Protraction effects in radiation studies: basic biophysics.
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Biophysics↗
Biomedical subjects
R K Sachs
Publications and source records attributed to R K Sachs.
A more robust biologically based ranking criterion for treatment plans.
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Algorithms↗
Locations of radiation-produced DNA double strand breaks along chromosomes: a stochastic cluster process formalism.
Ionizing radiation produces DNA double strand breaks (DSBs) in chromosomes. For densely ionizing radiation, the DSBs are not spaced randomly along a chromosome: recent data for size distributions of DNA fragments indicate break clustering on kbp-Mbp scales. Different DSB clusters on a chromosome are typically made by different, statistically independent, stochastically structured radiation tracks, and the average number of tracks involved can be small. We therefore model DSB positions along a chromosome as a stationary Poisson cluster process, i.e. a stochastic process consisting of secondary point processes whose locations are determined by a primary point process that is Poisson. Each secondary process represents a break cluster, typically consisting of 1-10 DSBs in a comparatively localized stochastic pattern determined by chromatin geometry and radiation track structure. Using this Poisson cluster process model, which we call the randomly located clusters (RLC) formalism, theorems are derived for how the DNA fragment-size distribution depends on radiation dose. The RLC dose-response relations become non-linear when the dose becomes so high that DSB clusters from different tracks overlap or adjoin closely. The RLC formalism generalizes previous models, fits current data adequately and facilitates mechanistically based extrapolations from high-dose experiments to the much lower doses of interest for most applications.
Chromosome Aberrations↗
Clustering of radiation-produced breaks along chromosomes: modelling the effects on chromosome aberrations.
PURPOSE: For high-LET radiations, and perhaps even for hard X-rays, DNA double-strand breaks (dsb) are clustered nonrandomly along chromosomes; disproportionately, many inter-dsb segments are less than a few Mbp (10(6) base pairs). The implications of such dsb clustering for chromosome aberrations are analysed. METHODS: Chromosome segments between different dsb within one dsb cluster are assumed too small to detect in the aberration assay. Enumeration or Monte-Carlo computer simulations are used to compute the relative frequencies of many observable aberration patterns: apparently simple or visibly complex. The theoretical predictions are compared with X-ray data for human fibroblasts, involving painted chromosomes 1, 2, 4, 5, 7 or 13. RESULTS AND CONCLUSIONS: Surprisingly, cryptic dsb multiplicity does not affect the frequency ratios predicted for aberration patterns by a random breakage-and-rejoining model. The model is generally consistent with current data on many different types of aberrations, whether or not dsb usually occur in cryptic clusters. For a Revell-type exchange model, however, the predictions do depend on clustering configurations; they gradually approach the predictions of the breakage-and-rejoining model as average cluster multiplicity increases. The model is consistent with the data, for example with the ratio of visibly complex to apparently simple aberrations, only if there is considerable dsb clustering even at low-LET, with approximately 1.5 or more reactive dsb per cluster on average.
Chromosome Aberrations↗
Polymer chromosome models and Monte Carlo simulations of radiation breaking DNA.
MOTIVATION: Chromatin breakage by ionizing radiation is relevant to studies of carcinogenesis, tumor radiotherapy, biodosimetry and molecular biology. This article focuses on computer analysis of chromosome irradiation in mammlian cells. METHODS: Polymer physics and Monte Carlo numerical methods are used to develop a coarse-grained computational approach. Chromatin is modeled as a random walk on a cubic lattice, and the radiation tracks hitting the chromatin are modeled as straight lines hitting lattice sites. Each track can make a cluster of DSBs on a chromosome. RESULTS: The results obtained replace conjectured DNA fragment-size distribution functions in the recently developed RLC formalism by more mechanistically motivated distributions. The discrete lattice algorithm reproduces features of current radiation experiments relevant to chromatin on large scales. It approximates the continuous formalism and experimental data with adequate precision. It was also found that assuming either fixed chromatin with correlations among different clusters of DSBs or moving chromatin with no such correlations gives virtually identical numerical predictions.
