Analysis of non-linearities in mutation frequency curves

Mutation frequency curves for ultraviolet light and other mutagens often exhibit non-linear, as well as linear components. A common pattern observed for UV-induced reversion of auxotrophy in yeast is a biphasic, linear-quadratic (or higher order) response. The non-linear component in such a biphasic frequency curve can arise in two distinct, but non-mutually exclusive, ways: (i) as a result of the existence of two-hit processes in the molecular mechanism(s) of mutagenesis; and (ii) as a result of the possible stochastic dependence of mutation and killing, such that the probability of clone formation by the mutant cells differs from that of the non-mutant cells in the population. We describe here a simple mathematical method for distinguishing between these two sources of non-linearity. It is based on the calculation of a quantity that we call ‘apparent survival’. This is given, for any mutagen dose x, by the ratio of the mutant yield to the corresponding linear component of mutation frequency. If the apparent survival rises to values greater than unity before declining at high doses, then there must exist positive two-hit (or higher order) components in the mutational mechanism. If the final slope of the apparent survival curve differs from that of the measured survival curve, then there also exists some degree of stochastic dependence between mutation and killing.     

High-frequency transformation of human repair-deficient cell lines by an Epstein-Barr virus-based cDNA expression vector.

We constructed a human cDNA expression vector by combining an episomal Epstein-Barr virus (EBV) vector with the expression cassette from the transient-expression vector, pCDM8. This new vector, designated pEBS7, exhibited high-level expression of reporter genes in normal and repair-deficient xeroderma pigmentosum cell lines. Reconstruction experiments indicated that marker genes diluted to a frequency of 10(-5) can be rescued on a single transfection dish. Moreover, derivative cell lines that constitutively express the gene encoding EBV nuclear antigen 1 exhibited a tenfold enhancement in the frequency of rescue of marker genes. The feasibility of preparing large-scale directional or nondirectional cDNA libraries in pEBS7 was demonstrated and reconstruction experiments indicated that marker genes could be rescued from either library with equal efficiency. These results establish a high-efficiency system for the isolation of genes by direct phenotypic selection in human mutant cell lines.     

Time-dependent ROC curves for censored survival data and a diagnostic marker

ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.     

Cell inactivation by ionizing particles and the shapes of survival curves

Recent experiments concerning the survival of monolayer cells irradiated by different parts of ion Bragg peaks opened a way to a deeper mechanistic understanding of cell inactivation. A new theoretical formula for survival curves has been derived reflecting two basic phases of the given mechanism, i.e. energy transfer to a cell nucleus and subsequent biological effect (depending on the amount of imparted energy). The survival ratio for a given dose has been expressed as a function of inactivation probabilities of individual cells after different numbers of nucleus hits (a given amount of energy being transferred to a cell nucleus in each ion traversal). Having used the experimental data for V79 cells irradiated by protons, deuterons and helium ions in different parts of Bragg peaks preliminary values of these inactivation probabilities for individual cells at different LET values have been established.     

Derivation of the frequency distributions of cycle durations from continuous labeling curves

In cell populations that are continuously exposed to radioactive thymidine over a long period, all proliferating cells become labeled as they pass through their DNA-replicating phase. The continuous labeling curve (CLC) shows the percentage of labeled cells versus time. Expected CLCs are calculated for cell populations with arbitrary frequency distributions of cycle durations. By optimizing the parameter values of a general probability function in the formula for CLC, frequency distributions of cycle durations are estimated from experimental CLCs. The analysis of several fetal rat tissues shows that the cycle durations vary over quite a wide range within the same tissue.     

