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PubMed2006

The depolymerizing kinesin MCAK uses lattice diffusion to rapidly target microtubule ends.

The microtubule cytoskeleton is a dynamic structure in which the lengths of the microtubules are tightly regulated. One regulatory mechanism is the depolymerization of microtubules by motor proteins in the kinesin-13 family. These proteins are crucial for the control of microtubule length in cell division, neuronal development and interphase microtubule dynamics. The mechanism by which kinesin-13 proteins depolymerize microtubules is poorly understood. A central question is how these proteins target to microtubule ends at rates exceeding those of standard enzyme-substrate kinetics. To address this question we developed a single-molecule microscopy assay for MCAK, the founding member of the kinesin-13 family. Here we show that MCAK moves along the microtubule lattice in a one-dimensional (1D) random walk. MCAK-microtubule interactions were transient: the average MCAK molecule diffused for 0.83 s with a diffusion coefficient of 0.38 microm2 s(-1). Although the catalytic depolymerization by MCAK requires the hydrolysis of ATP, we found that the diffusion did not. The transient transition from three-dimensional diffusion to 1D diffusion corresponds to a "reduction in dimensionality" that has been proposed as the search strategy by which DNA enzymes find specific binding sites. We show that MCAK uses this strategy to target to both microtubule ends more rapidly than direct binding from solution.

Adenosine Triphosphate↗
PubMed2002

Pattern formation by a cell surface-associated morphogen in Myxococcus xanthus.

In response to starvation, an unstructured population of identical Myxococcus xanthus cells rearranges into an asymmetric, stable pattern of multicellular fruiting bodies. Central to this pattern formation process are changes in organized cell movements from swarming to aggregation. Aggregation is induced by the cell surface-associated C-signal. To understand how aggregation is accomplished, we have analyzed how C-signal modulates cell behavior. We show that C-signal induces a motility response that includes increases in transient gliding speeds and in the duration of gliding intervals and decreases in stop and reversal frequencies. This response results in a switch in cell behavior from an oscillatory to a unidirectional type of behavior in which the net-distance traveled by a cell per minute is increased. We propose that the C-signal-dependent regulation of the reversal frequency is essential for aggregation and that the remaining C-signal-dependent changes in motility parameters contribute to aggregation by increasing the net-distance traveled by starving cells per minute. In our model for symmetry-breaking and aggregation, C-signal transmission is a local event involving direct contacts between cells that results in a global organization of cells. This pattern formation mechanism does not require a diffusible substance or other actions at a distance. Rather it depends on contact-induced changes in motility behavior to direct cells appropriately

Bacterial Proteins↗
PubMed2005

Facilitated diffusion in chromatin lattices: mechanistic diversity and regulatory potential.

The interaction between a protein and a specific DNA site is the molecular basis for vital processes in all organisms. Location of the DNA target site by the protein commonly involves facilitated diffusion. Mechanisms of facilitated diffusion vary among proteins; they include one- and two-dimensional sliding along DNA, direct transfer between uncorrelated sites, as well as combinations of these mechanisms. Facilitated diffusion has almost exclusively been studied in vitro. This review discusses facilitated diffusion in the context of the living cell and proposes a theoretical model for facilitated diffusion in chromatin lattices. Chromatin structure differentially affects proteins in different modes of diffusion. The interplay of facilitated diffusion and chromatin structure can determine the rate of protein association with the target site, the frequency of association-dissociation events at the target site, and, under particular conditions, the occupancy of the target site. Facilitated diffusion is required in vivo for efficient DNA repair and bacteriophage restriction and has potential roles in fine-tuning gene regulatory networks and kinetically compartmentalizing the eukaryotic nucleus.

Chromatin↗
PubMed1979

Two-carrier influx of neutral amino acids into rabbit ileal mucosa.

1. The influx of serine, alanine and methionine across the brush border membrane of the rabbit ileal mucosa has been measured during short periods of incubation. 2. A kinetic analysis of the uptake data, assuming one mediated entry mechanism or one mediated entry mechanism plus a diffusion component to be present, does not provide an adequate explanation for the results obtained. Methionine inhibition of serine uptake provided direct evidence that the diffusive entry of serine into the rabbit ileum was small or non-existent. 3. Data taken from amino acid inhibition and substrate-uptake experiments, fitted simultaneously to a double hyperbolic model of amino acid uptake, give good agreement between predicted and experimental results. There is also good quantitative agreement between computer-derived kinetic constants in the present work and similar constants obtained previously using a different method of analysis. 4. Present work supports the general hypothesis that neutral amino acids use two mediated pathways to enter the rabbit ileal mucosa. The possible physiological significance of these results and their probable effect on currently held concepts of how amino acids cross the brush border membrane of the rabbit intestinal mucosa is discussed.

