The clonogen content of murine intestinal crypts: dependence on radiation dose used in its determination.

The number of colony-forming (clonogenic) cells in each of the crypts in mouse small intestine was deduced using a two-dose irradiation technique. The number was 7.5 +/- 0.8 cells using two equal doses each less than 9 Gy and 38 +/- 7 cells using 9 Gy or more per dose. The significant dose dependence could not be accounted for by considerations of intra- or intercrypt variability, or by the factor introduced to correct the sampling frequency for the influence of crypt size. The results suggest that more colony-forming cells may be recruited when the injury is more severe.     

Scoring mitotic activity in longitudinal sections of crypts of the small intestine

Various counts have been made of the number of mitotic figures in whole crypts and sections of crypts of the small intestine of the mouse. Samples were analysed from animals killed at different times of the day and at different times after administration of vincristine. Measurements have been made of the size of mitotic and interphase nuclei and of the radial position of mitotic figures. The correction factor, f, which is required to take into account the enhancement of mitotic counts in sections as a consequence of their centripetal position has been investigated. The results indicate the following: (1) transverse sections of the crypt differ from longitudinal sections if they involve cutting the intestine before fixation which may result in a relaxation of the crypt and its widening by 25%; (2) columnar cell nuclei have a shape that resembles a sphere flattened so that the average diameter is 20% greater in crypt transverse sections; (3) mitotic nuclei tend to be about half-way between the crypt edge and the central axis of the crypt; (4) between about four and seven times more mitotic figures have their mitotic axis parallel to the long axis of the crypt; (5) about one-third of all mitotic figures in a crypt are seen in a longitudinal section of the crypt. If this is related to the number of cells in the crypt as a whole and in a section, a correction factor fD for the mitotic index of 0.59 is obtained; (6) the correction factor fT derived from the shape and position of the mitotic figures measured in 3 microns longitudinal sections is 0.53; (7) relating cell cycle and mitotic accumulation data using a computer-based model of the crypt also permits a correction factor fmod to be estimated. This gives a value of 0.66. When sectioned material is used to calculate a mitotic index the most appropriate correction factor is fD; for mouse small intestine it is 0.59.     

Estimates of the number of clonogenic cells in crypts of murine small intestine

There is a proliferative cell hierarchy in the mouse intestinal crypt with ancestral stem cells which can regenerate all components of the lineage after injury (clonogenic cells). The number of these clonogenic or regenerative cells per crypt can be estimated from radiobiological experiments where doses of radiation are used to kill cells and ablate crypts. Various approaches can be adopted which provide different estimates of this number of cells. One of the conventional approaches used in the past provided estimates of about 70-80 clonogenic cells per crypt (i.e. about 50% of the proliferative or 30% of all crypt cells). A technically simpler approach has recently been suggested. This has been used here to provide many independent estimates of the number of crypt clonogenic cells. These suggest about 32 clonogenic cells exist per crypt i.e. about half the previous estimate and about twice the number of putative "functional" stem cells (those which operate as stem cells in the normal steady-state crypt). The reasons for the differences are discussed. The new estimates are compatible with the hypothesis that the crypt contains a ring of about 16 functional stem cells which are expected to be clonogenic, besides which there is a second ring of 16 clonogenic cells which represent early transit cells (the immediate daughters of the stem cells) which can act as clonogenic cells if required after radiation injury.     

Differences in survival of mouse colon crypts after whole- or partial-body irradiation.

The survival of mouse colon crypts after X-irradiation has been studied by the microcolony technique. The Do for crypt survival was 266 rad after whole-body irradiation in air, but when the colon alone was irradiated, the Do was 340 rad. In mice which were breathing 95 per cent oxygen, the Do values were 238 rad for whole-body and 302 rad for colon irradiation. The survival curves were all extrapolated to the same number, and the DQ was also increased with colon irradiation. There was, therefore an enhancement of colon crypt survival of about 27 per cent by local as opposed to whole-body irradiation. These results might be explained by a circulating repair promoter or by the production of a toxin after whole-body irradiation.     

