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.     

Stochastic theory of compartments: An open,two compartment,reversible system with independent poisson arrivals

This paper discusses two compartment models with interaction allowed between the compartments. The total number of particles in the system at any time is discussed along with the number to the found in each separate compartment. An interesting result is that the number of particles in each of the two compartments areindependent random variables. Some asymptotic results are also given. The paper is a continuation of some earlier work by the author.     

Cell tracing reveals a dorsoventral lineage restriction plane in the mouse limb bud mesenchyme

Regionalization of embryonic fields into independent units of growth and patterning is a widespread strategy during metazoan development. Compartments represent a particular instance of this regionalization, in which unit coherence is maintained by cell lineage restriction between adjacent regions. Lineage compartments have been described during insect and vertebrate development. Two common characteristics of the compartments described so far are their occurrence in epithelial structures and the presence of signaling regions at compartment borders. Whereas Drosophila compartmental organization represents a background subdivision of embryonic fields that is not necessarily related to anatomical structures, vertebrate compartment borders described thus far coincide with, or anticipate, anatomical or cell-type discontinuities. Here, we describe a general method for clonal analysis in the mouse and use it to determine the topology of clone distribution along the three limb axes. We identify a lineage restriction boundary at the limb mesenchyme dorsoventral border that is unrelated to any anatomical discontinuity, and whose lineage restriction border is not obviously associated with any signaling center. This restriction is the first example in vertebrates of a mechanism of primordium subdivision unrelated to anatomical boundaries. Furthermore, this is the first lineage compartment described within a mesenchymal structure in any organism, suggesting that lineage restrictions are fundamental not only for epithelial structures, but also for mesenchymal field patterning. No lineage compartmentalization was found along the proximodistal or anteroposterior axes, indicating that patterning along these axes does not involve restriction of cell dispersion at specific axial positions.     

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.     

Cell-free reconstitution of vacuole membrane fragmentation reveals regulation of vacuole size and number by TORC1

Size and copy number of organelles are influenced by an equilibrium of membrane fusion and fission. We studied this equilibrium on vacuoles-the lysosomes of yeast. Vacuole fusion can readily be reconstituted and quantified in vitro, but it had not been possible to study fission of the organelle in a similar way. Here we present a cell-free system that reconstitutes fragmentation of purified yeast vacuoles (lysosomes) into smaller vesicles. Fragmentation in vitro reproduces physiological aspects. It requires the dynamin-like GTPase Vps1p, V-ATPase pump activity, cytosolic proteins, and ATP and GTP hydrolysis. We used the in vitro system to show that the vacuole-associated TOR complex 1 (TORC1) stimulates vacuole fragmentation but not the opposing reaction of vacuole fusion. Under nutrient restriction, TORC1 is inactivated, and the continuing fusion activity then dominates the fusion/fission equilibrium, decreasing the copy number and increasing the volume of the vacuolar compartment. This result can explain why nutrient restriction not only induces autophagy and a massive buildup of vacuolar/lysosomal hydrolases, but also leads to a concomitant increase in volume of the vacuolar compartment by coalescence of the organelles into a single large compartment.     

A class of general stochastic compartmental systems

In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.     

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.     

Methylation of nuclear DNA in Physarum polycephalum.

The restriction endonucleases HpaII and HhaI, whose action is inhibited by the presence of methylated base analogues at the recognition sequences in the DNA substrate, were used to investigate the distribution of 5-methylcytosine in nuclear DNA from Physarum polycephalum. Physarum DNA is digested into two fractions by these enzymes: a low-molecular-weight (M--) compartment comprising 80% of the DNA, and a high-molecular-weight (M+) compartment containing 20% of the DNA. The DNA fraction showing resistance to digestion by restriction endonuclease HpaII is cleaved by its isoschizomer MspI, indicating that methylated endonuclease-HpaII-specific sites are present in M + DNA. Additional properties of sequences in the M+ compartment were investigated.     

Immunocytochemical analysis of Uukuniemi virus budding compartments: role of the intermediate compartment and the Golgi stack in virus maturation.

