On the stochastic theory of compartments: Solution forn-compartment systems with irreversible,time-dependent transition probabilities

The bivariate distribution of a two-compartment stochastic system with irreversible, time-dependent transition probabilities is obtained for any point in time. The mean and variance of the number of particles in any compartment and the covariance between the number of particles in each of the two compartments are exhibited and compared to existing results. The two-compartment system is then generalized to ann-compartment catenary and to ann-compartment mammillary system. The multivariate distributions of these two systems are obtained under two sets of initial conditions: (1) the initial distribution is known; and (2) the number of particles in each compartment of the system at timet=0 is determined. The moments of these distributions are also produced and compared with existing results.     

Cytoplasmic motions, rheology, and structure probed by a novel magnetic particle method

The motions of magnetic particles contained within organelles of living cells were followed by measuring magnetic fields generated by the particles. The alignment of particles was sensed magnetometrically and was manipulated by external fields, allowing non-invasive detection of particle motion as well as examination of cytoplasmic viscoelasticity. Motility and rheology data are presented for pulmonary macrophages isolated from lungs of hamsters 1 d after the animals had breathed airborne gamma-Fe2O3 particles. The magnetic directions of particles within phagosomes and secondary lysosomes were aligned, and the weak magnetic field produced by the particles was recorded. For dead cells, this remanent field was constant, but for viable macrophages, the remanent field decreased rapidly so that only 42% of its initial magnitude remained 5 min after alignment. A twisting field was applied perpendicular to the direction of alignment and the rate at which particles reoriented to this new direction was followed. The same twisting was repeated for particles suspended in a series of viscosity standards. Based on this approach, the low-shear apparent intracellular viscosity was estimated to be 1.2-2.7 X 10(3) Pa.s (1.2-2.7 X 10(4) poise). Time-lapse video microscopy confirmed the alignment of ingested particles upon magnetization and showed persistent cellular motility during randomization of alignment. Cytochalasin D and low temperature both reduced cytoplasmic activity and remanent-field decay, but affected rheology differently. Magnetic particles were observed in association with the microtubule organizing center by immunofluorescence microscopy; magnetization did not affect microtubule distribution. However, both vimentin intermediate filaments and f-actin reorganized after magnetization. These data demonstrate that magnetometry of isolated phagocytic cells can probe organelle movements, rheology, and physical properties of the cytoskeleton in living cells.     

Influence of apolipoprotein A-I and apolipoprotein A-II availability on nascent HDL heterogeneity

It is important to understand HDL heterogeneity because various subspecies possess different functionalities. To understand the origins of HDL heterogeneity arising from the existence of particles containing only apoA-I (LpA-I) and particles containing both apoA-I and apoA-II (LpA-I+A-II), we compared the abilities of both proteins to promote ABCA1-mediated efflux of cholesterol from HepG2 cells and form nascent HDL particles. When added separately, exogenous apoA-I and apoA-II were equally effective in promoting cholesterol efflux, although the resultant LpA-I and LpA-II particles had different sizes. When apoA-I and apoA-II were mixed together at initial molar ratios ranging from 1:1 to 16:1 to generate nascent LpA-I+A-II HDL particles, the particle size distribution altered, and the two proteins were incorporated into the nascent HDL in proportion to their initial ratio. Both proteins formed nascent HDL particles with equal efficiency, and the relative amounts of apoA-I and apoA-II incorporation were driven by mass action. The ratio of lipid-free apoA-I and apoA-II available at the surface of ABCA1-expressing cells is a major factor in determining the contents of these proteins in nascent HDL. Manipulation of this ratio provides a means of altering the relative distribution of LpA-I and LpA-I+A-II HDL particles.     

Behavior of magnetic particles in hamster lungs: estimates of clearance and cytoplasmic motility

Ferrimagnetic particles suspended in saline were instilled intratracheally into the lungs of Syrian golden hamsters. The particles were magnetized and aligned by applying an external magnetic field. Upon removal of the external field, the particles produced a remanent magnetic field from the lungs which decayed due to random misalignment of the particles (relaxation). Magnetization and relaxation measurements were performed immediately after instillation, then repeatedly during the first 24 h, and finally at intervals of several days up to 30 days after the instillation. The size of the initial remanent magnetic field immediately following each external magnetization is a measure of the amount of iron oxide in the lungs. It decreased with time, reflecting particle clearance. The rate of relaxation increased steeply during the first 12 h after the instillation and decreased slowly between the 5th and 30th day. Changes in the location of particles from extracellular to intracellular sites and movements from ectoplasmic to endoplasmic sites within cells may be responsible for the observed changes in relaxation rates with time.     