Algorithms↗
Size distributions of misrejoining DNA fragments in irradiated cells.
When ionizing radiation strikes a cell it induces DNA double strand breaks (DSBs). Subsequently, some of the DSBs misrejoin and thus cause alterations in the size distribution of the DNA fragments. We derive a system of non-linear integro-differential equations describing the misrejoining interactions of five classes of DNA fragments, including rings and various types of linear fragments. The fragment classes are represented by density functions; the shape of a density function determines the probability that a fragment has a particular size and the amplitude (integral) equals the expected number of such fragments per cell. The equations are solved: analytically for exponentially distributed initial fragment sizes (corresponding to high doses) and numerically for arbitrary initial conditions. Computed final fragment size distributions are applied to situations representative of flow karyotypes and pulsed-field gel assays. For human flow karyotypes, the model can be used to obtain misrejoining estimates at doses too high for conventional methods of data analysis. For pulsed-field gel assays in which human chromosomes are digested with restriction endonucleases to form 'cut-somes' (restriction fragments), the model provides a means of misrejoining estimation when the cut-some sizes are non-random. The model suggests that if the cut-some size distribution for unirradiated cells is completely random, misrejoining of radiation-induced DSBs will not be detectable in the final size distribution.
Chromosome Breakage↗
A formalism for analysing large-scale clustering of radiation-induced breaks along chromosomes.
PURPOSE: To model intrachromosomal clustering of DSB (DNA double strand breaks) induced by ionizing radiation. That DSB are located non-randomly along chromosomes after high LET irradiation, with clustering even at extremely large scales, has been confirmed by recent pulsed field gel electrophoresis data for size distributions of DNA fragments. We therefore extend the standard random-breakage model for DNA fragment-size distributions to a more general 'clustered-breakage' formalism, which can take correlations of DSB locations along a chromosome into account. METHODS: The new formalism is based mainly on a one-track probability distribution, describing the DNA fragment-size pattern due to a single primary high-energy particle, a pattern determined by track structure and chromatin geometry. Multi-track fragment-size distributions are derived mathematically from the one-track distribution, so that dose response relations are obtained. RESULTS: The clustered-breakage formalism is applicable to any chromosomal geometry and any radiation track structure. It facilitates extrapolations of high-dose data to the much lower doses of interest for most applications. When applied to recently published data for irradiation of mammalian cells with ions of LET approximately 100 keV microm(-1) it indicates a pattern of Mbp-scale DSB clusters, each containing a number of DSB and corresponding to a very large-scale, multiply-damaged chromatin site. Although DSB are bunched, DSB clusters are scattered almost at random throughout the genome. Estimates of DSB yield are markedly increased by resolving such clusters into individual DSB. The dose response relation for fragments of a given size becomes non-linear when clusters from different tracks interlace or adjoin, as can occur for high doses and large sizes. CONCLUSIONS: DSB clustering along chromosomes, which influences important radiobiological endpoints, is described quantitatively by the clustered-breakage formalism.
Alpha Particles↗
Radiation-induced total-deletion mutations in the human hprt gene: a biophysical model based on random walk interphase chromatin geometry.
PURPOSE: To develop a biophysical model that explains the sizes of radiation-induced hprt deletions. METHODS: Key assumptions: (1) Deletions are produced by two DSB that are closer than an interaction distance at the time of DSB induction; (2) Interphase chromatin is modelled by a biphasic random walk distribution; and (3) Misrejoining of DSB from two separate tracks dominates at low-LET and misrejoining of DSB from a single track dominates at high-LET. RESULTS: The size spectra for radiation-induced total deletions of the hprt gene are calculated. Comparing with the results of Yamada and coworkers for gamma-irradiated human fibroblasts the study finds that an interaction distance of 0.75 microm will fit both the absolute frequency and the size spectrum of the total deletions. It is also shown that high-LET radiations produce, relatively, more total deletions of sizes below 0.5 Mb. The model predicts an essential gene to be located between 2 and 3 Mb from the hprt locus towards the centromere. Using the same assumptions and parameters as for evaluating mutation frequencies, a frequency of intra-arm chromosome deletions is calculated that is in agreement with experimental data. CONCLUSIONS: Radiation-induced total-deletion mutations of the human hprt gene and intrachange chromosome aberrations share a common mechanism for their induction.