Scoring Mitotic Activity In Longitudinal Sections of Crypts of the Small Intestine

Abstract. Various counts have been made of the number of mitotic figures in whole crypts and sections of crypts of the small intestine of the mouse. Samples were analysed from animals killed at different times of the day and at different times after administration of vincristine. Measurements have been made of the size of mitotic and interphase nuclei and of the radial position of mitotic figures. the correction factor, f, which is required to take into account the enhancement of mitotic counts in sections as a consequence of their centripetal position has been investigated. the results indicate the following: (1) transverse sections of the crypt differ from longitudinal sections if they involve cutting the intestime before fixation which may result in a relaxation of the crypt and its widening by 25%; (2) columnar cell nuclei have a shape that resembles a sphere flattened so that the average diameter is 20% greater in crypt transverse sections; (3) mitotic nuclei tend to be about half-way between the crypt edge and the central axis of the crypt; (4) between about four and seven times more mitotic figures have their mitotic axis parallel to the long axis of the crypt; (5) about one-third of all mitotic figures in a crypt are seen in a longitudinal section of the crypt. If this is related to the number of cells in the crypt as a whole and in a section, a correction factor f_d for the mitotic index of 0.59 is obtained; (6) the correction factor f_T derived from the shape and position of the mitotic figures measured in 3 μm longitudinal sections is 0.53; (7) relating cell cycle and mitotic accumulation data using a computer-based model of the crypt also permits a correction factor f_mod to be estimated. This gives a value of 0.66. When sectioned material is used to calculate a mitotic index the most appropriate correction factor is f_D; for mouse small intestine it is 0.59.     

Ionizing radiation and genetic risks. XIII. Summary and synthesis of papers VI to XII and estimates of genetic risks in the year 2000

This paper recapitulates the advances in the field of genetic risk estimation that have occurred during the past decade and using them as a basis, presents revised estimates of genetic risks of exposure to radiation. The advances include: (i) an upward revision of the estimates of incidence for Mendelian diseases (2.4% now versus 1.25% in 1993); (ii) the introduction of a conceptual change for calculating doubling doses; (iii) the elaboration of methods to estimate the mutation component (i.e. the relative increase in disease frequency per unit relative increase in mutation rate) and the use of the estimates obtained through these methods for assessing the impact of induced mutations on the incidence of Mendelian and chronic multifactorial diseases; (iv) the introduction of an additional factor called the "potential recoverability correction factor" in the risk equation to bridge the gap between radiation-induced mutations that have been recovered in mice and the risk of radiation-inducible genetic disease in human live births and (v) the introduction of the concept that the adverse effects of radiation-induced genetic damage are likely to be manifest predominantly as multi-system developmental abnormalities in the progeny.For all classes of genetic disease (except congenital abnormalities), the estimates of risk have been obtained using a doubling dose of 1 Gy. For a population exposed to low LET, chronic/ low dose irradiation, the current estimates for the first generation progeny are the following (all estimates per million live born progeny per Gy of parental irradiation): autosomal dominant and X-linked diseases, approximately 750-1500 cases; autosomal recessive, nearly zero and chronic multifactorial diseases, approximately 250-1200 cases. For congenital abnormalities, the estimate is approximately 2000 cases and is based on mouse data on developmental abnormalities. The total risk per Gy is of the order of approximately 3000-4700 cases which represent approximately 0.4-0.6% of the baseline frequency of these diseases (738,000 per million) in the population.     

