On the stochastic theory of compartments: I. A single-compartment system

A stochastic model is developed for a compartment with a single time-dependent input, and generalized to include inputs from several sources. With the number of particles of a given molecular species in the compartment as the random variable, the mean, variance and third central moment of this variable are calculated from its generating function, and compared with previous results. The behavior of the calculated moments is discussed, and the possibility of applying the model to chemical and biological systems is considered.     

Theoretical basis for the interpretation of surface permeability data by a transient method

Surface permeability data are frequently required when the system under study consists of a multiple zone membrane. Rotunno et al. (1970) developed a transient method to determine surface permeabilities in which the solute from one compartment is fully absorbed by the membrane without being transferred to the other. The theoretical analysis of the various possible situations is presented here to show that: (1) a linear plot of uptake vs. contact time can be expected for the most simple case (quasi-steady state in the external zone) even in the presence of considerable boundary layer resistance, and (2) a linear display of experimental data is not exclusive for that case, but it can also occur in the more complex situation of a composite resistance of a semi-infinite medium plus boundary layer. On this basis, different alternatives to interpret the data are suggested, according to the physical situation and the equations developed for each case.     

The adaptation of a two-compartment cell renewal system to external demands

Summary The inner enamel epithelium (IEE) covers the labial tooth aspect as a one cell layer which, when cut sagittally, appears as a longitudinal cell column extending from the tooth origin toward the periphery. Following sudden tooth shortening, the IEE responds by an increased cell production which later declines below normal values. The perturbation affects all cell kinetic parameters; the progenitor compartment, which initially increases, diminishes in size toward end of the experiment. The cell cycle transition times, which initially decline, rise toward the end of the experiment. The mean normal daily cell production rate of 70 cell % (i.e. 70 cells are produced by 100 progenitors) increases to 111 cell % and then declines to a low of 51 cell %. The IEE response typifies the behavior of other cell renewal systems such as intestinal epithelium and epidermis.     

On the Forkker-Planck equation in the stochastic theory of mortality: I

This paper, consisting of two parts, gives all the mathematical details that were omitted in a previous work by G. A. Sacher and E. Trucco (“The Stochastic Theory of Mortality.”Ann. N. Y. Acad. Sci.,96, 985–1007, cited here as ST). We assume that the reader is familiar with ST, where the stochastic theory of mortality, originally proposed by Sacher, is discussed at length. We recall that the basic model presented there refers to an ensemble of particles performing Brownian motion in one dimension, with the added constraint of two absorbing barriers. These two points, collectively, are designated as the “lethal bound.” Part I (section 1 to 4) deals with the special case in which the two absorbing barriers are symmetrically located at a finite distance from the origin. The solution of the Fokker-Planck equation is obtained from the theory of eigenvalue problems. Quite generally, the eigenfunctions functions belong to the family of Kummer's confluent hypergeometric functions, but the symmetry condition imposed here results in considerable simplification and makes it possible to estimate the first few eigenvalues by a graphical procedure. In section 3 we show how perturbation theory can be applied in the limiting case of “weak homeostasis,” and section 4 deals with the opposite extreme of “strong homeostasis.” A rigorous proof is given for the result corresponding to equation (28) of ST (asymptotic or quasi-static approximation for the “force of mortality”). This work was performed under the auspices of the U.S. Atomic Energy Commission.     

On the time-dependent reversible stochastic compartmental model—I. The general two-compartment system

The distribution of the two-compartment, reversible system with time-dependent transitions is proposed and verified. Inasmuch as the required probabilities cannot, in general, be expressed in closed form, a method of approximating these probabilities is described. An example with specific inverse functions of time is presented.     

On the probability of reaching a threshold in a stochastic mammillary system

The multivariate distribution over time of a particular stochastic mammillary compartmental model is obtained for any point in time. The maximum expectation of the peripheral compartments is then derived and used to determine lower bounds on the probability that the maximum of the peripheral compartments reaches any arbitrary threshold level. A bound on the probability is illustrated by an example and some of its implications are explored.     

CellLine, a stochastic cell lineage simulator

Summary: We present CellLine, a simulator of the dynamics ofgene regulatory networks (GRN) in the cells of a lineage. Fromuser-defined reactions and initial substance quantities, itgenerates cell lineages, i.e. genealogic pedigrees of cellsrelated through mitotic division. Each cell's dynamics is drivenby a delayed stochastic simulation algorithm (delayed SSA),allowing multiple time delayed reactions. The cells of the lineage can be individually subject to ‘perturbations’,such as gene deletion, duplication and mutation. External interventions,such as adding or removing a substance at a given moment, canbe specified. Cell differentiation lineages, where differentiationis stochastically driven or externally induced, can be modeledas well. Finally, CellLine can generate and simulate the dynamicsof multiple copies of any given cell of the lineage. As examples of CellLine use, we simulate the following systems:cell lineages containing a model of the P53-Mdm2 feedback loop,a differentiation lineage where each cell contains a 4 generepressilator (a bistable circuit), a model of the differentiationof the cells of the retinal mosaic required for color visionin Drosophila melanogaster, where the differentiation pathwaydepends on one substance's concentration that is controlledby a stochastic process, and a 9 gene GRN to illustrate theadvantage of using CellLine rather than simulating multipleindependent cells, in cases where the cells of the lineage aredynamically correlated. Availability: The CellLine program, instructions and examplesare available at http://www.cs.tut.fi/~sanchesr/CellLine/CellLine.html Contact: andre.sanchesribeiro{at}tut.fi Associate Editor: Limsoon Wong     

