Mathematical Aspects of a New Synergy Theory Applicable to Malstressor-Dominated Mixtures which Include Damage-Ameliorating Countermeasures.

In radiobiology, and throughout translational biology, synergy theories for multi-component agent mixtures use 1-agent dose-effect relations (DERs) to calculate baseline neither synergy nor antagonism mixture DERs. The most used synergy theory, simple effect additivity, is not self-consistent when curvilinear 1-agent DERs are involved, and many alternatives have been suggested. In this paper we present the mathematical aspects of a new alternative, generalized Loewe additivity (GLA). To the best of our knowledge, generalized Loewe additivity is the only synergy theory that can systematically handle mixtures of agents that are malstressors (tend to produce disease) with countermeasures - agents that oppose malstressors and ameliorate malstressor damage. In practice countermeasures are often very important, so generalized Loewe additivity is potentially far-reaching. Our paper is a proof-of-principle preliminary study. Unfortunately, generalized Loewe additivity's scope is restricted, in various unwelcome but perhaps unavoidable ways. Our results illustrate its strengths and its weaknesses. One area where our methodology has potentially important applications is analyzing counter-measure mitigation of galactic cosmic ray damage to astronauts during interplanetary travel.

Evidence for the organization of chromatin in megabase pair-sized loops arranged along a random walk path in the human G0/G1 interphase nucleus.

We determined the folding of chromosomes in interphase nuclei by measuring the distance between points on the same chromosome. Over 25,000 measurements were made in G0/G1 nuclei between DNA sequences separated by 0.15-190 megabase pairs (Mbp) on three human chromosomes. The DNA sequences were specifically labeled by fluorescence in situ hybridization. The relationship between mean-square interphase distance and genomic separation has two linear phases, with a transition at approximately 2 Mbp. This biphasic relationship indicates the existence of two organizational levels at scales > 100 kbp. On one level, chromatin appears to be arranged in large loops several Mbp in size. Within each loop, chromatin is randomly folded. On the second level, specific loop-attachment sites are arranged to form a supple, backbonelike structure, which also shows characteristic random walk behavior. This random walk/giant loop model is the simplest model that fully describes the observed large-scale spatial relationships. Additional evidence for large loops comes from measurements among probes in Xq28, where interphase distance increases and then locally decreases with increasing genomic separation.

Hypo-fractionated boost in locally advanced non-small cell lung cancer: temporal distribution of boost fractions.

To propose new schemas for radiation boosting of primary tumors, in locally advanced non-small cell lung cancers (NSCLC), in conjunction with standard chemoradiotherapy. To investigate the effect of temporal distributions of the boost fractions on tumor control. NSCLC cases, previously treated with 60 Gy in 30 fractions, were retrospectively planned by adding a radiation boost (25 Gy in 5 fractions) to the primary tumor. Several integrated and sequential boosting schedules were considered. Biological doses were calculated for targets and organs at risk (OAR). Tumor control probabilities (TCP) were calculated using an empirical model and a stochastic model that accounts more systematically for tumor growth kinetics and cell kill. For heterogeneous patient populations, the TCPs for different boost schedules ranged from 82% to 84% and from 73% to 74% for integrated and sequential boosting respectively. For individual tumors with specific growth parameters, the TCP varied by up to 19% between the different schedules. The TCP for sequential boosting was expected to be up to 67% lower than front integrated boosting. The gap in TCP between schedules was higher for tumors with higher clonogenic cell numbers, lower radio-sensitivity, shorter doubling times and lower cell loss. The proposed boosting schemas are dosimetrically feasible and biologically effective. We suggest that the boosts are most effective when given during the first week of treatment and least effective when given sequentially after the end of treatment. The effect of boost scheduling and the effectiveness of front boosting are expected to be most significant for tumors with high clonogenic cell numbers, fast growing rates, low cell loss and low radio-sensitivity. Ultimately, animal studies and clinical trials, guided by biology modeling as presented in the present work, will be needed to verify the effectiveness of fine tuning temporal distributions of radiotherapy fractions.