Sampling effects, noise, and photobleaching in temporal image correlation spectroscopy

We present an extensive investigation of the accuracy and precision of temporal image correlation spectroscopy (TICS). Using simulations of laser scanning microscopy image time series, we investigate the effect of spatiotemporal sampling, particle density, noise, sampling frequency, and photobleaching of fluorophores on the recovery of transport coefficients and number densities by TICS. We show that the recovery of transport coefficients is usually limited by spatial sampling, while the measurement of accurate number densities is restricted by background noise in an image series. We also demonstrate that photobleaching of the fluorophore causes a consistent overestimation of diffusion coefficients and flow rates, and a severe underestimation of number densities. We derive a bleaching correction equation that removes both of these biases when used to fit temporal autocorrelation functions, without increasing the number of fit parameters. Finally, we image the basal membrane of a CHO cell with EGFP/alpha-actinin, using two-photon microscopy, and analyze a subregion of this series using TICS and apply the bleaching correction. We show that the photobleaching correction can be determined simply by using the average image intensities from the time series, and we use the simulations to provide good estimates of the accuracy and precision of the number density and transport coefficients measured with TICS.     

Intestinal crypt clonogens: a new interpretation of radiation survival curve shape and clonogenic cell number

Estimates of the clonogen content (number of microcolony-forming cells) of murine intestinal crypts using microcolony assays show an apparent dependence on the radiation dose used in the assay of clonogen content. Crypt radiation survival curves often show increased curvature beyond that expected on the basis of the conventional linear-quadratic model. A novel form of crypt survival curve shape is proposed based on two contributory mechanisms of crypt killing. Six previously published sets of microcolony data were re-analysed using a dual-kill model, where target cells are killed by two contributory mechanisms, each described by a linear-quadratic function of dose. The data were analysed as two series--high-dose rate and low-dose rate irradiation. The data were fitted to the models using direct maximization of a quasi-likelihood, explicitly allowing for overdispersion. The dual-kill model can reproduce both the apparent dose-dependence of the clonogen estimates and the high-dose curvature of the dose-response curves. For both series of data the model was a significantly better fit to the data than the standard linear-quadratic model, with no evidence of any systematic lack of fit. The parameters of the clonogenic cell component of the model are consistent with other studies that suggest a low clonogen number (somewhat less than five) per crypt. The model implies that there is a secondary mechanism decreasing clonogen survival, and hence increasing clonogen number estimates, at high doses. The mechanisms underlying the modification of the dose-response are unclear, and the implied mechanisms of, for example, slow growth, induced either directly in the surviving cells or indirectly through stromal injury or bystander effects are only speculative. Nevertheless, the model fits the data well, demonstrating that there is greater kill at high doses in these experimental series than would be expected from the conventional linear-quadratic model. This alternative model, or another model with similar behaviour, needs to be considered when analysing in detail and interpreting microcolony data as a function of dose. The implied low number of < or = 5 of these regenerative and relatively radioresistant clonogenic cells is distinct from a similar number of much more radiosensitive precursor stem cells which undergo early apoptosis after doses around 1 Gy.     

The decay of autoradiographic grain number over crypt base columnar cells in murine ileum as a measure of their generation time

The decay in the number of grains over [3H]-thymidine labelled crypt base columnar cells (BCC) in autoradiographs of the ileum of BDF1 mice has been studied. The results revealed that using the conventional grain count halving (GCH) method it is possible to obtain an estimation of the generation time (Tc) of the proliferative BCC cells in the Paneth cell zone (PC-zone) of 18.8 +/- 0.74 h. This lies within the range obtained by the percent labelled mitoses (PLM) method, but is shorter than most values obtained by stathmokinetic methods. The present data show no evidence for a shortening of the cell cycle 3 days after irradiation (8 Gy) which is contrary to some earlier observations. Some reasons for this discrepancy are discussed. The comparatively high labelling index of the BCC allows a larger amount of data to be easily collected, compared with the PLM technique, and correction factors which take into account the complicated shape of the bottom of the crypt are not required.     

Evaluation of standard error and confidence interval of estimated multilocus genotype probabilities, and their implications in DNA forensics.

