimentally using LTQ FT LC-MS and LC-MS/MS data obtained earlier for Escherichia coli. The HPLC system calibration was performed using peptide retention standards. The results received show a linear correlation between predicted and experimental retention times, with a correlation coefficient, R2, of 0.97 for a peptide standard mixture and 0.9 for E. coli data, respectively, with the standard error below 1 min. The work presents the first description of a BioLCCC approach for high-throughput peptide characterization and preliminary results of its feasibility tests.

Adsorption↗
PubMed2007

Pore-scale dispersion in electrokinetic flow through a random sphere packing.

The three-dimensional velocity field and corresponding hydrodynamic dispersion in electrokinetic flow through a random bulk packing of impermeable, nonconducting spheres are studied by quantitative numerical analysis. First, a fixed bed with interparticle porosity of 0.38 is generated using a parallel collective-rearrangement algorithm. Then, the interparticle velocity field is calculated using the lattice-Boltzmann (LB) method, and a random-walk particle-tracking method is finally employed to model advection-diffusion of an inert tracer in the LB velocity field. We demonstrate that the pore-scale velocity profile for electroosmotic flow (EOF) is nonuniform even under most ideal conditions, including a negligible thickness of the electrical double layer compared to the mean pore size, a uniform distribution of the electrokinetic potential at the solid-liquid interface, and the absence of applied pressure gradients. This EOF dynamics is caused by a nonuniform distribution of the local electrical field strength in the sphere packing and engenders significant hydrodynamic dispersion compared to pluglike EOF through a single straight channel. Both transient and asymptotic dispersion behaviors are analyzed for EOF in the context of packing microstructure and are compared to pressure-driven flow in dependence of the average velocity through the bed. A better hydrodynamic performance of EOF originates in a still much smaller amplitude of velocity fluctuations on a mesoscopic scale (covering several particle diameters), as well as on the microscopic scale of an individual pore.

Journal Article↗
PubMed2000

A theoretical description of microdialysis with mass transport coupled to chemical events.

A random-walk simulation of microdialysis is used to examine how a reaction that consumes analyte in the medium external to the probe affects the extraction and recovery processes. The simulations suggest that such a reaction can promote the extraction process while simultaneously inhibiting the recovery process, which appears to be consistent with recent experimental evidence of asymmetry in the extraction and recovery of the neurotransmitter, dopamine, during brain microdialysis. This suggests that quantitative microdialysis strategies that rely on the extraction fraction as a measure of the probe recovery value, such as the no-net-flux method, will produce an underestimate of the analyte concentration in the external medium when that analyte is consumed by a reaction in the external medium. Furthermore, if experimental conditions arise under which the kinetics of the reaction are changed, then changes in the extraction and recovery processes are likely to occur as well. The implications of these theoretical findings for the quantitative interpretation of in vivo microdialysis results obtained for the neurotransmitter dopamine are examined.

Algorithms↗
PubMed1997

Rapid-reaction analysis of plasmid DNA cleavage by the EcoRV restriction endonuclease.

Rapid-reaction methods have been used previously to identify intermediates in the reaction of the EcoRV restriction endonuclease on oligonucleotide substrates. In this study, the pathway on macromolecular DNA was elucidated by using the quench-flow method to analyze EcoRV reactions on a plasmid with one recognition site. Some reactions were carried out by first allowing the EcoRV enzyme to bind nonspecifically to the DNA and then initiating DNA cleavage by adding magnesium ions. The subsequent transfer of the enzyme from nonspecific to specific sites was extremely rapid, at a random walk rate of at least 5 x 10(5) base pairs per second. The two strands of the DNA at the EcoRV recognition site were then cleaved sequentially, at rates that were faster than the turnover number of the enzyme. The rates recorded for the cleavage steps were direct measurements of phosphodiester hydrolysis, while the turnover is limited by the dissociation of the product cleaved in both strands. Other reactions were initiated by adding EcoRV and MgCl2 to the DNA: these revealed not only the processes observed in reactions starting from DNA-bound enzyme but also the bimolecular association of the protein with the plasmid. The association rate was limited by diffusion but its rate constant, 1.2 x 10(8) M(-1) s(-1), was unusually small for the binding of a protein to DNA. The slowness of this diffusion-controlled process may be due to a rapid oscillation of the protein between closed and open conformations, with only the open form capable of binding DNA.

Binding Sites↗
PubMedDate not supplied

Graph kernels for molecular structure-activity relationship analysis with support vector machines.

