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.     

A stochastic model for then-compartment irreversible system

This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.     

A stochstic model for a two-compartment reversible system

This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.     

Quantifying immunogold labelling patterns of cellular compartments when they comprise mixtures of membranes (surface-occupying) and organelles (volume-occupying)

In quantitative immunoelectron microscopy, subcellular compartments that are preferentially labelled with colloidal gold particles can be identified by estimating labelling densities (LDs) and relative labelling indices (RLIs). Hitherto, this approach has been limited to compartments which are either surface occupying (membranes) or volume occupying (organelles) but not a mixture of both (membranes and organelles). However, some antigens are known to translocate between membrane and organelle compartments and the problem then arises of expressing gold particle LDs in a consistent manner (e.g., as number per compartment profile area). Here, we present one possible solution to tackle this problem. With this method, each membrane is treated as a volume-occupying compartment and this is achieved by creating an acceptance zone at a fixed distance on each side of membrane images. Gold signal intensity is then expressed as an LD within the membrane profile area so created and this LD can be compared to LDs found in volume-occupying compartments. Acceptance zone width is determined largely by the expected dispersion of gold labelling. In some cases, the zone can be applied to all visible membrane images but there is a potential problem when image loss occurs due to the fact that membranes are not cut orthogonal to their surface but are tilted within the section. The solution presented here is to select a subset of clear images representing orthogonally sectioned membranes (so-called local vertical windows, LVWs). The fraction of membrane images forming LVWs can be estimated in two ways: goniometrically (by determining the angle at which images become unclear) or stereologically (by counting intersections with test lines). The fraction obtained by either method can then be used to calculate a factor correcting for membrane image loss. In turn, this factor is used to estimate the total gold labelling associated with the acceptance zone of the entire (volume-occupying) membrane. However calculated, the LDs over the chosen (membrane and organelle) compartments are used to obtain observed and expected gold particle counts. The observed distribution is determined simply by counting gold particles associated with each compartment. Next, an expected distribution is created by randomly superimposing test points and counting those hitting each compartment. LDs of the chosen compartments are used to calculate RLI and chi-squared values and these serve to identify those compartments in which there is preferential labelling. The methods are illustrated by synthetic and real data.     

Molecular Analysis of Bacterial Communities in a Three-Compartment Granular Activated Sludge System Indicates Community-Level Control by Incompatible Nitrification Processes

Bacterial community structure and the predominant nitrifying activities and populations in each compartment of a three-compartment activated sludge system were determined. Each compartment was originally inoculated with the same activated sludge community entrapped in polyethylene glycol gel granules, and ammonium nitrogen was supplied to the system in an inorganic salts solution at a rate of 5.0 g of N liter of granular activated sludge⁻¹ day⁻¹. After 150 days of operation, the system was found to comprise a series of sequential nitrifying reactions (K. Noto, T. Ogasawara, Y. Suwa, and T. Sumino, Water Res. 32:769–773, 1998), presumably mediated by different bacterial populations. Activity data showed that all NH₄-N was completely oxidized in compartments one and two (approximately half in each), but no significant nitrite oxidation was observed in these compartments. In contrast, all available nitrite was oxidized to nitrate in compartment three. To study the microbial populations and communities in this system, total bacterial DNA isolated from each compartment was analyzed for community structure based on the G+C contents of the component populations. Compartment one showed dominant populations having 50 and 67% G+C contents. Compartment two was similar in structure to compartment one. The bacterial community in compartment three had dominant populations with 62 and 67% G+C contents and retained the 50% G+C content population only at a greatly diminished level. The 50% G+C content population from compartment one hybridized strongly with amo (ammonia monooxygenase) and hao (hydroxylamine oxidoreductase) gene probes from Nitrosomonas europaea. However, the 50% G+C content population from compartment two hybridized strongly with the hao probe but only weakly with the amo probe, suggesting that the predominant ammonia-oxidizing populations in compartments one and two might be different. Since different activities and populations come to dominate in each compartment from an identical inoculum, it appears that the nitrification processes may be somewhat incompatible, resulting in a series of sequential reactions and different communities in this three-compartment system.     