Previous studies have suggested that Uukuniemi virus, a bunyavirus, matures at the membranes of the Golgi complex. In this study we have employed immunocytochemical techniques to analyze in detail the budding compartment(s) of the virus. Electron microscopy of infected BHK-21 cells showed that virus particles are found in the cisternae throughout the Golgi stack. Within the cisternae, the virus particles were located preferentially in the dilated rims. This would suggest that virus budding may begin at or before the cis Golgi membranes. The virus budding compartment was studied further by immunoelectron microscopy with a pre-Golgi intermediate compartment marker, p58, and a Golgi stack marker protein, mannosidase II (ManII). Virus particles and budding virus were detected in ManII-positive Golgi stack membranes and, interestingly, in both juxtanuclear and peripheral p58-positive elements of the intermediate compartment. In cells incubated at 15 degrees C the nucleocapsid and virus envelope proteins were seen to accumulate in the intermediate compartment. Immunoelectron microscopy demonstrated that at 15 degrees C the nucleocapsid is associated with membranes that show a characteristic distribution and tubulo-vesicular morphology of the pre-Golgi intermediate compartment. These membranes contained virus particles in the lumen. The results indicate that the first site of formation of Uukuniemi virus particles is the pre-Golgi intermediate compartment and that virus budding continues in the Golgi stack. The results raise questions about the intracellular transport pathway of the virus particles, which are 100 to 120 nm in diameter and are therefore too large to be transported in the 60-nm-diameter vesicles postulated to function in the intra-Golgi transport. The distribution of the virus in the Golgi stack may imply that the cisternae themselves have a role in the vectorial transport of virus particles.     

An analytical solution for a class of delay-differential equations in pharmacokinetic compartment modeling

The authors obtain the analytic expression for the solution of a differential system with time lags for any n-compartment linear model with a single input, and, by convolution, for all intakes. The theoretical result is applied to the case of one-, two-, and three-compartment models and gives insight into the pharmacokinetics of drug undergoing enterohepatic circulation: the amount of drug in any compartment is expressed for all time. Statistical results, such as the mean residence time of drug, are obtained by the same calculation.     

On the distribution of the general irreversiblen-compartmental model having time-dependent transition probabilities

The cumulant generating function and first two moments are derived for the stochastic distribution of units in a general irreversiblen-compartment model with time-dependent transition probabilities. In this model, a unit in the first compartment can transfer to any one of the remainingn−1 compartments and a unit in the second compartment can transfer to any of the remainingn−2 compartments and so on. In addition, a unit can enter or leave the system through any compartment. The work is related to previous research and a numerical example is given.     

Development of the Drosophila genital disc requires interactions between its segmental primordia

In both sexes, the Drosophila genital disc comprises three segmental primordia: the female genital primordium derived from segment A8, the male genital primordium derived from segment A9 and the anal primordium derived from segments A10-11. Each segmental primordium has an anterior (A) and a posterior (P) compartment, the P cells of the three segments being contiguous at the lateral edges of the disc. We show that Hedgehog (Hh) expressed in the P compartment differentially signals A cells at the AP compartment border and A cells at the segmental border. As in the wing imaginal disc, cell lineage restriction of the AP compartment border is defined by Hh signalling. There is also a lineage restriction barrier at the segmental borders, even though the P compartment cells of the three segments converge in the lateral areas of the disc. Lineage restriction between segments A9 and A10-11 depends on factors other than the Hh, En and Hox genes. The segmental borders, however, can be permeable to some morphogenetic signals. Furthermore, cell ablation experiments show that the presence of all primordia (either the anal or the genital primordium) during development are required for normal development of genital disc. Collectively, these findings suggest that interaction between segmental primordia is required for the normal development of the genital disc.     