Multilocus genotype probabilities, estimated using the assumption of independent association of alleles within and across loci, are subject to sampling fluctuation, since allele frequencies used in such computations are derived from samples drawn from a population. We derive exact sampling variances of estimated genotype probabilities and provide simple approximation of sampling variances. Computer simulations conducted using real DNA typing data indicate that, while the sampling distribution of estimated genotype probabilities is not symmetric around the point estimate, the confidence interval of estimated (single-locus or multilocus) genotype probabilities can be obtained from the sampling of a logarithmic transformation of the estimated values. This, in turn, allows an examination of heterogeneity of estimators derived from data on different reference populations. Applications of this theory to DNA typing data at VNTR loci suggest that use of different reference population data may yield significantly different estimates. However, significant differences generally occur with rare (less than 1 in 40,000) genotype probabilities. Conservative estimates of five-locus DNA profile probabilities are always less than 1 in 1 million in an individual from the United States, irrespective of the racial/ethnic origin.     

On the significance of sequence alignments when using multiple scoring matrices

MOTIVATION: Pairwise local sequence alignment is commonly used to search data bases for sequences related to some query sequence. Alignments are obtained using a scoring matrix that takes into account the different frequencies of occurrence of the various types of amino acid substitutions. Software like BLAST provides the user with a set of scoring matrices available to choose from, and in the literature it is sometimes recommended to try several scoring matrices on the sequences of interest. The significance of an alignment is usually assessed by looking at E-values and p-values. While sequence lengths and data base sizes enter the standard calculations of significance, it is much less common to take the use of several scoring matrices on the same sequences into account. Altschul proposed corrections of the p-value that account for the simultaneous use of an infinite number of PAM matrices. Here we consider the more realistic situation where the user may choose from a finite set of popular PAM and BLOSUM matrices, in particular the ones available in BLAST. It turns out that the significance of a result can be considerably overestimated, if a set of substitution matrices is used in an alignment problem and the most significant alignment is then quoted. RESULTS: Based on extensive simulations, we study the multiple testing problem that occurs when several scoring matrices for local sequence alignment are used. We consider a simple Bonferroni correction of the p-values and investigate its accuracy. Finally, we propose a more accurate correction based on extreme value distributions fitted to the maximum of the normalized scores obtained from different scoring matrices. For various sets of matrices we provide correction factors which can be easily applied to adjust p- and E-values reported by software packages.     

Addressing Temporal Variability in Bird Calling with Design and Estimation: A Northern Bobwhite Example

Imprecise or biased density estimates can lead to inadequate conservation action, overexploitation of game species, or lost recreational opportunities. Common approaches to estimating density of avian populations often either ignore the probability that an individual is present within the sampling area but is not available to be sampled (e.g., not vocalizing), or do not consider covariates that could influence availability. Additionally, management decisions made at the management unit scale are often informed by inadequate monitoring practices, such as limited sampling intensity. In such cases, management agencies calculate density by applying correction factors (e.g., detection probabilities estimated using empirical data from a different study system) to count data, rather than estimating a detection function directly using statistical models. We conducted a simulation study using northern bobwhite (Colinus virginianus; bobwhite) as a model species to quantify the consequences of mis-specifying avian point count models on bias and precision of density estimates. We compared bias and precision of estimates from a fully specified distance-sampling model that estimates availability and detection to 4 different mis-specified approaches, including 2 approaches to calculating density using correction factors. Using correction factors to calculate density produced estimates with low bias but relatively lower precision compared to the fully specified model (CV of density estimates at 35 sites over 5 years: fully specified = 10%, correction factors = 25% and 30%). Although the mean precision and bias of the fully specified model improved with more data (70 sites over 5 years, CV = 9%; 35 sites over 10 years, CV = 9%), precision of correction factors did not (70 sites over 5 years, CV = 22% and 27%; 35 sites over 10 years, CV = 24% and 29%). The fully specified model captured the underlying temporal variation in detection and availability. Increasing sampling duration from 5 to 10 years improved modeled estimates of growth rate, even for mis-specified models, but not derived growth rates using pre-determined detection functions. We demonstrated that conducting point counts 3 times/year at a feasible number of sites can produce relatively unbiased estimates of bobwhite density. Pre-determined detection functions can be fortuitously unbiased for certain years, but they are not a reliable method for determining density or identifying trends in density over time. © 2020 The Wildlife Society.     