Biophysical Phenomena↗
The mechanistic basis of the linear-quadratic formalism.
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Biophysical Phenomena↗
Recent data obtained by pulsed-field gel electrophoresis suggest two types of double-strand breaks.
The temporal evolution of unrejoined and misrejoined DNA double-strand breaks (DSBs) produced by high doses (80-160 Gy) of X rays has been estimated using pulsed-field gel electrophoresis (PFGE) (Löbrich et al., Proc. Natl. Acad. Sci. USA 92, 12050-12054, 1995). We attempted to fit these data to three models. An RBM ("Revell binary misrejoining") model, based on the usual repair-misrepair and lethal-potentially lethal models, appears to be inconsistent with the data. The main discrepancies are the following: (1) The RBM model predicts that 90% of the misrejoined DSBs form by the time 75% of the DSBs have disappeared, while the data indicate that only 50% are formed by this time; and (2) the model predicts an increasing fraction of DSBs misrejoined at 160 Gy compared to 80 Gy, while the data support approximately equal fractions misrejoined. These discrepancies are alleviated in the Sax subset (SS) and Revell subset (RS) models. In the SS and RS models, two types (or subsets) of DSBs exist: those that are active in misrejoining and those that are not. In the SS model, active DSBs misrejoin by the breakage-and-reunion mechanism described by Sax; in the RS model, active DSBs either repair, or misrejoin according to the complete exchange misrejoining mechanism described by Revell. Both models are consistent with the data set considered.
Animals↗
Misrejoining of double-strand breaks after X irradiation: relating moderate to very high doses by a Markov model.
Misrejoining of double-strand breaks (DSBs) detected with pulsed-field gel electrophoresis (PFGE) after X irradiation of human cells at very high doses (80-160 Gy) is related to dose-response relationships for chromosome aberrations at moderate doses (1-5 Gy) by the Sax-Markov binary eurejoining/misrejoining (SMBE) model. The SMBE model applies Sax's breakage-and-reunion hypothesis to a subset of DSBs active in binary misrejoining and in binary eurejoining (accidental restitution). The model is numerically consistent with both data on chromosome aberrations and the data obtained by PFGE if proximity effects (restrictions on the range of interactions of DSB free ends) are present. Proximity effects are modeled by partitioning the cell's nucleus into approximately 400 interaction sites, with two active DSB free ends capable of rejoining only if they were produced within the same site. Neglecting one-track action, the SMBE model predicts a quadratic-linear dose-response relationship for DSB misrejoining after exposure to low-LET radiation; i.e., there is a quadratic response at moderate doses which becomes linear as the dose becomes large, rather than vice versa. The linear region results because at very high doses almost all of the active DSB free ends misrejoin rather than eurejoin.
DNA↗
The linear-quadratic model and most other common radiobiological models result in similar predictions of time-dose relationships.
One of the fundamental tools in radiation biology is a formalism describing time-dose relationships. For example, there is a need for reliable predictions of radiotherapeutic isoeffect doses when the temporal exposure pattern is changed. The most commonly used tool is now the linear-quadratic (LQ) formalism, which describes fractionation and dose-protraction effects through a particular functional form, the generalized Lea-Catcheside time factor, G. We investigate the relationship of the LQ formalism to those describing other commonly discussed radiobiological models in terms of their predicted time-dose relationships. We show that a broad range of radiobiological models are described by formalisms in which a perturbation calculation produces the standard LQ relationship for dose fractionation/protraction, including the same generalized time factor, G. This approximate equivalence holds not only for the formalisms describing binary misrepair models, which are conceptually similar to LQ, but also for formalisms describing models embodying a very different explanation for time-dose effects, namely saturation of repair capacity. In terms of applications to radiotherapy, we show that a typical saturable repair formalism predicts practically the same dependences for protraction effects as does the LQ formalism, at clinically relevant doses per fraction. For low-dose-rate exposure, the same equivalence between predictions holds for early-responding end points such as tumor control, but less so for late-responding end points. Overall, use of the LQ formalism to predict dose-time relationships is a notably robust procedure, depending less than previously thought on knowledge of detailed biophysical mechanisms, since various conceptually different biophysical models lead, in a reasonable approximation, to the LQ relationship including the standard form of the generalized time factor, G.
