Biomedical subjects

M J Saxton

Publications and source records attributed to M J Saxton.

At least 19 recordsLinked to original sources

PubMed2001

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study.

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster.

Diffusion↗

PubMed1997

Single-particle tracking: the distribution of diffusion coefficients.

In single-particle tracking experiments, the diffusion coefficient D may be measured from the trajectory of an individual particle in the cell membrane. The statistical distribution of single-trajectory diffusion coefficients is examined by Monte Carlo calculations. The width of this distribution may be useful as a measure of the heterogeneity of the membrane and as a test of models of hindered diffusion in the membrane. For some models, the distribution of the short-range diffusion coefficient is much narrower than the observed distribution for proteins diffusing in cell membranes. To aid in the analysis of single-particle tracking measurements, the distribution of D is examined for various definitions of D and for various trajectory lengths.

Animals↗

PubMed1997

Heat generation and dissipation in plants: can the alternative oxidative phosphorylation pathway serve a thermoregulatory role in plant tissues other than specialized organs?

A number of hypothetical physiological roles have been proposed for the cyanide-insensitive alternative pathway in plants (Palmer, 1976; Laties, 1982; Meeuse, 1984; Purvis and Shewfelt, 1994; Wagner and Krab, 1995). The calorimetric observations of Raskin and co-workers (Ordentlich et al., 1991; Nevo et al., 1992; Moynihan et al., 1995) are significant contributions showing an interesting metabolic, chilling-induced response of the alternative pathway activity and differences in the low-temperature response among species adapted to different climates. Since different oxidative pathways do not have large differences in enthalpy, and observed heat rate increases are insufficient to cause significant temperature increases of physiological importance in nonthermogenic plants, other explanations must be developed for the relationship between the partitioning of electron flow and physiological conditions such as low temperature. The induction and engagement of the alternative respiratory pathway is involved in metabolic stasis, maintaining proper balance between carbon flow, ATP-ADP ratio, and electron flow during fluctuating or extreme temperature conditions. The alternative oxidase is engaged when ATP requirements are adequately met, as discussed by Palmer (1976), Meeuse (1983), Lambers (1985), and Wagner and Krab (1995). The expression and kinetic activity of the alternative oxidase are regulated by concentrations of key metabolites (Day and Wiskich, 1995; Siedow and Umbach, 1995; Wagner and Krab, 1995; Day et al., 1996). Dynamic partitioning of electron flow between Cyt oxidase and the alternative oxidase depends on the kinetic behavior of the two oxidases and the substrate dehydrogenases (Day and Wiskich, 1995; Siedow and Umbach, 1995; Wagner and Krab, 1995; Day et al., 1996). Furthermore, Moynihan et al. (1995) found that Episces cupreata Hook, adapted to the tropics, has very little alternative oxidase activity compared with wheat (Nevo et al., 1992), adapted to a large range of temperature climates. This results is consistent with the general relation between the apparent alternative oxidase activity and the climate of origin of the species.

Hot Temperature↗

PubMed1997

Single-particle tracking: applications to membrane dynamics.

Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.

Diffusion↗

PubMed1996

Anomalous diffusion due to binding: a Monte Carlo study.

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.

Animals↗

PubMed1995

Single-particle tracking: effects of corrals.

Structural proteins of the membrane skeleton are thought to form "corrals" at the membrane surface, and these corrals may restrict lateral diffusion of membrane proteins. Recent experimental developments in single-particle tracking and laser trapping make it possible to examine the corral model in detail. Techniques to interpret these experiments are presented. First, escape times for a diffusing particle in a corral are obtained from Monte Carlo calculations and analytical solutions for various corral sizes, shapes, and escape probabilities, and reduced to a common curve. Second, the identification of corrals in tracking experiments is considered. The simplest way to identify corrals is by sight. If the walls are impermeable enough, a trajectory fills the corral before the diffusing particle escapes. The fraction of distinct sites visited before escape is calculated for corrals of various sizes, shapes, and escape probabilities, and reduced to a common curve. This fraction is also a measure of the probability that the diffusing species will react with another species in the corral before escaping. Finally, the effect of the sampling interval on the measurement of the short-range diffusion coefficient is examined.

Biophysical Phenomena↗

PubMed1994

Single-particle tracking: models of directed transport.

Single-particle tracking techniques make it possible to measure motion of individual particles on the cell surface. In these experiments, individual trajectories are observed, so the data analysis must take into account the randomness of individual random walks. Methods of data analysis are discussed for models combining diffusion and directed motion. In the uniform flow model, a tracer simultaneously diffuses and undergoes directed motion. In the conveyor belt model, a tracer binds and unbinds to a uniform conveyor belt moving with constant velocity. If a tracer is bound, it moves at the velocity of the conveyor belt; if it is unbound, it diffuses freely. Trajectories are analyzed using parameters that measure the extent and asymmetry of the trajectory. A method of assessing the usefulness of such parameters is presented, and pitfalls in data analysis are discussed. Joint probability distributions of pairs of extent and asymmetry parameters are obtained for a pure random walk. These distributions can be used to show that a trajectory is not likely to have resulted from a pure random walk.

