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PubMed2006

Non-random associations and vascular fields in neurofibromatosis 1: a pathogenetic hypothesis.

Neurofibromatosis type 1 (NF1) is an autosomal dominant disorder with highly variable expression generally ascribed to random factors. However, evidence is presented for patterns suggesting non-stochastic processes as follows: (1) We have seen a MZ twin pair concordant for renal vascular hypertension, and another for unilateral ptosis. Other concordances have been reported, including both malformations and tumors, and combinations as well. (2) Four children were seen with a distinct ipsilateral association of glaucoma or iris anomaly, optic glioma, plexiform neurofibromas arising from the trigeminal nerve and its branches, and sphenoid dysplasia. Other cases in the literature support milder forms of this association. (3) We saw six children with apparent gynecomastia or premature thelarche without endocrine abnormalities. Tissue samples from four of these showed an unusual fibrous plexiform neurofibroma. Interestingly, five of the six cases were African Americans, and constitutional factors affecting fibrous reactions may also be involved here.A tentative hypothesis is presented suggesting vascular fields involving defined areas that can: (1) Support tumor growth. They would be the "soil" determining the ability and the extent of growth. There would, however, still be a need for a "second hit" tumor transformation. (2) Affect blood supply to organs, creating structural anomalies. NF1 involves a vasculopathy, and would predispose to vulnerabilities of such fields. Genetic factors could induce superimposed susceptibilities of specific fields, leading to twin concordances. "Hits" affecting specific fields would increase the likelihood of multiple abnormalities that could include both tumors and structural findings. Finally, tumors may follow the contours of existing fields. The breast is an area normally primed for growth, and the observation of clitoromegally secondary to tumor involvement suggests that such fields exist elsewhere.

Child↗

PubMed1988

Effects of English admixture and geographic distance on anthropometric variation and genetic structure in 19th-century Ireland.

The analysis of anthropometric data often allows investigation of patterns of genetic structure in historical populations. This paper focuses on interpopulational anthropometric variation in seven populations in Ireland using data collected in the 1890s. The seven populations were located within a 120-km range along the west coast of Ireland and include islands and mainland isolates. Two of the populations (the Aran Islands and Inishbofin) have a known history of English admixture in earlier centuries. Ten anthropometric measures (head length, breadth, and height; nose length and breadth; bizygomatic and bigonial breadth; stature; hand length; and forearm length) on 259 adult Irish males were analyzed following age adjustment. Discriminant and canonical variates analysis were used to determine the degree and pattern of among-group variation. Mahalanobis' distance measure, D2, was computed between each pair of populations and compared to distance measures based on geographic distance and English admixture (a binary measure indicating whether either of a pair of populations had historical indications of admixture). In addition, surname frequencies were used to construct distance measures based on random isonymy. Correlations were computed between distance measures, and their probabilities were derived using the Mantel matrix permutation method. English admixture has the greatest effect on anthropometric variation among these populations, followed by geographic distance. The correlation between anthropometric distance and geographic distance is not significant (r = -0.081, P = .590), but the correlation of admixture and anthropometric distance is significant (r = 0.829, P = .047). When the two admixed populations are removed from the analysis the correlation between geographic and anthropometric distance becomes significant (r = 0.718, P = .025). Isonymy distance shows a significant correlation with geographic distance (r = 0.425, P = .046) but not with admixture distance (r = -0.052, P = .524). The fact that anthropometrics show past patterns of gene flow and surnames do not reflects the greater impact of stochastic processes on surnames, along with the continued extinction of surnames. This study shows that 1) anthropometrics can be extremely useful in assessing population structure and history, 2) differential gene flow into populations can have a major impact on local genetic structure, and 3) microevolutionary processes can have different effects on biological characters and surnames.

Adult↗

PubMed2005

Joint modelling of repeated transitions in follow-up data--a case study on breast cancer data.

In longitudinal studies where time to a final event is the ultimate outcome often information is available about intermediate events the individuals may experience during the observation period. Even though many extensions of the Cox proportional hazards model have been proposed to model such multivariate time-to-event data these approaches are still very rarely applied to real datasets. The aim of this paper is to illustrate the application of extended Cox models for multiple time-to-event data and to show their implementation in popular statistical software packages. We demonstrate a systematic way of jointly modelling similar or repeated transitions in follow-up data by analysing an event-history dataset consisting of 270 breast cancer patients, that were followed-up for different clinical events during treatment in metastatic disease. First, we show how this methodology can also be applied to non Markovian stochastic processes by representing these processes as "conditional" Markov processes. Secondly, we compare the application of different Cox-related approaches to the breast cancer data by varying their key model components (i.e. analysis time scale, risk set and baseline hazard function). Our study showed that extended Cox models are a powerful tool for analysing complex event history datasets since the approach can address many dynamic data features such as multiple time scales, dynamic risk sets, time-varying covariates, transition by covariate interactions, autoregressive dependence or intra-subject correlation.