Alanine↗
PubMed2006

Modeling cardiac electrical activity at the cell and tissue levels.

Significant tissue structures exist in cardiac ventricular tissue, which are of supracellular dimension. It is hypothesized that these tissue structures contribute to the discontinuous spread of electrical activation, may contribute to arrhythmogenesis, and also provide a substrate for effective cardioversion. However, the influences of these mesoscale tissue structures in intact ventricular tissue are difficult to understand solely on the basis of experimental measurement. Current measurement technology is able to record at both the macroscale tissue level and the microscale cellular or subcellular level, but to date it has not been possible to obtain large volume, direct measurements at the mesoscales. To bridge this scale gap in experimental measurements, we use tissue-specific structure and mathematical modeling. Our models, which can incorporate ion channel models at the cell level into the reaction-diffusion equations at the tissue level, have enabled us to consider key hypotheses regarding discontinuous activation.

Heart↗
PubMed1989

Restricted expression of CD2 among subsets of sheep thymocytes and T lymphocytes.

A monoclonal antibody (mAb) generated against sheep T-cell blasts, called I/35 A, blocks sheep autologous E rosetting and competes with purified T11 target structure (TS), the sheep form of LFA3, for binding sites on the sheep T-cell surface. Immunoprecipitation from lysates of surface iodinated sheep T cells identifies the cell surface molecule recognized by mAb I/35 A as a single chain polypeptide migrating as a diffuse band of MW 55,000. From its binding properties and the biochemical nature of the target antigen, we conclude that mAb I/35 A is directed at sheep CD2. This finding makes sheep the first animal model in which the CD2-LFA3 (T11TS) system is defined by mAbs to both receptor and ligand. When analysed by two-colour flow cytometry and by immunohistochemistry, the cellular expression of CD2 in sheep differs significantly to that reported in humans. In peripheral blood, CD2 is found exclusively on CD4+8- and CD4-8+ T cells, while the third, CD4-8- (predominantly SBU-T19+) subset of sheep T cells (around 20% in peripheral blood) is CD2-. In thymus, only low to moderate levels of CD2 expression occurs on 80% of cells. Among these, medullary 'single positive' thymocytes express the highest level of CD2, whereas the CD4-8- 'double negative' population (which in contrast to peripheral CD4-8- T cells contains only very few SBU-T19+ cells) consists of CD2- and weakly positive cells. In peripheral lymphoid organs, CD2+ lymphocytes occur in the T-cell regions of spleen, lymph nodes and jejunal Peyer's patches (JPP). Tissue macrophages found in B-cell follicles of lymph nodes and JPP are also CD2+. The implications of these findings are discussed in terms of the role CD2 plays in the proliferation of immature thymocytes and of the possible importance of CD2/LFA3 interactions in lymphocyte recirculation.

Animals↗
PubMed2003

Monte Carlo modeling of an integrating sphere reflectometer.

The Monte Carlo method has been applied to numerical modeling of an integrating sphere designed for hemispherical-directional reflectance factor measurements. It is shown that a conventional algorithm of backward ray tracing used for estimation of characteristics of the radiation field at a given point has slow convergence for small source-to-sphere-diameter ratios. A newly developed algorithm that substantially improves the convergence by calculation of direct source-induced irradiation for every point of diffuse reflection of rays traced is described. The method developed is applied to an integrating sphere reflectometer for the visible and infrared spectral ranges. Parametric studies of hemispherical radiance distributions for radiation incident onto the sample center were performed. The deviations of measured sample reflectance from the actual reflectance as a result of various factors were computed. The accuracy of the results, adequacy of the reflectance model, and other important aspects of the algorithm implementation are discussed.

Journal Article↗
PubMed1999

The binding of arachidonic acid in the cyclooxygenase active site of mouse prostaglandin endoperoxide synthase-2 (COX-2). A putative L-shaped binding conformation utilizing the top channel region.