Patterns of growth, axonal extension and axonal arborization of neuronal lineages in the developing Drosophila brain

The Drosophila central brain is composed of approximately 100 paired lineages, with most lineages comprising 100-150 neurons. Most lineages have a number of important characteristics in common. Typically, neurons of a lineage stay together as a coherent cluster and project their axons into a coherent bundle visible from late embryo to adult. Neurons born during the embryonic period form the primary axon tracts (PATs) that follow stereotyped pathways in the neuropile. Apoptotic cell death removes an average of 30-40% of primary neurons around the time of hatching. Secondary neurons generated during the larval period form secondary axon tracts (SATs) that typically fasciculate with their corresponding primary axon tract. SATs develop into the long fascicles that interconnect the different compartments of the adult brain. Structurally, we distinguish between three types of lineages: PD lineages, characterized by distinct, spatially separate proximal and distal arborizations; C lineages with arborizations distributed continuously along the entire length of their tract; D lineages that lack proximal arborizations. Arborizations of many lineages, in particular those of the PD type, are restricted to distinct neuropile compartments. We propose that compartments are “scaffolded” by individual lineages, or small groups thereof. Thereby, the relatively small number of primary neurons of each primary lineage set up the compartment map in the late embryo. Compartments grow during the larval period simply by an increase in arbor volume of primary neurons. Arbors of secondary neurons form within or adjacent to the larval compartments, resulting in smaller compartment subdivisions and additional, adult specific compartments.     

Preference for structured environment in zebrafish (Danio rerio) and checker barbs (Puntius oligolepis)

Information about the welfare and husbandry of pet and laboratory fish is scarce although millions of fish are sold in pet shops and used in laboratory research every year. Inadequate housing conditions can cause behavioural problems also in fish since they are complex animals with sophisticated behaviour. In this study, we investigated the influence of environmental complexity on compartment preference and behaviour in zebrafish (Danio rerio) and checker barbs (Puntius oligolepis). For the preference test, large aquaria were divided by two semi-transparent walls of Plexiglas into an empty compartment, a structured compartment enriched with plants and clay pots, and a smaller compartment in-between, where food was provided. For observation, the empty and structured compartments were divided into six zones of similar size by defining three vertical layers and two horizontal areas (back vs. front area). Seven groups of six to nine zebrafish and seven groups of seven or eight checker barbs were observed on four days each (within a time period of ten days) to assess compartment use and activity, and to assess behavioural diversity and use of zones within compartments. Both zebrafish and checker barbs showed a significant preference for the structured compartment. Nevertheless, in neither species did behavioural diversity differ between the empty and structured compartment. Zebrafish used all zones in both compartments to the same extent. Checker barbs, however, used the structured compartment more evenly than the empty compartment, where they mainly used the lower and middle zones. These results suggest that zebrafish and checker barbs have a preference for complex environments. Furthermore, they indicate that the behavioural and ecological needs of fish may vary depending on species, and recommendations for husbandry should be specified at species level.     

On transfer times in tracer experiments

A compartment is defined as a pool of material whose behavior can be described by a deterministic or by a stochastic equation; these two equations are used to define the transit time through the compartment, the total residence time, the time of entrance and the time of exit.If in a complex system one or more compartments are accessible, the transport of material through it can be studied using a tracer. Then the transfer time between any two compartments, or through the cycle around a compartment, can be analyzed under certain hypotheses, even if the transport along the route considered cannot be described by compartment equations.     

