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EN
Ab initio methods of DNA regulatory sequence region prediction known as transcription factor binding sites (TFBS) are a very big challenge to modern bioinformatics. Although the currently available methods are not perfect they are fairly reliable and can be used to search for new potential protein-DNA interaction sites. The biggest problem of ab initio approaches is the very high false positive rate of predicted sites which results mainly from the fact that TFBS are very short and highly degenerate. Because of that they can occur by chance every few hundred bases making the task of computational prediction extremely difficult if one aims to reduce the high false positive rate keeping highest possible sensitivity to predict biologically meaningful sequence regions. In this work we present a new application that can be used to predict TFBS regions in very large datasets based on position weight matrix models (PWM’s) using one of the most popular prediction methods. The presented application was used to predict the concentration of TFBS in a set of nearly 2.2 thousand unique sequences of human gene promoter regions. The study revealed that the concentration of TFBS further than 1kbp from the transcription initiation site is constant but it decreases rapidly while getting closer to the transcription initiation site. The decreasing TFBS concentration in the vicinity of genes might result from evolutionary selection which keeps only sites responsible for interactions with proteins being part of a specific regulatory mechanism leading to cells survival.
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.
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.
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.
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.
EN
Proper classification of cancer is a crucial aspect in diagnosis and choosing optimal medical therapy. It has been suggested, in recent years, that classification process of cancer can be done using gene expression monitoring. Usefulness of this approach has increased due to the new technique of gene expression monitoring – using so called "expression chips". Recently in [1, 3] a heuristic method of cancer classification, called weighted voting (WV) method, based on gene expression levels has been proposed and tested on a set of samples of acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). Here a more traditional approach to feature selection and classification is presented and tested on the same data set. Feature selection is performed using modified Sebestyen criterion and classification is done using linear classifying function trained by modified perception algorithm. Obtained results are better than results of the WV method. In cross-validation of initial set all 38 samples were classified correctly (WV – 1 incorrect) and only one sample from independent set was classified incorrectly (WV – 2 incorrect).
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