Effect of degree of uniformity on predicted visual cortical response tuning curves

 The different cortical visual cells exhibit a large repertoire of responses to sinusoidal gratings, depending on their receptive field structure and the stimulation parameters. It has been shown previously that the tuning curves and histogram shapes of cell responses are affected by subunit distances. One receptive field model (Spitzer and Hochstein 1985b) incorporated subunit distance but assigned it as a constant parameter, for ease of calculation. Here we investigate different tuning curve properties of various primary cortical cell types during testing of 10 deg of nonuniform distances of the receptive fields’ subunits. The effect of nonuniformity was compared for average responses, tuning curve shapes, maximum peak responses, and bandwidths across four cell types of different sizes. The shapes and other properties of tuning curves are usually found to be retained also when the degree of uniformity is not very high for most of the cell types. In addition, the effect of uniformity is compared across these different response properties. The maximum peak responses of the tuning curve are found to display a lower coefficient of variation than the bandwidth, for all cell types, for most degrees of uniformity. Received: 15 June 1993/Accepted in revised form: 5 August 1994     

A model-free way of representing hyperthermia cell survival data

We present a method of fitting curves to cell survival data that is free from all model assumptions, requiring only that the fitted curves be decreasing and reasonably smooth, where the degree of smoothness is determined from considerations of experimental error. The fitted curves are then differentiated to yield frequency distributions of cell killing times, which may be of value in defining subpopulations with different sensitivities to the cytotoxic agent under study. In addition, confidence intervals on the fitted curves and frequency distributions are obtained by Monte Carlo simulation. The results allow the objective and model-free assessment of the effects of various experimental interventions on cell survival.     

A versatile method for simultaneous analysis of families of curves

We have developed a versatile new approach to the simultaneous analysis of families of curves, which combines the simplicity of empirical methods with several of the advantages of mathematical modeling, including objective comparison of curves and statistical hypothesis testing. The method uses weighted smoothing cubic splines; the degree of smoothing is adjusted automatically to satisfy constraints on curve chape (monotonicity, number of inflection points). By simultaneous analysis of a family of curves, one can extract the shape common to all the curves. Up to four linear scaling parameters are used to match the shape to each curve, and to provide optimal superimposition of the several curves. By applying constraints to these scaling factors, one can test a variety of hypotheses concerning comparisons of curves (e.g., identity, parallelism, or similarity of shape of two or more curves), and thus evaluate the effects of experimental manipulation. By optimal pooling of data one can avoid the need for arbitrary selection of a typical experiment, and can detect subtle but reproducible effects that might otherwise be overlooked. This approach can facilitate the development of an appropriate model. The method has been implemented in a Turbo-Pascal program for IBM-PC compatible microcomputers, and in FORTRAN-77 for the DEC-10 mainframe, and has been utilized successfully in a wide variety of applications.     

Segregation studies in CHO hybrid cells: I. Spontaneous and mutagen-induced segregation events of two recessive drug-resistant loci

The process of segreation or phenotypic expression of two recessive drug-resistant loci from heterozygous Chinese hamster ovary hybrid lines is examined. The spontaneous segregation rates of phytohaemagglutinin resistance (Phar) and a temperature-dependent 8-azaguanine-resistant locus (Azarts) from heterozygous quasitetraploid lines using Luria-Delbruck fluctuation analysis were 5 X 10(-5) and 10(-5) events/cell/generation, respectively. In quasihexaploid lines, the latter rates increased 40- and 200-fold, respectively, and were dependent on the number of presumptive drug-sensitive allelel. The mutagens EMS, MNNG, ICR-170, ICR-191, and gamma rays significantly increased the frequency of segregation events. The mutagen-induced frequency of dominant mutations to ouabain (Ouar) and alpha-amanitin (Amar) rsistance in the same hybrid line was much lower in comparison to segregation events and was mutagen specific. The chromosome number per metaphase cell was more variable than DNA content in quasitetraploid lines. These properties of marker segregation are consistent with mechanisms of either restricted chromosome loss, rearrangement, or mutation.     

Rescue of marker phenotypes: effects of BUdR sensitization, hypoxia and high LET.

