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1
Content available Sensitivity analysis of deterministic signaling pathways models
Puszyński K., Lachor P., Kardyńska M., Śmieja J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2012
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Vol. 60, nr 3
471-479
EN
The paper is focused on application of sensitivity methods to analysis of signaling pathway models. Two basic methods are compared: local, based on standard sensitivity functions, and global, based on Sobol indices. Firstly, a general outline of modeling of signaling pathways by means of ordinary differential equations is briefly described. Afterwards, the methods of sensitivity analysis, known from literature, are introduced and illustrated with a simple example of a dynamical system of the second order. Subsequently, the analysis of the p53/Mdm2 regulatory module, which is a key element of any pathway involving p53 protein, is presented. The results of this analysis suggest that no single method should be chosen for investigation of any signaling pathway model but several of them should be applied to answer important questions about sources of heterogeneity in cells behavior, robustness of signaling pathways and possible molecular drug targets.
2
Content available remote Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes
Śmieja J.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 4
781-788
EN
The paper deals with the analysis of signaling pathways aimed at uncovering new regulatory processes regulating cell responses. First, general issues of comparing simulation and experimental data are discussed, and various aspects of data normalization are covered. Then, a model of a particular signaling pathway, induced by Interferon-\beta, is briefly introduced. It serves as an example illustrating how mathematical modeling can be used for inferring the structure of a regulatory system governing the dynamics of intracellular processes. In this pathway, experimental results suggest that a hitherto unknown process is responsible for a decrease in the levels of one of the important molecules used in the pathway. Then, equilibrium points of the model are analyzed, allowing the rejection of all but one explanation of the phenomena observed experimentally. Numerical simulations confirm that the model can mimic the dynamics of the processes in the pathway under consideration. Finally, some remarks about the applicability of the method based on an analysis of equilibrium points are made.
3
Content available remote Transkrypcja genów jako ciągły lub dyskretny proces produkcyjny
Śmieja J.
Przegląd Elektrotechniczny
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2008
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R. 84, nr 9
93-95
PL
W komórkach żywych organizmów zachodzi wiele procesów biochemicznych podlegających skomplikowanym mechanizmom regulacji. Jednym z nich jest proces produkcji cząsteczek mRNA, zachodzący w jądrze komórkowym. Z praktycznego punktu widzenia jest to proces dyskretny. W niektórych przypadkach może być on jednak opisywany modelami ciągłymi. W niniejszej pracy pokazane są warunki, w jakich zarówno opis dyskretny, jak i ciągły prowadzą do takich samych jakościowo wyników.
EN
Biochemical processes in living cells are controlled by complex regulatory systems. One of such processes is production of mRNA molecules during gene transcription, taking place in the nucleus. The nature of this production process is discrete but in some cases it can be described by means of continuous models. This work presents cases in which both discrete and continuous models lead to qualitatively equivalent results.
4
Content available remote Model based analysis of signaling pathways
Śmieja J.
International Journal of Applied Mathematics and Computer Science
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2008
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Vol. 18, no 2
139-145
EN
The paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including unknown processes activating gene transcription by means of first-order lag elements is introduced and discussed. Then, a particular interferon-ß induced pathway is introduced, limited to early events that precede activation of gene transcription. It is shown how to simplify the system description based on the goals of modeling. Further, a computational analysis is presented, facilitating better understanding of the mechanisms underlying regulation of key components in the pathway. The analysis is illustrated by a comparison of simulation and experimental data.
5
Content available Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?
Świerniak A., Kimmel M., Śmieja J., Rzeszowska-Wolny J.
Journal of Medical Informatics & Technologies
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2004
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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.
6
Content available remote Different Models of Chemotherapy Taking Into Account Drug Resistance Stemming from Gene Amplification
Śmieja J., Świerniak A.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 3
297-305
EN
This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the other is infinite dimensional and tridiagonal. A methodology of the analysis of such models, based on system decomposition, is presented. An optimal control problem is defined in the l1 space. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
7
Content available Asymptotic analysis of three random branching walk models arising in molecular biology
Świerniak A., Polański A., Śmieja J., Kimmel M., Rzeszowska-Wolny J.
Control and Cybernetics
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2003
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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.
8
Content available Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification
Śmieja J., Świerniak A.
Journal of Medical Informatics & Technologies
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2002
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Vol. 3
MI13--19
EN
The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.
9
Modelling of cell aging - system theoretic approach
Świerniak A., Kimmel M., Śmieja J., Rzeszowska-Wolny J.
Journal of Medical Informatics & Technologies
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2001
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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.
10
Cancer treatment optimisation under evolving drug resistance-control theoretic approach
Świerniak A., Śmieja J., Duda Z.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Elektryka
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2000
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Z. 35
53-60
EN
Optimmision of treatment protocols for resistant cancer population is formulated as an optimal control problem for infinite dimensional model which takes into account gene amplification. From mathematical point of view the model is similar to the one for the RC ladder infinite systems nevertheless the control variable is introduced as a multiplier in the state equations that makes the control problem bilinear. The necessary conditions for optimal control of drug resistant population are found. To achieve this, the primary model in the form of infinietely many state equations is transformed into one described by single integro-differential equation. A gradient method base approach for finding the solution of the stated problem is presented.
PL
Optymalizacja protokołów leczenia lekoopornych populacji nowotworowych została sformułowana jako zadanie sterowania nieskończenie wymiarowym modelem biorącym pod uwagę amplifikację genów. Z matematycznego punktu widzenia model jest podobny do modelu nieskończonego układu drabinkowego RC ze sterowaniem wprowadzonym multiplikatywnie. co powoduje hi liniowość problemu optymalizacyjnego. W celu znalezienia warunków koniecznych pierwotny model w postaci nieskończenie wielu równań stanu przekształcono do jednego równania różniczkowo całkowego i zastosowano odpowiednią wersję abstrakcyjnej zasady maksimum. Następnie zaproponowano algorytm numerycznego wyznaczania optymalnych harmonogramów chemioterapii oparty na odpowiedniej metodzie gradientowej.
11
Content available Qualitative analysis of controlled drug resistance model - inverse Laplace and and semigroup approach
Świerniak A., Polański A., Kimmel M., Bobrowski A., Śmieja J.
Control and Cybernetics
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1999
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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.
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