Radiation-produced chromosome aberrations: colourful clues.

Ionizing radiation produces many chromosome aberrations. A rich variety of aberration types can now be seen with the technique of chromosome painting. Apart from being important in medicine and public health, radiation-produced aberrations act as colorful molecular clues to damage-processing mechanisms and, because juxtaposition of different parts of the genome is involved, to interphase nuclear organization. Recent studies using chromosome painting have helped to identify DNA double-strand-break repair and misrepair pathways, to determine the extent of chromosome territories and motions, and to characterize different aberration patterns left behind by different kinds of radiation.

Detection of an intrinsic marker in hypoxic cells.

An autoradiographic method is presented for detecting, within a cell population, those cells which have been subjected to chronic hypoxia. No radioisotope is administered; rather the photographic emulsion is chemically reduced by intrinsic constituents of the cells. Hypoxic regions in the sandwich system, a multicellular in vitro tumor model, were detected in this manner. These regions were then compared with hypoxic sandwich regions as demonstrated by [3H]misonidazole labeling. Auxiliary studies, including studies on hypoxic monolayers, were consistent with the sandwich results. In all cases, the intracellular distribution of the chemographic grains was found to be cytosolic. Often the grains were clustered near the nucleus, perhaps in the region of the endoplasmic reticulum and the Golgi. We conclude that cells in a state of hypoxia and nutrient deprivation similar to that found in solid tumors retain a detectably altered biology for a significant period after reoxygenation. Therefore systematic methods of detecting previous hypoxia in histological tumor sections are feasible.

Defining AML and MDS second cancer risk dynamics after diagnoses of first cancers treated or not with radiation.

Risks of acute myeloid leukemia (AML) and/or myelodysplastic syndromes (MDS) are known to increase after cancer treatments. Their rise-and-fall dynamics and their associations with radiation have, however, not been fully characterized. To improve risk definition we developed SEERaBomb R software for Surveillance, Epidemiology and End Results second cancer analyses. Resulting high-resolution relative risk (RR) time courses were compared, where possible, to results of A-bomb survivor analyses. We found: (1) persons with prostate cancer receiving radiation therapy have increased RR of AML and MDS that peak in 1.5-2.5 years; (2) persons with non-Hodgkin lymphoma (NHL), lung and breast first cancers have the highest RR for AML and MDS over the next 1-12 years. These increased RR are radiation specific for lung and breast cancer but not for NHL; (3) AML latencies were brief compared to those of A-bomb survivors; and (4) there was a marked excess risk of acute promyelocytic leukemia in persons receiving radiation therapy. Knowing the type of first cancer, if it was treated with radiation, the interval from first cancer diagnosis to developing AML or MDS, and the type of AML, can improve estimates of whether AML or MDS cases developing in this setting are due to background versus other processes.

3H-misonidazole labeling and viability of hypoxic cells in the sandwich system, an in vitro tumor analogue.

3H-misonidazole was used as a marker of hypoxic cells in an in vitro tumor analogue, the sandwich system. MISO binding was assessed in situ, using autoradiography. Binding profiles indicate that there are regions of radiobiological hypoxia surrounding the necrotic center in sandwiches of the V79 cell line and in sandwiches of the 9L cell line. Grains per cell were counted and detailed statistics on the variation of intrinsic binding among cells in the same microenvironment are presented. There is a systematic decrease in the standard deviation of grains per cell as one examines populations of cells further and further from the nutrient and oxygen source. Kinetic studies show that the growth fraction of the cell population also decreases with distance from the nutrient source. These findings taken together suggest that MISO binding is proportional to cell size and cells in the inner noncycling portion of the sandwich are more nearly uniform in size. Sandwich cells which exhibit heavy MISO binding, and are presumably radiobiologically hypoxic, were shown to be still viable if restored to good nutrient and oxygen conditions.

Comparison of 3H-misonidazole binding between CHO and 9L cells using the sandwich system.

