Ewa Gudowska-Nowak

Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, that represent here populations of cells involved in cancerous proliferation and cytotoxic response of the immune system, the overall kinetics can be approximated by a one-dimensional overdamped Langevin equation. The modulating activity of the immune response is here modeled as a dichotomous random process of the relative rate of neoplastic cell destruction. We discuss physical aspects of environmental noises acting in such a system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together. We explain the underlying mechanisms by analyzing the behavior of the variance of first passage times as a function of the noise intensity.

Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment

We investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells populations is based on the generic Michaelis-Menten kinetics depicting interaction and competition between the tumor and the immune system. The appropriate phenomenological equation modeling cell-mediated immune surveillance against cancer is of the predator-prey form and exhibits bistability within a given choice of the immune response-related parameters. Under the influence of weak external fluctuations, the model may be analyzed in terms of a stochastic differential equation bearing the form of an overdamped Langevin-like dynamics in the external quasi-potential represented by a double well. We analyze properties of the system within the range of parameters for which the potential wells are of the same depth and when the additional perturbation, modeling a periodic treatment, is insufficient to overcome the barrier height and to cause cancer extinction. In this case the presence of a small amount of noise can positively enhance the treatment, driving the system to a state of tumor extinction. On the other hand, however, the same noise can give rise to return effects up to a stochastic resonance behavior. This observation provides a quantitative analysis of mechanisms responsible for optimization of periodic tumor therapy in the presence of spontaneous external noise. Studying the behavior of the extinction time as a function of the treatment frequency, we have also found the typical resonant activation effect: For a certain frequency of the treatment, there exists a minimum extinction time.

Lévy-Brownian motion on finite intervals : mean first passage time analysis

We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by Lévy stable noises. The complexity of the first passage time statistics (mean first passage time, cumulative first passage time distribution) is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non-Gaussian noises. The validity of the method is tested numerically and compared against analytical formulas when the stability index alpha approaches 2, recovering in this limit the standard results for the Fokker-Planck dynamics driven by Gaussian white noise.

High-LET-induced chromosome aberrations in V79 cells analysed in first and second post-irradiation metaphases

Purpose : As an extension of previous studies, the time-course of high-LET-induced chromosomal damage was investigated in first- and second-cycle V79 Chinese hamster cells. Materials and methods : Cells were exposed in G 1 to 10.4MeV/u Ar ions (LET=1226keV/mum) and chromosomal damage was measured at 2h sampling intervals between 10h and 34h after irradiation. To distinguish between cells in different post-irradiation cycles, the fluorescence-plus-Giemsa technique was applied. Results : For first- and second-generation cells, the number of aberrant metaphases and aberrations per metaphase were found to increase markedly with sampling time, demonstrating that cell cycle progression was delayed according to the number of lesions carried by the cell. To account for the time-dependent expression of chromosomal damage a mathematical approach was used based on the integrated flux of aberrant cells entering mitosis. Moreover, the analysis of Ar ion-induced chromosome lesions confirmed that high-LET radiation results in specific changes in the spectrum of aberration types. In particular, an increased rate of chromatid-type aberrations as well as a high frequency of chromosomal breaks was found, although the cells were exposed in G 1. Conclusions : Due to the fact that cells collected at one sampling time are not representative of the entire population, the complete time-course of chromosomal damage has to be taken into account for the determination of a meaningful RBE value. Otherwise, the analysis of chromosomal damage can result in a pronounced over- or underestimation of the RBE depending on the subpopulation of cells entering mitosis at that particular sampling time.PURPOSE As an extension of previous studies, the time-course of high-LET-induced chromosomal damage was investigated in first- and second-cycle V79 Chinese hamster cells. MATERIALS AND METHODS Cells were exposed in G1 to 10.4 MeV/u Ar ions (LET = 1226 keV/microm) and chromosomal damage was measured at 2h sampling intervals between 10 h and 34 h after irradiation. To distinguish between cells in different post-irradiation cycles, the fluorescence-plus-Giemsa technique was applied. RESULTS For first- and second-generation cells, the number of aberrant metaphases and aberrations per metaphase were found to increase markedly with sampling time, demonstrating that cell cycle progression was delayed according to the number of lesions carried by the cell. To account for the time-dependent expression of chromosomal damage a mathematical approach was used based on the integrated flux of aberrant cells entering mitosis. Moreover, the analysis of Ar ion-induced chromosome lesions confirmed that high-LET radiation results in specific changes in the spectrum of aberration types. In particular, an increased rate of chromatid-type aberrations as well as a high frequency of chromosomal breaks was found, although the cells were exposed in G1. CONCLUSIONS Due to the fact that cells collected at one sampling time are not representative of the entire population, the complete time-course of chromosomal damage has to be taken into account for the determination of a meaningful RBE value. Otherwise, the analysis of chromosomal damage can result in a pronounced over- or underestimation of the RBE depending on the subpopulation of cells entering mitosis at that particular sampling time.

