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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 30 (1992), S. 493-511 
    ISSN: 1432-1416
    Keywords: Chromosome aberrations ; Ionizing radiation damage to DNA ; Markov chain models ; Chemical kinetics master equation ; Radiation cell survival
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ionizing radiation damage to a mammalian genome is modeled using continuous time Markov chains. Models are given for the initial infliction of DNA double strand breaks by radiation and for the enzymatic processing of this initial damage. Damage processing pathways include DNA double strand break repair and chromosome exchanges. Linear, saturable, or inducible repair is considered, competing kinetically with pairwise interactions of the DNA double strand breaks. As endpoints, both chromosome aberrations and the inability of cells to form clones are analyzed. For the post-irradiation behavior, using the discrete time Markov chain embedded at transitions gives the ultimate distribution of damage more simply than does integrating the Kolmogorov forward equations. In a representative special case explicit expressions for the probability distribution of damage at large times are given in the form used for numerical computations and comparisons with experiments on human lymphocytes. A principle of branching ratios, that late assays can only measure appropriate ratios of repair and interaction functions, not the functions themselves, is derived and discussed.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-1416
    Keywords: Chromosome aberration ; Ionizing radiation damage to DNA ; Markov chain models ; Stochastic chemical kinetics ; Radiation cell survival
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ionizing radiation damage to the genome of a non-cycling mammalian cell is analyzed using continuous time Markov chains. Immediate damage induced by the radiation is modeled as a batch Poisson arrival process of DNA double strand breaks (DSBs). Different kinds of radiation, for example gamma rays or alpha particles, have different batch probabilities. Enzymatic modulation of the immediate damage is modeled as a Markov process similar to the processes described by the master equation of stochastic chemical kinetics. An illustrative example is the restitution/complete exchange model, which postulates that radiation induced DSBs can subsequently either undergo enzymatically mediated repair (restitution) or can participate pairwise in chromosome exchanges, some of which make irremediable lesions such as dicentric chromosome aberrations. One may have rapid irradiation followed by enzymatic DSB processing or have prolonged irradiation with both DSB arrival and enzymatic DSB processing continuing throughout the irradiation period. A complete solution of the Markov chain is known for the case that the exchange rate constant is negligible so that no irremediable chromosome lesions are produced and DSBs are the only damage to the genome. Using PDEs for generating functions, a perturbation calculation is made assuming the exchange rate constant is small compared to the repair rate constant. Some non-perturbative results applicable to very prolonged irradiation are also obtained using matrix methods: Perron-Frobenius theory, variational methods and numerical approximations of eigenvalues. Applications to experimental results on expected values, variances and statistical distributions of DNA lesions are briefly outlined. Continuous time Markov chain models are the most systematic of those current radiation damage models which treat DSB-DSB interactions within the cell nucleus as homogeneous (e.g. ignore diffusion limitations). They contain most other homogeneous models as special cases, limiting cases or approximations. However, applying the continuous time Markov chain models to studying spatial dependence of DSB interactions, which is generally believed to be very important in some situations, presents difficulties.
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  • 3
    ISSN: 1432-2099
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Summary When cells are subjected to ionizing radiation the specific energy rate (microscopic analog of dose-rate) varies from cell to cell. Within one cell, this rate fluctuates during the course of time; a crossing of a sensitive cellular site by a high energy charged particle produces many ionizations almost simultaneously, but during the interval between events no ionizations occur. In any cell-survival model one can incorporate the effect of such fluctuations without changing the basic biological assumptions. Using stochastic differential equations and Monte Carlo methods to take into account stochastic effects we calculated the dose-survival relationships in a number of current cell survival models. Some of the models assume quadratic misrepair; others assume saturable repair enzyme systems. It was found that a significant effect of random fluctuations is to decrease the theoretically predicted amount of dose-rate sparing. In the limit of low dose-rates neglecting the stochastic nature of specific energy rates often leads to qualitatively misleading results by overestimating the surviving fraction drastically. In the opposite limit of acute irradiation, analyzing the fluctuations in rates merely amounts to analyzing fluctuations in total specific energyvia the usual microdosimetric specific energy distribution function, and neglecting fluctuations usually underestimates the surviving fraction. The Monte Carlo methods interpolate systematically between the low dose-rate and high dose-rate limits. As in other approaches, the slope of the survival curve at low dose-rates is virtually independent of dose and equals the initial slope of the survival curve for acute radiation.
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  • 4
    ISSN: 1432-2099
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract  DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from 〉100 Mbp down to 〈0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.
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