The authors have declared that no competing interests exist.
Conceived and designed the experiments: IS ED. Performed the experiments: IS ED. Analyzed the data: IS. Contributed reagents/materials/analysis tools: IS ED. Wrote the paper: IS ED.
Microbial population responses to combined effects of chronic irradiation and other stressors (chemical contaminants, other sub-optimal conditions) are important for ecosystem functioning and bioremediation in radionuclide-contaminated areas. Quantitative mathematical modeling can improve our understanding of these phenomena. To identify general patterns of microbial responses to multiple stressors in radioactive environments, we analyzed three data sets on: (1) bacteria isolated from soil contaminated by nuclear waste at the Hanford site (USA); (2) fungi isolated from the Chernobyl nuclear-power plant (Ukraine) buildings after the accident; (3) yeast subjected to continuous γ-irradiation in the laboratory, where radiation dose rate and cell removal rate were independently varied. We applied generalized linear mixed-effects models to describe the first two data sets, whereas the third data set was amenable to mechanistic modeling using differential equations. Machine learning and information-theoretic approaches were used to select the best-supported formalism(s) among biologically-plausible alternatives. Our analysis suggests the following: (1) Both radionuclides and co-occurring chemical contaminants (e.g. NO2) are important for explaining microbial responses to radioactive contamination. (2) Radionuclides may produce non-monotonic dose responses: stimulation of microbial growth at low concentrations vs. inhibition at higher ones. (3) The extinction-defining critical radiation dose rate is dramatically lowered by additional stressors. (4) Reproduction suppression by radiation can be more important for determining the critical dose rate, than radiation-induced cell mortality. In conclusion, the modeling approaches used here on three diverse data sets provide insight into explaining and predicting multi-stressor effects on microbial communities: (1) the most severe effects (e.g. extinction) on microbial populations may occur when unfavorable environmental conditions (e.g. fluctuations of temperature and/or nutrient levels) coincide with radioactive contamination; (2) an organism’s radioresistance and bioremediation efficiency in rich laboratory media may be insufficient to carry out radionuclide bioremediation in the field—robustness against multiple stressors is needed.
Understanding radionuclide effects on non-human biota is important for environmental protection and bioremediation after accidental (e.g. from nuclear power plants or waste storage facilities) or malicious (“dirty bomb” attacks) radionuclide releases [
The objective of this paper is to use quantitative mathematical modeling to identify general patterns of microbial responses to radioactive contamination. Understanding and predicting such patterns can guide research on environmental protection and bioremediation after radionuclide releases [
Unfortunately, data on multi-stressor combinations involving chronic ionizing radiation exposure are limited [
The first data set was generated by bacteriological analysis of vadose sediments located under a high-level radioactive waste storage tank at the Hanford site, near Richland, Washington [
We used this information (presented mainly in Tables 1 and 3 and in Figs. 1 and 2 of reference [
Using this data set we sought to evaluate whether the toxicity of nuclear waste to soil bacteria was driven mainly by radionuclides (137Cs, 99Tc), or whether chemical toxicants (Cr, NO3, NO2) were also important. In addition, we sought to evaluate how variability of responses to the various toxicants among different bacterial taxa could affect community composition in contaminated soil: for example, would the most radioresistant taxa gain a competitive advantage over radiosensitive ones.
The second data set was generated by mycological analysis of 24 samples collected within the Chernobyl nuclear power plant buildings 11–12 years after the accident [
Using this data set, we sought to evaluate how the approximately 10-fold difference in radiation dose rate within the reactor buildings affected fungal community composition. Specifically, we intended to identify which fungal taxa are most robust under chronic irradiation and oligotrophic conditions, and would therefore be potentially useful as radioactive waste bioremediators.
The third data set was produced by continuous 60Co γ-irradiation of diploid yeast (
In this third data set we sought to investigate how the critical radiation dose rate, above which population extinction occurs, is modulated by an experimentally-controlled adverse factor–the cell removal rate. The liquid culture medium flowed through the chemostat at a constant rate (the dilution rate) fixed by the experimenters. The dilution rate thus represented the cell removal rate, which acted as an additional stressor–an example of unfavorable conditions which increase mortality in the population. Since dilution rate and dose rate were varied independently, the effects of each stressor could be readily assessed and disentangled.