Algorithms↗

PubMed2002

Probability distributions of enantiomeric excess in unstirred and stirred crystallization of 1,1'-binaphthyl melt.

Crystallization of 1, l'-binaphthyl from its melt can generate optical activity spontaneously. Since crystallization is a stochastic process, the enantiomeric excess (ee) generated in each crystallization varies randomly. We investigated the qualitative features of probability distribution of the ee for crystallization at two temperatures, 150 degrees C and 152 degrees C, at which conglomerate crystallization occurs. No clear transparent crystals were produced at either temperature, indicating that the solid states formed in the melt were polycrystalline. The ee randomly fluctuated from run to run, with an average of 26.9% and 2.7% when the crystallization was carried out at 152 degrees C, and 150 degrees C, respectively. The spread of the probability distribution is also substantially different. We also studied the probability distribution of ee in stirred crystallization at different stirring RPM. The results show probability distribution's broadening and evolution to a bimodality with increasing stirring RPM--a typical behavior in symmetry-breaking transitions. These results shed light on the nature of enantioselectivity in secondary nucleation and crystal growth.

Journal Article↗

PubMed1997

Influences on the lifespan of B cell subpopulations defined by different phenotypes.

The turnover of mature and immature B cells defined by a range of cell surface markers was investigated by feeding normal or bcl-2-transgenic (bcl-2-Tg) mice 5'-bromo-2-deoxyuridine (BrdUrd) for up to 6 weeks. In peripheral lymphoid tissue, B cells accumulated BrdUrd with a 50% labeling time of 4.3 weeks and a pattern of uptake indicative of the presence of both long-lived and short-lived cells. These two kinetic populations could be resolved into immature B220lo/heat-stable antigen (HSA)hi cells which labeled rapidly, and B220hiHSAlo cells which were uniformly long-lived with a half-life of about 6 weeks. During loading and pulse-chase experiments, BrdUrd uptake by cells within the mature B220hiHSAlo population clearly followed an exponential kinetic pattern, suggesting that their loss was governed by stochastic processes. Using other surface markers, the long-lived population could also be defined by high expression of IgD, representing cells in the follicular mantle zone of the spleen, and by the phenotype IgMhiIgDloHSAlo which most likely represented marginal zone memory B cells. CD23 expression on B cells did not differentiate well between long and short-lived cells. Only about half of newly labeled B cells appearing in the spleen progressed to the long-lived compartment, a proportion which was not altered significantly in bcl-2-Tg mice. The most likely explanation was that a combination of both positive and negative selection was operating at this site which was mediated by pathways not regulated by bcl-2. On the other hand, overexpression of bcl-2 did result in a two- to threefold increase in the rate of appearance of newly labeled B cells in the spleen, consistent with a possible role for this protein during early selection events within the bone marrow. Selection processes appeared to be very active in young mice during the shaping of the B cell repertoire, since B cells from 6-week-old non-Ig mice displayed a rapid rate of turnover irrespective of their surface phenotype, and a significant population of long-lived cells did not become evident until the mice had reached about 12 weeks of age.

Animals↗

PubMed1997

Defects of the respiratory chain in the normal human liver and in cirrhosis during aging.

Defects of the respiratory chain are a typical feature of mitochondrial diseases and occur also during normal aging where they have been described in postmitotic tissues. The present study addresses the question of defect expression in the normal and cirrhotic liver. Randomly distributed defects of complex III (ubiquinone-cytochrome-c-oxidoreductase) and of complex IV (cytochrome-c-oxidase) of the respiratory chain have been detected with age-related increasing frequency both in normal and cirrhotic livers. No defects were present for complex II (succinate-dehydrogenase) and complex V (adenosine triphosphate-synthase) and in liver cell carcinomas. Sixty-one of 107 normal livers (57%) showed defects of the respiratory chain. The defects occurred in advanced age (over 50 years) in 87%. In contrast 50 of 64 cirrhotic livers (78%) had defects and approximately 60% occurred after age 50. The defects were caused by a loss of enzyme protein involving both nuclearly and mitochondrially coded subunits. Ninety-four percent of the defects (n = 275) involved complex IV selectively. In 4% selective defects of complex III were found and combined defects of both complexes occurred in only 2%. In situ hybridization and polymerase chain reaction (PCR) studies for the detection of the common deletion (4.977 bp) and of various point mutations of mitochondrial DNA (mtDNA) revealed no consistent molecular genetic abnormalities in microdissected respiratory chain defective liver cell areas. Single point mutations at nt 3243 and/or 5692 were found only in 7 of 18 microdissected probes from 6 patients. The results show that defects of the respiratory chain occur already in normal livers most probably during cell aging and at a higher rate in cirrhosis. The random defect pattern favors a stochastic process, e.g., free radical damage. However, the role of mutations of mtDNA remains to be established.