Distribution of Intramembrane Particles and Its Changes during the Acrosome Reaction in Spermatozoa of the Japanese Abalone

The distribution of intramembrane particles in the plasma and acrosomal membranes of sperm of the Japanese abalone, Haliotis discus , and its changes during the acrosome reaction were studied by the freeze-fracture replica technique. The P face of the plasma membrane covering the acrosome has sparse membrane particles except in the apical region, which includes the trigger and 'truncated cone' regions. Large particles with an average diameter of 10 nm are located in this apical region. The E face of the plasma membrane has only a few particles. On the outer acrosomal membrane, many particles are randomly distributed throughout the P face, but only a small number of particles are found on the E face. Numerous particles on the P face of the inner acrosomal membrane show a regular arrangement as a dense lattice or with a concentric circular pattern. The initial change in the acrosome reaction is clearance of membrane particles from both the P and E faces of the plasma and outer acrosomal membranes around the apical region, where fusion of the two membranes occurs. As the acrosomal process elongates, the dense arrangement of particles on the inner acrosomal membrane changes via a loose lattice arrangement to a patchy distribution with particle-free areas. Then the arrangement is further disorganized becoming a sparse, random distribution.     

Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-time distribution for the local exchange model

Fine particles suspended in turbulent water exhibit highly irregular trajectories as they are buffeted by fluid eddies. The Local Exchange Model provides a stochastic diffusion approximation to the randomlike motion of such particles (e.g. dispersing benthic organisms in a stream). McNair et al. (1997, J. theor. Biol.188, 29) used this model to derive equations governing the mean hitting time, which is the expected time until a particle hits bottom for the first time from a given initial elevation. The present paper derives equations governing the probability distribution of the hitting time, then studies the distribution's dependence on a particle's initial elevation and two dimensionless parameters. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-time distribution is strongly skewed to the right, with mode相似文献   

Electro-optic decay analysis for polydisperse systems

The decay curves of electro-optic transients are generally used to measure the rotary diffusion contants (D) of colloidal particles in suspension or biopolymers in solution. Analysis usually is made by plotting the logarithm of the decay as a function of time, t. Curvature in such plots the presence of several values of D and hence a distribution of particle sizes. In this case, analysis of the complete curve to yield the distribution is severely restricted by lack of precision in the experimental data. The most reliable and reproducible part of the decay curve is the initial (t =0)slope. This paper develops theory for the initial slope for dilute suspensions of long thin cylinders with various electrical properties. It is shown that the inital slope depends not only on the particle-size distribution and electric field strength, but also on the nature of the electrical properties of the molecules. Futhermore, for an identical polydisperse system. transient electric birefringence, electric optical rotation, and electric dichroism on the one hand, and transient electric light scattering on the other, yield different initial slopes and hence apperently different values for D. These important conclusions have not been appereciated in previous studies and indicate the need for caution when comparing data from different experimental methods. I11ustrative calculations are presented for a polydisperse system of long thin cylinders having a normal distribution in lengths, but of uniform diameter. Some preliminary measurement support the theory.     

The kinetics of cellular aggregation induced by turbulent flow

A theoretical treatment for the aggregation of cellular dispersions in a turbulent fluid is proposed based on the work of Saffman &; Turner (1956). The use of an expression for the rate of collisions between cells and cell aggregates which is dependent on the size of the colliding cell particles gives theoretical results which markedly reflect many of the features of cellular aggregation as found experimentally by pulse height analysis using a Coulter counter and particle size discriminator. In particular the shape of the distribution curves, the rate of change of single cell population and the attainment of an equilibrium state as well as the occurrence of cell aggregate redistribution during aggregation are shown to be consistent with aggregation in a turbulent field.It is also shown that the nature of the initial cell aggregate distribution has a very significant effect on subsequent aggregation kinetics.The theory has been applied to the aggregation of two Chinese hamster cell lines and gives a satisfactory explanation of the experimental results.     

Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-distance problem for the local exchange model

The local exchange model developed by McNair et al. (1997) provides a stochastic diffusion approximation to the random-like motion of fine particles suspended in turbulent water. Based on this model, McNair (2000) derived equations governing the probability distribution and moments of the hitting time, which is the time until a particle hits the bottom for the first time from a given initial elevation. In the present paper, we derive the corresponding equations for the probability distribution and moments of the hitting distance, which is the longitudinal distance a particle has traveled when it hits the bottom for the first time. We study the dependence of the distribution and moments on a particle's initial elevation and on two dimensionless parameters: an inverse Reynolds number M (a measure of the importance of viscous mixing compared to turbulent mixing of water) and the Rouse number ?(a measure of the importance of deterministic gravitational sinking compared to stochastic turbulent mixing in governing the vertical motion of a particle). We also compute predicted hitting-distance distributions for two published data sets. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-distance distribution is strongly skewed to the right, with mode相似文献   

The critical electric field in heated SF<Subscript>6</Subscript>

The critical electric field at which the ionization rate is equal to the rate of electron attachment to neutral particles in heated sulfur hexafluoride (SF₆) is calculated by numerically solving the Boltzmann equation for electrons. It is shown that the main causes of a decrease in the critical field with increasing gas temperature are the change in the electron energy distribution due to gas dissociation and the reduction in the rate of electron attachment to neutral particles. The calculated results are in qualitative agreement with the available experimental data.     

Image segmentation for automatic particle identification in electron micrographs based on hidden Markov random field models and expectation maximization

Three-dimensional reconstruction of large macromolecules like viruses at resolutions below 10 A requires a large set of projection images. Several automatic and semi-automatic particle detection algorithms have been developed along the years. Here we present a general technique designed to automatically identify the projection images of particles. The method is based on Markov random field modelling of the projected images and involves a pre-processing of electron micrographs followed by image segmentation and post-processing. The image is modelled as a coupling of two fields--a Markovian and a non-Markovian. The Markovian field represents the segmented image. The micrograph is the non-Markovian field. The image segmentation step involves an estimation of coupling parameters and the maximum á posteriori estimate of the realization of the Markovian field i.e, segmented image. Unlike most current methods, no bootstrapping with an initial selection of particles is required.     

Coulomb explosion in a cluster plasma

The energy spectra of particles in a cluster plasma produced during the Coulomb explosion of spherically symmetric clusters with an arbitrary initial density distribution are investigated. A relationship is found between the energy spectrum of the ions and the density profile of the atoms in the cluster.     

Implicit Estimation of Ecological Model Parameters

We introduce an implicit method for state and parameter estimation and apply it to a stochastic ecological model. The method uses an ensemble of particles to approximate the distribution of model solutions and parameters conditioned on noisy observations of the state. For each particle, it first determines likely values based on the observations, then samples around those values. This approach has a strong theoretical foundation, applies to nonlinear models and non-Gaussian distributions, and can estimate any number of model parameters, initial conditions, and model error covariances. The method is called implicit because it updates the particles without forming a predictive distribution of forward model integrations. As a point of comparison for different assimilation techniques, we consider examples in which one or more bifurcations separate the true parameter from its initial approximation. The implicit estimator is asymptotically unbiased, has a root-mean-squared error comparable to or less than the other methods, and is accurate even with small ensemble sizes.     

On the thermodynamic characterization of membrane gating particles by their Boltzmann distribution

The characterizations of gating particles of ionic channels in nerve membranes by their equivalent valencies and their electric dipole moment changes are compared. The gating particle is represented as a system of electric charges in fixed positions in an external electric field and the potential energy of such a system is calculated in the approximation of a constant electric field. The proper expression of the Boltzmann distribution of the gating particles is presented. It is shown that the dipole moment of transition of the gating particle is the only proper thermodynamic (macroscopic) characteristics of the gating particles based on the available experimental information and does not depend on any microscopic assumption as the equivalent valency does.     

The dispersal of an initial concentration of motile bacteria.

The dispersal of an initial concentration of identical Brownian particles is accurately described by the solution of the conventional diffusion equation, and a diffusion coefficient can be assigned to the assembly of particles. However, the dispersal of an initial concentration of motile bacteria is not well described by the same solution, in spite of the similarity between the random motion of a bacterium and a Brownian particle. Reasons for the failure of the Gaussian solution of the diffusion equation to describe the dispersal of Escherichia coli are discussed. An equation is formulated which gives the concentration of dispersing organisms as a function of space and time if the speed distribution function of the assembly of organism is known and reproduction is suppressed. For three assumed speed distributions the results are compared with concentrations measured by previous authors.     