The three data sets were purposely selected to be diverse and to include a wide range of microbial taxa, exposure conditions, and stressors. Our goal was to integrate the analysis results from each data set by formulating general conclusions with potentially broad applicability to environmental protection and radioactive waste bioremediation. We used descriptive and (whenever possible) mechanistic mathematical modeling, which involved machine learning and/or information theoretic model selection, to analyze the three data sets and provide insight into environmental effects of radionuclides combined with other stressors [
We modeled the probability of detecting a given bacterial taxon in each soil sample using logistic regression, where the radionuclides, chemical toxicants and measured soil properties (e.g. conductivity) were the predictor variables. To account for potential differences in how strongly different taxa respond to particular stressors (e.g. 137Cs), we used generalized linear mixed-effects models (GLMMs), which extend logistic regression to include both fixed and random effects. Using matrix notation, GLMM structure is summarized as follows, where logit(
Here,
Because the measured radionuclides (137Cs, 99Tc) and chemical contaminants (Cr, NO3, NO2) were released from the same source (the ruptured nuclear waste tank), their distributions in soil were correlated (e.g. the correlation coefficient of Cr with NO2 was 0.83). Consequently, several different combinations of variables could potentially describe the outcome equally well, and multi-collinearity was a potentially important problem. To identify those variables with the strongest main effects, we employed a customized approach (called, for convenience, the “filter procedure”). This procedure, described in detail in the
We modeled the probability for detection of each fungal species in each sample using the same GLMM approach as described above. Since only one environmental variable–radiation dose rate–was reported, there was no need for the filter procedure. Oligotrophic conditions, which probably had an important impact on fungal growth, were not described in quantitative terms and therefore could not be modeled. Unfortunately, there was no information provided in reference [
We used a GLMM with a fixed effect of radiation (coded as a binary variable: 0 = low and 1 = high dose rate) and random effects (intercepts and slopes) for two taxonomic variables: order and species. The sum of fixed and random effects for each species produced the net model coefficient for radiation effect on the given species. This coefficient was converted to the odds ratio for detection of a given species in high vs. low radiation locations. This predicted odds ratio was compared to the observed odds ratio (with 95% confidence intervals estimated by Fisher’s exact test with Type I error threshold of 0.05). Absolute goodness of fit (GOF) for the GLMMs was assessed by marginal R2, which represents the variance explained by fixed effects, and conditional R2, which represents variance explained by both fixed and random effects (i.e. by the entire model) [
We also investigated whether the lethal dose of acute irradiation, taken from reference [
Since the GLMM analysis does not explicitly account for inter-specific interactions, we calculated the bias-corrected Chao2 species richness estimator [
The endpoints of interest in this data set were: (1) the equilibrium cell concentration, i.e. the number of cells per ml of growth medium when a steady-state of the system has been achieved and no further changes were detectable; and (2) the critical dose rate above which population extinction occurred (i.e. no steady-state could be achieved). To model these endpoints, we used mechanistic approaches, which provides important advantages over purely descriptive ones [
This data set provides detailed information on how a bacterial community, which exists under harsh conditions (in sub-surface sediments with low water content and nutrient concentrations), responded to severe contamination with radionuclides and chemical toxicants [
Eight potential predictor variables for the probability to detect each bacterial taxon (water content, conductivity, temperature, 137Cs, 99Tc, Cr, NO3 and NO2) were identified as having important main effects using machine learning methods implemented as part of the filter procedure described in
The variance inflation factors (VIF) were high (>5) for temperature, Cr and NO3. Consequently, these three variables were removed from the model to alleviate multi-collinearity. The resulting confidence set of fixed-effect models contained only water content, conductivity, 137Cs, 99Tc, and NO2, with VIFs of 1.12, 1.09, 1.10, 1.79, and 1.79, respectively. Multi-model inference (MMI, described in
Cond = conductivity. SE = standard errors of the model coefficients. NA = non-applicable. Details are provided in the main text and in
Variable (units) | MMI using confidence set of fixed-effect models | Best-fitting mixed-effect model | Standard deviation of random effect | |||||
---|---|---|---|---|---|---|---|---|
Impor- tance | Coeffi- cient | SE | p-value | Coeffi- cient | SE | p-value | ||
Water content (%) | 0.57 | -0.0301 | 0.037 | 0.418 | ||||
Cond (mS/cm) | 0.85 | 0.0167 | 0.010 | 0.107 | 0.0215 | 0.008 | 0.008 | NA |
137Cs (μCi/g) | 0.99 | -0.0763 | 0.033 | 0.023 | 0.0247 | |||
99Tc (μCi/L) | 0.62 | -0.0046 | 0.005 | 0.363 | ||||
NO2 (mg/L) | 0.70 | -0.0118 | 0.011 | 0.273 | -0.0160 | 0.007 | 0.021 | NA |
Intercept | NA | –1.9122 | 0.505 | 1.6×10−4 | -2.8369 | 0.337 | 2×10−16 | 0.6181 |
These results suggest that conductivity had a marginally positive effect on bacteria (
The best-supported fixed effect model contained only conductivity, 137Cs and NO2 as predictors. The VIFs for these variables were 1.04, 1.04 and 1.08, respectively. Eight observations (out of 460) exceeded the Cook's distance threshold for outlier data points (defined in
Even though the best-supported fixed-effect model assumes that the responses of all taxa to a given predictor are identical, it achieved fair GOF (R2 = 0.512) and predictive accuracy: area under the Receiver Operating Characteristic (ROC) curve [