The support vector machine algorithm together with graph kernel functions has recently been introduced to model structure-activity relationships (SAR) of molecules from their 2D structure, without the need for explicit molecular descriptor computation. We propose two extensions to this approach with the double goal to reduce the computational burden associated with the model and to enhance its predictive accuracy: description of the molecules by a Morgan index process and definition of a second-order Markov model for random walks on 2D structures. Experiments on two mutagenicity data sets validate the proposed extensions, making this approach a possible complementary alternative to other modeling strategies.

Algorithms↗
PubMed2006

UV reactor performance modeling by Eulerian and Lagrangian methods.

A study was performed to investigate the influence of hydrodynamics on the performance of ultraviolet (UV) reactors. Two general UV disinfection models were developed by integrating fluence rate models and inactivation kinetics within a commercial computational fluid dynamics (CFD) software package to predict reactor performances. Both a particle tracking (Lagrangian) random walk model and a volumetric reaction rate based (Eulerian) model were implemented. Simulations were performed for two characteristic annular single-lamp UV reactor configurations, with inlets concentric (L-shape) and normal (U-shape) to the reactor axis. Two fluence rate models, the infinite line source assumption and the finite line or multiple point source summation (MPSS), were used. First-order inactivation kinetics was assumed for disinfection, with rate constants from MS2 bacteriophage assays. The simulation results provided detailed information on the velocity profiles, reaction rates, range of absorbed dose, and areas of short circuiting of the UV reactors. Model predictions based on both the Lagrangian dose distribution and Eulerian concentration distribution were in good agreement with each other at high flow rates but showed some discrepancies at lower flow rates. Experimental verification of the general models was performed by simulating the disinfection performance of an industrial prototype UV reactor. Results from both integration approaches were shown to be in good agreement with the provided biodosimetry data.

Kinetics↗
PubMed2006

The role of exciton hopping and direct energy transfer in the efficient quenching of conjugated polyelectrolytes.

The dynamics of fluorescence quenching of a conjugated polyelectrolyte by a cyanine dye are investigated by femtosecond fluorescence up-conversion and polarization resolved transient absorption. The data are analyzed with a model based on the random walk of the exciton within the polymer chain and a long-range direct energy transfer between polymer and dye. We find that rapid intrachain energy migration toward complex sites with the dye leads to the highly efficient energy transfer, whereas the contribution from direct, long-range energy transfer is negligible. We determine the actual density of complexes with the dye along the polymer chain. A clear deviation from calculations based on a constant complex association constant is found and explained by a reduced effective polymer concentration due to aggregation. Altogether, the quenching efficiency is found to be limited by (i) the energetic disorder within the polymer chain and (ii) the formation of loose polymer aggregates.

Adsorption↗
PubMed2005

Motion of single DNA molecules at a liquid-solid interface as revealed by variable-angle evanescent-field microscopy.

A variable-angle total-internal-reflection fluorescence microscope (VATIRFM) capable of providing a large range of incident angles was constructed for imaging single DNA molecule dynamics at a solid/liquid interface. An algorithm using a public-domain image-processing program, ImageJ, was developed for single-molecule counting. The experimental counts at various incident angles with different evanescent-field layer (EFL) thicknesses are affected by molecular diffusion. The dynamics of molecules near the surface and the observed counts in the VATIRFM are elucidated using a limited one-dimensional random-walk diffusion model. The simulation fits well with the experimental counting results. Further analysis using the simulation reveals the details of single-molecule motion. One implication is that the measured intensities cannot be used directly to determine the distances of molecules from the surface, though the majority of fluorescence does come from the EFL. Another implication is that rather than providing molecular concentrations within EFL the experimental counting results depict the distance-dependent dynamics of molecules near the surface. Thus, the VATIRFM could be a powerful technique to study the surface repulsion/attraction of molecules within a few hundred nanometers of the surface. Further studies show that molecules at low ionic strengths experience electrostatic repulsion at distances much further away from the surface than the calculated thickness of the electrical double layer.

DNA↗
PubMed2005

Influence of vacancy ordering on the percolative behavior of (Li(1)(-x)Na(x))(3y)La(2/3-y)TiO(3) perovskites.