The chemical mandates for arachidonic acid conversion to prostaglandin G(2) within the cyclooxygenase (COX) active site predict that the substrate will orient in a kinked or L-shaped conformation. Molecular modeling of arachidonic acid in sheep COX-1 confirms that this L-shaped conformation is possible, with the carboxylate moiety binding to Arg-120 and the omega-end positioned above Ser-530 in a region termed the top channel. Mutations of Gly-533 to valine or leucine in the top channel of mCOX-2 abolished the conversion of arachidonic acid to prostaglandin G(2), presumably because of a steric clash between the omega-end of the substrate and the introduced side chains. A smaller G533A mutant retained partial COX activity. The loss of COX activity with these mutants was not the result of reduced peroxidase activity, because the activity of all mutants was equivalent to the wild-type enzyme and the addition of exogenous peroxide did not restore full COX activity to any of the mutants. However, the Gly-533 mutants were able to oxidize the carbon 18 fatty acid substrates linolenic acid and stearidonic acid, which contain an allylic carbon at the omega-5 position. In contrast, linoleic acid, which is like arachidonic acid in that its most omega-proximal allylic carbon is at the omega-8 position, was not oxidized by the Gly-533 mutants. Finally, the ability of Gly-533 mutants to efficiently process omega-5 allylic substrates suggests that the top channel does not serve as a product exit route indicating that oxygenated substrate diffuses from the cyclooxygenase active site in a membrane proximal direction.

Animals↗
PubMed2003

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect.

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.

Animals↗
PubMed2001

Iontophoretic transport of oligonucleotides across human epidermal membrane: a study of the Nernst-Planck model.

The objective of this study was to investigate the transport behavior of a series of oligonucleotides with human epidermal membrane (HEM) and to examine the applicability of the modified NERNST-PLANCK model to transdermal iontophoresis of these macromolecules. Iontophoretic transport experiments were first carried out in a synthetic model membrane system (Nuclepore membranes) with a four-electrode potentiostat to examine the baseline modified NERNST-PLANCK model. The modified NERNST-PLANCK model derived from the Einstein relation and the Stokes-Einstein equation taken from previous work did not hold for the oligonucleotides. Results obtained in the Nuclepore studies were, however, consistent with predictions of the modified NERNST-PLANCK model using the experimentally determined electromobilities and diffusion coefficients. The electromobilities of the oligonucleotides (determined by capillary electrophoresis) were found to be more than a factor of two smaller than expected from the Einstein relation between electromobilities and diffusion coefficients (the latter determined in diffusion cell experiments). A correlation between these electromobilities and the theoretical electromobilities estimated by considering the effects of counterion binding and the effects of mobility reduction according to colloid theory was also observed. These results suggest that the modified NERNST-PLANCK model predictions are satisfactory only when the electromobilities and the effective molecular size of the oligonucleotides are known and are used directly to predict the iontophoretically enhanced transport. Results with the HEM experiments generally agreed with model predictions based on the experimental electromobilities. The oligonucleotide HEM flux data also suggest the existence of pores with effective pore radii greater than the effective radii estimated in previous studies with small molecular weight model permeants.

Biological Transport↗
PubMed1987

[Experimental evaluation of dura mater permeability on a model of peridural analgesia with morphine and dikain].

The permeability of spinal dura mater (DM) in 14 people after sudden death was studied on the model of peridural analgesia with morphine and dikain. The DM permeability was found to linearly increase in caudal direction and within the limits of 10 segments of thoracolumbar section of the peridural space (from T2-3 to L1-2) it is increased by 170% for morphine and 200% for dikain. The diffusion of 14-18% of the epidurally injected dosage of morphine and 18-27% of dikain through the dura mater takes place depending on the segmentary level. This correlation should be taken into account for the achievement of the most pronounced antinociceptive effect and prevention of complications.

Adult↗
PubMed2006

Head-mounted goggles for murine form deprivation myopia.

Recently a murine model has been developed for use in form deprivation myopia experiments. Due to the small size of the head and eye, methods to blur visual input to the mouse eye are challenging. Previous methods to induce form deprivation include lid suture and gluing diffuser goggles directly to the fur around the eye. In this paper we describe a new method of goggling using a head pedestal and goggle, which improves compliance and allows for better ocular health. Nob mice, previously shown to be highly susceptible to form deprivation myopia, were used for these experiments. Immediately following baseline refraction using an infrared automated photorefractor, mice were either goggled with a diffuser attached directly to the fur or with a head-mounted goggling apparatus. The goggle apparatus consists of five main components: goggle and frame, head pedestal, acrylic cube for stabilization, and balancing bar. Mice were goggled for 2 weeks in which ocular health and goggle position was monitored and then had a final refraction. The use of head-mounted goggles resulted in 75% fewer instances of goggle loss and 55% fewer ocular complications compared to goggles glued to the fur. Both goggling methods induced a myopic shift of approximately 5 diopters. The head-mounted goggle apparatus provides an improved method for inducing form deprivation in mice and offers the ability to easily take repeated refractive measurements as well as allowing for the use of defocusing lenses.

