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At least 739 records · Page 41Linked to original sources
PubMed2000

Tumour control probability: a formulation applicable to any temporal protocol of dose delivery.

An analytic expression for the tumour control probability (TCP), valid for any temporal distribution of dose, is discussed. The TCP model, derived using the theory of birth-and-death stochastic processes, generalizes several results previously obtained. The TCP equation is [equation: see text] where S(t) is the survival probability at time t of the n clonogenic tumour cells initially present (at t = 0), and b and d are, respectively, the birth and death rates of these cells. Equivalently, b = 0.693/Tpot and d/b is the cell loss factor of the tumour. In this expression t refers to any time during or after the treatment; typically, one would take for t the end of the treatment period or the expected remaining life span of the patient. This model, which provides a comprehensive framework for predicting TCP, can be used predictively, or--when clinical data are available for one particular treatment modality (e.g. fractionated radiotherapy)--to obtain TCP-equivalent regimens for other modalities (e.g. low dose-rate treatments).

Brachytherapy↗
PubMed2000

Using Bayesian networks to analyze expression data.

DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a "snapshot" of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biological features of cellular systems. In this paper, we propose a new framework for discovering interactions between genes based on multiple expression measurements. This framework builds on the use of Bayesian networks for representing statistical dependencies. A Bayesian network is a graph-based model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. We then describe a method for recovering gene interactions from microarray data using tools for learning Bayesian networks. Finally, we demonstrate this method on the S. cerevisiae cell-cycle measurements of Spellman et al. (1998).

Algorithms↗
PubMed2002

Rate4Site: an algorithmic tool for the identification of functional regions in proteins by surface mapping of evolutionary determinants within their homologues.

MOTIVATION: A number of proteins of known three-dimensional (3D) structure exist, with yet unknown function. In light of the recent progress in structure determination methodology, this number is likely to increase rapidly. A novel method is presented here: 'Rate4Site', which maps the rate of evolution among homologous proteins onto the molecular surface of one of the homologues whose 3D-structure is known. Functionally important regions often correspond to surface patches of slowly evolving residues. RESULTS: Rate4Site estimates the rate of evolution of amino acid sites using the maximum likelihood (ML) principle. The ML estimate of the rates considers the topology and branch lengths of the phylogenetic tree, as well as the underlying stochastic process. To demonstrate its potency, we study the Src SH2 domain. Like previously established methods, Rate4Site detected the SH2 peptide-binding groove. Interestingly, it also detected inter-domain interactions between the SH2 domain and the rest of the Src protein that other methods failed to detect.

Algorithms↗
PubMed1989

SDSE: a software package to simulate the evolution of a pair of DNA sequences.

An algorithm to simulate DNA sequence evolution under a general stochastic model, including as particular cases all the previously used schemes of nucleotide substitution, is described. The stimulation is carried out on finite, variable length, DNA sequences through a strict stochastic process, according to the particular substitution rates imposed by each scheme. Five FORTRAN programs, running on an IBM PC and compatibles, carry out all the tasks needed for the simulation. They are menu driven and interfaced to the system through a principal menu. All sequence data files used and generated by the SDSE package conform to the standard GenBank database format, thus allowing the use of any sequence retrieved from this databank, as well as the application of other packages to analyse, manipulate or retrieve stimulated sequences.

Algorithms↗
PubMed2000

Joint modelling of longitudinal measurements and event time data.

This paper formulates a class of models for the joint behaviour of a sequence of longitudinal measurements and an associated sequence of event times, including single-event survival data. This class includes and extends a number of specific models which have been proposed recently, and, in the absence of association, reduces to separate models for the measurements and events based, respectively, on a normal linear model with correlated errors and a semi-parametric proportional hazards or intensity model with frailty. Special cases of the model class are discussed in detail and an estimation procedure which allows the two components to be linked through a latent stochastic process is described. Methods are illustrated using results from a clinical trial into the treatment of schizophrenia.