Brachytherapy↗
A two-backbone polymer model for interphase chromosome geometry.
A polymer model for the overall geometric structure of a human chromosome during the G0/G1 portion of cell-cycle interphase is constructed, based on fluorescence in situ hybridization data on distances between defined genomic sequences. The model consists of flexible giant loops, averaging about 6 million base pairs, with two random-walk backbones; it involves essentially three parameters. Numerical results based on properly selected values of parameters fit the data well.
Chromosomes, Human↗
The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair.
PURPOSE: To review current opinion on the production and temporal evolution of low-LET radiobiological damage. METHODS: Standard cell survival models which model repair/misrepair kinetics in order to quantify dose-response relations and dose-protraction effects are reviewed and interrelated. Extensions of the models to endpoints other than cell survival, to multiple or compound damage processing pathways, and to stochastic intercellular damage fluctuations are surveyed. Various molecular mechanisms are considered, including double strand breaks restitution and binary misrepair. CONCLUSIONS: (1) Linking dose-response curves to the underlying damage production/processing kinetics allows mechanistic biological interpretations of observed curve parameters. (2) Various damage processing pathways, with different kinetics, occur. (3) Almost every current kinetic model, whether based on binary misrepair or saturable repair, leads at low or intermediate doses to the LQ (linear-quadratic) formalism, including the standard (generalized Lea-Catcheside) dependence on dose protraction. (4) Two-track (beta) lethal damage is largely due to dicentric chromosome aberrations, but one-track (alpha) lethal damage is largely caused by other mechanisms such as point mutations in a vital gene, small deletions, residual chromosome breaks, induced apoptosis, etc. (5) A major payoff for 50 years of radiobiological modelling is identifying molecular mechanisms which underly the broadly applicable LQ formalism.
Animals↗
Centric rings, acentric rings and excess acentric fragments based on a random-walk interphase chromosome model.
Excess acentric fragments, consisting of acentric rings and acentric linear fragments, are among the most frequent kinds of chromosome-type aberrations produced by radiation. The frequency of acentric rings cannot be obtained directly by experiment but is estimated here from the ratio of acentric to centric rings, evaluated using a random-walk model for the organization of chromatin during interphase and an assumption that the probability of an exchange formation is proportional to the rate of collision between two DSB. This ratio is calculated to be 2.5 in low-LET irradiated human fibroblasts, significantly greater than the ratio if proximity effects are not considered. The calculated frequency of acentric rings is insufficient to account for all the observed excess acentric fragments. Assuming that the rest of the excess acentric fragments are due to incomplete exchanges, all possible recombinations between two DSB that result in acentric rings and acentric linear fragments have been identified. From the chromosome aberration data, the incompleteness parameter has been estimated. Intra-arm chromosome exchanges, either complete or incomplete, were estimated to account for more than 50% of the excess acentric fragments in human fibroblasts.
Chromosome Aberrations↗
Review: proximity effects in the production of chromosome aberrations by ionizing radiation.