Parameter identification in N-compartment mamillary models

We consider a general mamillary model with a central compartment (compartment 1) and n?1 peripheral compartments, each bidirectionally connected to the first. Elimination is allowed from any compartment and effectively occurs from the system. With input introduced into an arbitrary compartment and measurement performed in an arbitrary compartment, explicit equations are given to derive the parameters of the model from the input-output procedure. The calculations include essentially the determination of the roots of a polynomial plus some elementary algebra. If input and measurement are performed in the same compartment, then a set of 2n elementary combinations of the model parameters can be uniquely determined. However, the model parameters themselves can only be localized, each within an interval. These intervals are explicitly calculated and their width discussed.     

Architectural and histochemical analysis of the semitendinousus muscle in mice,rats, guinea pigs,and rabbits

The architectural and histochemical properties of the anatomically distinct compartments of the semitendinosus muscle (ST) of mice, rats, guinea pigs, and rabbits show that the ST is composed of two separate compartments aligned in series—a destal compartment (STd) and a proximal one (STp). The STp is further subdivided into a ventral head (STpv) and a dorsal head (STpd). The muscle fibers were arranged in parallel to the line of muscle pull within each compartment. The STd has the longest and the STpv the shortest fibers in all species. The physiological cross-sectional area and the estimated tetanic tension was greatest in the STd. Based on the staining pattern for myosin ATPase (alkaline preincubation) and an oxidative indicator (NADH or SDH), the STpv has the highest percentage of slow-oxidative (SO) or SO plus fast-oxidative-glycolytic (FOG) fibers of any portion of the muscle. The differences in fiber-type distributions and architectural designs of the separate compartments suggest a specialization of function of the individual compartments.     

The Kinetics of Distribution of the Fat-Soluble Inert Gas Cyclopropane in the Body

A kinetic analysis is made of the experimentally measured time course of respiratory uptake of the highly fat-soluble, inert gas cyclopropane by normal human subjects. The analysis is based on the well-known perfusion-limited model in which a number of body compartments are arranged in parallel with the lungs via the circulating blood. Three distinct body compartments are derived from the data. These are tentatively identified as: (a) adipose tissue (b) fat-poor tissue of low perfusion such as resting muscle, skin, and connective tissue (c) fat-poor tissue of high perfusion such as brain, heart, gut, liver, and kidney. Blood flow rates to the several compartments are also derived from the data. The rates to compartments (a) and (b) are each approximately 10 per cent of the estimated total cardiac output. The derived perfusion (blood flow rate/compartment weight) of the three compartments are in the range, respectively, (a) 2 to 4, (b) 1 to 2.5, (c) 25 to 75 ml/min/100 gm. Uncertainties arising from the experimental data and from simplifications of the model (neglect of lung fill-up phase of uptake and gross diffusion of cyclopropane from one tissue into another) are discussed. The present type of uptake experiment is significant for the problems of total body fat determination, of gross body composition in relation to weight change, of gross shunting of blood flow from one compartment to another, of anesthesia by fat-soluble substances, and of decompression sickness.     

Generation of nonidentical compartments in vesicular transport systems

How can organelles communicate by bidirectional vesicle transport and yet maintain different protein compositions? We show by mathematical modeling that a minimal system, in which the basic variables are cytosolic coats for vesicle budding and membrane-bound soluble N-ethyl-maleimide–sensitive factor attachment protein receptors (SNAREs) for vesicle fusion, is sufficient to generate stable, nonidentical compartments. A requirement for establishing and maintaining distinct compartments is that each coat preferentially packages certain SNAREs during vesicle budding. Vesicles fuse preferentially with the compartment that contains the highest concentration of cognate SNAREs, thus further increasing these SNAREs. The stable steady state is the result of a balance between this autocatalytic SNARE accumulation in a compartment and the distribution of SNAREs between compartments by vesicle budding. The resulting nonhomogeneous SNARE distribution generates coat-specific vesicle fluxes that determine the size of compartments. With nonidentical compartments established in this way, the localization and cellular transport of cargo proteins can be explained simply by their affinity for coats.     