A physical analogy of the genetic toggle switch.

We show that there is a physical analogy between a stochastic model of a genetic toggle switch system and a thermostated particle moving in a potential field, derived from the probability distribution of the toggle switch. This result suggests that one can actually simulate the dynamics of a more complex gene network by considering an ensemble of thermostated particles moving in a potential field, derived from the stationary distribution of the chemical stochastic model describing the gene network.     

Erythrocyte sedimentation rate in diluted suspensions and their electrophoretic mobility in a vertical electrical field

The sedimentation rates (SR) of human red blood cells (RBC) were measured in diluted suspensions using the thin plate chamber. If the suspension medium was phosphate buffer saline or 0,18 M NaCl the SR-dependence on the distance to the chambers wall corresponded to SR distribution of small particles without interaction. The more NaCl content was decreased down to 0.145 M, the more temperature-dependent variations of SR were noted, while SR distribution became distinct with the predicted one for the non-interacting particles. The use of SR distribution is discussed for testing the RBC interaction in diluted suspensions caused by sedimentation. The electrophoretic measurements carried out under vertical oriented electrical field showed the rate of RBC movement to be the linear function of the field gradient and to be not influenced under the SR modifying conditions.     

Splitting of the spectra of MHD waves and the structure of a satellite alfvén resonance in a cold plasma in a strong axial magnetic field and a weak helical field

The possibility is demonstrated of splitting the eigenfrequencies of MHD plasma waves in a stellarator with a weakly rippled helical confining magnetic field. The distribution of the fields of an Alfvén wave in the satellite Alfvén resonance region is investigated when the influence of the helical ripple in a confining magnetic field on the resonance structure is comparable with the effects of the finite ion Larmor radius, electron inertia, and collisions between plasma particles.     

On the excess energy of nonequilibrium plasma

The energy that can be released in plasma due to the onset of instability (the excess plasma energy) is estimated. Three potentially unstable plasma states are considered, namely, plasma with an anisotropic Maxwellian velocity distribution of plasma particles, plasma with a two-beam velocity distribution, and an inhomogeneous plasma in a magnetic field with a local Maxwellian velocity distribution. The excess energy can serve as a measure of the degree to which plasma is nonequilibrium. In particular, this quantity can be used to compare plasmas in different nonequilibrium states.     

Causal basis of gravity stimulus nullification by clinostat rotation

Using appropriate clinostat rotation methods, it has been shown that increases in root growth and geotropic curvature of oat coleoptiles are related to and explained (within the limits of auxin economy) by increased rates of plant respiration imparted by nullification of the gravitational stimulus. Increased respiration with decreased gravitational stimulus, in turn, is explained by increased uniformity in intracellular distribution of metabolically active graviprecipitable particles.

Oat seedlings grown with nullification of the gravitational stimulus show a more uniform distribution of graviprecipitable protoplasmic inclusions. Respiration involves reactions between particles of sufficient mass to be precipitated in 1 × g unidirectional force field and particles of such size that they are distributed throughout the protoplasm due to thermal energy. When plants are grown without nullification of the gravitational stimulus, graviprecipitable protoplasmic inclusions tend to accumulate in the lower portions of the cells. Respiration rates are consequently limited due to a relatively low concentration of the smaller particles in the region of high concentration of the larger particles. Distribution of the larger particles throughout the protoplasm negates the reaction rate limiting effects of these intracellular concentration gradients.

It has been shown using starch particles to index graviprecipitation of intracellular particles that enhancement of respiration by nullification of the gravitational stimulus may be induced, maintained, discontinued, and reinduced by treatments which concomitantly result in the more uniform distribution of graviprecipitable protoplasmic inclusions, the maintenance of this uniform distribution, the discontinuation of this uniform distribution and its reinduction.

The degree of uniformity of intracellular particle distribution in response to treatments only partially nullifying the gravitational stimulus is shown wholly consonant with growth responses of roots and coleoptiles when the growth is measured as the expression of increased respiration in the absence of auxin limitation.

The findings collectively indicate that gravity sensing by plants is broadly based on the physicochemical relationship between particle distribution and the expression of respiratory metabolism as growth.