Journal Article↗
PubMed2002

Mathematical models of vaccination.

Mathematical models of epidemics have a long history of contributing to the understanding of the impact of vaccination programmes. Simple, one-line models can predict target vaccination coverage that will eradicate an infectious agent, whilst other questions require complex simulations of stochastic processes in space and time. This review introduces some simple ordinary differential equation models of mass vaccination that can be used to address important questions about the predicted impact of vaccination programmes. We show how to calculate the threshold vaccination coverage rate that will eradicate an infection, explore the impact of vaccine-induced immunity that wanes through time, and study the competitive interactions between vaccine susceptible and vaccine resistant strains of infectious agent.

Child↗
PubMed1987

Optimal recombination rate in fluctuating environments.

The optimal recombination rate which maximizes the long-term geometric average of the population fitness is studied for a two-locus haploid model, assuming that the fitnesses of genotypes AB, Ab, aB and ab are 1 + s(t), 1 - s(t), 1 - s(t), and 1 + s(t), respectively, where s(t) follows various stationary stochastic processes with the average zero. With positive recombination, the polymorphism is stably maintained at both loci. After an initial transient phase, the dynamics are reduced to one dimension, and are analyzed for weak selection limit, strong selection limit, and selection with two state Markovian jump. Results are: (1) If the environmental fluctuation has a predominant periodic component, ropt is approximately inversely proportional to the period irrespective of selection intensity. (2) If the fluctuation is a superposition of many periodic components, the one with the longest period is the most effective in determining ropt because the genetic dynamics cannot track very quick fluctuations (low pass filter effect). (3) If the power spectrum density is decreasing with the frequency, as in pink, or 1/f noises, ropt is small when selection is weak, and increases with the selection intensity. Numerical calculation of the genetic dynamics of a recombination modifier supports all these predictions for the evolutionarily stable recombination rate.

Alleles↗
PubMed1998

Analysis of genetic structure and dispersal patterns in a population of sea beet.

A model of the migration pattern in a metapopulation of sea beet (Beta vulgaris L. ssp. maritima), based on the continuous distributions of seed and pollen movements, is fitted to gene frequency data at 12 isozyme and RFLP loci by maximum likelihood by using an approximation of the simultaneous equilibrium distribution of the gene frequencies generated by the underlying multivariate stochastic process of genetic drift in the population. Several alternative restrictions of the general model are fitted to the data, including the island model, a model of complete isolation, and a model in which the seed and pollen dispersal variances are equal. Several likelihood ratio tests between these alternatives are performed, and median bias in the estimated parameters is corrected by using parametric bootstrapping. To assess the fit of the selected model, the predicted covariances are compared with covariances computed from the data directly. The dependency of estimated parameters on the ratio between effective and absolute subpopulation sizes, which is treated as a known parameter in the analysis, is also examined. Finally, we note that the data also appear to contain some information about this ratio.

Alleles↗
PubMed2002

Recombination at his-3 in Neurospora declines exponentially with distance from the initiator, cog.

By deletion of 1.8 kb of sequence between cog(L) and his-3 and replacement with sequences of different lengths, we have generated a set of Neurospora strains in which the distance between cog(L) and the site at which recombination is selected varies from 1.7 to nearly 6 kb. Each of the manipulated strains includes cog(L), a highly active recombination hotspot, and rec-2, thus allowing high-frequency recombination. In addition, each is a his-3 mutant, either K26 or K480. The frequency of His(+) recombinants in progeny of these crosses is inversely proportional to the distance between his-3 and cog. Specifically, there is a linear relationship between log(10) (recombination frequency) and the distance in base pairs, indicating that as distance decreases, the rate of interallelic recombination increases exponentially. An exponential relationship between distance separating markers and the chance of co-conversion has been found in both Drosophila and fission yeast, indicating that the extension of recombination events may be a stochastic process in most organisms. On the basis of these and additional data presented in this article, we conclude that recombination is initiated at cog(L) in >17% of meioses, that most conversion tracts are very short, and that few extend >14 kb.