The survival curve of colony-forming ability of Chinese hamster wg3h cells has been compared with the dose-response curve for the expression of an active thymidine kinase (TK) gene from these cells. The TK+ phenotype was measured by hybrid colony formation after fusion of wg3h (TK+) cells with Chinese hamster A23 (TK-) cells. The TK+ survival data fitted a multi-target curve up to 3 krad of 137 Cs irradiation, when a highly resistant fraction of hybrid colonies was seen at about 1 per cent survival. The Do of TK+ survival for the multi-target region was 3.1-4.0 times greater, than that of wg3h survival, even when the Do for cell survival varied between 136 and 545 rad by 14 MeV neutrons and hypoxia respectively. This parallel modification of cell and TK+ sensitivities suggests that the lesions causing cell inactivation are of the same type as those that cause marker inactivation. Using 14 MeV neutron data the approximate target size for TK inactivation was calculated to be 0.54-0.91 per cent of the DNA content of the cell (or about one-fifth to one-tenth of a chromosome). The data support the idea that marker inactivation results primarily from damage occurring outside the marker gene. BUdR labelling of wg3h cells before irradiation caused slight toxicity (30 per cent reduction in plating efficiency) and a twofold increase in cell sensitivity. However, the sensitivity of the TK+ phenotype increases by only 30 per cent. The increased cell sensitivity thus appeared to result from synergism between increased sensitivity of DNA to strand breakage and metabolic toxicity, the latter being largely overcome by fusion with normal cells.     

Initial slope of radiation survival curves is characteristic of the origin of primary and established cultures of human tumor cells and fibroblasts

The published survival curves of 110 human tumor cell lines and 147 nontransformed human fibroblast strains have been reanalyzed using three different statistical methods: the single hit multitarget model, the linear-quadratic model, and the mean inactivation dose. The 110 tumor cell lines were classified in two ways: (a) into three categories defined by clinical radiocurability criteria, and (b) into seven categories based on histopathology. The 147 fibroblast strains were divided into eight genetic groups. Differences in the radiosensitivities of both the tumor cell and fibroblast groups could be demonstrated only by parameters that describe the slopes of the initial part of the survival curves. The capacity of the survival level to identify significant differences between groups was dose dependent over the range 1 to 6 Gy. This relationship showed a bell-shaped curve with a maximum at 1.5 Gy for the tumor cell lines and 3 Gy for the fibroblasts. Values for intrinsic radiosensitivity for a number of groups of tumors have also been obtained by primary culture of tumor cells. These values are strictly comparable to those obtained by clonogenic methods. This confirms that intrinsic radiosensitivity is a determinant of the response of tumor cells to radiotherapy and suggests that tissue culture methods may be used as a predictive assay.     

A novel strategy for the generation of T cell lines lacking expression of endogenous alpha- and/or beta-chain T cell receptor genes

Mutant T cell lines that do not express the endogenous alpha- and/or beta-chain genes of the TCR were generated from the alpha beta TCR/CD3+ tumor cell line C6VL with a combination of classical mutagenesis methods and selection of somatic hybrid variants. This novel strategy obviated the need for repeated mutagenesis and screening of a large number of individual clones. The loss of either the alpha- or the beta-chain expression in the mutant cells was associated with the loss of surface TCR/CD3 complex, which could be rescued by the transfection of appropriate exogenous alpha- and/or beta-chain gene constructs. Because these cells express a single TCR molecule on the cell surface, they are useful for the study of the assembly and function of the alpha beta TCR. This strategy is also generally applicable for the generation of homozygous mutant cell lines lacking other gene products.     

Analysis of non-linearities in frequency curves for UV-induced mitotic recombination in wild-type and excision-repair-deficient strains of yeast

Frequency curves for UV-induced mitotic recombination often are linear at low doses. As dose increases, these curves either increase at higher powers of dose and/or reach a maximum induced frequency and then decline. Similar dose-response patterns have been observed previously for mutation. The non-linearities can arise from higher order effects inherent in the molecular mechanisms of mutagenesis and/or from 'delta-effects' (Eckardt and Haynes, 1977a), i.e., differential probabilities of clone formation for mutant and non-mutant cells. Previously, we have shown that one can distinguish between these two possibilities by plotting the ratio of the induced mutant yield to the linear component of frequency as a function of dose (Haynes et al., 1985). In this study, we have used this ratio, a quantity we call 'apparent survival', to analyse the non-linear regions of the dose-response curves for UV-induced mitotic crossing-over and gene conversion in wild-type (RAD) and excision-repair-deficient (rad3) strains of yeast. Plots of apparent survival versus dose reveal the existence of a positive, non-linear component associated with UV-induced gene conversion in RAD, but not rad3, cells. A high dose decline in frequency, which is observed for UV-induced recombination in both strains, can be attributed to delta-effects.     

