Wyniki wyszukiwania - Biblioteka Nauki

1

Early detection of lung cancer by computed tomography and biomarkers: estimating the course of disease and population impact of treatment

100%

Kimmel M.

Journal of Medical Informatics & Technologies

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2000

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tom Vol. 1

IP 15--25

2

Model matematyczny procesu rekombinacji chromosomów

63%

Polańska J. , Kimmel M.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

|

1998

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tom z. 122

167-182

PL

W pracy przedstawiono model matematyczny ewolucji rozkładów alleli dla dwóch genów typu VNTR (Variable Number of Tandem Repeats). W procesie tworzenia modelu uwzględnionio wszystkie możliwe zdarzenia, z jednoczesnym występowaniem trzech oddziaływań genetycznych: mutacji, dryfu genetycznego i rekombinacji. Otrzymane wzory mogą z powodzeniem znaleźć zastosowanie w analizie statystycznej danych eksperymentalnych.

EN

The mathematical model of two-linked microsatellite loci evolution is presented. The described population model is a time-continuous Marcov chain. It is tranformed into differential equations' system of probablity generating function. The obtained model is very complicated because of considering all possible events, and including three genetic processes: mutation, genetic drift, and recombination. Appropriate specification of hypotheses leads to the well-known formulae. The equations could be successfully applied to the stochastic analysis of experimental data.

3

A model of dynamics of mutation, genetic drift and recombination in DNA-repeat genetic loci

63%

Polańska J. , Kimmel M.

Archives of Control Sciences

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1999

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tom Vol. 9, no. 1/2

143-157

EN

We present a model of genetic dynamics of a population of chromosomes, involving mutation, drift and recombination at a pair of repeat-DNA sequences. Such sequences, known as microsatellites and VNTR's, are commonly used as markers in studies in forensics, molecular evolution and gene mapping. The model we use has the form of a time-continuous Markov chain. It is further transformed to the form of a differential equation for probability generating functions. This description allows to follow dynamics with a variety of initial conditions. It allows, among other, to model the so called linkage disequilibrium, i.e. the state in which, due to processes like newly arisen mutation, selection, or population admixture, there exists a dependence between alleles at two loci. Recombination gradually dissolves the linkage disequilibrium, with additional contributions from drift and mutation. The model, in its complete form, is rather involved, since it includes all possible occurrences related to three genetic forces: mutation, genetic drift and recombination. However, we find explicit solutions to special cases which allow to understand the dynamics of dissolution of linkage disequilibrium. Other special cases of the model include the previously known relationships involving mutations and genetic drift. Also, we derive equations for the moments of the random variables present in the model. The moments can be used to define distance measures between distributions of alleles.

4

Analysis of dynamics of gene exspression using singular value decomposition

63%

Simek K. , Kimmel M.

Journal of Medical Informatics & Technologies

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2002

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tom Vol. 3

MI31--40

EN

Recently, data on multiple gene expression at sequential time points were analyzed, using Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by fitting of a linear discrete-time dynamical model in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model we formulate a nonlinear optimization problem and present how to solve it numerically using standard MATLAB procedures. We use publicly available data to test the approach. Then, we investigate the sensitivity of the method to missing measurements and its possibilities to reconstruct missing data. Summarizing we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics but may also lead to unexpected difficulties.

5

Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance

63%

Kimmel M. , Świerniak A.

Archives of Control Sciences

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2004

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tom Vol. 14, no. 2

105-145

EN

Two major obstacles against successful chemotheraphy of cancer are (1) the cell-cycle-phase dependence of treatment, and (2) the emergence of resistance of cancer cells to cytotoxic agents. One way to understand and overcome these two problems is to apply optimal control theory to mathematical models of cell cycle dynamics. These models should include division og the cell cycle into subphase and/or the mechanisms of drug resistance. we review our relevant results in mathematical modelling and control of the cell cycle and the mechanisms of gene amplification, and estimation of parameters of the constructed models.

6

Dynamics of the life history of a DNA-repeat sequence

63%

Bobrowski A. , Kimmel M.