Adenosine Triphosphatases↗

PubMed1991

Differentiation and heterogeneity in T-antigen immortalized precursor cell lines from mouse cerebellum.

Recently, various techniques have been developed to transfer oncogenes into brain cells in order to generate immortalized neural cell lines. It is of interest to establish how well such cell lines reflect their cellular origin. Here we report the characterization of sixteen cell lines from mouse cerebellum and, as a control, six cell lines from skin. Lines were established by immortalizing postnatal primary cell cultures with a retrovirus carrying a modified temperature-sensitive variant of SV40 large T antigen. The cell lines reflect many properties of the cell type from which they were derived. All of the sixteen cerebellar lines expressed one or more markers of the neural precursor cells, namely, nestin and epitopes for NG2 and A2B5. In contrast, none of the six skin lines expressed neural precursor markers. Both types of cell lines expressed vimentin and fibronectin. Differentiation occurred in some of the cerebellar lines and was enhanced in defined medium. A small percentage of cerebellar cells, usually less than 5%, was positive for a marker of differentiation, e.g., glial fibrillary acidic protein (GFAP), galactocerebroside (GalC), or L1. Expression of GFAP colocalized with that of nestin at varying levels of intensity, indicating a gradual replacement of nestin by GFAP in the cytoskeleton. Both the cells positive for precursor markers and those positive for differentiation markers tended to be located in clusters, suggesting that stochastic processes or cell-cell interactions are important for the determination of the fate of cells within a clonal cell line in vitro. The degree of differentiation seemed to correlate with a shift from serum-containing to defined medium, but not with a shift from the permissive to the nonpermissive temperature for T antigen expression. The immortalization approach described here thus allows the establishment of cell lines which are "captured" in the precursor state of the developing mouse neuroepithelium.

Animals↗

PubMed1988

Model analysis of factors influencing the prediction of muscle forces at the knee.

A three-dimensional stochastic mathematical muscle model of the knee joint has been developed and applied to a study in which the influence of both mechanical and physiological factors were examined in relation to the prediction of muscular forces about the joint. The model includes a representation of the proximal portion of the tibia and distal portion of the femur along with a mathematical expression of the patellar mechanism and 13 muscles crossing the knee joint. The model accounts for the rolling and gliding movement of the tibial-femoral articulation. The computational technique involves equilibrating three components of external moments at the knee joint to the internal moments generated by muscular forces and soft tissue. The variables contained in the moment equilibrium equation are randomly chosen based on the choice of the tibial-femoral contact point. The randomness of the variables, reflected in the final solution, defines a stochastic process in the context of the present model. Studies with the model indicated that a very important mechanical aspect of the model was the capability to simulate the moving contact point between the tibia and femur. The moving contact point increased the mechanical advantage of the quadriceps muscles by 50%, which corresponded to in vivo EMG measurements. Muscle force predictions during normal gait have shown the capability of the model to determine the presence of synergistic and antagonistic muscle action.

Biomechanical Phenomena↗

PubMed1988

Fatigue-related changes in neuromuscular excitability of rat hindlimb muscles.

Brief repetitive trains of supramaximal nerve stimulation produce intermittent muscle activation and, in time, a progressive decline in force (i.e., neuromuscular fatigue) and depression of the electromyogram (EMG). These changes may include within-train reductions in EMG due to a failure of neuromuscular propagation. The aim of the present study was to investigate changes in EMG during a 360-second stimulus regimen designed to fatigue soleus and extensor digitorum longus muscles of anesthetized rats by activating the muscle with repetitive trains of 40 Hz stimuli. Measurements included peak force for each tetanus, variation of the within-train EMG (coefficient of variation for area), and magnitude of the first EMG waveform (area) of each train. Fatigue was characterized as the relative decline in force over the course of the test. The responses of the test muscles were categorized, based on an absolute scale of fatigability, into five groups: potentiated, nonfatigable, low fatigability, intermediate fatigability, and high fatigability. Fatigable muscles (low, intermediate, and high fatigability groups) demonstrated a decreased EMG magnitude and an increased EMG-area variation with repetitive activation. This increased variation, however, was nonmonotonically related to fatigability such that the least and most fatigable muscles had the smallest within-train EMG variation. We suggest that these data can be explained by considering the EMG (compound muscle action potential) as a stochastic process that represents a composite of single-fiber events (axonal to sarcolemmal transmission) with variable probabilities.

