A note on the use of a stochastic mammillary compartmental model as an environmental safety model

Environmental safety testing typically requires procedures for extrapolating from the relatively high experimental to the very low use doses of potentially harmful substances. In the present paper, a stochastic mammillary compartmental model for environmental safety testing is proposed and extrapolation procedures based on its dose-response relationship are developed. The proposed model is a direct generalization of one of the basic safety models, the one-hit model, in that a harmful reaction is assumed to occur if at any time any of the peripheral compartments attains a specified threshold of particles. Consideration of a closed model yields an upper bound on the probability of attaining a certain threshold level, thus providing a conservative procedure for extrapolating to a low dose, while a lower bound obtained from a related open model provides a useful monitoring device as to the sharpness of the upper, bound. The extrapolation procedure is illustrated with simulated data and approximations for initial values are developed.     

The stochastic theory of compartments—A mammillary system

A stochastic mammalillary model with arbitrary holding times for each of the compartments is analyzed here both with and without input. Several results found earlier by other authors for a special case of this model are generalized and some new results are also added. In particular the distribution of the system content is determined at a finite time and also in the steady state. Computable bounds for the probability of exceeding a given threshold in the peripheral compartments are given. The time until the system becomes empty is also discussed.     

Beta-very low density lipoprotein is sequestered in surface-connected tubules in mouse peritoneal macrophages

beta-very low density lipoprotein (VLDL) is a large lipoprotein with multiple apoprotein E (apoE) molecules that bind to the LDL receptors on mouse macrophages. Even though they bind to the same receptor, the endocytic processing of beta-VLDL differs from low density lipoprotein (LDL). LDL is rapidly delivered to perinuclear lysosomes and degraded, but much of the beta-VLDL is retained in peripheral compartments for several minutes. We have investigated the properties of these peripheral compartments. Measurement of the pH was made using FITC- phosphatidylethanolamine incorporated into the beta-VLDL, and we found that the peripheral compartments were near neutral in pH. These peripheral, beta-VLDL containing compartments were poorly accessible to antibodies, but a low molecular weight fluorescence quencher (trypan blue) entered the compartments within a few seconds. Intermediate voltage EM of cells labeled with colloidal-gold-beta-VLDL revealed that the peripheral compartments are tubular, surface-connected invaginations. Kinetic studies with fluorescent beta-VLDL showed that the compartments become fully sealed with a half-time of 6 min, and the beta-VLDL is then delivered rapidly to perinuclear lysosomes. By monitoring fluorescence energy transfer between lipid analogs incorporated into the beta-VLDL, some processing of the lipoprotein in the peripheral tubular compartments is demonstrated. The novel mode of uptake of beta-VLDL may account for the high cholesterol ester accumulation induced by this lipoprotein.     

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.     

Glial Plasticity in the Trigeminal Root Entry Zone of a Rat Trigeminal Neuralgia Animal Model

Neurochemical Research - The trigeminal root entry zone (TREZ) is the transitional zone of central and peripheral tissue compartments in the trigeminal root. Microvascular compression on the TREZ...     

Nonrandom Distribution of Hepatitis C Virus Quasispecies in Plasma and Peripheral Blood Mononuclear Cell Subsets

The existence of an extrahepatic reservoir of hepatitis C virus (HCV) is suggested by differences in quasispecies composition between the liver, peripheral blood mononuclear cells, and serum. We studied HCV RNA compartmentalization in the plasma of nine patients, in CD19(+), CD8(+), and CD4(+) positively selected cells, and also in the negatively selected cell fraction (NF). HCV RNA was detected in all plasma samples, in seven of nine CD19(+), three of eight CD8(+), and one of nine CD4(+) cell samples, and in seven of eight NF cells. Cloning and sequencing of HVR1 in two patients showed a sequence grouping: quasispecies from a given compartment (all studied compartments for one patient and CD8(+) and NF for the other) were statistically more genetically like each other than like quasispecies from any other compartment. The characteristics of amino acid and nucleotide substitutions suggested the same structural constraints on HVR1, even in very divergent strains from the cellular compartments, and homogeneous selection pressure on the different compartments. These findings demonstrate the compartmental distribution of HCV quasispecies within peripheral blood cell subsets and have important implications for the study of extrahepatic HCV replication and interaction with the immune system.     