Theoretical basis of the Beavis effect

The core of statistical inference is based on both hypothesis testing and estimation. The use of inferential statistics for QTL identification thus includes estimation of genetic effects and statistical tests. Typically, QTL are reported only when the test statistics reach a predetermined critical value. Therefore, the estimated effects of detected QTL are actually sampled from a truncated distribution. As a result, the expectations of detected QTL effects are biased upward. In a simulation study, William D. Beavis showed that the average estimates of phenotypic variances associated with correctly identified QTL were greatly overestimated if only 100 progeny were evaluated, slightly overestimated if 500 progeny were evaluated, and fairly close to the actual magnitude when 1000 progeny were evaluated. This phenomenon has subsequently been called the Beavis effect. Understanding the theoretical basis of the Beavis effect will help interpret QTL mapping results and improve success of marker-assisted selection. This study provides a statistical explanation for the Beavis effect. The theoretical prediction agrees well with the observations reported in Beavis's original simulation study. Application of the theory to meta-analysis of QTL mapping is discussed.     

Theoretical basis of the plant domestication

Summary Plant domestication is stimulated by economic demands. Crop plant formation is controlled primarily by natural selection in cultivation; artificial selection is only a useful addition. The ecotypical nature of the initial material has great bearing on the success of domestication. The weeds of a convergent group were well adapted to being cultivated; weeds of a divergent group can be domesticated only with difficulty. Wild plants in nature are extremely varied ecotypically: some can be domesticated easily, others with difficulty. Some wild plants and weeds can be cultivated without genetic change (naturalization), while a genetic transmutation is necessary for the domestication of others (acclimatization). New domesticated ecotypes can be produced: 1. as a result of reconstruction of the initial populations and new ecotype synthesis on the basis of individual genotypes; 2. by means of hybridization of wild or weed initial genotypes with cultivated ones; 3. by use of new mutations in cultivation and further plant breeding.     

The cellular basis of self renewal in culture by human acute myeloblastic leukemia blast cell progenitors

Blast cells from patients with Acute Myeloblastic Leukemia (AML) were separated according to cell size using velocity sedimentation under unit gravity. Fractions obtained in this way were plated in methyl cellulose with a growth stimulator present in media conditioned by leukocytes in the presence of phytohemagglutinin (PHA-LCM). Colonies of blast cells form under these conditions. Pooled cell suspensions from such colonies were plated in microwells; the plating efficiency of such suspensions is a measure of blast progenitor self-renewal occurring in the original blast colonies. Self-renewal assays on each fraction indicated that self renewal among blast progenitors is heterogeneously distributed with subpopulations differing in renewal capacities. The results are consistent with the view that blast cell subpopulations in AML undergo a series of transitions associated with decreasing self renewal capacity, analogous to that observed in normal hemopoiesis, where proliferative capacity decreases with increasing differentiation.     

Angiotensin II cell signaling: physiological and pathological effects in the cardiovascular system

The renin-angiotensin system is a central component of the physiological and pathological responses of cardiovascular system. Its primary effector hormone, angiotensin II (ANG II), not only mediates immediate physiological effects of vasoconstriction and blood pressure regulation, but is also implicated in inflammation, endothelial dysfunction, atherosclerosis, hypertension, and congestive heart failure. The myriad effects of ANG II depend on time (acute vs. chronic) and on the cells/tissues upon which it acts. In addition to inducing G protein- and non-G protein-related signaling pathways, ANG II, via AT₁ receptors, carries out its functions via MAP kinases (ERK 1/2, JNK, p38MAPK), receptor tyrosine kinases [PDGF, EGFR, insulin receptor], and nonreceptor tyrosine kinases [Src, JAK/STAT, focal adhesion kinase (FAK)]. AT₁R-mediated NAD(P)H oxidase activation leads to generation of reactive oxygen species, widely implicated in vascular inflammation and fibrosis. ANG II also promotes the association of scaffolding proteins, such as paxillin, talin, and p130Cas, leading to focal adhesion and extracellular matrix formation. These signaling cascades lead to contraction, smooth muscle cell growth, hypertrophy, and cell migration, events that contribute to normal vascular function, and to disease progression. This review focuses on the structure and function of AT₁ receptors and the major signaling mechanisms by which angiotensin influences cardiovascular physiology and pathology. vascular smooth muscle; NAD(P)H oxidase; tyrosine and nontyrosine receptor kinases; endothelial dysfunction; vascular disease     

Conformational behaviours of 2-substituted cyclohexanones: a complete basis set,hybrid-DFT study and NBO interpretation