Animals↗

PubMed2006

Substructural cooperativity and parallel versus sequential events during protein unfolding.

According to the "old view," proteins fold along well-defined sequential pathways, whereas the "new view" sees protein folding as a highly parallel stochastic process on funnel-shaped energy landscapes. We have analyzed parallel and sequential processes on a large number of molecular dynamics unfolding trajectories of the protein CI2 at high temperatures. Using rigorous statistical measures, we quantify the degree of sequentiality on two structural levels. The unfolding process is highly parallel on the microstructural level of individual contacts. On a coarser, macrostructural level of contact clusters, characteristic parallel and sequential events emerge. These characteristic events can be understood from loop-closure dependencies between the contact clusters. A correlation analysis of the unfolding times of the contacts reveals a high degree of substructural cooperativity within the contact clusters.

Amino Acid Sequence↗

PubMed2006

A mixed effects Markov model for repeated binary outcomes with non-ignorable dropout.

In many areas of research, repeated binary measures often represent a two-state stochastic process, where individuals can transition among two states. In a behavioural or physical disability setting, individuals can flow from susceptible or subthreshold state, to an infectious or symptomatic state, and back to a subthreshold state. Quite often the transition among the states happens in continuous time but is observed at discrete, irregularly spaced timepoints which may be unique to each individual. Methods for analyses of such data are typically based on the Markov assumption. Cook (Biometrics 1999; 55:915-920) introduced a conditional Markov model that accommodates the subject-to-subject variation in the model parameters with random effects. We extend this model by adding a non-ignorable dropout component to the model. Specification of the distribution of the random effects is made to guarantee a closed form expression of the marginal likelihood. This methodology is illustrated by applications to a data set from a parasitic field infection survey, a data set from a cocaine treatment study, and a data set from an aging study. Simulations suggest that the shared parameter model is robust with respect to at least one alternative non-ignorable model.

Activities of Daily Living↗

PubMed1988

A random walk model for evaluating clinical trials involving serial observations.

For clinical trials where the variable of interest is ordered and categorical (for example, disease severity, symptom scale), and where measurements are taken at intervals, it might be possible to achieve a greater discrimination between the efficacy of treatments by modelling each patient's progress as a stochastic process. The random walk is a simple, easily interpreted model that can be fitted by maximum likelihood using a maximization routine with inference based on standard likelihood theory. In general the model can allow for randomly censored data, incorporates measured prognostic factors, and inference is conditional on the (possibly non-random) allocation of patients. Tests of fit and of model assumptions are proposed, and application to two therapeutic trials of gastroenterological disorders are presented. The model gave measures of the rate of, and variability in, improvement for patients under different treatments. A small simulation study suggested that the model is more powerful than considering the difference between initial and final scores, even when applied to data generated by a mechanism other than the random walk model assumed in the analysis. It thus provides a useful additional statistical method for evaluating clinical trials.

Algorithms↗

PubMed1990

Statistical analysis of quality of life data in cancer clinical trials.

In clinical trials endpoints other than total and/or disease-free survival are gaining more and more interest. In particular, quality of life (QOL) or the well-being of patients has emerged as a synonym for variables describing the subjective reactions of patients towards their disease and its treatment. The statistical analysis of such QOL data is complicated firstly by the large number of variables measured and their obvious lack of objectivity. The construction of suitable aggregate measures allowing a reduction of the measurements into a (preferably) unidimensional index are discussed in the context of an analysis at a fixed time point during the course of treatment. A second problem arises from the consideration that a patient's well-being is subject to changes over time. We discuss the modelling of QOL by suitable stochastic processes which are extensions of a multistate disease process. This allows QOL events to be incorporated into methods of survival analysis by either estimating the relevant transition probabilities between states or calculating quality-adjusted survival times. Finally, some brief guidelines for the planning of clinical trials including QOL measurements will be proposed.

Attitude to Health↗

PubMed1991

Assessment of quality of life in clinical trials.