Biological Transport, Active↗

PubMed1994

Anomalous diffusion due to obstacles: a Monte Carlo study.

In normal lateral diffusion, the mean-square displacement of the diffusing species is proportional to time. But in disordered systems anomalous diffusion may occur, in which the mean-square displacement is proportional to some other power of time. In the presence of moderate concentrations of obstacles, diffusion is anomalous over short distances and normal over long distances. Monte Carlo calculations are used to characterize anomalous diffusion for obstacle concentrations between zero and the percolation threshold. As the obstacle concentration approaches the percolation threshold, diffusion becomes more anomalous over longer distances; the anomalous diffusion exponent and the crossover length both increase. The crossover length and time show whether anomalous diffusion can be observed in a given experiment.

Biophysical Phenomena↗

PubMed1993

Lateral diffusion in an archipelago. Dependence on tracer size.

In a pure fluid-phase lipid, the dependence of the lateral diffusion coefficient on the size of the diffusing particle may be obtained from the Saffman-Delbrück equation or the free-volume model. When diffusion is obstructed by immobile proteins or domains of gel-phase lipids, the obstacles yield an additional contribution to the size dependence. Here this contribution is examined using Monte Carlo calculations. For random point and hexagonal obstacles, the diffusion coefficient depends strongly on the size of the diffusing particle, but for fractal obstacles--cluster-cluster aggregates and multicenter diffusion-limited aggregates--the diffusion coefficient is independent of the size of the diffusing particle. The reason is that fractals have no characteristic length scale, so a tracer sees on average the same obstructions, regardless of its size. The fractal geometry of the excluded area for tracers of various sizes is examined. Percolation thresholds are evaluated for a variety of obstacles to determine how the threshold depends on tracer size and to compare the thresholds for compact and extended obstacles.

Biophysical Phenomena↗

PubMed1993

Lateral diffusion in an archipelago. Single-particle diffusion.

Several laboratories have measured lateral diffusion of single particles on the cell surface, and these measurements may reveal an otherwise inaccessible level of submicroscopic organization of cell membranes. Pitfalls in the interpretation of these experiments are analyzed. Random walks in unobstructed systems show structure that could be interpreted as free diffusion, obstructed diffusion, directed motion, or trapping in finite domains. To interpret observed trajectories correctly, one must consider not only the trajectories themselves but also the probabilities of occurrence of various trajectories. Measures of the asymmetry of obstructed and unobstructed random walks are calculated, and probabilities are evaluated for random trajectories that resemble either directed motion or diffusion in a bounded region.

Cell Membrane↗

PubMed1992

Gaps in the erythrocyte membrane skeleton: a stretched net model.

The geometry of spectrin-free regions in the erythrocyte membrane skeleton is modeled using Monte Carlo calculations for an incomplete triangular lattice of entropy springs under tension. Intact springs correspond to normal spectrin molecules, and cut springs correspond to spectrin that is missing or unable to associate normally. As springs are cut and the network is allowed to relax to mechanical equilibrium, gaps in the network appear. Geometrical properties of these gaps are obtained as a function of the fraction of springs cut. The most important property modeled is the area of the largest spectrin-free region; this area increases approximately exponentially as the fraction of normal spectrin decreases from 100% to approximately 50%. The effect of these gaps on lateral diffusion and vesiculation is discussed.

Erythrocyte Membrane↗

PubMed1992

Lateral diffusion and aggregation. A Monte Carlo study.

Aggregation in a lipid bilayer is modeled as cluster-cluster aggregation on a square lattice. In the model, clusters carry out a random walk on the lattice, with a diffusion coefficient inversely proportional to mass. On contact, they adhere with a prescribed probability, rigidly and irreversibly. Monte Carlo calculations show that, as expected, rotational diffusion of the aggregating species is highly sensitive to the initial stages of aggregation. Lateral diffusion of an inert tracer obstructed by the aggregate is a sensitive probe of the later stages of aggregation. Cluster-cluster aggregates are much more effective barriers to lateral diffusion of an inert tracer than the same area fraction of random point obstacles is, but random point obstacles are more effective barriers than the same area fraction of compact obstacles. The effectiveness of aggregates as obstacles is discussed in terms of particle-particle correlation functions and fractal dimensions. Results are applicable to aggregation of membrane proteins, and at least qualitatively to aggregation of gel-phase lipid during lateral phase separation.