The generalised anomeric effect (GAE) and gauche effect (GE) associated with donor–acceptor delocalisations, dipole–dipole interactions and total steric exchange energies (TSEE) on the conformational properties of 2-methoxy- (1), 2-methylthio- (2), 2-methylseleno- (3), 2-fluoro- (4), 2-chloro- (5) and 2-bromocyclohexanone (6) have been studied by means of ab initio and hybrid density functional theory methods and natural bond orbital (NBO) analysis. All methods used showed that the axial conformation stability increased from 2-methoxy- (1) to 2-methylselenocyclohexanone (3) and also from 2-fluoro- (4) to 2-bromocyclohexanone (6), which is in agreement with reported NMR data. The results obtained by complete basis set 4 (CBS-4), B3LYP/6-311+G** and HF/6-311+G** levels for compounds 1, 5 and 6 are very similar, but the CBS-4 results for compound 4 are not in agreement with the reported experimental data (vapour phase). The NBO analysis showed that the GAE increases from compounds 1 to 3 and also from compounds 4 to 6. The low axial conformer populations of compounds 1 and 4 can be reasonably explained by their small GAE. GE does not have significant impact on the conformational behaviours of compounds 1–6 and GAE succeeds in accounting qualitatively for the increase in the axial preferences in both series of compounds. The results showed that the calculated Δ(TSEE_eq–ax) values decrease from compounds 4 to 6 which contradicts the suggested arguments in the literature about these compounds. On the other hand, the calculated differences between the dipole moment values of the axial and equatorial conformations, Δ(μ_eq ? μ_ax), increase from compounds 1 to 2, but decrease from compounds 2 to 3 and also decrease from compounds 4 to 6. The calculated GAE values are more significant for the explanation of the conformational preferences of compounds 1–6 than the dipole–dipole repulsion effects. The correlations between the GAE, GE, dipole–dipole interactions, Wiberg Bond Index, TSEE, donor and acceptor orbital energies and occupancies, structural parameters and conformational behaviour of compounds 1–6 have been investigated.     

RASSF1C modulates the expression of a stem cell renewal gene, PIWIL1

ABSTRACT: BACKGROUND: RASSF1A and RASSF1C are two major isoforms encoded by the Ras association domain family 1 (RASSF1) gene through alternative promoter selection and mRNA splicing. RASSF1A is a well established tumor suppressor gene. Unlike RASSF1A, RASSF1C appears to have growth promoting actions in lung cancer. In this article, we report on the identification of novel RASSF1C target genes in non small cell lung cancer (NSCLC). METHODS: Over-expression and siRNA techniques were used to alter RASSF1C expression in human lung cancer cells, and Affymetrix-microarray study was conducted using NCI-H1299 cells over-expressing RASSF1C to identify RASSF1C target genes. RESULTS: The microarray study intriguingly shows that RASSF1C modulates the expression of a number of genes that are involved in cancer development, cell growth and proliferation, cell death, and cell cycle. We have validated the expression of some target genes using qRT-PCR. We demonstrate that RASSF1C over-expression increases, and silencing of RASSF1C decreases, the expression of PIWIL1 gene in NSCLC cells using qRT-PCR, immunostaining, and Western blot analysis. We also show that RASSF1C over-expression induces phosphorylation of ERK1/2 in lung cancer cells, and inhibition of the MEK-ERK1/2 pathway suppresses the expression of PIWIL1 gene expression, suggesting that RASSF1C may exert its activities on some target genes such as PIWIL1 through the activation of the MEK-ERK1/2 pathway. Also, PIWIL1 expression is elevated in lung cancer cell lines compared to normal lung epithelial cells. CONCLUSIONS: Taken together, our findings provide significant data to propose a model for investigating the role of RASSF1C/PIWIL1 proteins in initiation and progression of lung cancer.     

The repair rate of radiation-induced DNA damage: a stochastic interpretation based on the gamma function

There is a large body of evidence that stress-induced DNA damage may be responsible for cell lethality, cancer proneness and/or immune reaction. However, statistical features of their repair rate remain poorly documented. In order to interpret the shape of the radiation-induced DNA damage repair curves with a minimum of biological assumptions, we introduced the concept of repair probability, specific to any individual radiation-induced DNA damage, whatever its biochemical type. We strengthened the apparent paradox that the repair rate of a population of DNA damage is time-dependent even if the repair rate of the individual DNA damage is constant. Hence, the existing models, based on a dual approach of the DNA repair may be insufficient for describing the DNA repair rate over a large range of repair times. Since the repair probability of DNA damage cannot be assessed individually, the measurement of the DNA repair rate is assumed to consist in determining the instantaneous mean of all repair probabilities. The relevance of this model was examined with different endpoints: cell species, genotypes, radiation type and chromatin condensation. The Euler's Gamma function was shown to provide the distribution the most consistent with such hypotheses. Furthermore, formulas, deduced from the Gamma distribution, were found to be compatible with our previous model, empirically defined but based on a variable repair half-time.