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R K Sachs

Publications and source records attributed to R K Sachs.

At least 55 records · Page 3Linked to original sources
PubMed1996

Dose timing in tumor radiotherapy: considerations of cell number stochasticity.

A typical tumor radiotherapy regimen using external beam X rays consists of doses on weekdays for 4-7 weeks. During the final weeks, the tumor may contain only a few cells capable of regenerating the tumor and may be growing exponentially between doses. Stochastic fluctuations of the cell number can influence the optimal time pattern of dose delivery. If the total dose is fixed, a deterministic model of exponential tumor growth, neglecting stochastic effects, predicts that the way the radiation dose is spread out in time does not affect the average number of tumor cells at the end. However, we here show, within the framework of a birth-death model, that when stochastics are taken into account, the earlier the dose is given (consistent with other constraints imposed by quite different considerations), the better. The proof uses a transformation that simplifies the characteristic equation of the partial differential equation governing the probability generating function for a birth-death process with time-dependent rates. The theorem that earlier is better holds for any statistical distribution of cell number from patient to patient at the start of the exponential growth phase and for virtually any cell-killing model. Numerical results indicate the stochastic effects, although not dominant, are not negligible.

Cell Count↗
PubMed1996

Interpretation of inverse dose-rate effects for mutagenesis by sparsely ionizing radiation.

An inverse dose-rate effect has sometimes been observed for mutagenesis in cells exposed to gamma-rays. We model such data quantitatively with the key assumption that the effect is caused in cycling cells by correlated variations in sensitivity across the cell cycle, for both mutation and killing. We quantify this approach using the LQR (linear-quadratic + resensitization) formalism, which describes the response to radiation of a heterogeneous cell population. This model is applied to an exponentially growing population. We compare its predictions with dose- and dose-rate dependent mutation data and show that it can well fit the observed inverse dose-rate effect, as well as providing an explanation of why inverse dose-rate effects have been seen in some experiments, but not in others. The actual values of the model parameters emerging from the analysis are reasonable in magnitude, based on their biological interpretations. We conclude that the LQR model can quantify cell-cycle redistribution effects without overparameterization, and that the data favour a correlation explanation of inverse dose-rate effects for mutagenesis by low-LET radiation. It is less clear that this explanation is appropriate to high-LET radiation-induced oncogenic transformation, although all potential explanations of inverse dose-rate effects predict that, at appropriately low doses, no dose-rate effects of any kind are expected.

Cell Cycle↗
PubMed1996

Proximity effects for chromosome aberrations measured by FISH.

A Monte Carlo simulation computer program for radiation-produced chromosome aberrations, based on the breakage-and-reunion model, was extended to include proximity effects due to localization of chromosomes and limited range for break-break interactions. Two adjustable parameters were used. One corresponds to total dose: the other determines proximity effects by specifying the number of 'interaction regions' in a cell nucleus. The use of additional adjustable parameters was avoided by assuming randomness of break induction and aberration production. FISH chromosome painting data were obtained from 1.9 Gy 60Co gamma-rays-irradiated human lymphocytes. The data were compared with the computer simulation results, taking individual chromosome lengths into account. With about 13 interaction regions, agreement between the experiment and the simulation was good, even when detailed categories of damage were scored. An estimated average dsb-dsb interaction distance, based on 13 interaction regions, is about 1.3 micron. Monte Carlo methods give useful quantitative estimates of relative aberration yields, with a minimum of adjustable parameters and the theoretical assumptions, and indicated proximity effects. Computer simulation of FISH experiments can be adapted to any number of colours, any scoring criteria and any method of grouping aberrations into categories. Simulation allows systematic extrapolation of aberration data on painted chromosomes to whole-genome aberration frequencies.

Chromosome Aberrations↗
PubMed1996

Theoretical predictions on the equality of radiation-produced dicentrics and translocations detected by chromosome painting.

Existing models of chromosome aberrations produced by ionizing-radiation predict equal numbers of dicentrics and translocations if the dose is so low that complex aberrations can be ignored. We show that, for a specific subset of aberrations detected by FISH, dicentric/translocation equality is predicted even at higher doses. Assuming one-colour whole-chromosome painting (with unpainted chromosomes counterstained and centromeres recognizable) the relevant restriction is that the final metaphase pattern be, in the terminology of Simpson and Savage, 'apparently simple'. This means that the painted pattern is required to have the colour/centromere appearance corresponding to a single complete reciprocal exchange but its actual formation, as reflected for example in lengths, is allowed to be more complicated. The restriction to apparent simplicity is significantly less limiting than ignoring all complex aberrations. Our analysis of predicted dicentric/translocation equality in this case uses examples, a combinatorial counting method, Monte Carlo computer programs, and a duality proof. However, we argue that for 'visibly complex' dicentrics or translocations, no similar equality is expected in general. Corresponding experimental results are briefly surveyed. Checking dicentric/translocation equality experimentally can provide a significant test of current chromosome aberration models.