Archives of Control Sciences

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1999

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tom Vol. 9, no. 1/2

57-67

EN

We consider a model of evolution of a DNA-repeat sequence, which takes into account stepwise extension/contraction events occurring with intensities proportional to the sequence length and the possibility of catastrophic breakdowns. The model was originally introduced by Kruglyak et al. [Proc. Natl. Acad. Sci. USA, 1998, 95: 10774-10778], in a slightly different form, and used for between-species comparisons of short DNA-repeat data. In the present paper, we investigate the dynamics of absorption in the model, which is equivalent to the elimination of the DNA-repeat sequence. Using the theory of Markov chains and stochastic semigroups, we obtain explicit expressions for the distributions of the process and for the time to absorption. We estimate median times to absorption for a range of coefficient values and discuss their relevance in view of known data for human and chimpanzee DNA-repeat sequences.

7

Spatial and Stochastic Effects in a Model of Viral Infection

63%

Bertolusso R. , Kimmel M.

Fundamenta Informaticae

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2012

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tom Vol. 118, nr 4

327-343

EN

Recently, Haseltine et al. published a mathematical model of dynamics of viral infection that has consisted of reaction-diffusion type differential equations for wild-type and infected cells, virions and interferon. The model serves as a mathematical description for two-dimensional viral infection spread experiments. We built a model which is different from Haseltine’s and is an ex- tension of another model by Getto et al. We investigated its deterministic and stochastic versions, using modeling software sbioPN created by Bertolusso. We found that in the range of parameters, which may be called “critical”, the stochastic model seems to display complex effects qualitatively different from its deterministic counterpart. Also, the rates of infection in the stochastic model are generally slower than in the deterministic model, an effect, which can be traced to Jensen inequality known best in probability calculus. Although a direct experimental confirmation of these effects is still missing, they seem sufficiently interesting to deserve discussion.

8

Population Genetics Models for the Statistics of dna Samples Under Different Demographic Scenarios-Maximum Likelihood Versus Approximate Methods

63%

Polański A. , Kimmel M.

International Journal of Applied Mathematics and Computer Science

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2003

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tom Vol. 13, no 3

347-355

EN

The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.

9

Stochastic Models of Progression of Cancer and Their Use in Controlling Cancer-Related Mortality

63%

Kimmel M. , Gorlova O. Y.

International Journal of Applied Mathematics and Computer Science

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2003

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tom Vol. 13, no 3

279-287

EN

A construction of a realistic statistical model of lung cancer risk and progression is proposed. The essential elements of the model are genetic and behavioral determinants of susceptibility, progression of the disease from precursor lesions through early (localized) tumors to disseminated disease, detection by various modalities, and medical intervention. Using model estimates as a foundation, mortality reduction caused by early-detection and intervention programs can be predicted under different scenarios. Genetic indicators of susceptibility to lung cancer should be used to define the highest-risk subgroups of the high-risk behavior population (smokers). The calibration and validation of the model requires applying our techniques to a variety of data sets available, including public registry data of the SEER type, data from the NCI lung cancer chest X-ray screening studies, and the recent ELCAP CT-scan screening study.

10

Testing for signatures of natural selection at molecular genes level

51%

Cyran K. , Polańska J. , Kimmel M.

Journal of Medical Informatics & Technologies

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2004

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tom Vol. 8

MM31--40

EN

The paper presents the methodology used for detecting the signatures of natural selection at the molecular level from single nucleotide polymorphism data. The results obtained from widely used approach, based on statistical testing departures from neutral evolution model, can be obscured by the presence of alternative hypotheses generating the similar to natural selection results of the tests. These hypotheses include population growth and geographic substructure. Especially for human population these alternatives are of non-negligible importance. In the paper we show how to deal with this problem, both by the analysis of a battery of statistical tests giving indication about the age of the predominant mutations, and by application of non conventional null hypotheses that assume different population scenarios. Since the critical values of the tests are known only for panmicting, constant size population, the second approach demands the intensive computer simulations of coalescence process to obtain analogous critical values for different scenarios used as a null. The methodology with the problem of detecting signatures of natural selection in four genes implicated in human familial cancers has been illustrated.

11

Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?

51%

Świerniak A. , Kimmel M. , Śmieja J. , Rzeszowska-Wolny J.

Journal of Medical Informatics & Technologies

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2004

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tom Vol. 8

MM3--10

EN

Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.

12

Single nucleotide polymorphisms applied in statistical inference of population growth

51%

Polański A. , Starosolski Z. , Świerniak A. , Kimmel M.

