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Simple data-driven models of intracellular calcium dynamics with predictive power.

Biology is complex. However, it is not clear how much of this complexity must necessarily translate into complicated mathematical models of biological processes. Simple models can be appealing to physicists but are usually deceiving for biologists. Complicated models, on the other hand, depend on too many parameters whose values are frequently unknown. Therefore, complicated models, although in principle more realistic, can lead to erroneous results if they are sensitive to these unknown parameter values. Intracellular calcium signals provide an example of utmost biological importance in which the issue of "simple vs complex" can be explored. In this paper we show that simple models describing the dynamics of intracellular calcium can be directly inferred from experimental data, without no a priori information on unknown parameters. A similar approach can be followed to study other reaction-diffusion systems. In spite of their simplicity, these models can provide quantitative information on some of the processes that shape calcium signals, such as the calcium current that underlies an experimental observation. This shows that simple models of biological systems are not limited to qualitative descriptions.

Animals↗

Bidirectional membrane transport: simulations of transport inhibition in uptake studies explain data obtained with flavonoids.

The purpose of the simulations was to obtain an estimate of concentration-dependent uptake curves when two counteracting transporters are present. On the basis of this experimental data obtained with a pair of ovarian carcinoma cell lines, one of which was not expressing the exsorptive transporter P-glycoprotein and one of which was an MDR1-transfected, P-glycoprotein expressing variant, the kinetics of cellular uptake of the radiolabel (3)H-talinolol were calculated and the inhibitory constants at P-gp were determined for different flavonoids. With respect to the inhibition of P-gp function, among others, naringenin and isoquercitrin were identified as inhibitors, yet estimation of the inhibitory constant was only possible for uptake values corrected for non-P-glycoprotein-mediated processes. It was assumed that an additional inside-directed transporting protein (Carrier B), which is inhibited by the presence of test compounds, uptake of radiolabel was simulated as a function of the concentration of test-compound, with exemplary parameters for the rate constant (k(B)) of the additional Carrier B and the inhibition constants (K(I)-values) for both transporting proteins. The obtained uncorrected experimental data, which showed either inhibition or enhancement of radiolabel uptake as a function of the inhibitor concentration, were appropriately explained by the respective model. The respective model included an exsorptive transporter as well as carrier-mediating facilitated diffusion. It is concluded that flavonoids, such as naringenin and isoquercitrin, inhibit an inside-directed process in addition to their inhibition of P-glycoprotein-mediated exsorption.

ATP Binding Cassette Transporter, Subfamily B, Mem↗

Anisometric transport of ions and particles in anisotropic tissue spaces.

The results of time-lapse measurements and electron microscopic observations on the diffusion of histological dyes, colloidal particles, and heavy metal salts in excised chicken breast tendon are reported. In all cases, the transport was found to be anisometric, the extent of the spreading being much greater parallel than perpendicular to the collagen fibers. The diffusion of colloidal gold was shown to be governed by a random diffusion process, with coefficients of 3 to 5 x 10(-7) and 1 to 2 x 10(-7) cm(2)/sec for the parallel and perpendicular directions, respectively; the anisotropy was attributed to steric hindrance. In the diffusion of uranyl nitrate, a sharp boundary appeared at the leading edge of the diffusate and advanced at a rate proportional to the square root of time. Electron micrographs showed uranyl nitrate clusters localized in space on the surface of the collagen fibrils and tightly bound to the polar amino acid regions of the macromolecule. A model was proposed involving diffusion with attrition, and predicted a sharp boundary advancing proportionally to the square root of time and to the 0.65 power of the initial diffusate concentration. Application of the model to the experimental results for uranyl nitrate gave a diffusion coefficient of 10 x 10(-7) and 4 x 10(-7) cm(2)/sec for the parallel and perpendicular directions, respectively, and a possible explanation of this large difference was advanced. The importance of anisometric transport in anisotropic tissues was indicated.

Animals↗

Facilitated diffusion of a DNA binding protein on chromatin.