3H-misonidazole binding of 9L cells was compared with that of CHO cells using an in vitro tumor analog, the sandwich system. In sandwiches there is a gradient of microenvironments, with cells adjacent to the necrotic center subjected to low concentrations of oxygen and glucose and to high concentrations of metabolites. Mixed sandwiches, having 9L and CHO cells interspersed, were used along with sandwiches of each individual cell line. MISO binding was assessed in situ, using autoradiography. Grains per cell were counted and detailed statistics were obtained on the variation in MISO binding among cells located in the same microenvironment. In all cases binding in the regions near the necrotic center was more than 50 times the binding found at the sandwich edge and found in control monolayers, indicating radiobiological hypoxia near the necrotic center. 9L cells began to significantly increase binding of MISO metabolites at a somewhat higher oxygen concentration than did CHO cells. At all oxygen tensions, average per cell binding of the 9L cells was 3 times or more that of the CHO cells, a factor greater than can be explained by the ratio of cell volumes alone. Statistical analyses of the variation in binding among cells in a given microenvironment give some evidence that in the mixed CHO/9L sandwiches there are interactions between the cells of the two different lines which affect the growth patterns of the cells. No preferred binding of misonidazole in the nucleus or cytoplasm was noted within the cells.

Optimizing the time course of brachytherapy and other accelerated radiotherapeutic protocols.

PURPOSE: It is likely that early-responding tissues, such as tumors, repair sublethal damage more rapidly than do late-responding tissues. This difference can be exploited to design protocols with a significantly improved therapeutic advantage for accelerated radiotherapeutic regimens, including brachytherapy. METHODS AND MATERIALS: The time course of potential protocols is computer optimized, maximizing the therapeutic difference between tumor-control probability (TCP), and normal-tissue complication probability (NTCP). These quantities are evaluated with the linear-quadratic model, using clinically derived parameters. The optimization is performed by individually adjusting doses in different parts of the treatment, maximizing the therapeutic advantage. In the main calculations, half times for damage repair were T1/2(late) = 4 h, T1/2(early) = 0.5 h. Two component (fast/slow) repair processes were also investigated. RESULTS: Protocols determined by optimization have significantly greater therapeutic advantage than continuous low-dose rate (CLDR) protocols of the same overall dose and time. The optimized protocols are either (a) acute-dose/gap/CLDR/gap/acute-dose; or (b) a series of acute doses separated by 3-4 h. As a typical example, results are given for 60 Gy/120 h CLDR brachytherapy, which is assumed to give NTCP = 0.2 and TCP = 0.8. Under our assumptions, optimized regimes, with the same overall time and dose, produce an NTCP of approximately 0.11 and TCP of approximately 0.83, a significant therapeutic gain over CLDR. CONCLUSION: Difference in repair rates between early- and late-responding tissues can be exploited to produce clinically practical protocols that are significantly superior to current regimens. Such optimized protocols produce slightly better tumor control than CLDR with the same overall dose and time, significantly less late damage, and similar early normal-tissue sequellae. Temporal optimization, thus, promises to be a powerful tool in designing better treatment protocols.

A convenient extension of the linear-quadratic model to include redistribution and reoxygenation.

PURPOSE: At present, the linear-quadratic model for cellular response to radiation can incorporate sublethal damage repair and repopulation. We suggest an extension, termed LQR, to include also the other two "Rs" of radiobiology, cell cycle redistribution, and reoxygenation. METHODS AND MATERIALS: In this approach, redistribution and reoxygenation are both regarded as aspects of a single phenomenon, which we term resensitization. After the first portion of a radiation exposure has decreased the average radiosensitivity of a diverse cell population by preferentially sparing less sensitive cells, resensitization gradually restores the average sensitivity of the population towards its previous value. The proposed LQR formula is of the same form as the original LQ formula, but with two extra parameters, an overall resensitization magnitude and a characteristic resensitization time. The LQR model assumes that resensitization is monotonic rather than oscillatory in time, i.e., always tends to increase average cellular sensitivity as overall time increases. We argue that this monotonicity assumption is likely to hold in clinical situations, though a possible extension is discussed to account for oscillatory decay of resensitization effects. RESULTS: The LQR model gives reasonable fits to relevant experimental data in the literature, reproducing an initial rise in cell survival, due to repair, as the treatment time is increased, followed by a resensitization-related decrease in survival due to redistribution and/or reoxygenation for treatment times of the order of the cell cycle time, and a final survival increase due to repopulation as the treatment time is increased still further. CONCLUSION: The LQR model is a simple and potentially useful extension of the LQ model for computing more realistic isoeffect relations for early responding tissues, including tumors, when comparing different radiotherapeutic protocols.