Infinite products of large random matrices and matrix-valued diffusion

Abstract We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large Hermitian matrices. The infinite product case allows us to define a natural matrix-valued multiplicative diffusion process. In both cases of Hermitian and complex matrices, we observe the emergence of a “topological phase transition”, when a hole develops in the eigenvalue spectrum, after some critical diffusion time τ crit is reached. In the case of a particular product of two Hermitian ensembles, we observe also an unusual localization–delocalization phase transition in the spectrum of the considered ensemble. We verify the analytical formulas obtained in this work by numerical simulation.

Analysis of Ar-ion and X-ray-induced chromatin breakage and repair in V79 plateau-phase cells by the premature chromosome condensation technique

Purpose : The premature chromosome condensation technique has been used to compare chromatin breakage and repair in noncycling V79 cells following high and low LET radiation. Materials and methods : Plateau-phase V79 cells were exposed to graded doses of low energy Ar ions (LET 1233 keV / μ m) and X-rays. Cells were fused to mitotic V79 cells immediately after exposure to examine initial chromatin breakage or after various time intervals of post-irradiation incubation to investigate the kinetics of chromatin break rejoining as well as the fraction of unrejoined fragments. Results and conclusions : For both radiation qualities an average initial number of about 2.4 excess PCC fragments per cell per Gy was found increasing linearly with dose. The distributions of PCC chromosomes plus excess fragments among cells followed Poisson statistics after X-ray irradiation, while an overdispersion of the frequencies was observed after Ar-irradiation indicating that a single particle traversal through a cell nucleus can produce multiple chromatin lesions. Moreover, for both radiation types the rejoining of excess fragments has been examined. Both data sets could be fitted well to first-order kinetics with a single component. Despite similar rates of rejoining cellular repair was noticeably less effective for Ar ions than for X-rays. While after 10h of post-irradiation incubation 60% of Ar ion induced excess fragments remained unrejoined, only 14% of X-ray-induced lesions were not rejoined. Furthermore, comparison of the residual number of excess PCC fragments with recently published data on the yield of chromosome aberrations in first post-irradiation metaphases shows that for both radiation types more aberrations are detected in interphase than in metaphase cells. Yet, for comparable doses this difference is more pronounced for Ar ions indicating that scoring of high LET induced aberrations in metaphase cells might result in a significant underestimation of the produced damage.PURPOSE The premature chromosome condensation technique has been used to compare chromatin breakage and repair in noncycling V79 cells following high and low LET radiation. MATERIALS AND METHODS Plateau-phase V79 cells were exposed to graded doses of low energy Ar ions (LET 1233 keV/microm) and X-rays. Cells were fused to mitotic V79 cells immediately after exposure to examine initial chromatin breakage or after various time intervals of post-irradiation incubation to investigate the kinetics of chromatin break rejoining as well as the fraction of unrejoined fragments. RESULTS AND CONCLUSIONS For both radiation qualities an average initial number of about 2.4 excess PCC fragments per cell per Gy was found increasing linearly with dose. The distributions of PCC chromosomes plus excess fragments among cells followed Poisson statistics after X-ray irradiation, while an overdispersion of the frequencies was observed after Ar-irradiation indicating that a single particle traversal through a cell nucleus can produce multiple chromatin lesions. Moreover, for both radiation types the rejoining of excess fragments has been examined. Both data sets could be fitted well to first-order kinetics with a single component. Despite similar rates of rejoining cellular repair was noticeably less effective for Ar ions than for X-rays. While after 10 h of post-irradiation incubation 60% of Ar ion induced excess fragments remained unrejoined, only 14% of X-ray-induced lesions were not rejoined. Furthermore, comparison of the residual number of excess PCC fragments with recently published data on the yield of chromosome aberrations in first post-irradiation metaphases shows that for both radiation types more aberrations are detected in interphase than in metaphase cells. Yet, for comparable doses this difference is more pronounced for Ar ions indicating that scoring of high LET induced aberrations in metaphase cells might result in a significant underestimation of the produced damage.