Facilitated diffusion accounts for the rapid rate of association of many bacterial DNA binding proteins with specific DNA sequences in vitro. In this mechanism the proteins bind at random to non-specific sites on the DAN and diffuse (by 'sliding' or 'hopping') along the DNA chain until they arrive at their specific functional sites. We have investigated whether such a mechanism can operate in chromatin by using a bacterial DNA binding protein, Escherichia coli RNA polymerase, that depends on linear diffusion to locate initiation sites on DNA. We have measured the competition between chromatin and its free DNA for the formation of initiation complexes. Only the short linker segments exposed by the removal of histone H1 are available for interaction with the polymerase, but the sparsely distributed promoter sites on the linker DNA of such a polynucleosome chain are located at the same rate as those on DNA. We conclude that the polymerase is free to migrate between the separate linker DNA segments of a polynucleosome chain to reach a promoter site. This chain thus permits the 'hopping' of proteins between neighboring linker segments in their search for a target site on the accessible DNA.

Animals↗

Hydrolytic degradation and morphologic study of poly-p-dioxanone.

The in vitro hydrolytic degradation of 2-0 size PDS monofilament suture was studied for the purpose of revealing its morphologic structure and degradation mechanism. The sutures were immersed in phosphate buffer of pH 7.44 for up to 120 days at 37 degrees C. These hydrolyzed sutures were examined by the changes in tensile properties, weight, thermal properties, x-ray diffraction structure, surface morphology, and dye diffusion phenomena. It was found that hydrolysis had significant effects on the change of PDS fiber morphology and properties. Hydrolysis, however, had no significant effect on overall molecular orientation of the fiber until the very late stage. PDS suture fibers retained their skeleton throughout the earlier periods of hydrolysis concurrent with mass and tensile strength losses. PDS sutures exhibited an absorption delay of 120 days. Both heat of fusion and melting point exhibited a maximum function of hydrolysis time. Hydrolysis of PDS suture fibers proceeded through two stages: random scission of chain segments located in the amorphous regions of microfibrils and intermicrofibrillar space, followed by stepwise scission of chain segments located in the crystalline regions of microfibrils. Dye diffusion data showed that the passage along the longitudinal direction of the fiber was relatively easier than the lateral direction as evident in the diffusion coefficient, activation energy, and flexibility of chain segments. Swiss-cheese model of fiber structure appears to describe the observed dye diffusion phenomena and their dependence on hydrolysis time and dying temperature.

Adsorption↗

How to get from A to B: strategies for analysing protein motion on DNA.

Essentially all genetic events require proteins to move from one location in a DNA polymer to another location in the same chain. A protein will seldom bind to a specific site in the DNA by colliding directly with that site. Instead, the protein will almost always collide first with a random site anywhere in the DNA and then migrate to the specific site by a facilitated-diffusion process that is constrained to the zone of that DNA molecule. Thereafter, many proteins bound to their target sites translocate in a specified direction along the DNA by a energy-dependent vectorial mechanism. This review will discuss some of the strategies that have been developed to analyse the motion of proteins on DNA, with respect to both the random diffusion processes involved in target-site location by DNA-binding proteins and the vectorial processes involved in unidirectional translocation along DNA.

DNA↗

A stochastic metapopulation model accounting for habitat dynamics.

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Animals↗

The locomotion of mouse fibroblasts in tissue culture.

Time-lapse cinematography was used to investigate the motion of mouse fibroblasts in tissue culture. Observations over successive short time intervals revealed a tendency for the cells to persist in their direction of motion from one 2.5 hr time interval to the next. Over 5.0-hr time intervals, however, the direction of motion appeared random. This fact suggested that D, the diffusion constant of a random walk model, might serve to characterize cellular motility if suitably long observation times were used. We therefore investigated the effect of "persistence" on the pure random walk model, and we found theoretically and confirmed experimentally that the motility of a persisting cell could indeed be characterized by an augmented diffusion constant, D*. A method for determining confidence limits on D* was also developed. Thus a random walk model, modified to comprehend the persistence effect, was found to describe the motion of fibroblasts in tissue culture and to provide a numerical measure of cellular motility.