Impact of protein binding on receptor occupancy: A two-compartment model

In this paper we analyse the impact of protein-, lipid- and receptor-binding on receptor occupancy in a two-compartment system, with proteins in both compartments and lipids and receptors in the peripheral compartment only. We do this for two manners of drug administration: a bolus administration and a constant rate infusion, both into the central compartment. We derive explicit approximations for the time-curves of the different compounds valid for a wide range of realistic values of rate constants and initial concentrations of proteins, lipids, receptors and the drug. These approximations are used to obtain both qualitative and quantitative insight into such critical properties as the distribution of the drug over the two compartments, the maximum receptor occupancy and the area under the drug-receptor complex curve. In particular we focus on assessing the impact of the dissociation constants, K_P, K_L and K_R of the drug with, respectively, the proteins, the lipids and the receptors, the permeability and the surface area of the membrane between compartments, and the rate the drug is eliminated from the system.     

On dispersion in tracer experiments

Extending the results of a previous paper (Rescigno, 1973), the dispersion between two compartments or through the cycle around a compartment is defined in terms of the transport time of the particles flowing through the system.Some of the properties of the dispersion are analyzed, and the method for computing it is described.     

Detection of stored-grain insect infestation in wheat transported in railroad hopper-cars

Levels of insect infestation, insect spatial distribution, and the relationship between the number of insect-damaged kernels (IDK) and the number of insects present in grain samples in three-hopper railcars transporting wheat from country elevators to a mill were studied. Six of eight sampled railcars were infested with more than two species of insects. The most abundant species collected were the lesser grain borer, Rhyzopertha dominica (F.), and rusty grain beetle, Cryptolestes ferrugineus (Stephens), with the larval stage of the two species being the most prevalent (>90%). The spatial distributions of these two species within the grain mass were typically clumped in railcar compartments containing >0.4 insect/2.75-kg sample of wheat, and these foci of high-infestation levels varied in compartments within the railcars and among the sampled railcars. There were no significant correlations between IDK and insect density for any of the different stage-specific insect populations that were collected in the grain samples. Mean numbers of immatures and IDK differed among railcars and compartments within railcars, but not among grain depths. Number of insects in the first discharge sample was not correlated with mean numbers of insects in the entire compartment. This indicates that each compartment of a railcar should be sampled to determine level of insect infestation but that sampling at different depths within a compartment is less important.     

A rapid method for assessing the distribution of gold labeling on thin sections.

Particulate gold labeling on ultrathin sections is in widespread use for antigen localization at the EM level. To extend the usefulness of gold labeling technology, we are evaluating different methods for sampling and estimating quantities of gold labeling. Here we present a simple, rapid, and unbiased method for assessing the relative pool sizes of immunogold labeling distributed over different cell compartments. The method uses a sampling approach developed for stereology in which a regular array of microscopic fields or linear scans is positioned randomly on labeled sections. From these readouts, gold particles are counted and assigned to identifiable cell structures to construct a gold labeling frequency distribution of those labeled compartments. Here we use ultrathin cryosections labeled for a range of different proteins and for a signaling lipid. We show by scanning labeled sections at the electron microscope that counting 100-200 particles on each of two grids is sufficient to obtain a reproducible and rapid assessment of the pattern of labeling proportions over 10-16 compartments. If more precise estimates of labeling proportions over individual compartments are required (e.g., to achieve coefficients of error of 10-20%), then 100-200 particles need to be counted over each compartment of interest.     