Biocybernetics and Biomedical Engineering

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2003

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tom Vol. 23, no. 4

45-61

EN

We have evaluated probability distributions of estimates of parameters of population growth, based on data on frequencies of alleles of unlinked SNP sites in DNA, modeled with the use of time dependent coalescence process acting together with mutation of a very low intensity. Probability distributions of maximum likelihood estimates of the product parameter of the present population effective size and exponent coefficient, for exponential scenario, have atoms at zero and long tails to the right. For stepwise scenario, log likelihood functions typically exhibit very long lines, covering many decades of the scale, of almost the same value of log likelihood. Observational data from [14] are consistent with the hypothesis of the population growth.

13

Modelling of cell aging - system theoretic approach

51%

Świerniak A. , Kimmel M. , Śmieja J. , Rzeszowska-Wolny J.

Journal of Medical Informatics & Technologies

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2001

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tom Vol. 2, Part. 1

MI3--MI8

EN

We characterize the asymptotic behavior of telomeres shortening of which is supposed to be the mechanism of aging and death. The problem is described by models in the form of infinitely many differential linear first order equations, resulting from branching random walk processes used to represent the evolution of particles in this problem, under different assumptions dealing with stochastic characterization of the process. We use control theoretical machinery based on Laplace transforms, Tauberian theorems and transfer loop reduction.

14

Identification and identifiability of models of cell signalling pathways

51%

Fujarewicz K. , Kimmel M. , Świerniak A.

Przegląd Elektrotechniczny

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2008

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tom R. 84, nr 5

91-94

EN

The dynamical behaviour of a cell signalling pathway may be described by means of a set of nonlinear ordinary differential equations. The data for parameter estimation are collected only at discrete time moments that are relatively rare. We show a gradient-based algorithm for parameter estimation. We also present some considerations about identifiability of cell signalling pathways. The approach is illustrated on a model of NF?B transcription factor pathway.

PL

Dynamiczne zachowanie komórkowych szlaków sygnałowych może być modelowane za pomocą nieliniowych równań różniczkowych zwyczajnych. Dane potrzebne do identyfikacji zbierane są w nielicznych, dyskretnych chwilach czasu. W artykule zamieszczamy gradientową metodę identyfikacji parametrów oraz przedstawiamy rozważania dotyczące identyfikowalności parametrów. Podejście jest zilustrowane na przykładzie modelu szlaku sygnałowego czynnika transkrypcyjnego NF?B.

15

Improved classification of microarray gene expression data using support vector machines

51%

Fujarewicz K. , Kimmel M. , Rzeszowska-Wolny J. , Świerniak A.

Journal of Medical Informatics & Technologies

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2001

|

tom Vol. 2, Part. 1

MI9--MI17

EN

Microarrays are new technique of gene expression measurements that attracted a great deal of research interest in recent years. It has been suggested that gene expression data from microarrays (biochips) can be utilized in many biomedical areas, for example in cancer classification. Whereas several, new and existing, methods of classification has been tested, a selection of proper (optimal) set of genes, which expression serves during classification, is still an open problem. In this paper we propose a heuristic method of choosing suboptimal set of genes by using support vector machines (SVMs). Obtained set of genes optimizes one-leave-out cross-validation error. The method is tested on microarray gene expression data of samples of two cancer types: acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). The results show that quality of classification of selected set of genes is much better than for sets obtained using another methods of feature selection.

16

Qualitative analysis of controlled drug resistance model - inverse Laplace and and semigroup approach

45%

Świerniak A. , Polański A. , Kimmel M. , Bobrowski A. , Śmieja J.

Control and Cybernetics

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1999

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tom Vol. 28, no 1

61-73

EN

In this paper we study some properties of infinite models of the controlled evolution of drug resistance. We combine asymptotic techniques used in previous studies of similar models with methods of control theory and of semigroup theory. It enables us to find conditions for stability of the model both when the sensitive population is annihilated and when there exists a permanent influx from the sensivite compartment into drug resistant one. The conditions are expressed in terms of relationships between amplification and deamplification ratios as well as average life times of cells and intensity of anticancer drug action.

17

Asymptotic analysis of three random branching walk models arising in molecular biology

45%

Świerniak A. , Polański A. , Śmieja J. , Kimmel M. , Rzeszowska-Wolny J.

Control and Cybernetics

|

2003

|

tom Vol. 32, no 1

147-162

EN

Using asymptotic techniques based on Laplace transforms, spectral analysis and theory of feedback systems, we characterise the asymptotic behaviour of the repeat loci in microsatellite DNA and cancer cells with increasing number of copies of genes responsible for coding proteins causing drug removal or metabolisation as well as telomeres shortening, which is supposed to be the mechanism of ageing and death. These three problems are described by models in the form of infinitely many differential linear or bilinear first order equations, resulting from branching random walk processes used to represent the evolution of particles in these problems.