Influence of the vacancy concentration on the Li conductivity of the (Li(1-x)Na(x))(0.2)La(0.6)TiO(3) and (Li(1-x)Na(x)(0.5)La(0.5)TiO(3) perovskite series, with 0 < or = x < 1, has been investigated by neutron diffraction (ND), impedance spectroscopy (IS), nuclear magnetic resonance (NMR), and Monte Carlo simulations. In both series, Li(+) ions occupy unit cell faces, but Na(+) ions are located at A sites of the perovskite. From this fact, the amount of vacant A sites that participate in Li conductivity is given by the expression n(v) = [Li] + square, where square is the nominal vacancy concentration. Substitution of Li by Na decreases the amount of vacancies, reducing drastically the Li conductivity when n(v) approaches the percolation threshold of the perovskite conduction network. In disordered (Li(1-x)Na(x))(0.5)La(0.5)TiO(3) perovskites, the percolation threshold is 0.31; however, in ordered (Li(1-x)Na(x))(0.2)La(0.6)TiO(3) perovskites, this parameter changes to 0.26. Near the percolation threshold, the amount of mobile Li species deduced by (7)Li NMR spectroscopy is lower than that derived from structural formulas but higher than deduced from dc conductivity measurements. Conductivity values have been explained by Monte Carlo simulations, which assume a random walk for Li ions in the conduction network of the perovskite. In these simulations, distribution of vacancies conforms to structural models deduced from ND experiments.

Journal Article↗
PubMed2005

The mechanism of proton transfer between adjacent sites exposed to water.

The surface of a protein, or a membrane, is spotted with a multitude of proton-binding sites, some of which are only a few angstroms apart. When a proton is released from one site, it propagates through the water by a random walk under the bias of the local electrostatic potential determined by the distribution of the charges on the protein. Some of the released protons disperse into the bulk, but during the first few nanoseconds, the released protons can be trapped by encounter with nearby acceptor sites. This process resembles a scenario which corresponds with the time-dependent Debye-Smoluchowski equation. In the present study, we investigated the mechanism of proton transfer between sites that are only a few angstroms apart, using as a model the proton exchange between sites on a small molecule, fluorescein, having two, spectrally distinguishable, proton-binding sites. The first site is the oxyanion on the chromophore ring structure. The second site is the carboxylate moiety on the benzene ring of the molecule. Through our experiments, we were able to reconstruct the state of protonation at each site and the velocity of proton transfer between them. The fluorescein was protonated by a few nanosecond long proton pulse under specific conditions that ensured that the dye molecules would be protonated only by a single proton. The dynamics of the protonation of the chromophore were measured under varying initial conditions (temperature, ionic strength, and different solvents (H(2)O or D(2)O)), and the velocity of the proton transfer between the two sites was extracted from the overall global analysis of the signals. The dynamics of the proton transfer between the two proton-binding sites of the fluorescein indicated that the efficiency of the site-to-site proton transfer is very sensitive to the presence of the screening electrolyte and has a very high kinetic isotope effect (KIE = 55). These two parameters clearly distinguish the mechanism from proton diffusion in bulk water. The activation energy of the reaction (E(a) = 11 kcal mol(-1)) is also significantly higher than the activation energy for proton dissociation in bulk water (E(a) approximately 2.5 kcal mol(-1)). These observations are discussed with respect to the effect of the solute on the water molecules located within the solvation layer.

Anions↗
PubMed2005

Grain morphology and trapping effects on electron transport in dye-sensitized nanocrystalline solar cells.

We have examined the combined effects of grain morphology and electron trapping on the transient response of photoelectrons moving through the TiO2 grains in a dye-sensitized nanocrystalline solar cell using a multi-time-scale random walk Monte Carlo model. Our use of a multi-time-scale approach enables us to simulate transport for electrons moving through spherical connected grains in a three-dimensional (3D) voided network and look at the effect of the size of interparticle boundaries on carrier dynamics. We can also address similar times to those over which measurements are taken, namely, 0.1 ms. These times are long because of deep traps in the TiO2 grains. The grains have 2-fold connectivity in one dimension (linear chains) or 4-fold or 6-fold connectivity in three dimensions and traps with an exponential distribution of energies. Photoelectrons are generated by a light pulse of short duration. The spatial distribution of the photogenerated electron density from this pulse either has a uniform profile or is peaked on the electrolyte side. We show that the constrictions at the grain necks slow the electrons, making trapping more likely and hence further delaying their passage to the extracting electrode. By comparing our results for 4-fold and 6-fold coordinated particles on a cubic lattice with 2-fold coordinated particles on linear chains, we show that transport is slowed in the former case due to the additional paths available to the electrons in the 3D network. We also find that the charge and current transients cannot be fit to an analytical solution of the continuum equations with an effective diffusion coefficient even at long times. Therefore, caution must be exercised when attempting to fit experimental transient data with an effective diffusion coefficient.

Journal Article↗
PubMed2005

Transient absorption studies and numerical modeling of iodine photoreduction by nanocrystalline TiO2 films.