Hydro-Lyases↗
PubMed1999

Methylation profiling of CpG islands in human breast cancer cells.

CpG island hypermethylation is known to be associated with gene silencing in cancer. This epigenetic event is generally accepted as a stochastic process in tumor cells resulting from aberrant DNA methyltransferase (DNA-MTase) activities. Specific patterns of CpG island methylation could result from clonal selection of cells having growth advantages due to silencing of associated tumor suppressor genes. Alternatively, methylation patterns may be determined by other, as yet unidentified factors. To explore further the underlying mechanisms, we developed a novel array-based method, called differential methylation hybridization (DMH), which allows a genome-wide screening of hypermethylated CpG islands in tumor cells. DMH was used to determine the methylation status of >276 CpG island loci in a group of breast cancer cell lines. Between 5 and 14% of these loci were hypermethylated extensively in these cells relative to a normal control. Pattern analysis of 30 positive loci by Southern hybridization indicated that CpG islands might differ in their susceptibility to hypermethylation. Loci exhibiting pre-existing methylation in normal controls were more susceptible to de novo methylation in these cancer cells than loci without this condition. In addition, these cell lines exhibited different intrinsic abilities to methylate CpG islands not directly associated with methyltransferase activities. Our study provides evidence that, aside from random DNA-MTase action, additional cellular factors exist that govern aberrant methylation in breast cancer cells.

Base Sequence↗
PubMed2005

Engineering translocations with delayed replication: evidence for cis control of chromosome replication timing.

Certain chromosome rearrangements, found in cancer cells or in cells exposed to ionizing radiation, exhibit a chromosome-wide delay in replication timing (DRT) that is associated with a delay in mitotic chromosome condensation (DMC). We have developed a chromosome engineering strategy that allows the generation of chromosomes with this DRT/DMC phenotype. We found that approximately 10% of inter-chromosomal translocations induced by two distinct mechanisms, site-specific recombination mediated by Cre or non-homologous end joining of DNA double-strand breaks induced by I-Sce1, result in DRT/DMC. Furthermore, on certain balanced translocations only one of the derivative chromosomes displays the phenotype. Finally, we show that the engineered DRT/DMC chromosomes acquire gross chromosomal rearrangements at an increased rate when compared with non-DRT/DMC chromosomes. These results indicate that the DRT/DMC phenotype is not the result of a stochastic process that could occur at any translocation breakpoint or as an epigenetic response to chromosome damage. Instead, our data indicate that the replication timing of certain derivative chromosomes is regulated by a cis-acting mechanism that delays both initiation and completion of DNA synthesis along the entire length of the chromosome. Because chromosomes with DRT/DMC are common in tumor cells and in cells exposed to ionizing radiation, we propose that DRT/DMC represents a common mechanism responsible for the genomic instability found in cancer cells and for the persistent chromosomal instability associated with cells exposed to ionizing radiation.

Cell Line, Tumor↗
PubMedDate not supplied

Neural networks in the analysis of episodic growth hormone release.

