Andrzej Świerniak

CELL CYCLE AS AN OBJECT OF CONTROL

This chapter is devoted to models of cancer growth and anticancer therapies that put special emphasis on the dependence of therapy efficiency on cell cycle. First, biological background is introduced and detailed description of a cell cycle is given, based on the review of biological literature. It is supplemented with information about chosen chemotherapeutic drugs and their efficacy with respect to the cell cycle. Next, pharmacokinetic and pharmacodynamics aspects of chemotherapeutics are briefly described. They along with cell cycle specificity of drugs may lead to various phenomena of resonances and aftereffects that need to be taken into account in therapy and synchronization of treatment protocols. These issues are mentioned in a separate section of this chapter. Finally, models that incorporate evolution of drug resistance are presented. For all models, the problem of finding a suitable treatment protocol is formulated as a problem of control optimization and some results of application of optimization theory to solve these problems are presented.

Using SVD and SVM methods for selection, classification, clustering and modeling of DNA microarray data

Abstract DNA microarray technology is the latest and the most advanced tool for parallel measuring of the activity and interactions of thousands of genes. This modern technology promises new insight into mechanisms of living systems, for example only two high-density oligonucleotide microarrays are sufficient to inspect the whole human genome. However, it provides unprecedented amount of data that require application of advanced computational methods. The appropriate choice of data analysis technique depends both on data and on goals of an experiment. In this paper we focus on two promising methods: singular value decomposition and support vector machines. We discuss the possibility of application of these methods for different purposes; particularly for clustering, classification, feature selection and modeling of dynamics of gene expression. We use for testing presented approaches existing data sets, which are widely available via Internet, and one new tumor/normal thyroid microarray data set.

On direct controllability of discrete time jump linear system

In this paper we consider a problem of controllability of discrete time linear system with randomly jumping parameters which can be described by finite state Markov chain. Necessary and sufficient conditions for existence of control which governs the system from any initial conditions to zero, from zero initial condition to any final value and from any initial condition to any final value in given time and with probability one are given. The relations between such kinds of controllability and stochastic stabilizability are discussed.

Upper Bounds on the Solution of Coupled Algebraic Riccati Equation

Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE) and discrete time coupled algebraic Riccati equation (DCARE) are developed as special cases of bounds for the uni...ed coupled algebraic Riccati equation (UCARE). They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.

Regulation of p53 by siRNA in radiation treated cells

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive correlation between the radiation dose and the number of apoptotic cancer cells, radiation has to be limited because of extensive side effects. Therefore, additional control signals whose role will be to maximize the cancer cells death-ratio while minimizing the radiation dose and by that the potential side effects are worth considering. In this work we present the results of simulation studies showing possibilities of single gene regulation by small interfering RNA (siRNA) that can increase radio-sensitivity of malignant cells showing aberrations in the p53 signaling pathway, responsible for DNA damage-dependant apoptosis. By blocking the production of the p53 inhibitor Mdm2, radiation treated cancer cells are pushed into the apoptotic state on a level normally achievable only with high radiation doses. The presented approach, based on a simulation study originating from experimentally validated regulatory events, concerns one of the basic problems of radiotherapy dosage limitations, which, as will be shown, can be partially avoided by using the appropriate siRNA based control mechanism.

Control Problems Arising in Chemotherapy Under Evolving Drug Resistance

Abstract In this paper, we present our recent results which may play a role in improving the situation in the practical implications of mathematical modeling of cancer chemotherapy. We are concerned with control problems for a model of the dynamics of emergence of resistance of cancer cells to chemotherapy, as understood based on recent progress in molecular biology. In some special cases of this model, their asymptotic behavior and the stability problem for the infinite dimensional case were studied. In the case of finite initial condition the stability conditions were derived by asymptotical analysis of the analytical solution to the system of equations. In the case of initial condition with infinite number of elements the stability verification was based on the spectral properties of the infinitesimal generator of the system.

Development of a population of cancer cells: Observation and modeling by a Mixed Spatial Evolutionary Games approach.

Living cells, like whole living organisms during evolution, communicate with their neighbors, interact with the environment, divide, change their phenotypes, and eventually die. The development of specific ways of communication (through signaling molecules and receptors) allows some cellular subpopulations to survive better, to coordinate their physiological status, and during embryonal development to create tissues and organs or in some conditions to become tumors. Populations of cells cultured in vitro interact similarly, also competing for space and nutrients and stimulating each other to better survive or to die. The results of these intercellular interactions of different types seem to be good examples of biological evolutionary games, and have been the subjects of simulations by the methods of evolutionary game theory where individual cells are treated as players. Here we present examples of intercellular contacts in a population of living human cancer HeLa cells cultured in vitro and propose an evolutionary game theory approach to model the development of such populations. We propose a new technique termed Mixed Spatial Evolutionary Games (MSEG) which are played on multiple lattices corresponding to the possible cellular phenotypes which gives the possibility of simulating and investigating the effects of heterogeneity at the cellular level in addition to the population level. Analyses performed with MSEG suggested different ways in which cellular populations develop in the case of cells communicating directly and through factors released to the environment.

A Holistic Approach to Testing Biomedical Hypotheses and Analysis of Biomedical Data

Testing biomedical hypotheses is performed based on advanced and usually many-step analysis of biomedical data. This requires sophisticated analytical methods and data structures that allow to store intermediate results, which are needed in the subsequent steps. However, biomedical data, especially reference data, often change in time and new analytical methods are created every year. This causes the necessity to repeat the iterative analyses with new methods and new reference data sets, which in turn causes frequent changes of the underlying data structures. Such instability of data structures can be mitigated by the use of the idea of data lake, instead of traditional database systems.

Extended Spatial Evolutionary Games and Induced Bystander Effect

The main goal of the study is modelling of radiation induced bystander effect using evolutionary game theory. A payoff table for three different phenotypes (game-theoretic strategies) contains: costs/profits of bystander effect, choice of apoptotic pathway, producing growth factors and resistance against bystander effect. Games are played on a lattice and for that purpose two kinds of spatial evolutionary games are presented and compared. Moreover different polymorphic equilibrium points dependent on model parameters and cells reproductions are discussed.

Multidimensional extended spatial evolutionary games

The goal of this paper is to study the classical hawk-dove model using mixed spatial evolutionary games (MSEG). In these games, played on a lattice, an additional spatial layer is introduced for dependence on more complex parameters and simulation of changes in the environment. Furthermore, diverse polymorphic equilibrium points dependent on cell reproduction, model parameters, and their simulation are discussed. Our analysis demonstrates the sensitivity properties of MSEGs and possibilities for further development. We discuss applications of MSEGs, particularly algorithms for modelling cell interactions during the development of tumours.