Reliability of aneuploidy estimates in human sperm: Results of fluorescence in situ hybridization studies using two different scoring criteria

Aneuploidy estimates for chromosomes 1, 12, X, and Y were obtained in human sperm from five donors using multicolor fluorescence in situ hybridization (FISH) analysis. Disomy frequencies were obtained by scoring a minimum of 10,000 sperm for each chromosome probe per donor. This analysis was replicated for two scoring criteria: one used one half of a signal domain as the minimum distance between two signals to be counted as two and thus disomic; the other set one signal domain as the minimum distance between two signals. A total of 120,870 sperm were assessed using one half of a domain as the criterion, and 113,478 were scored using one domain as the criterion. The percentage of disomy for chromosomes 1, 12, X, Y, and XY was 0.18, 0.16, 0.15, 0.19, and 0.25, respectively, using the one-half-domain criterion, and 0.08, 0.17, 0.07, 0.12, and 0.16, respectively, using the one-domain criterion. The percentage of disomy decreased significantly with use of one domain as the minimum distance for signal separation for all chromosomes except for chromosome number 12. These lower disomy frequencies correlated well with frequencies derived from human sperm karyotypes analyzed in our laboratory. This suggests that the fluorescent signals for chromosomes 1, X, and Y split into more than one domain in decondensed interphase sperm, and that the use of the one-half-domain criterion would lead to an overestimate of aneuploidy frequencies. The factors known to affect aneuploidy estimates derived from FISH studies are discussed, and recommendations for stringent scoring criteria are proposed. © 1995 wiley-Liss, Inc.     

Bias and Sampling Error of the Estimated Proportion of Genotypic Variance Explained by Quantitative Trait Loci Determined From Experimental Data in Maize Using Cross Validation and Validation With Independent Samples

Cross validation (CV) was used to analyze the effects of different environments and different genotypic samples on estimates of the proportion of genotypic variance explained by QTL (p). Testcrosses of 344 F(3) maize lines grown in four environments were evaluated for a number of agronomic traits. In each of 200 replicated CV runs, this data set was subdivided into an estimation set (ES) and various test sets (TS). ES were used to map QTL and estimate p for each run (p(ES)) and its median (p(ES)) across all runs. The bias of these estimates was assessed by comparison with the median (p(TS.ES)) obtained from TS. We also used two independent validation samples derived from the same cross for further comparison. The median p(ES) showed a large upward bias compared to p(TS.ES). Environmental sampling generally had a smaller effect on the bias of p(ES) than genotypic sampling or both factors simultaneously. In independent validation, p(TS.ES) was on average only 50% of p(ES). A wide range among p(ES) reflected a large sampling error of these estimates. QTL frequency distributions and comparison of estimated QTL effects indicated a low precision of QTL localization and an upward bias in the absolute values of estimated QTL effects from ES. CV with data from three QTL studies reported in the literature yielded similar results as those obtained with maize testcrosses. We therefore recommend CV for obtaining asymptotically unbiased estimates of p and consequently a realistic assessment of the prospects of MAS.     

Bias and Sampling Error of the Estimated Proportion of Genotypic Variance Explained by Quantitative Trait Loci Determined From Experimental Data in Maize Using Cross Validation and Validation With Independent Samples.