Pulsatile secretion of growth hormone (GH) has been observed in healthy controls as well as acromegalic patients. In healthy adults, highly regulated secretory pulses of GH occur 4-8 times within 24 h. This episodic pattern of secretion seems to be related to the optimal induction of physiological effects at the peripheral level. In contrast to normal subjects, acromegalic patients demonstrate an irregular pattern of excessive GH release. This pattern of secretion is responsible for many systemic effects, such as the stimulation of connective tissue growth, cardiovascular and cerebrovascular disease, diabetes mellitus and arthritis. Standard methods for the analysis of pulsatile patterns of hormone secretion did not consistently separate the temporal dynamics of GH release in healthy controls and acromegalic patients under various study conditions. Using the cutting edge technology of artificial neural networks for time series prediction, we were able to achieve significant separation of both groups under various conditions by means of the predictability of their GH secretory dynamics. Improving the predictive results by using a more refined system of multiple neural networks acting in parallel (adaptive mixtures of local experts), we found that this system performed a self-organized segmentation of hormone pulsatility. It separated phases of secretory bursts and quiescence without any prior knowledge of the form of a GH pulse or a model of secretion. Comparing the predictive results for the GH dynamics with those for computer-stimulated stochastic processes, we were able to define the irregular pattern of GH secretion in acromegaly as a random autonomous process. The introduction of neural networks to the analysis of dynamic endocrine systems might help to expand the existing analytical approaches beyond counting frequency and amplitude of hormone pulses.

Acromegaly↗
PubMed2003

Parallel functional changes in the digestive RNases of ruminants and colobines by divergent amino acid substitutions.

A morphological or physiological trait may appear multiple times in evolution. At the molecular level, similar protein functions may emerge independently in different lineages. Whether these parallel functional changes are due to parallel amino acid substitutions has been a subject of debate. Here, I address this question using digestive ribonucleases (RNases) of two groups of foregut-fermenting mammals: ruminant artiodactyls and colobine monkeys. The RNase1 gene was duplicated twice in ancestral ruminants at least 40 MYA, and it was also duplicated in the douc langur, an Asian colobine, approximately 4 MYA. After duplication, similar functional changes occurred in the ruminant and monkey enzymes. Interestingly, five amino acid substitutions in ruminant RNases that are known to affect its catalytic activity against double-stranded (ds) RNA did not occur in the monkey enzyme. Rather, a similar functional change in the monkey was caused by a different set of nine substitutions. Site-directed mutagenesis was used to make three of the five ruminant-specific substitutions in the monkey enzyme. Functional assays of these mutants showed that one of the three substitutions has a similar effect in monkeys, the second has a stronger effect, and the third has an opposite effect. These results suggest that (1) an evolutionary problem can have multiple solutions, (2) the same amino acid substitution may have opposite functional effects in homologous proteins, (3) the stochastic processes of mutation and drift play an important role even at functionally important sites, and (4) protein sequences may diverge even when their functions converge.

Amino Acid Sequence↗
PubMed2003

The relationship between microsatellite slippage mutation rate and the number of repeat units.

Microsatellite markers are widely used for genetic studies, but the relationship between microsatellite slippage mutation rate and the number of repeat units remains unclear. In this study, microsatellite distributions in the human genome are collected from public sequence databases. We observe that there is a threshold size for slippage mutations. We consider a model of microsatellite mutation consisting of point mutations and single stepwise slippage mutations. From two sets of equations based on two stochastic processes and equilibrium assumptions, we estimate microsatellite slippage mutation rates without assuming any relationship between microsatellite slippage mutation rate and the number of repeat units. We use the least squares method with constraints to estimate expansion and contraction mutation rates. The estimated slippage mutation rate increases exponentially as the number of repeat units increases. When slippage mutations happen, expansion occurs more frequently for short microsatellites and contraction occurs more frequently for long microsatellites. Our results agree with the length-dependent mutation pattern observed from experimental data, and they explain the scarcity of long microsatellites.

Algorithms↗
PubMed1991

Cancer metastasis.

The process of metastasis consists of a series of linked, sequential steps that must be completed by tumour cells if a metastasis is to develop. Although some of the steps in this process contain stochastic elements, metastasis as a whole favors the survival and growth of a few subpopulations of tumour cells that pre-exist within the heterogeneous parent neoplasm. Metastases can have a clonal origin, and different metastases can originate from the proliferation of single cells. The outcome of metastasis depends on the interaction of metastatic cells with different organ environments. Organ-specific metastases have been demonstrated in a variety of experimental tumour systems, and tumour growth can be specific to a particular site within one organ. The factors that regulate metastasis are the intrinsic properties of some tumour cells and host factors involved in homeostasis. Understanding these factors should allow for the development of more effective treatment of cancer metastasis.