Quantitative analysis of radiation-induced chromosome aberrations.

We review chromosome aberration modeling and its applications, especially to biodosimetry and to characterizing chromosome geometry. Standard results on aberration formation pathways, randomness, dose-response, proximity effects, transmissibility, kinetics, and relations to other radiobiological endpoints are summarized. We also outline recent work on graph-theoretical descriptions of aberrations, Monte-Carlo computer simulations of aberration spectra, software for quantifying aberration complexity, and systematic links of apparently incomplete with complete or truly incomplete aberrations.

Chromosomal "fingerprints" of prior exposure to densely ionizing radiation.

A biomarker that would distinguish radiation-induced biological damage from damage produced by other agents has long been a goal in radiation biology. We suggest that densely ionizing radiations such as alpha particles from radon daughters, or fission neutrons, leave a distinctive chromosomal marker that may be detected and measured long after radiation exposure. Specifically, they produce an anomalously low ratio (F) of interchromosomal to intrachromosomal, interarm exchange-type chromosome aberrations, in comparison with either X rays or chemical carcinogens. For densely ionizing radiations and for other agents, experimental values of this F ratio, determined both in vitro and in vivo, are quantitatively consistent with theoretical expectations based on considerations of chromosomal geometry and radiation track structure. The use of fluorescence in situ hybridization to measure F values in stable chromosomal aberrations, together with recent developments in techniques for harvesting viable human cells, makes the application of this biological marker quite feasible. For example, the use of this marker could greatly facilitate epidemiological studies of radon-exposed cohorts.

The ratio of dicentrics to centric rings produced in human lymphocytes by acute low-LET radiation.

Chromosome aberrations produced by ionizing radiation are assumed to develop from DNA double-strand breaks (DSBs) which interact pairwise, in an exchange event. Dicentrics and centric rings are aberrations that exemplify inter- and intrachromosomal exchanges, respectively. We show from a survey of published data that for acute low-LET irradiation of resting human lymphocytes the observed ratio of dicentrics to centric rings is approximately five times smaller than predicted by a pairwise interaction model which assumes complete randomness. Such a low ratio can be interpreted as evidence for a proximity effect, favoring exchanges of an intrachromosomal type. That is, since DSBs induced close together have an above-average chance of pairwise interaction, the observed excess of centric rings indicates that at the time of irradiation there is some degree of spatial confinement for the two arms of a single chromosome. Assuming the excess of centric rings is indeed due to proximity effects, the data are used to estimate that the volume of a domain, within which any one lymphocyte chromosome is localized at one instant during the G0/G1 phase, is at most approximately 20% of the nuclear volume.

Chromosome aberrations produced by radiation: the relationship between excess acentric fragments and dicentrics.

Most chromosome aberrations produced by ionizing radiation develop from DNA double-strand breaks (DSBs). Published data on the yield and variance of excess acentric fragments after in vitro irradiation of human lymphocytes were compared with corresponding data on dicentrics. At low LET the number of excess acentric fragments is about 60% of the number of dicentrics, independent of dose and perhaps of dose rate, suggesting that dicentrics and excess acentric fragments arise from similar kinetics rather than from fundamentally different reactions. Only a weak dependence of the ratio on LET is observed. These results are quantified using generalizations of models for pairwise DSB interactions suggested by Brewen and Brock based on data for marsupial cells. By allowing singly incomplete and some "doubly incomplete" exchanges, the models can also account for the experimental observation that the dispersion for excess acentric fragments, a measure of cell-to-cell variance, is systematically larger than the dispersion for dicentrics. Numerical estimates of an incompleteness parameter are derived.