Animals↗
PubMed2004

Compartmental modeling of transdermal iontophoretic transport: I. In vitro model derivation and application.

PURPOSE: The objective of this study was to develop a family of compartmental models to describe in a strictly quantitative manner the transdermal iontophoretic transport of drugs in vitro. METHODS: Two structurally different compartmental models describing the in vitro transport during iontophoresis and one compartmental model describing the in vitro transport in post-iontophoretic period are proposed. These models are based on the mass transfer from the donor compartment to the acceptor compartment via the skin as an intermediate compartment. In these models, transdermal iontophoretic transport is characterized by 5 parameters: 1) kinetic lag time (tL), 2) steady-state flux during iontophoresis (Jss), 3) skin release rate constant (K(R)), 4) the first-order rate constant of the iontophoretic driving force from the skin to the acceptor compartment (I1), and 5) passive flux in the post-iontophoretic period (Jpas). The developed models were applied to data on the iontophoretic transport in human stratum corneum in vitro of R-apomorphine after pretreatment with phosphate buffered saline pH 7.4 (PBS) and after pretreatment with surfactant (SFC), as well as the iontophoretic transport of 0.5 mg ml(-1) rotigotine at pH 5 (RTG). RESULTS: All of the proposed models could be fitted to the transport data of PBS, SFC, and RTG groups both during the iontophoresis and in the post-iontophoretic period. The incorporation of parameter I1 failed to improve the fitting performance of the model. This might indicate a negligible contribution of iontophoretic driving force to the mass transfer in the direction from the skin to the acceptor compartment, although it plays an important role in loading the skin with the drug. The estimated values of Jss of PBS, SFC, and RTG were identical (p > 0.05) to the values obtained with the diffusion lag time method. Moreover, time required to achieve steady-state flux can be estimated based on the parameter tL and the reciprocal value of parameter K(R). In addition, accumulation of drug molecules in the skin is reflected in a reduction of the value of the K(R) parameter. CONCLUSIONS: The developed in vitro models demonstrated their strength and consistency to describe the drug transport during and post-iontophoresis.

Administration, Cutaneous↗
PubMed1994

Analysis and correction of motion artifacts in diffusion weighted imaging.

For diffusion-weighted magnetic resonance imaging and under circumstances where patient movement can be modeled as rigid body motion, it is shown both theoretically and experimentally that translations and rotations produce phase errors which are zero- and first-order, respectively, in position. While a navigator echo can be used to correct the imaging data for arbitrary translations, only when the diffusion gradient is applied in the phase encode direction is there sufficient information to correct for rotations around all axes, and therefore for general rigid body motion. Experiments in test objects and human brain imaging confirm theoretical predictions and demonstrate that appropriate corrections dramatically improve image quality in vivo.

Algorithms↗
PubMed2004

Scientific approach to the optimization of protein crystallization conditions for microgravity experiments.

The National Space Development Agency of Japan (NASDA) developed a practical protocol to optimize protein crystallization conditions for microgravity experiments. This protocol focuses on the vapor diffusion method using high density protein crystal growth (HDPCG)--hardware developed by the University of Alabama, Birmingham--that flew on the STS-107 mission. The objective of this development was to increase the success rate of microgravity experiments by setting crystallization conditions based on knowledge of crystal growth and fluid dynamics. The protocol consists of four steps: (1) phase diagram preparation, (2) estimation of condensation rate in the vapor diffusion method, (3) fluid dynamic property measurement, and (4) fluid dynamic simulation. First, a phase diagram was constructed. Crystallization characteristics were investigated by a microbatch method. The data were recalculated based on classical nucleation theory and the crystallization boundary was determined as a function of time. The second step was to develop a practical model to estimate the condensation rate of the crystallizing solution, including protein and precipitant, as a function of the precipitant concentration and solution volume. By considering the crystallization map and the vapor diffusion condensation model we were able to optimize the crystallization conditions that generate crystals in the desired time. This was particularly important in a shuttle mission whose mission duration is limited. The third step was fluid dynamic property measurement necessary for fluid dynamics simulation and crystal growth study. The last step was to estimate the mass transport in space on the basis of the fluid dynamics simulation transport model. It turned out that neither the vapor phase nor the solution phase was seriously affected by gravity until nucleation provided the hardware was set in a normal direction. Therefore, we concluded that the optimized crystallization conditions could be directly applied to microgravity experiments. By completing the approach, we were able to control the time for nucleation in the vapor diffusion method.