Chromosome Aberrations↗
PubMed1995

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.

Animals↗
PubMed1995

A random-walk/giant-loop model for interphase chromosomes.

Fluorescence in situ hybridization data on distances between defined genomic sequences are used to construct a quantitative model for the overall geometric structure of a human chromosome. We suggest that the large-scale geometry during the G0/G1 part of the cell cycle may consist of flexible chromatin loops, averaging approximately 3 million bp, with a random-walk backbone. A fully explicit, three-parametric polymer model of this random-walk/giant-loop structure can account well for the data. More general models consistent with the data are briefly discussed.

Base Composition↗
PubMed1995

Ionizing radiation damage to cells: effects of cell cycle redistribution.

If a population of cycling cells is exposed to a fixed dose of ionizing radiation delivered over time T, it is sometimes observed that increasing T increases the amount of cell killing. This is essentially because at first the radiation preferentially kills cells in a sensitive portion of the cycle and the surviving, more resistant cells then have time to reach more sensitive stages. We refer to this effect as population resensitization, caused by redistribution within the cell cycle. We investigate the effect theoretically by employing the McKendrick-von Foerster equation for age-structured proliferating cell populations, generalized by introducing a radiation damage term. Within our formalism, we show that population resensitization occurs whenever: (a) prior to irradiation the cell population has the stable age-distribution approached asymptotically by an unirradiated population, and (b) T is sufficiently small. Examples and other cases are outlined. The methods of Volterra integral equations, renewal theory, and positive semigroup theory are applied. The effect of varying T is evaluated by considering the ultimate amplitude of the stable age-distribution population at times much greater than both the irradiation duration and the average cell-cycle time. The main biological limitations of the formalism are the following: considering only radiation damage which is not subject to enzymatic repair or quadratic misrepair, using an overly naive method of ensuring loss of cell cycle synchrony, neglecting nonlinear effects such as density inhibition of growth, and neglecting radiatively induced perturbations of the cell cycle. Possible methods for removing these limitations are briefly discussed.

Animals↗
PubMed1995

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.

Cell Cycle↗
PubMed1995

Chromosome aberrations produced by ionizing radiation: Monte Carlo simulations and chromosome painting data.

Monte Carlo simulations are used to analyze the reshuffling of chromosome segments which occurs when DNA is damaged by ionizing radiation. Programs are based on either Sax's classic breakage-and-reunion model or Revell's exchange model for chromosome aberrations. The simulations quantify the predictions of the two models in complete detail, using only one adjustable parameter which corresponds to total radiation dose. While testing subroutines, new analytic results on the chromosome/arm/break method of classifying aberrations were obtained. The model predictions were tested by using three-color fluorescence in situ hybridization (FISH) 'chromosome painting' on human lymphocyte cells irradiated with gamma-rays. Some of the per-cell aberration frequencies were observed to be intermediate between the predictions of the two models. This result indicates proximity 'effects', due to localization of chromosome interactions in space and time. Predictions based on chromosome arm lengths were found to be in good agreement with experiment. Monte Carlo simulations are a powerful, flexible way to compare models of chromosome aberration production with experiments quantitatively, using a minimum of theoretical presumptions.

Algorithms↗
PubMed1995

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.

Chromosome Aberrations↗
PubMed1994

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.

Animals↗
PubMed1994

Track structure, chromosome geometry and chromosome aberrations.

The joint role of radiation track structure and chromosome geometry in determining yields of chromosome aberrations is discussed. Ideally, the geometric models of chromosomes used for analyzing aberration yields should have the same degree of realism as track structure models. However, observed chromosome aberrations are produced by processes on comparatively large scales, e.g., misrepair involving two DSB located on different chromosomes or two DSB separated by millions of base pairs on one chromosome, and quantitative models for chromatin on such large scales have to date almost never been attempted. We survey some recent data on large-scale chromosome geometry, mainly results obtained with fluorescence in situ hybridization ("chromosome painting") techniques. Using two chromosome models suggested by the data, we interpret the relative yields, at low and high LET, of inter-chromosomal aberrations compared to intra-chromosomal, inter-arm aberrations. The models consider each chromosome confined within its own "chromosome localization sphere," either as a random cloud of points in one model or as a confined Gaussian polymer in the other. In agreement with other approaches, our results indicate that at any given time during the G0/G1 part of the cell cycle a chromosome is largely confined to a sub-volume comprising less than 10% of the volume of the cell nucleus. The possible significance of the ratio of inter-chromosomal aberrations to intra-chromosomal, inter-arm aberrations as an indicator of previous exposure to high LET radiation is outlined.