Humans↗
PubMed1996

Molecular divergence and phylogeny: rates and patterns of cytochrome b evolution in cranes.

Analyses of complete cytochrome b sequences from all species of cranes (Aves: Gruidae) reveal aspects of sequence evolution in the early stages of divergence. These DNA sequences are > or = 89% identical, but expected departures from random substitution are evident. Silent, third-position pyrimidine transitions are the dominant substitution type, with transversion comprising only a small fraction of sequence differences. Substitution patterns are not clearly manifested until divergence has reached a moderate level (> 3%), as expected for a stochastic process. Variation in the frequency of mismatch types among lineages decreases at larger divergences, but the level of bias does not decay. Divergence varies up to fivefold among gene regions but is not correlated with structural domain. All protein structural domains except extramembrane 4 display < 20% variable residues. Regions corresponding to putative functional domains show the excepted conservation of amino acids, although the C-terminal portion of the Q0 reaction center displays several nonconservative replacements. Phylogenetic analyses incorporating substitution asymmetries produced mixed results. Distances estimated with multiple parameters (transition, codon-position, composition, and pyrimidine-transition biases) yielded identical additive tree topologies with comparable bootstrap values, all consistent with uncontroversial species relationships. Maximum likelihood analysis incorporating these biases, as well as equally weighted parsimony analysis, produced similar results. Static, differential weighting for parsimony did not improve the phylogenetic signal but produced unusual trees with low bootstraps. The overall rate of nucleotide substitution varies slightly but significantly among cranes, and calibration of distances against fossil dates suggests divergence rates of 0.7%-1.7% per million years.

Animals↗
PubMed1998

The frequency distribution of gene family sizes in complete genomes.

We compare the frequency distribution of gene family sizes in the complete genomes of six bacteria (Escherichia coli, Haemophilus influenzae, Helicobacter pylori, Mycoplasma genitalium, Mycoplasma pneumoniae, and Synechocystis sp. PCC6803), two Archaea (Methanococcus jannaschii and Methanobacterium thermoautotrophicum), one eukaryote (Saccharomyces cerevisiae), the vaccinia virus, and the bacteriophage T4. The sizes of the gene families versus their frequencies show power-law distributions that tend to become flatter (have a larger exponent) as the number of genes in the genome increases. Power-law distributions generally occur as the limit distribution of a multiplicative stochastic process with a boundary constraint. We discuss various models that can account for a multiplicative process determining the sizes of gene families in the genome. In particular, we argue that, in order to explain the observed distributions, gene families have to behave in a coherent fashion within the genome; i.e., the probabilities of duplications of genes within a gene family are not independent of each other. Likewise, the probabilities of deletions of genes within a gene family are not independent of each other.

Algorithms↗
PubMed1996

Communication patterns and expressed emotion in families of persons with mental disorders.

Interaction in 40 families of persons with bipolar disorders or schizophrenia was analyzed as a stochastic process to examine communication patterns between patients and parents relative to parents' level of expressed emotion (EE). Interaction sequences were coded with the Relational Control Coding System, and Markov process characteristics of order (degree of sequential dependency), stationarity, and role homogeneity were assessed with log-linear analysis. Communication patterns in high-EE families with both disorders showed more serial dependence--were more "tightly joined"--than low-EE families. However, both low- and high-EE families of persons with bipolar disorders competed for control, while there were marked differences in control patterns in low- and high-EE families of persons with schizophrenia, with low-EE families not at all competitive and high-EE families highly competitive. Difference in both responsiveness and competition for control were much stronger in dual-parent families. It was concluded that high-EE families have a family system that combines over-responsiveness with conflict about "who's in charge".

Adolescent↗