Searching for the most cost-effective strategy for controlling epidemics spreading on regular and small-world networks

We present a combined epidemiological and economic model for control of diseases spreading on local and small-world networks. The disease is characterized by a pre-symptomatic infectious stage that makes detection and control of cases more difficult. The effectiveness of local (ring-vaccination or culling) and global control strategies is analysed by comparing the net present values of the combined cost of preventive treatment and illness. The optimal strategy is then selected by minimizing the total cost of the epidemic. We show that three main strategies emerge, with treating a large number of individuals (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. If the disease spreads within the well-defined neighbourhood, the local strategy is optimal unless the cost of a single vaccine is much higher than the cost associated with hospitalization. In the latter case, it is most cost-effective to refrain from prevention. Destruction of local correlations, either by long-range (small-world) links or by inclusion of many initial foci, expands the range of costs for which the NS is most cost-effective. The GS emerges for the case when the cost of prevention is much lower than the cost of treatment and there is a substantial non-local component in the disease spread. We also show that local treatment is only desirable if the disease spreads on a small-world network with sufficiently few long-range links; otherwise it is optimal to treat globally. In the mean-field case, there are only two optimal solutions, to treat all if the cost of the vaccine is low and to treat nobody if it is high. The basic reproduction ratio, R0, does not depend on the rate of responsive treatment in this case and the disease always invades (but might be stopped afterwards). The details of the local control strategy, and in particular the optimal size of the control neighbourhood, are determined by the epidemiology of the disease. The properties of the pathogen might not be known in advance for emerging diseases, but the broad choice of the strategy can be made based on economic analysis only.

Resonant activation in the presence of nonequilibrated baths.

We study the generic problem of the escape of a classical particle over a fluctuating barrier under the influence of non-Gaussian noise mimicking the effects of nonequilibrated bath. The model system is described by a Langevin equation with two independent noise sources, one of which stands for the dichotomous process and the other describes external driving by alpha-stable noise. Our attention focuses on the effect of the structure of stable noises on the mean escape time and on the phenomenon of resonant activation. Possible physical interpretation of the occurrence of Lévy noises and the relevance of the model for chemical kinetics is briefly discussed.

Fundamental building blocks of eumelanins: electronic properties of indolequinone-dimers.

Abstract We present results from the theoretical INDO calculations of the electronic structure for stacked eumelanins’ monomers. As basic indolic components of the eumelanin structure 5,6-dihydroxyindole (DHI or HQ) and its oxidized forms (SQ and IQ) were chosen. The results reveal dependency of electronic properties of such aggregates on monomers’ redox states. They point out also a tendency to localize an extra charge on one of dimers’ subunits that could be suggestive of an electron hopping as a model mechanism for the electron transfer in eumelanins.

Stationary states in Langevin dynamics under asymmetric Lévy noises

Properties of systems driven by white non-Gaussian noises can be very different from these of systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by alpha-stable Lévy-type noises, which provide natural extension to the Gaussian noise having, however, a new property, namely a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic, and in generic double well potential models subjected to the action of alpha-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.