We have used transient absorption spectroscopy to study the reaction between photogenerated electrons in a dye-free nanocrystalline titanium dioxide film and an iodine/iodide redox couple. Recombination kinetics was measured by recording the transient optical signal following band gap excitation by a UV laser pulse. In the presence of a methanol hole scavenger in the electrolyte, a long-lived (0.1-1 s) red/infrared absorbance is observed and assigned to photogenerated electrons forming Ti(3+) species. In the presence of iodine and excess iodide in the electrolyte, the signal decays on a millisecond-microsecond time scale, assigned to reduction of the redox couple by photogenerated electrons in the TiO(2). The electron lifetime decreases inversely with increasing iodine concentration, indicating that the back reaction is first order in [I(2)]. No evidence for I(2)(-) is observed, indicating that the reaction mechanism does not involve the formation of I(2)(-) as an intermediate. The shape of the kinetics evolves from monoexponential at low [I(2)] to stretched-exponential as [I(2)] increases. A Monte Carlo continuous-time random walk model is implemented to simulate the kinetics and its [I(2)] dependence and used to address the order of the recombination reaction with respect to electron density, n. The model incorporates the diffusion of oxidized species from the electrolyte toward the TiO(2) surface as well as electron trapping and transport in the TiO(2). In the limit of low [I(2)], the monoexponential kinetics is explained by the recombination reaction being rate limited by the diffusion of the oxidized species in the electrolyte. The stretched-exponential behavior at high [I(2)] can be explained by the reaction being rate limited by the transport of electrons through a distribution of trap states toward reactive sites at the TiO(2)-electrolyte interface, similar to the mechanism proposed previously for the kinetics of electron-dye cation recombination. Such trap-limited recombination can also explain the superlinear dependence of electron recombination rate on electron density, which has been reported elsewhere, without the need for a reaction mechanism that is second order in n. In contrast, a second-order reaction mechanism in a trap-free medium cannot explain the observed kinetics, although a second-order mechanism incorporating electron trapping cannot be conclusively ruled out by the data. We propose that the most likely reaction scheme, that is first order in both [I(2)] and n, is the dissociative reduction of I(2) onto the metal oxide surface, followed by a second electron reduction of the resulting adsorbed iodine radical, and that empirical second-order behavior of the electron lifetime is most likely explained by electron trapping rather than by a second-order recombination mechanism.

Journal Article↗
PubMed2006

Influence of subdiffusive motion on spin relaxation and spin effects in radical pairs.

Specific features of spin relaxation and the kinetics of spin effect generation in radical pairs (RPs) undergoing subdiffusive relative motion are studied in detail. Two types of processes are analyzed: (1) spin relaxation in biradicals, resulting from anomalously slow subdiffuisive reorientation (with the correlation function P(t) approximately (wt)(-alpha), where 0 < alpha < 1) and (2) spin effect generation in subdiffusion-assisted RP recombination. Analysis is made with the use of the non-Markovian stochastic Liouville equation (SLE) derived within the continuous time random walk approach. The SLE predicts anomalous (very slow and nonexponential) spin relaxation in biradicals which results in some peculiarities of the spectrum of the system. In RP recombination, the subdiffusive relative motion shows itself in slow dependence of the reaction yield Y(r)() on reactivity and parameters of the RP spin Hamiltonian and anomalous electron spin polarization of escaped radicals. The spectrum of the reaction yield detected magnetic resonance, that is, the Y(r)() dependence on the frequency omega of microwave field, is found to be strongly non-Lorenzian with the width determined by the field strength omega(1) and very broad wings depending on alpha. Analysis shows that the majority of interesting, specific features of the observables in both systems are controlled only by the parameter alpha.

Journal Article↗
PubMed2005

Dynamics of imbibition into a pore with a heterogeneous surface.

We use large-scale molecular dynamics simulations to study the dynamics of liquid penetration into a cylindrical pore having a randomly heterogeneous surface comprising areas of differing wettability. Our results confirm that the equilibrium contact angle in the heterogeneous pore is well described by Cassie's law. As in the case of the uniform pore studied previously, the dynamics of penetration can be described by the Lucas-Washburn equation corrected to include the effect of a dynamic contact angle. The dissipation at the three-phase line, which gives rise to the dynamic contact angle, may be characterized in terms of a friction coefficient. Interestingly, the wetting-line friction on the heterogeneous surface also turns out to be a linear function of the fractional concentration of the areas of different wettability, analogous to Cassie's law. These results can be interpreted in terms of an independent random walk mechanism.

Journal Article↗