This paper is intended as an overview of developments in the assessment of quality of life (QOL) in clinical trials over the last decade from the viewpoint of clinical biostatistics. In the first part we deal with aspects of obtaining adequate measurements of quality of life. A literature survey shows that a large number of quite heterogeneous measurement approaches for use in clinical trials exist, a substantial percentage of which cannot be regarded as sufficient for their actual measuring purpose. In the second part we review statistical methods applied to and adapted for the analysis of QOL data. Underlying the analysis should be the assumption of QOL as a stochastic process. Applied analysis procedures are again investigated in a literature survey. Finally, critical conclusions are outlined and suggestions for further research are given.

Activities of Daily Living↗

PubMed1997

A Dynamic Model for the Attachment of a Brownian Particle Mediated by Discrete Macromolecular Bonds

A model is presented for the attachment of a Brownian particle to a surface mediated by both the conservative colloidal forces and the formation of macromolecular bonds. By considering Brownian motion and bond formation as coupled stochastic processes, the model derives a governing equation for the time-dependent probability density of having a given number of bonds and separation distance from the surface. The model predicts the deposition rate of particles to a surface as a function of the physicochemical parameters of the binding molecules, including the density, interaction length, stiffness, and formation and dissociation kinetic rate constants. Furthermore, two limiting simplifications of the full model are explored which correspond to particle attachment rate limited by the rate of Brownian motion or by the rate of bond formation.

Journal Article↗

PubMed1996

Reproducible nonlinear population dynamics and critical points during replicative competitions of RNA virus quasispecies.

RNA virus evolution is generally considered to be highly unpredictable, but tests of determinism in the evolution of competing populations during viral infections have not been performed. Here we study the fate of two closely related evolving quasispecies of vesicular stomatitis virus, by determining the relative concentration of a wild-type clone and a surrogate marked virus subclone (MARM-C) upon extensive competitive replication in a constant cell culture environment. A highly predictable nonlinear behaviour of the two competing populations was found. In addition, the presence of critical points, which are defined as points from which viral competitions may follow different trajectories, has been documented. Critical points were reached after nearly constant periods of time. The dynamics of relative fitness values for both competing populations were calculated during the replication passages. Concomitant with expected fitness gain of both competing viral populations (which follow the Red Queen hypothesis) a tendency for the MARM-C to gain less fitness than the wild-type was observed. Although fitness variations were noisy, this tendency was seen in all evolutionary replicas. Thus, despite the stochastic process of mutation that leads to a continuous generation of mutant genomes during RNA virus replication, a nonlinear, nearly deterministic evolutionary behaviour has been observed. It is proposed that such a behaviour is mediated by a low-pass filter (averaging of mutational noise signals) due to competitive selection among variants.

Analysis of Variance↗

PubMed1998

Spin Echo Attenuation of Restricted Diffusion as a Discord of Spin Phase Structure

By using the particle probability density we analyze the spin echo attenuation of particles, diffusing in a bounded region. It provides a means to expand a nonuniform spin phase distribution into a series of waves that characterize the geometry and boundary conditions of confinement. Random motion disrupts the initial phase structure created by applied gradients and consequently discords its structure waves. By assuming the spin phase fluctuation and/or the randomness of spin phase distribution in the subensemble as a Gaussian stochastic process, we derive a new analytical expression for the echo attenuation related to the particle velocity correlation. For a diffusion in porous structure we get the expression featuring the same "diffusive diffraction" patterns as those being found and explained by P. T. Callaghan and A. Coy ("Principles of Nuclear Magnetic Resonance Microscopy," Oxford Univ. Press, Oxford (1991); J. Chem. Phys. 101, 4599-4609 (1994)) with the use of propagator theory. With the new approach we cast a new light on the phenomena and derive analitically how the diffusive diffractions appear when the sequence of finite or even modulated gradients are applied. The method takes into account the non-Markovian character of restricted diffusion, and therefore the echo dependence on the diffusion lengths and on the strength of applied gradient differs from the results of authors assuming the Markovian diffusion either by dealing with the diffusion propagators or by the computer simulation of Fick's diffusion. Copyright 1998 Academic Press.

Journal Article↗

PubMed1997

Continuous stability and evolutionary convergence.

A stochastic process of long-term evolution due to mutation and selection is defined over an asexually reproducing population, with selection according to a population game with a one-dimensional continuity of pure strategies. Limiting the analysis to mutations of small effect, it is shown that long-term dynamic stability in such a process is equivalent to continuous stability in the relevant population game. In the case of a one-dimensional strategy set (but not necessarily if the strategy set is multi-dimensional), this result is virtually independent of the distribution of mutations.

Animals↗