Cell Cycle↗
PubMed1994

Influence of time-dependent stochastic heterogeneity on the radiation response of a cell population.

A solid tumor is a cell population with extensive cellular heterogeneity, which severely complicates tumor treatment by therapeutic agents such as ionizing radiation. We model the response to ionizing radiation of a multicellular population whose cells have time-dependent stochastic radiosensitivity. A reaction-diffusion equation, obtained by assuming a random process with the radiation response of a cell partly determined by competition between repair and binary misrepair of DNA double-strand breaks, is used. By a suitable transformation, the equation is reduced to that of an Ornstein-Uhlenbeck process so explicit analytic solutions are available. Three consequences of the model's assumptions are that (1) response diversity within a population increases resistance to radiation, that is, the population surviving is greater than that anticipated from considering an average cell; (2) resistant cell subpopulations preferentially spared by the first part of a prolonged radiation protocol are driven biologically into more radiosensitive states as time increases, that is, resensitization occurs; (3) an inverse dose-rate effect, that is, an increase in cell killing as overall irradiation time is increased, occurs in those situations where resensitization dominates effects due to binary misrepair of repairable damage. The results are consistent with the classic results of Elkind and coworkers on extra cell killing attributed to cell-cycle redistribution and are in agreement with some recent results on in vitro and in vivo population radiosensitivity. They also generalize the therapeutic paradigm that low dose rate or fractionated radiation can help overcome hypoxic radioresistance in tumors.

Animals↗
PubMed1994

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.

Biomarkers↗
PubMed1993

Polymer models for interphase chromosomes.

The overall geometry of chromosomes in mammalian cells during interphase is analyzed. On scales larger than approximately 10(5) bp, a chromosome is modeled as a Gaussian polymer subjected to additional forces that confine it to a subvolume of the cell nucleus. An appropriate partial differential equation for the polymer Green's function leads to predictions for the average geometric length between two points on the chromosome. The model reproduces several of the experimental observations: (i) a square root dependence of average geometric distance between two marked chromosome locations on their genomic separation over genomic length scales from approximately 10(5) to approximately 10(6) bp; (ii) an approach of the geometric distance to a maximum value for still larger genomic separations of the two points; (iii) overall chromosome localization in subdomains of the cell nucleus, as suggested by fluorescent labeling of whole chromosomes and by radiobiological evidence. The model is also consistent with known properties of the 30-nm chromatin fiber. It makes a testable prediction: that for two markers a given number of base pairs apart on a given chromosome, the average geometric separation is larger if the configuration is near one end of the chromosome than if it is near the center of the chromosome.

Animals↗
PubMed1993

Using three-color chromosome painting to test chromosome aberration models.

Ionizing radiation induces DNA double-strand breaks (DSB), which interact pairwise to produce chromosome aberrations. There have long been two main competing theories of such pairwise DSB-DSB interactions. The "classical" theory asserts that an unrepaired DSB makes two ends that separate within the cell nucleus, with each end subsequently able to join any similar (nontelomeric) end. The "exchange" theory asserts that at a DSB the chromatin does not separate completely; rather the DSB ends remain associated until repair, or an illegitimate recombination involving another DSB, occurs. The DSB-DSB interaction mechanism was tested by using three-color fluorescence in situ hybridization to paint chromosomes and observe "three-color triplets": three broken and misrejoined chromosomes having cyclically permuted colors. We observed 18 "three-color triplets" in 2000 cells after 2.25 Gy of gamma-irradiation. On the exchange model in its standard form such three-color triplets cannot occur, so this model is inconsistent with the observations. On the classical model, formalized as a discrete time Markov chain embedded at the transitions of a continuous time Markov chain, the frequency of occurrence of three-color triplets can be computed by Monte Carlo simulations. The number of three-color triplets predicted mathematically by the classical model was found to be slightly larger than the observed number. Thus our data, together with our computer simulations, exclude the standard form of the exchange model but are compatible with the classical model. The results are also compatible with other, more complicated models.

Chromosome Aberrations↗