Myosin-Powered Membrane Compartment Drives Cytoplasmic Streaming,Cell Expansion and Plant Development

Using genetic approaches, particle image velocimetry and an inert tracer of cytoplasmic streaming, we have made a mechanistic connection between the motor proteins (myosins XI), cargo transported by these motors (distinct endomembrane compartment defined by membrane-anchored MyoB receptors) and the process of cytoplasmic streaming in plant cells. It is shown that the MyoB compartment in Nicotiana benthamiana is highly dynamic moving with the mean velocity of ~3 μm/sec. In contrast, Golgi, mitochondria, peroxisomes, carrier vesicles and a cytosol flow tracer share distinct velocity profile with mean velocities of 0.6–1.5 μm/sec. Dominant negative inhibition of the myosins XI or MyoB receptors using overexpression of the N. benthamiana myosin cargo-binding domain or MyoB myosin-binding domain, respectively, resulted in velocity reduction for not only the MyoB compartment, but also each of the tested organelles, vesicles and cytoplasmic streaming. Furthermore, the extents of this reduction were similar for each of these compartments suggesting that MyoB compartment plays primary role in cytosol dynamics. Using gene knockout analysis in Arabidopsis thaliana, it is demonstrated that inactivation of MyoB1-4 results in reduced velocity of mitochondria implying slower cytoplasmic streaming. It is also shown that myosins XI and MyoB receptors genetically interact to contribute to cell expansion, plant growth, morphogenesis and proper onset of flowering. These results support a model according to which myosin-dependent, MyoB receptor-mediated transport of a specialized membrane compartment that is conserved in all land plants drives cytoplasmic streaming that carries organelles and vesicles and facilitates cell growth and plant development.     

Architecture and consequent physiological properties of the semitendinosus muscle in domestic goats

Morphological and physiological analyses confirm that the semitendinosus muscle of goats contains two separate compartments in series, each with distinct innervation. These compartments of the muscle are in turn composed of short fibers (approximately four fibers in series in the proximal compartment and seven to eight fibers in the distal compartment) which overlap each other for more than 30% of their length, with much of the overlapping portions consisting of slender tails that terminate at one-tenth of the midfiber diameter. Groups of fibers are associated into relatively narrow bands that run end-to-end in each compartment. The data suggest that the maximum length of muscle fibers may be limited; even the fibers of parallel-fibered muscles may not scale with the dimension of the animal.     

HIV-1 buds and accumulates in "nonacidic" endosomes of macrophages

Macrophages represent viral reservoirs in HIV-1-infected patients and accumulate viral particles within an endosomal compartment where they remain infectious for long periods of time. To determine how HIV-1 survives in endocytic compartments that become highly acidic and proteolytic and to study the nature of these virus-containing compartments, we carried out an ultrastructural study on HIV-1-infected primary macrophages. The endosomal compartments contain newly formed virions rather than internalized ones. In contrast to endocytic compartments free of viral proteins within the same infected cells, the virus containing compartments do not acidify. The lack of acidification is associated with an inability to recruit the proton pump vacuolar ATPase into the viral assembly compartment. This may prevent its fusion with lysosomes, since acidification is required for the maturation of endosomes. Thus, HIV-1 has developed a strategy for survival within infected macrophages involving prevention of acidification within a devoted endocytic virus assembly compartment.     

Studies on peroxisomes III. Further studies on the intraparticulate localization of peroxisomal components in the liver of the rat

The peroxisome-rich fraction prepared from rat liver homogenate was treated by various procedures and the behavior of the peroxisomal core on sucrose density gradient centrifugation was investigated.Peroxisomes were destroyed by various treatments, such as pH 9.0, VirTis blender, sonication and deoxycholate, resulting in the solubilization of catalase from the particles. Urate oxidase was not solubilized at all such treatments. Although D-amino acid oxidase was solubilized by treatments with deoxycholate and VirTis blender, this enzyme was found to be resistant to solubilization by treatment with pH 9.0 or sonication, in contrast to catalase.When the peroxisomal core was investigated, using urate oxidase activity as a marker, its density proved to be changed when submitted to various treatments. These results indicated that the peroxisomes consist of four compartments: a catalase-containing compartment (matrix), a urate oxidase containing compartment (core), a D-amino acid oxidase containing compartment and a low density compartment which is proposed for the first time in the present paper. Furthermore, it was also found that the last two compartments seem to be bound to the core, though the binding might be weak.