A generalization of the clonal survival models: Equations for the families of curves obtained with fractionated irradiation

Summary The survival curves obtained when cellular recovery follows various first radiation dose deliveriesDI seem, when semi-logarithmically plotted, to be translated from the part of the curve corresponding to an unfractionated irradiation beyond a doseDR. A possible assumption consistent with such experimental observations is proposed which allows the generalization of any survival modelS = f(D). The derived equationS = f(DR + D - DI)f(DI)/f(DR) is convenient for the whole family of experimental survival curves involving cellular damage repairs when the first radiation doses vary. All the parameters of the family equation can be simultaneously fitted so that their reliability is increased. The generalized equations are given for the four following models: two-hits targets, Chadwick and Leenhouts, Green and Burki, Wideröe. As an example, the Chadwick and Leenhouts generalized model parameters are fitted to a family of experimental survival curves concerningChlorella cells exposed to fractionated and continuous gamma irradiation. The fittings are presented with their confidence limits and are briefly discussed.     

Gene flow by immigrants into isolated recipient populations: a laboratory model using flour beetles

The effectiveness of immigrants as agents of gene flow was investigated in a laboratory model, using mutant marker strains of the flour beetle, Tribolium castaneum (Herbst).We show that immigrants had an advantage over residents. The proportion of hybrid offspring (PHO), resulting from immigrant mating with residents, was higher than expected from their frequency in the parental population. This advantage was observed regardless of immigrant sex and immigrant strain. The advantage seems to result from immigrant mating advantage (although not a rare-male phenomenon) and not from better survival of hybrid offspring. However, hybrid offspring seem to be more resistant to sporozoan infection, resulting in higher PHO in sporozoan-infected cultures.     

Characterization of a Chinese hamster-human hybrid cell line with increased system L amino acid transport activity.

We have studied leucine transport in several Chinese hamster-human hybrid cell lines obtained by fusion of a temperature-sensitive line of Chinese hamster ovary cells, ts025C1, and normal human leukocytes. A hybrid cell line exhibiting a twofold increase in L-leucine uptake over that in the parental cell line was found. This hybrid cell line, 158CnpT-1, was temperature resistant, whereas the parental Chinese hamster ovary mutant, ts025C1, contained a temperature-sensitive leucyl-tRNA synthetase mutation. An examination of the different amino acid transport systems in this hybrid cell line revealed a specific increase of system L activity with no significant changes in systems A and ASC. The Vmax for L-leucine uptake exhibited by the hybrid 158CnpT-1 was twice that in the CHO parental mutant, ts025C1. Cytogenetic analysis showed that the hybrid 158CnpT-1 contains four complete human chromosomes (numbers 4, 5, 10, and 21) and three interspecific chromosomal translocations in a total complement of 34 chromosomes. Biochemical and cytogenetic analysis of segregant clones obtained from hybrid 158CnpT-1 showed that the primary temperature resistance and high system L transport phenotypes can be segregated from this hybrid independently. The loss of the primary temperature resistance was associated with the loss of the human chromosome 5, as previously reported by other laboratories, whereas the loss of the high leucine transport phenotype, which is associated with a lesser degree of temperature resistance, was correlated with the loss of human chromosome 20.     

Exponential or shouldered survival curves result from repair of DNA double-strand breaks depending on postirradiation conditions

The yeast mutant rad54-3 is temperature conditional for the rejoining of DNA double-strand breaks, but cells do proliferate at both the restrictive and permissive temperatures. Thus, after irradiation with 30 MeV electrons, survival curves can be obtained which may or may not involve double-strand break rejoining under certain experimental conditions. Because of this special property of rad54-3 cells, it was possible to demonstrate that rejoining of radiation-induced double-strand breaks under nongrowth conditions yields exponential survival curves the slopes of which decrease as a function of the rejoining time. These survival data suggest that, under nongrowth conditions, the rejoining of double-strand breaks is an unsaturated process and lacks binary misrepair. In contrast, whenever rejoining of double-strand breaks occurs under growth conditions, shouldered survival curves are observed. This is true for immediate plating as well as for delayed plating survival curves. It is proposed that it is the unsaturated rejoining of double-strand breaks under nongrowth conditions, lacking binary misrepair, which is responsible for potentially lethal damage repair.     