Animals↗
PubMed2001

Non-ideality by sedimentation velocity of halophilic malate dehydrogenase in complex solvents.

We have investigated the potential of sedimentation velocity analytical ultracentrifugation for the measurement of the second virial coefficients of proteins, with the goal of developing a method that allows efficient screening of different solvent conditions. This may be useful for the study of protein crystallization. Macromolecular concentration distributions were modeled using the Lamm equation with the approximation of linear concentration dependencies of the diffusion constant, D = D(o) (1 + k(D)c), and the reciprocal sedimentation coefficient s = s(o)/(1 + k(s)c). We have studied model distributions for their information content with respect to the particle and its non-ideal behavior, developed a strategy for their analysis by direct boundary modeling, and applied it to data from sedimentation velocity experiments on halophilic malate dehydrogenase in complex aqueous solvents containing sodium chloride and 2-methyl-2,4-pentanediol, including conditions near phase separation. Using global modeling for three sets of data obtained at three different protein concentrations, very good estimates for k(s) and s degrees and also for D degrees and the buoyant molar mass were obtained. It was also possible to obtain good estimates for k(D) and the second virial coefficients. Modeling of sedimentation velocity profiles with the non-ideal Lamm equation appears as a good technique to investigate weak inter-particle interactions in complex solvents and also to extrapolate the ideal behavior of the particle.

Diffusion↗
PubMed1989

The simulation of continuous arteriovenous hemodialysis with a mathematical model.

We have developed a mathematical model that predicts the performance of continuous arteriovenous hemodialysis. Given patient (plasma protein concentration, hematocrit, mean arterial pressure, central venous pressure) and circuit (flow resistance, membrane hydraulic permeability, dialyzer mass transfer coefficient, ultrafiltrate column height, dialysate flow rate) characteristics as inputs, predictions of hydraulic and oncotic pressure distribution, filtration rate, blood flow, total, diffusive, and convective urea clearances are provided. The model was tested by perfusing a circuit with bovine blood under conditions of pure ultrafiltration, zero net ultrafiltration and dialysis, or combined ultrafiltration and dialysis (countercurrent dialysate flow at rates of 10, 20, and 30 ml/min). In order to permit computation, membrane hydraulic permeability and flow resistances were measured. Dialyzer mass transfer coefficient for urea could not be measured directly and so was determined by fitting model predictions to measured urea clearances. For all conditions of operation, a urea mass transfer coefficient of 0.014 cm/min successfully simulated the data. Predictions of blood flow, filtrate generation rate, and circuit pressure distribution were accurate. At lower dialysate flow rates, urea clearance approximated the sum of dialysate flow and filtration rate. At higher dialysate flows, however, departure from this ideal blood-dialysate equilibrium was observed. Model predictions regarding the relative contributions of diffusion and convection to urea clearance were explored. Under conditions of nearly perfect equilibration of urea between blood and dialysate at the blood inlet, the model predicts that the diffusive clearance of urea will increase with increasing rate of filtration and may exceed the rate of dialysate inflow.

Hemofiltration↗
PubMed1994

Significance of viable skin layers in percutaneous permeation and its implication in mathematical models: theoretical consideration based on parameters for betamethasone 17-valerate.

The role of viable skin layers (viable epidermis and dermis) is examined by the three-layer model using parameter values for betamethasone 17-valerate. The mathematical three-layer diffusion model indicates that the lag time and half-life after vehicle removal in epidermis and split-thickness skin are longer than those in stratum corneum without viable layers, even if drug flux at steady-state is minimally altered. The theoretical values of the lag time and half-life predicted for epidermis and split-thickness-skin samples are compatible with the values observed in another in vitro study. The results predicted by the three-layer model indicate that the simplified model (single-layer or compartment model), which regards the whole skin as one diffusion layer or one compartment, may be warranted because all three skin layers have the same half-life after vehicle removal. The parameters used in the simplified model are estimated from some of the following values directly obtainable in the experiment: flux from skin and amount in the whole skin at steady-state, lag time, and drug concentration or amount maintained to be unchanged in the donor site. However, the simplified model often cannot resolve some discrepancy between the data and model (e.g., the ratio of the half-life to lag time) even if the data may be explained by the three-layer model.

Betamethasone Valerate↗