After ionizing radiation has induced double-strand DNA breaks (dsb), misrejoining produces chromosome aberrations. Aberration yields are influenced by "proximity' effects, i.e., by the dependence of misrejoining probabilities on initial dsb separations. We survey proximity effects, emphasizing implications for chromosome aberration-formation mechanisms, for chromatin geometry, and for dose-response relations. Evidence for proximity effects comes from observed biases for centric rings and against three-way interchanges, relative to dicentrics or translocations. Other evidence comes from the way aberration yields depend on radiation dose and quality, tightly bunched ionizations being relatively effective. We concludes (1) that misrejoining probabilities decrease as the distance between dsb at the time of their formation increases, and almost all misrejoining occurs among dsb initially separated by < 1/3 of a cell nucleus diameter; (2) that chromosomes occupy (irregular) territories during the G0/G1 phase of the cell cycle, having dimensions also roughly 1/3 of a cell nucleus diameter, (3) that proximity effects have the potential to probe how much different chromosomes intertwine on move relative to each other: and (4) that incorporation of proximity effects into the classic random breakage-and-reunion model allows quantitative interrelation of yields for many different aberration types and of data obtained with various FISH painting methods or whole-genome scoring.
Chromosome Aberrations↗
Intra-arm and interarm chromosome intrachanges: tools for probing the geometry and dynamics of chromatin.
Many chromosome-type, exchange-type chromosomal aberrations produced by radiation are intrachanges, i.e. involve only one chromosome. It is assumed such intrachanges are formed by illegitimate reunion of two double-strand breaks (DSBs) on the chromosome. The yield of intra-arm intrachanges (acentric rings or paracentric inversions) relative to that of interarm intrachanges (centric rings or pericentric inversions) is larger than would occur if production and illegitimate reunion of DSBs were spatially random. The excess of intra-arm intrachanges is presumably due to proximity effects for illegitimate reunions, i.e. enhancement of the intrachange probability when two DSBs are formed close to one another. Radiation track structure may also play a role. Using a polymer description for "large-scale" chromatin geometry (>2 Mb), and using two alternate (rapid or slow motion) models for the way that DSBs move after they are produced, theoretical estimates are given for size distributions of intrachanges at low or high linear energy transfer (LET). The ratio of intra-arm to interarm intrachanges is derived from the size distribution and compared with data from the literature on centric rings, inversions, interstitial deletions and excess acentric fragments. Proximity effects enhance yields of intra-arm relative to interarm intrachanges at least severalfold and perhaps as much as 10-fold compared to expectations based on spatial randomness. We argue that further measurements of intra-arm and interarm intrachanges would be informative about large-scale chromatin structure and chromosome motion. Because inversions are more frequent than estimates of randomness would indicate, and are transmissible to daughter cells, their size distribution could also help characterize past exposure to high-LET radiation.
Chromatin↗
Computer simulation of data on chromosome aberrations produced by X rays or alpha particles and detected by fluorescence in situ hybridization.
With fluorescence in situ hybridization (FISH), many different categories of chromosome aberrations can be recognized-dicentrics, translocations, rings and various complex aberrations such as insertions or three-way interchanges. Relative frequencies for the various aberration categories indicate mechanisms of radiation-induced damage and reflect radiation quality. Data obtained with FISH support a proximity version of the classic random breakage-and-reunion model for the formation of aberrations. A Monte Carlo computer implementation of the model, called the CAS (chromosome aberration simulator), is generalized here to high linear energy transfer (LET) and compared to published data for human cells irradiated with X rays or 238Pu alpha particles. For each kind of radiation, the CAS has two adjustable parameters: the number of interaction sites per cell nucleus and the number of reactive double-strand breaks (DSBs) per gray. Aberration frequencies for various painted chromosomes, of varying lengths, and for 11 different categories of simple or complex aberrations were simulated and compared to the data. The optimal number of interaction sites was found to be approximately 13 for X irradiation and approximately 25 for alpha-particle irradiation. The relative biological effectiveness (RBE) of alpha particles for the induction of reactive DSBs (which are a minority of all DSBs) was found to be approximately 4. The two-parameter CAS model adequately matches data for many different categories of aberrations. It can use data obtained with FISH for any one painting pattern to predict results for any other kind of painting pattern or whole-genome staining, and to estimate a suggested overall numerical damage indicator for chromosome aberration studies, the total misrejoining number.
Alpha Particles↗