The bystander effect in radiation oncogenesis: II. A quantitative model.

There is strong evidence that biological response to ionizing radiation has a contribution from unirradiated "bystander" cells that respond to signals emitted by irradiated cells. We discuss here an approach incorporating a radiobiological bystander response, superimposed on a direct response due to direct energy deposition in cell nuclei. A quantitative model based on this approach is described for alpha-particle-induced in vitro oncogenic transformation. The model postulates that the oncogenic bystander response is a binary "all or nothing" phenomenon in a small sensitive subpopulation of cells, and that cells from this sensitive subpopulation are also very sensitive to direct hits from alpha particles, generally resulting in a directly hit sensitive cell being inactivated. The model is applied to recent data on in vitro oncogenic transformation produced by broad-beam or microbeam alpha-particle irradiation. Two parameters are used in analyzing the data for transformation frequency. The analysis suggests that, at least for alpha-particle-induced oncogenic transformation, bystander effects are important only at small doses-here below about 0.2 Gy. At still lower doses, bystander effects may dominate the overall response, possibly leading to an underestimation of low-dose risks extrapolated from intermediate doses, where direct effects dominate.

Incorporating dose-rate effects in Markov radiation cell survival models.

Markov models for the survival of cells subjected to ionizing radiation take stochastic fluctuations into account more systematically than do non-Markov counterparts. Albright's Markov RMR (repair-misrepair) model (Radiat. Res. 118, 1-20, 1989) and Curtis's Markov LPL (lethal-potentially lethal) model [in Quantitative Mathematical Models in Radiation Biology (J. Kiefer, Ed.), pp. 127-146. Springer, New York, 1989], which assume acute irradiation, are here generalized to finite dose rates. Instead of treating irradiation as an instantaneous event we introduce an irradiation period T and analyze processes during the interval T as well as afterward. Albright's RMR transition matrix is used throughout for computing the time development of repair and misrepair. During irradiation an additional matrix is added to describe the evolving radiation damage. Albright's and Curtis's Markov models are recovered as limiting cases by taking T----0 with total dose fixed; the opposite limit, of low dose rates, is also analyzed. Deviations from Poisson behavior in the statistical distributions of lesions are calculated. Other continuous-time Markov chain models ("compartmental models") are discussed briefly, for example, models which incorporate cell proliferation and saturable repair models. It is found that for low dose rates the Markov RMR and LPL models give lower survivals compared to the original non-Markov versions. For acute irradiation and high doses, the Markov models predict higher survivals. In general, theoretical extrapolations which neglect some random fluctuations have a systematic bias toward overoptimism when damage to irradiated tumors is compared with damage to surrounding tissues.

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.

Extrapolation of the dna fragment-size distribution after high-dose irradiation to predict effects at low doses.

The patterns of DSBs induced in the genome are different for sparsely and densely ionizing radiations: In the former case, the patterns are well described by a random-breakage model; in the latter, a more sophisticated tool is needed. We used a Monte Carlo algorithm with a random-walk geometry of chromatin, and a track structure defined by the radial distribution of energy deposition from an incident ion, to fit the PFGE data for fragment-size distribution after high-dose irradiation. These fits determined the unknown parameters of the model, enabling the extrapolation of data for high-dose irradiation to the low doses that are relevant for NASA space radiation research. The randomly-located-clusters formalism was used to speed the simulations. It was shown that only one adjustable parameter, Q, the track efficiency parameter, was necessary to predict DNA fragment sizes for wide ranges of doses. This parameter was determined for a variety of radiations and LETs and was used to predict the DSB patterns at the HPRT locus of the human X chromosome after low-dose irradiation. It was found that high-LET radiation would be more likely than low-LET radiation to induce additional DSBs within the HPRT gene if this gene already contained one DSB.

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.

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.