Animals↗

Comparison of anandamide transport in FAAH wild-type and knockout neurons: evidence for contributions by both FAAH and the CB1 receptor to anandamide uptake.

The cellular inactivation of the endogenous cannabinoid (endocannabinoid) anandamide (AEA) represents a controversial and intensely investigated subject. This process has been proposed to involve two proteins, a transporter that promotes the cellular uptake of AEA and fatty acid amide hydrolase (FAAH), which hydrolyzes AEA to arachidonic acid. However, whereas the role of FAAH in AEA metabolism is well-characterized, the identity of the putative AEA transporter remains enigmatic. Indeed, the indirect pharmacological evidence used to support the existence of an AEA transporter has been suggested also to be compatible with a model in which AEA uptake is driven by simple diffusion coupled to FAAH metabolism. Here, we have directly addressed the contribution of FAAH to AEA uptake by examining this process in neuronal preparations from FAAH(-/-) mice and in the presence of the uptake inhibitor UCM707. The results of these studies reveal that (i) care should be taken to avoid the presence of artifacts when studying the cellular uptake of lipophilic molecules like AEA, (ii) FAAH significantly contributes to AEA uptake, especially with longer incubation times, and (iii) a UCM707-sensitive protein(s) distinct from FAAH also participates in AEA uptake. Interestingly, the FAAH-independent component of AEA transport was significantly reduced by pretreatment of neurons with the cannabinoid receptor 1 (CB1) antagonist SR141716A. Collectively, these results indicate that the protein-dependent uptake of AEA is largely mediated by known constituents of the endocannabinoid system (FAAH and the CB1 receptor), although a partial contribution of an additional UCM707-sensitive protein is also suggested.

Amidohydrolases↗

Accelerated progression of asbestos-induced mesotheliomas in heterozygous p53+/- mice.

Asbestos fibers produce diffuse malignant mesotheliomas in chronic rodent inhalation assays or after direct intrapleural or intraperitoneal injection. In vitro models have provided evidence that asbestos fibers are genotoxic carcinogens that can directly or indirectly generate reactive oxygen- and nitrogen-derived species that cause DNA damage. Heterozygous p53+/- mice show an increased incidence and reduced latency of malignant mesotheliomas induced by weekly intraperitoneal injections of crocidolite asbestos fibers. In this study, we investigated whether loss of heterozygosity (LOH) at the p53 tumor-suppressor gene locus contributes to accelerated tumor progression. LOH was found in 50% of the tumors produced in heterozygous p53+/- mice. In contrast to tumors that arise in p53+/+ mice or those that retained one p53 allele, LOH was associated with large tumor masses with central areas of necrosis, local invasion, and penetration of lymphatics. Increased tumor size was not associated with increased levels of cell proliferation as determined by BrdU incorporation, but it was correlated with a reduction in apoptosis as determined morphologically and by the TUNEL assay. Wild-type p53 protein is essential for cell cycle arrest in response to DNA damage and in maintenance of genomic stability. Cell lines established from tumors that showed LOH at the p53 tumor-suppressor gene locus were nearly tetraploid. These results suggest that p53 haplo-insufficiency sensitizes mice to the clastogenic or aneuploidogenic effects of crocidolite asbestos fibers, resulting in a shorter latent period. As solid tumors develop, spontaneous loss of the wild-type allele accompanied by decreased apoptosis and genetic instability is associated with accelerated tumor growth, invasion, and lymphatic dissemination.

Animals↗

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles.

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation, and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady state, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite-size system, however, continues to show a signature of the original transition, and we characterize the finite-size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.

Journal Article↗

Base-sequence-dependent sliding of proteins on DNA.

The possibility that the sliding motion of proteins on DNA is influenced by the base sequence through a base pair reading interaction, is considered. Referring to the case of the T7 RNA-polymerase, we show that the protein should follow a noise-influenced sequence-dependent motion which deviate from the standard random walk usually assumed. The general validity and the implications of the results are discussed.

Base Pairing↗

An error analysis of white matter tractography methods: synthetic diffusion tensor field simulations.