Diffusion↗

PubMed1991

Oligosaccharide signaling in plants. Specificity of oligouronide-enhanced plasma membrane protein phosphorylation.

The in vitro phosphorylation by [gamma-32P]ATP of a 34-kDa plasma membrane-associated protein (pp34) from tomato and potato is strongly enhanced in the presence of alpha-1,4-D-polygalacturonic acid (PGA) fragments (Farmer, E. E., Pearce, G., and Ryan, C. A. (1989) Proc. Natl. Acad. Sci. U. S. A. 86, 1539-1542) that activate the expression of defensive and developmental genes in plant tissues. [gamma-35S]ATP, but not [gamma-35S]GTP, has now been found to strongly label pp34 in the presence of the PGA fragments. PGA-enhanced phosphorylation of pp34 is at one or more threonine residue(s) and therefore is the product of a serine/threonine kinase. alpha-1,4-L-Polyguluronic acid (PGU) enhances thiophosphorylation of pp34, but is less effective than PGA. beta-1,4-D-Polymannuronic acid (PMA) is inactive. In vivo synthesis of proteinase inhibitors in tomato leaves in response to PGA, PGU, and PMA parallels enhancing activities in in vitro phosphorylation assays. The minimum oligogalacturonide lengths that enhance in vitro thiophosphorylation of pp34 are about 14-15 residues, which are near the minimum sizes of uronides required to elicit a variety of localized defensive and developmental responses in plants. The lengths of biologically active galacturonic acid oligomers are of the same length that form strong intermolecular complexes in solution with Ca2+. Uronide-Ca2+ complexes are proposed to be the active molecular species that initiate the signal transduction pathways regulating uronide-responsive genes.

Adenosine Triphosphate↗

PubMed1990

The membrane skeleton of erythrocytes: models of its effect on lateral diffusion.

The membrane skeleton, a network of structural proteins attached to the cytoplasmic surface of the plasma membrane, hinders lateral diffusion of integral proteins. 2. In some types of cells, such as epithelial cells and nerve cells, the obstruction of lateral diffusion by the membrane skeleton is one of the mechanisms by which proteins are localized to domains on the cell surface. 3. The effect of the membrane skeleton on lateral diffusion may involve steric hindrance, transient binding or both. Three pictures of the effect are reviewed, the discrete barrier model, the continuous barrier model and the transient binding model. 4. Experiments to distinguish the models are discussed.

Animals↗

PubMed1990

Lateral diffusion in a mixture of mobile and immobile particles. A Monte Carlo study.

The lateral diffusion coefficient for mixtures of mobile and immobile particles is obtained from Monte Carlo calculations of random walks by mobile tracers in the presence of immobile obstacles on a triangular lattice. The diffusion coefficient of the mobile species is obtained as a function of the area fractions of mobile and immobile species. The results are applied to diffusion of band 3 in the erythrocyte membrane, and indicate that obstruction of diffusion of mobile band 3 by band 3 and glycophorin attached to the membrane skeleton is not sufficient to explain the observed diffusion coefficient.

Animals↗

PubMed1990

The membrane skeleton of erythrocytes. A percolation model.

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.

Algorithms↗

PubMed1989

Concentration effects on reactions in membranes: rhodopsin and transducin.

The reaction rate of two laterally-diffusing species in a biological membrane shows a maximum at some concentration of reactants, because an increase in the concentration of reactants tends to increase the reaction rate by the law of mass action but decreases the diffusion rate of the reactants. The activation of transducin by rhodopsin in the disk membrane of the rod outer segment is described in terms of a steady-state diffusion model with concentration-dependent diffusion coefficients. The optimum concentrations of reactants are obtained from contour plots of the reaction rate as a function of rhodopsin and transducin concentrations, and the sensitivity of the results to the assumed values of the variables is examined. To determine whether the observed concentrations are in fact those yielding the maximum reaction rate, several variables must be known more accurately.

Diffusion↗

PubMed1989

Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient.

An understanding of the distance dependence of the lateral diffusion coefficient is useful in comparing the results of diffusion measurements made over different length scales, and in analyzing the kinetics of mobile redox carriers in organelles. A distance-dependent, concentration-dependent diffusion coefficient is defined, and it is evaluated by Monte Carlo calculations of a random walk by mobile point tracers in the presence of immobile obstacles on a triangular lattice, representing the diffusion of a lipid or a small protein in the presence of immobile membrane proteins. This work confirms and extends the milling crowd model of Eisinger, J., J. Flores, and W. P. Petersen (1986. Biophys J. 49:987-1001). Similar calculations for diffusion of mobile particles interacting by a hard-core repulsion yield the distance dependence of the self-diffusion coefficient. An expression for the range of short-range diffusion is obtained, and the distance scales for various diffusion measurements are summarized.

Diffusion↗