Cross validation (CV) was used to analyze the effects of different environments and different genotypic samples on estimates of the proportion of genotypic variance explained by QTL (p). Testcrosses of 344 F(3) maize lines grown in four environments were evaluated for a number of agronomic traits. In each of 200 replicated CV runs, this data set was subdivided into an estimation set (ES) and various test sets (TS). ES were used to map QTL and estimate p for each run (p(ES)) and its median (p(ES)) across all runs. The bias of these estimates was assessed by comparison with the median (p(TS.ES)) obtained from TS. We also used two independent validation samples derived from the same cross for further comparison. The median p(ES) showed a large upward bias compared to p(TS.ES). Environmental sampling generally had a smaller effect on the bias of p(ES) than genotypic sampling or both factors simultaneously. In independent validation, p(TS.ES) was on average only 50% of p(ES). A wide range among p(ES) reflected a large sampling error of these estimates. QTL frequency distributions and comparison of estimated QTL effects indicated a low precision of QTL localization and an upward bias in the absolute values of estimated QTL effects from ES. CV with data from three QTL studies reported in the literature yielded similar results as those obtained with maize testcrosses. We therefore recommend CV for obtaining asymptotically unbiased estimates of p and consequently a realistic assessment of the prospects of MAS.     

Simulated Sampling Strategies for Nematodes Distributed According to a Negative Binomial Model

A FORTRAN computer program was developed to simulate nematode soil sampling strategies consisting of various numbers of samples per field, with each sample consisting of various numbers of soil cores. The program assumes that the nematode species involved fit a negative binomial distribution. Required input data are estimates of the mean and k values, the number of samples per field and cores per sample in the strategy to be investigated, and the number of times the simulation is to be replicated. Output consists of simulated values of the relative deviation from the mean and standard error to mean ratio, both averaged over all replications. The program was used to compare 150 simulated sampling strategies for Meloidogyne incognita, involving all combinations of two mean values (2.0 and 10.0 la.rvae/10 cm³ soil), three k values (1.35, 0.544, and 0.294), five different numbers of samples per field (1, 2, 4. 10, 20), and five different numbers of cores per sample (1, 2, 4, 10, 20). Simulations resulting from different mean values were similar, but best results were obtained with higher k values and 20 cores per sample. Relatively few 20-core samples were needed to obtain average deviations from the mean of 20-25%.     

The effect of reducing the number of cells scored on the performance of the in vivo rat liver UDS assay

The most labour-intensive feature of the in vivo rat liver UDS assay is the scoring of hepatocyte autoradiograms by microscope. Even with image analyser and computer equipment the scoring phase of a full study might require half of the technical effort applied. Practice recommended by guidelines has been to score 50 cells/slide and two slides per animal. Now sufficient data have been accumulated, an evaluation was made to observe whether this procedure was necessary. An analysis of the accumulated UDS database in our laboratory was made to determine the sources of variability of mean net nuclear grain count, [N - C]. It was observed that the two largest components of variation in negative control animal mean [N - C]. were between-day and interanimal variability. The contribution from sampling error during slide scoring was relatively small. Theoretical calculations showed that the greater sampling error derived from scoring 30 rather than 50 cells/slide would result in only a marginal increase in total assay variation. To test this, 30 cells/slide were randomly selected from the 50 cells scored originally in negative control animals in each of 18 studies over an 18-month period. It was confirmed that reducing the number of cells had a negligible effect on the variation of negative control animal mean [N - C] values. Furthermore, analysis of data from 10 more studies confirmed that within-study variation would be essentially unaffected by scoring 30 cells/slide. The use of 30 rather than 50 cells per slide (a total of 60 cells per animal) has therefore been adopted for all current studies and scoring procedures modified to avoid operator bias during the selection of a smaller number of cells.     