White matter tractography using diffusion tensor MR images is a promising method for estimating the pathways of white matter tracts in the human brain. The success of this method ultimately depends upon the accuracy of the white matter tractography algorithms. In this study, a Monte Carlo simulation was used to investigate the impact of SNR, tensor anisotropy, and diffusion tensor encoding directions on the accuracy of six tractography algorithms. The accuracy was assessed in straight and curved tracts and tract geometries with divergence properties. In general, the tract dispersion increased with distance and decreased with SNR and anisotropy. The tract orientation with respect to the encoding scheme also influenced tract dispersion. Divergent tract geometries increased tract dispersion, whereas convergent tract geometries reduced dispersion. Analytic models of tract dispersion were constructed as a function of the tract distance, SNR, eigenvalues of the tracts, voxel size, and the relationship between the tract direction and the diffusion tensor encoding directions. In certain cases, the mean tract trajectory was found to deviate from the ideal pathway for curved trajectories. Analytical models of mean displacement were constructed as a function of the curvature, tract distance, step size, and tensor eigenvalues. These models may be used in future studies to assess the level of confidence associated with a tractography result.

Algorithms↗

Natural selection for within-generation variance in offspring number II. Discrite haploid models.

In the classical model of genetic drift in population genetics theory, use is made of a hypothetical "infinite-gametic pool". If, instead, the gametic pool is determined by the random number of offspring per individual, a new form of natural selection acting on the variance in offspring number occurs. A diffusion model of this selection process is derived and some of its properties are explored. It is shown that, independent of the sampling scheme used, the diffusion equation has the drift coefficient M(p) = p(1-p) (mul--mu2 + sigma2e2--sigma2el) and the diffusion coefficient v(p) equals p(1-p) [psigma2e2 + (l--p)sigma2el]. It is also pointed out that the Direct Product Branching process model of genetic drift introduces a non-biological interaction between individuals and is thus inappropriate for modeling natural selection.

Alleles↗

Design of a novel hydrogel-based intelligent system for controlled drug release.

The present work focused on the design of an assembled drug delivery system (DDS) to provide multifunctions, such as drug protection, self-regulated oscillatory release, and targeted uni-directional delivery by a bilayered self-folding gate and simple surface mucoadhesion. In this device, a pH-sensitive hydrogel together with a poly(hydroxyethyl methacrylate) (HEMA) barrier was used as a gate to control drug release. In addition, poly(HEMA) coated with poly(ethylene oxide)/poly(propylene oxide)/poly(ethylene oxide) (PEO-PPO-PEO) surfactant was utilized to enhance mucoadhesion on the device surface. The release profiles of two model drugs, acid orange 8 (AO8) and bovine serum albumin (BSA) were studied in this assembled system, which compared with the conventional drug-entrapped carriers and enteric-coating systems. Furthermore, targeted uni-directional release was demonstrated in a side-by-side diffusion cell. In conclusion, for such an assembled device, the poly(HEMA) layer not only affects the folding direction but also serves as a barrier to protect the model drugs. The release time can be controlled by the thickness of the bilayered gate and the drug reservoir. Due to the reversible swelling behavior of poly(methyacrylic acid-g-ethylene glycol) (p(MAA-g-EG)) gels, the bilayered gate can sense the environmental pH change and achieve an oscillatory release pattern. Moreover, the local targeting and uni-directional release have been successfully demonstrated in vitro.

Coloring Agents↗

Experimental evaluation of an anisotropic scattering model of a slab geometry.

A model has been developed based on random walk theory that allows the diffusion of light along a principal axis to differ from that in orthogonal directions. We present expressions that describe the time-resolved intensity measured across a slab and on the surface of a semi-infinite medium for a principal axis oriented parallel or perpendicular to the surface. The model of time-resolved transmittance is compared with experimental data acquired by use of a phantom consisting of wax fibers arranged within a solid cube of resin. It is shown that a single set of optical parameters is sufficient to model the experimental measurements acquired across all three orientations of the cube.

Algorithms↗