PL

Wykorzystując techniki asymptotyczne oparte na transformatach Laplace'a, analizę spektralną oraz teorię układów ze sprzężeniem zwrotnym w artykule scharakteryzowano zachowanie asymptotyczne powtórek w DNA mikrosatelitarnym oraz w komórkach rakowych z rosnącą liczbą kopii genów odpowiedzialnych za kodowanie białek powodujących usuwanie lub przemianę metaboliczną leków, a także skracanie telomerów, o którym się sądzi, że jest mechanizmem starzenia się i śmierci. Te trzy zagadnienia są opisywane przy pomocy modeli w postaci nieskończonej liczby liniowych lub biliniowych równań pierwszego rzędu, wynikających z procesów błądzenia, stosowanych do opisu ewolucji cząstek w tych zagadnieniach.

18

TNFalpha-induced activation of NFkappaB protects against UV-induced apoptosis specifically in p53-proficient cells

38%

Szoltysek K. , Pietranek K. , Kalinowska-Herok M. , Pietrowska M. , Kimmel M. , Widlak P.

Acta Biochimica Polonica

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2008

|

tom 55

|

nr 4

741-748

EN

The signaling pathways that depend on p53 or NFκB transcription factors are essential components of cellular responses to stress. In general, p53 is involved in either activation of cell cycle arrest or induction of apoptosis, while NFκB exerts mostly anti-apoptotic functions; both regulatory pathways apparently interfere with each other. Here we aimed to analyze the effects of NFκB activation on DNA damage-induced apoptosis, either p53-dependent or p53-independent, in a set of human cell lines. Four cell lines, HCT116 and RKO colon carcinoma, NCI-H1299 lung carcinoma and HL60 myeloblastoma, each of them in two congenic variants either containing or lacking transcriptionally competent p53, were used. Cells were incubated with TNFα cytokine to activate NFκB and then treated with ultraviolet or ionizing radiation to induce apoptosis, which was assessed by measurement of the sub-G1 cell fraction. We observed that treatment with TNFα resulted in a significant reduction in the frequency of apoptotic cells in UV-irradiated p53-proficient lines (with exception of the UV-resistant NCI-H1299 cells). This anti-apoptotic effect was lost when cells were pretreated with parthenolide, an inhibitor of NFκB activation. In marked contrast, TNFα-pretreatment of p53-deficient lines resulted in an increased frequency of apoptotic cells after UV irradiation (with exception of HL60 cells). Such anti- and pro-apoptotic influence of TNFα was less obvious in cells treated with ionizing radiation. The data clearly indicates functional interference of both signaling pathways upon the damage-induced apoptotic response, yet the observed effects are both cell type- and stimulus-specific.

19

Modeling of interactions between NFkappaB and p53 signaling pathways

38%

Szoltysek K. , Lanuszewska J. , Widlak P. , Smieja R. , Fujarewicz K. , Kimmel M.

Acta Biochimica Polonica

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2006

|

tom 53

|

nr Supplement 1

20

Sampling Properties of Estimators of Nucleotide Diversity at Discovered snp Sites

38%

Renwick A. , Bonnen P. E. , Trikka D. , Nelson D. L. , Chakraborty R. , Kimmel M.

International Journal of Applied Mathematics and Computer Science

|

2003

|

tom Vol. 13, no 3

385-394

EN

SNP sites are generally discovered by sequencing regions of the human genome in a limited number of individuals. This may leave SNP sites present in the region, but containing rare mutant nucleotides, undetected. Consequently, estimates of nucleotide diversity obtained from assays of detected SNP sites are biased. In this research we present a statistical model of the SNP discovery process, which is used to evaluate the extent of this bias. This model involves the symmetric Beta distribution of variant frequencies at SNP sites, with an additional probability that there is no SNP at any given site. Under this model of allele frequency distributions at SNP sites, we show that nucleotide diversity is always underestimated. However, the extent of bias does not seem to exceed 10-15% for the analyzed data. We find that our model of allele frequency distributions at SNP sites is consistent with SNP statistics derived based on new SNP data at ATM, BLM, RQL and WRN gene regions. The application of the theory to these new SNP data as well as to the literature data at the LPL gene region indicates that in spite of ascertainment biases, the observed differences of nucleotide diversity across these gene regions are real. This provides interesting evidence concerning the heterogeneity of the rates of nucleotide substitution across the genome.