Anti-tetherin activities of HIV-1 Vpu and Ebola virus glycoprotein do not involve removal of tetherin from lipid rafts

BST-2/tetherin is an interferon-inducible host restriction factor that blocks the release of newly formed enveloped viruses. It is enriched in lipid raft membrane microdomains, which are also the sites of assembly of several enveloped viruses. Viral anti-tetherin factors, such as the HIV-1 Vpu protein, typically act by removing tetherin from the cell surface. In contrast, the Ebola virus glycoprotein (GP) is unusual in that it blocks tetherin restriction without apparently altering its cell surface localization. We explored the possibility that GP acts to exclude tetherin from the specific sites of virus assembly without overtly removing it from the cell surface and that lipid raft exclusion is the mechanism involved. However, we found that neither GP nor Vpu had any effect on tetherin's distribution within lipid raft domains. Furthermore, GP did not prevent the colocalization of tetherin and budding viral particles. Contrary to previous reports, we also found no evidence that GP is itself a raft protein. Together, our data indicate that the exclusion of tetherin from lipid rafts is not the mechanism used by either HIV-1 Vpu or Ebola virus GP to counteract tetherin restriction.     

Stochastic modeling of controlled-drug release

A drug release process by the oral route is random in nature and thus is subject to constant fluctuations. Moreover, individuals have varied tolerances to such fluctuations. The objective of this work is to characterize these fluctuations by a stochastic formalism. The system under consideration, i.e., the gastrointestinal tract consists of four consecutive compartments, i.e., stomach, duodenum, jejunum, and ileum. The master equation of the system as well as the governing equations for the means, variances, and covariances of the random variables, each representing the number of microspheres in an individual compartment, have been derived through the probabilistic population balance. These equations have been numerically solved to predict the total release fraction of drug and its internal fluctuations, and the dynamic statistics (means, variances, and covariances) of the amount of drug in each compartment at any time after administration. The dissolution-intensity functions in the model have been recovered from the available in vitro dissolution data from controlled-release pellets of isosorbide-5-nitrate (IS-5-N) by assuming that the rate of release is of the first order. The residence times and transition-intensity functions of drug in the individual compartments have been estimated from the available data generated by the gamma scintigraphies of IS-5-N pellets labeled by ¹¹¹In. Based on these parameters, the total numbers of dissolved drug microspheres and their fluctuations at any instance have been calculated. The model is in accord with the existing in vivo dissolution data of the same drug independently obtained through plasma analysis. More important, the model predicts that fluctuations in terms of the standard deviations of the numbers of particles in the duodenum, jejunum, and ileum can be of the same orders of magnitude as the corresponding mean numbers when 100 microspheres are simultaneously administered orally; in practice, such fluctuations characterized by these deviations could result in an undesirable release profile. Discussion is given of the potential direct clinical application of the results obtained as well as the plausible indirect application of these results and the model derived to the analyses of chemical and biochemical reactors.     

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.     

Rearrangement of intramembrane particles as a possible mechanism for the release of acetylcholine

1. A chemiluminescent procedure for measuring acetylcholine (ACh) has recently been described. The procedure is based on the hydrolysis of ACh by acetylcholinesterase and on the oxidation of choline to betaine and H2O2 by choline oxidase. The H2O2 generated reacts with luminol in presence of peroxidase to produce a light emission. This method is sensitive in the pmol/ml range. 2. On isolated synaptosomes from electric organ, it is possible to obtain an estimate of the cytoplasmic ACh compartment by measuring the light emission after a single freezing and thawing cycle. The vesicular pool which resists several freezing and thawing cycles is then estimated by opening the compartment with a detergent. Increasing the intensity of stimulation of synaptosomes with different agents depletes the ACh content down to the vesicular pool. 3. The release of ACh is not associated with any change in the number of synaptic vesicles as seen in cryofractured synaptosomes. The only ultrastructural change detected common to all stimulations was a decreased density of P face intramembrane particles smaller than 11 nm and an increased density of E face 8 to 18 nm particles. The very significant particle changes were more intense for the conditions releasing more ACh. It is suggested that these particles are involved in the release of ACh from the cytoplasm. An attempt to directly correlate the release of ACh with intramembrane particle changes is discussed.     

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.