A stochastic compartmental model with continuous infusion

This paper deals with stochasticm-compartmental systems with continuous time-dependent infusions into all compartments and reversible time-independent flows between any two compartments. A methodology for the first two moments of the distribution of the number of units in the different compartments at any point in time is outlined without resorting to the usual techniques of generating functions and inverse Laplace transforms. A possible application to a systems analysis of the kidney transplant system is discussed.     

The influence of segmental compartmentalisation on the development of the larval peripheral nervous system in Drosophila melanogaster

Summary The peripheral nervous system of embryos homozygous for prd, ftz, en and bxd was examined for defects and transformations in the segment-specific pattern of sensilla and peripheral nerves. This analysis permitted me to assign a distinct subset of sensilla to any of the three genetically and morphologically defined compartments s, a and p of each segment. In the wild-type embryonic segments, sensory axons deriving from sensilla of different compartments form a part of the common peripheral nerves. In the composite segments of prd and ftz mutant embryos, subsets of sensilla of two neighbouring segments are combined. Nevertheless, the axons of sensilla of different segmental identity are able to fasciculate and to form afferent nerves, which connect in an apparently normal fashion to the central nervous system. It is concluded that in the Drosophila embryo compartmental and segmental identity of sensory organs has no influence on the trajectories of sensory axons.     

Mean residence times in linear compartmental systems. Symbolic formulae for their direct evaluation

A complete analysis has been performed of the mean residence times in linear compartmental systems, closed or open, with or without traps and with zero input. This analysis allows the derivation of explicit and simple general symbolic formulae to obtain the mean residence time in any compartment of any linear compartmental system, closed or open, with or without traps, as well as formulae to evaluate the mean residence time in the entire system like the above situations. The formulae are given as functions of the fractional transfer coefficients between the compartments and, in the case of open systems, they also include the excretion coefficients to the environment from the different compartments. The relationship between the formulae derived and the particular connection properties of the compartments is discussed. Finally, some examples have been solved.     

Granule development in a split-feed anaerobic baffled reactor

Operating anaerobic reactors at high organic loading rates during start-up can lead to instability, accumulation of volatile fatty acids and low pH, such problems being exacerbated in reactors that exhibit plug-flow characteristics. Moreover, plug-flow conditions increase the exposure of biomass to any toxic components in the feed. To overcome these limitations, an anaerobic baffled reactor (ABR), a reactor exhibiting partial plug-flow characteristics, was modified by splitting the feed between the individual compartments to produce the split-feed ABR (SFABR). Consequently, more favourable conditions were created in the initial compartments, such as lower, longer hydraulic retention time and longer cell retention time; conditions in the final compartments were also improved by the increased food availability for microorganisms. Other benefits included better gas mixing characteristics as a result of the more balanced gas production across the reactor. Granule development was compared in SFABR and normally fed ABR by analysing sludge samples, taken during start-up and continuous operation, using scanning electron microscopy. Photomicrographs allowed tentative conclusions to be made concerning the effect of split-feeding on the distribution of bacterial populations within the granule architecture and the role of extracellular polymers on granule formation.     

A law of small numbers for a mutation process

A system of particles will consist of 2n particles at time n, n = 0,1,2,...; each of the particles is either blue or white. At time 0 the particle is white. In the time interval (0,1) this particle mutates to blue with probability p. At time 1 the particle splits into two particles of the same color. At any time n greater than or equal to 1 the 2n particles act independently of each other and of their ancestral histories; during the time interval (n, n + 1) each white particle mutates to blue with probability p, and each blue particle mutates to white with probability alpha. The problem is to find the distribution of the number, Xn, of blue particles at time n - 0 when n is large and p = pn and alpha = alpha n are small.     