Estimating major gene effects with partial information using Gibbs sampling

A method for estimating major gene effects using Gibbs sampling to infer genotype of individuals with unknown values, was compared with a standard mixed-model analysis. The purpose of this study was to evaluate the effect of including information of individuals with unknown genotypes on the estimates and their error variances (Ve) of the single-gene effects. When genotypes were known for all the individuals, results using the Gibbs method (GS) were similar to those obtained with the mixed model (MM). In the absence of selection, when information from individuals with unknown genotypes was included, GS yielded unbiased estimates of the major gene effects while reducing the Ve associated with them. This reduction in Ve depended on the gene frequency and mode of action of the major locus. For the additive effect, the reduction in Ve ranged from 29 to 69% of the total reduction which would have been obtained if all individuals had had a known genotype. Similarly the reduction in Ve found for the dominance effect ranged from 12 to 58%. Estimates using GS generally had small detectable biases when the polygenic heritability used in the analysis was inflated or estimated simultaneously. However, the benefit of using information from individuals with unknown genotypes was still maintained when comparing the mean square error of the estimates using either GS or MM when genotypes are only known for a subset of the population. When the population has been under selection, the use of Gibbs sampling to incorporate information of individuals without genotypes reduced substantially the bias and mean square error found for MM analysis on partial data. Nevertheless, there was some bias detected using Gibbs sampling. The gene frequency of the major gene in the base population was also well estimated despite its change over generations due to selection.     

Evaluating Methods to Correct for Population Stratification when Estimating Paternity Indexes

The statistical interpretation of the forensic genetic evidence requires the use of allelic frequency estimates in the reference population for the studied markers. Differences in the genetic make up of the populations can be reflected in statistically different allelic frequency distributions. One can easily figure out that collecting such information for any given population is not always possible. Therefore, alternative approaches are needed in these cases in order to compensate for the lack of information. A number of statistics have been proposed to control for population stratification in paternity testing and forensic casework, Fst correction being the only one recommended by the forensic community. In this study we aimed to evaluate the performance of Fst to correct for population stratification in forensics. By way of simulations, we first tested the dependence of Fst on the relative sizes of the sub-populations, and second, we measured the effect of the Fst corrections on the Paternity Index (PI) values compared to the ones obtained when using the local reference database. The results provide clear-cut evidence that (i) Fst values are strongly dependent on the sampling scheme, and therefore, for most situations it would be almost impossible to estimate real values of Fst; and (ii) Fst corrections might unfairly correct PI values for stratification, suggesting the use of local databases whenever possible to estimate the frequencies of genetic profiles and PI values.     

The re-establishment of hypersensitive cells in the crypts of irradiated mouse intestine

Within 3-6 h of small doses of radiation (gamma-rays) the number of dead cells (apoptotic cells) in the crypts of the small intestine reaches peak values. These return to normal levels only after times later than 1 day. After higher doses elevated levels of cell death persist for longer times. The dead cells first occur most frequently at the lower positions of the crypt (median value for the distribution of apoptotic fragments is about cell position 6). At later times more dead cells are observed at higher positions. Two doses of radiation separated by various time intervals have been used to investigate when after irradiation the cell population susceptible to acute cell death is re-established. Dead cells were scored 3 or 6 h after the second dose. The yield of dead cells after two doses represents the sum of the dead cells produced by, and persisting from, the first dose and new apoptotic cells induced by the second dose. Since the temporal and dose-dependence aspects of the dead-cell yield after the first dose alone is known, the additional dead cells attributable to the second dose alone can be determined by subtraction. Within 1-2 days of small doses (0.5 Gy) the sensitive cells, recognized histologically as apoptotic cells, are re-established at the base of the crypt (around cell position 6). After higher doses (9.0 Gy) they are not re-established until about the fourth day after irradiation. Even in the enlarged regenerating crypts the sensitive cells are found at the same position at the crypt base. It has been estimated that the crypt contains five or six cells that are susceptible to low doses (0.5 Gy) (hypersensitive cells) and up to a total of only seven or eight susceptible cells that can be induced by any dose to enter the sequence of changes implicit in apoptosis. Between 4 and 10 days after an initial irradiation of 9.0 Gy the total number of susceptible cells increased from seven to eight to about 10 to 13 per crypt.