Genetic complementation between UV-sensitive CHO mutants and xeroderma pigmentosum fibroblasts

The purpose of this study was to determine the feasibility of doing complementation analysis between DNA-repair mutants of CHO cells and human fibroblasts based on the recovery of hybrid cells resistant to DNA damage. Two UV-sensitive CHO mutant lines, UV20 and UV41, which belong to different genetic complementation groups, were fused with fibroblasts of xeroderma pigmentosum in various complementation groups. Selection for complementing hybrids was performed using a combination of ouabain to kill the XP cells and mitomycin C to kill the CHO mutants. Because the frequency of viable hybrid clones was generally < 10⁻⁶ and the frequency of revertants of each CHO mutant was 2×10⁻⁷, putative hybrids required verification. The hybrid character of clones was established by testing for the presence of human DNA in a dot-blot procedure.

Hybrid clones were obtained from 9 of the 10 different crosses involving 5 complementation groups of XP cells. The 4 attempted crosses with 2 other XP groups yielded no hybrid colonies. Thus, a definitive complementation analysis was not possible. Hybrids were evaluated for their UV resistance using a rapid assay that measures differential cytotoxicity (DC). All 9 hybrids were more resistant than the parental mutant CHO and XP cells, indicating that in each case complementation of the CHO repair defect by a human gene had occurred. 3 hybrids were analyzed for their UV-radiation survival curves and shown to be much more resistant that the CHO mutants but less resistant than normal CHO cells. With 2 of these hybrids, sensitive subclones, which had presumably lost the complementing gene, were found to have similar sensitivity to the parental CHO mutants. We conclude that the extremely low frequency of viable hybrids in this system limits the usefulness of the approach. The possibility remains that each of the nonhybridizing XP strains could be altered in the same locus as one of the CHO mutants.     

The theory and practice of constructing calibration curves in biodozimetry

The methodical peculiarities of experimental construction of regression "dose-effect" relationships used for the dose reconstruction are discussed. The method of computer simulations is applied to study the efficiency of different statistical procedures for plotting regression curves as well as the dependence of errors in dose prediction on the volume of examined material and on the choice of doses for a calibration curve. The causes of essential variability of calibrations obtained by different teams of researchers are discussed. A number of methodical recommendations is given for statistical processing of cytogenetic data. The procedure of constructing calibration dose dependence of the frequency of dicentrics on the basis experiments with in vitro gamma-irradiation of lymphocytes from blood samples of 5 donors is considered in detail. The expressions for statistical errors occurring in the dose reconstruction made on the base of the frequency of aberrations were derived and checked by the computer experiment.     

CYTOKINETIC ANALYSIS OF THE JB-1 ASCITES TUMOUR AT DIFFERENT STAGES OF GROWTH

The cell kinetics of the murine JB-1 ascites tumour have been investigated on days 4, 7 and 10 after transplantation of 2·5 × 10⁶ cells. The experimental data, growth curve, percentage of labelled mitoses curves, continuous labelling curves and cytophotometric determination of single-cell DNA content have been analysed by means of a mathematical model for the cell kinetics. The important result was the existence of 8% non-cycling cells with G₂ DNA content in the 10-day tumour, while only 0·2 and 0% were observed in the 7- and 4-day tumours, respectively. The doubling times determined from the growth curve were 22·8, 70 and 240 hr, respectively, in the 4-, 7- and 10-day tumours. Growth fractions of 76, 67 and 44% were calculated for the same tumour ages. The mean cell cycle time increased from 14 to 44 hr from day 4 to 7 due to a proportional increase in the mean transit time of all phases in the cell cycle. In the 10-day tumour, the mean cell cycle changed to 41 hr and T _G1 decreased to 0·5 hr. The cell production rate was 4·3%/hr in the 4-day tumour, 1·2%/hr in the 7-day tumour and 1·0%/hr in the 10-day tumour. The cell loss rates in the same tumours were 1·3, 0·2 and 0·7%/hr, respectively. The analysis made it probable that the mode of cell loss was an age-specific elimination of non-cycling cells with postmitotic DNA content.