Endocytosis, intracellular trafficking, and processing of membrane IgG and monovalent antigen/membrane IgG complexes in B lymphocytes

Human B lymphoblastoid cell lines specific for tetanus toxin/toxoid were used in our earlier studies to demonstrate the rapid endocytosis of monovalent Ag and its processing, as a complex with mIgG. Here we show that the mIgGR for Ag is endocytosed in the presence or absence of Ag and that at any given time about 60% of this recycling pool of membrane (m) Ig is inside the cell. During the earliest detectable stages of Ag processing a high proportion of Ag fragments resolved on SDS gels were bound to intact mIg. However, at later times, as fragmented Ag accumulated, the fragments were precipitable only with antibodies against the Fab region of mIgG indicating proteolytic fragmentation of this receptor. Fractionation of cell homogenates on self-forming Percoll gradients revealed that at least two compartments are involved in Ag processing: a low density endosome compartment and a dense "late endosome"/lysosomal compartment. The spectrum of Ag fragments observed in each fraction differed: fragments produced at later times during processing were detected only in the late endosome/lysomal fraction whereas the earliest observed fragments were found both in this fraction and in the low density fractions. Monovalent Ag/mIgG complexes appear to have an increased probability, compared to unoccupied mIgG, of targeting to proteolytically active compartments leading to processing of the Ag/mIg complex and to accelerated degradation of the mIgG.     

Note on oscillations in a closed chain of compartments with linear,unidirectional transport

A closed chain of compartments in which there is unidirectional transport between adjacent members can exhibit damped oscillations. For a system ofn equivalent compartments, the value ofn which gives the greatest difference between the first maximum and first minimum isn=11, the difference being 1.57%. The greatest difference between the first maximum value and the steady state value is 4% and is obtained whenn=25. The results are illustrated graphically forn equal to 5, 10, 25 and 100.     

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.     

Susceptibility of Tribolium castaneum life stages exposed to elevated temperatures during heat treatments of a pilot flour mill: influence of sanitation, temperatures attained among mills floors, and costs

The influence of sanitation on responses of life stages of the red flour beetle, Tribolium castaneum (Herbst) (Coleoptera: Tenebrionidae), was investigated in a pilot flour mill subjected to three, 24-h heat treatments by using forced-air gas heaters fueled by propane. Two sanitation levels, dusting of wheat flour and 2-cm-deep flour, were created in 25 plastic bioassay boxes, each holding eggs, young larvae, old larvae, pupae, and adults of T. castaneum plus two temperature sensors. Data loggers (48) were placed on the five mill floors to record air temperatures. The time required to reach 50 degrees C, time above 50 degrees C, and the maximum temperature among mill floors and in bioassay boxes were measured. The maximum temperature in bioassay boxes and in the mill was lower on the first floor than on other floors. This trend was apparent in time required to reach 50 degrees C and time above 50 degrees C, especially in compartments with 2-cm-deep flour. The mean +/- SE mortality of T. castaneum life stages on the first floor was 55.5 +/- 12.9-98.6 +/- 0.8%; it was 93.2 +/- 6.7-100 +/- 0.0% on other floors. Adults were the least susceptible stage. Mortality of T. castaneum stages in compartments with 2-cm-deep flour was generally lower than those with flour dust. Costs for the three heat treatments ranged from US$27,438 to $28,838. An effective heat treatment can be conducted within 24 h, provided temperatures on mill floors reach 50 degrees C in 8-12 h and are held above 50 degrees C for at least 10-14 h, with maximum temperatures held between 50 and 60 degrees C.     

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.     

Implementation of group sequential logrank tests in a maximum duration trial

To control the Type I error probability in a group sequential procedure using the logrank test, it is important to know the information times (fractions) at the times of interim analyses conducted for purposes of data monitoring. For the logrank test, the information time at an interim analysis is the fraction of the total number of events to be accrued in the entire trial. In a maximum information trial design, the trial is concluded when a prespecified total number of events has been accrued. For such a design, therefore, the information time at each interim analysis is known. However, many trials are designed to accrue data over a fixed duration of follow-up on a specified number of patients. This is termed a maximum duration trial design. Under such a design, the total number of events to be accrued is unknown at the time of an interim analysis. For a maximum duration trial design, therefore, these information times need to be estimated. A common practice is to assume that a fixed fraction of information will be accrued between any two consecutive interim analyses, and then employ a Pocock or O'Brien-Fleming boundary. In this article, we describe an estimate of the information time based on the fraction of total patient exposure, which tends to be slightly negatively biased (i.e., conservative) if survival is exponentially distributed. We then present a numerical exploration of the robustness of this estimate when nonexponential survival applies. We also show that the Lan-DeMets (1983, Biometrika 70, 659-663) procedure for constructing group sequential boundaries with the desired level of Type I error control can be computed using the estimated information fraction, even though it may be biased. Finally, we discuss the implications of employing a biased estimate of study information for a group sequential procedure.     

A model-integrated multipoint Bayesian analysis of hypertension in the Framingham Heart Study data finds little evidence of linkage

This Genetic Analysis Workshop 13 contribution presents a linkage analysis of hypertension in the Framingham data based on the posterior probability of linkage, or PPL. We dichotomized the phenotype, coding individuals who had been treated for hypertension at any time, as well as those with repeated high blood pressure measurements, as affected. Here we use a new variation on the multipoint PPL that incorporates integration over the genetic model. PPLs were computed for chromosomes 1 through 5, 11, 14, and 17 and remained below the 2% assumed prior probability of linkage for 73% of the locations examined. The maximum PPL of 4.5% was obtained on chromosome 1 at 178 cM. Although this is more than twice the assumed prior probability of linkage, it is well below a level at which we would recommend committing substantial additional resources to molecular follow-up. While the PPL analysis of this data remains inconclusive, Bayesian methodology gives us a clear mechanism for using the information gained here in further studies.     

Complement factors in adult peripheral nerve: a potential role in energy metabolism

Complement cascade factors are known to play a critical role in myelin clearance after peripheral nerve injury. Here we show that components of both the classical (C1qa, C1qb, C1qc, C2 and C4) and alternative (C3, B and adipsin) pathways are expressed by uninjured peripheral nerve as well. mRNAs of components of the alternative pathway were predominantly found in the peri/epineurium, although factor C3 and factor B were also detected in the endoneurial compartment of adult nerve. Interestingly, adipsin mRNA was detected only in peri/epineurium, while adipsin protein was present in both peri/epineurium and endoneurium. This suggests that adipsin is transported to the endoneurium via the circulation from the peri/epineurium or outside of the nerve. Factor 5 and factor 9, necessary for the formation of the membrane-attack complex, were not detected in any part of the healthy peripheral nerve, which together with the observed presence of negative regulators of complement activation, is likely to prevent damage to the healthy nerve caused by complement activation. By analogy with the known role of complement factors in fat, we propose that local expression of these factors plays a role in the regulation of fatty acid homeostasis in the nerve and, thereby, in energy metabolism cross-talk between different compartments of the peripheral nerve.     

Gap junctional communication in the extraembryonic tissues of the gastrulating mouse embryo

We characterized gap junctional communication in the extraembryonic tissues of the 7.5-d gastrulating mouse embryo. At this stage of development, the extraembryonic tissues form a large part of the conceptus, and link the embryo proper to the maternal tissue. Using Lucifer yellow injections, cells in most extraembryonic tissues were observed to be very well dye coupled, the only exception being the peripheral regions of the ectoplacental cone. Of particular interest was the fact that no dye coupling was detected between the three major extraembryonic tissues. Thus, the extraembryonic ectoderm (EEC), the extraembryonic endoderm (EEN), and the ectoplacental cone (EPC) corresponded to separate communication compartments, with the EPC being further subdivided into three compartments. Interestingly, the EEN was observed to exhibit a very low level of dye coupling with the adjacent visceral embryonic endoderm (EN), and consistent with the latter dye coupling results was the finding that the EEN was ionically coupled to the EN, but not with any other extraembryonic tissues. However, in the EPC, ionic coupling studies show that the central region was well coupled ionically to the EEC, but only weakly coupled to the peripheral EPC. These findings, in conjunction with our previous study (1988. J. Cell Biol. 107:241-255), demonstrate that the 7.5-d mouse conceptus is subdivided into at least nine major Lucifer yellow-delineated communication compartments, with ionic coupling across some of these compartments effectively unifying the embryo into two large domains corresponding to the embryo proper and the major extraembryonic tissues.