A refined modeling approach, which allowed different taxa to respond differently by adding random intercepts and slopes for each predictor, one at a time, produced the best-fitting mixed-effect model. This model, with random effects for 137Cs and baseline abundance (
The y-axis represents: (1) the values of various stressors (bars), normalized (for convenience of presentation) by the maximum measured value within the data set; and (2) presence/absence data (points and lines) for bacterial genera. Two genera were selected in this illustration:
In the best-fitting mixed-effects model, the net regression coefficient for 137Cs (i.e. the sum of fixed and random effects) was negative for most bacterial genera (e.g. -0.0548 g/μCi for
This data set shows that multiple fungal taxa colonized the reactor buildings despite severe radioactive contamination and limited nutrient concentrations [
Analysis of detection probabilities for each fungal species supported the same conclusion. These probabilities [
Analysis of the data for all species using a GLMM suggested that most species isolated from the reactor buildings were more (rather than less) abundant in locations with high dose rates. This can be visualized by examining the observed and best-fit model-predicted odds ratios for detection of each species in high vs. low radiation locations (
Error bars indicate 95% confidence intervals (CIs) calculated by Fisher’s exact test with Type I error threshold of 0.05. The predictions are points, and they are connected by a line just for convenience to guide the eye. No points are shown when odds ratio estimates equaled zero or infinity, but CI bounds are shown in these cases. The species are: 1
The best-fit model coefficient for the fixed effect of increased radiation was positive, rather than negative, but not significantly different from zero: 0.35 (SE: 0.29, P = 0.23). This fixed effect explained very little of the variance: marginal R2 was 0.007. Random effects of radiation explained more, bringing conditional R2 to 0.285. However, this low value suggests that most of the variance remained unexplained and probably resulted from unmeasured factors: e.g. environmental variables other than radiation, interactions between fungal species, etc.
These results were not qualitatively altered when potential correlations between samples were investigated by merging data from randomly-selected samples into clusters of various sizes, and fitting the model to multiple synthetic data sets generated in this manner from the observed data set. The fixed effect of radiation fluctuated around zero, and the predicted odds ratios for detection in high vs. low radiation locations remained > 1 for several species.
At the most extreme case of inter-sample correlation (when the data from all samples at low dose rate were merged into a single presence/absence value and the same was done to all samples at high dose rate, reducing the data set to only two presence/absence values for each species), the coefficient for the fixed effect of increased radiation became negative, but not significantly different from zero: –0.66 (SE: 4.8, P = 0.89). Again, this fixed effect explained very little of the variance: marginal R2 was < 10−4. In contrast, random effects of order and species on the response to radiation explained most of the variance of this reduced data set, bringing conditional R2 to 0.998. Predicted odds ratios for detection in high vs. low radiation locations remained > 1 for 9 species:
The lethal dose of acute irradiation (in kGy), taken from reference [
This data set shows how the maximum radiation dose rate that a population can tolerate depends on another stressor–cell removal rate by chemostat dilution [
Solid circles are measurements of the equilibrium yeast cell concentration, which represents the steady-state number of cells/ml attained in the chemostat after multiple yeast generations (error bars are 95% CIs). Open squares are measurements of the critical dose rate above which the population became extinct. Solid curves are best-fit model predictions (from the best-supported model M1,
Details are provided in the main text and in
Model | Description | Mathematical expression for (dN/dt)/N | ΔAICc | |
---|---|---|---|---|
M1 | basic formalism with cell killing and suppression of proliferation by radiation | – |
0.00 | 0.544* |
M2 | radiation increases intraspecific competition | – |
3.37 | 0.096 |
M3 | dilution rate decreases radiation effect on cell proliferation | – |
3.83 | 0.076 |
M4 | radiation effect on cell proliferation is non-exponential | – |
4.08 | 0.067 |
M5 | dilution rate decreases cell killing by radiation | – |
4.74 | 0.048 |
M6 | cell killing by radiation is linear-quadratic | – |
5.29 | 0.037 |
M7 | intraspecific competition is affected by interaction of dilution rate with radiation | – |
5.44 | 0.034 |
M8 | radiation effect on cell proliferation is linear-quadratic | – |
5.52 | 0.033 |
M9 | radiation stimulates cell proliferation at low dose rates | – |
5.81 | 0.028 |
M10 | radiation increases intraspecific competition, but no radiation-independent cell proliferation rate component | – |
7.02 | 0.015 |
M11 | radiation increases intraspecific competition, but no cell killing by radiation | – |
8.68 | 0.007 |
M12 | radiation effect on intraspecific competition is linear-quadratic | – |
8.72 | 0.007 |
M13 | with separate non-exponential radiation effects on cell proliferation rate components | – |
9.91 | 0.004 |
M14 | dilution rate decreases radiation effects on cell proliferation and intraspecific competition | – |
10.07 | 0.003 |
M15 | with negative effect of dilution rate on cell killing by radiation and on intraspecific competition | – |
12.21 | 0.001 |
M16 | radiation effects are linear-quadratic for cell killing and for proliferation | – |
12.75 | 0.001 |
M17 | no direct killing by radiation | – |
18.61 | 0.000 |
M18 | no radiation-independent cell proliferation rate component | – |
23.17 | 0.000 |
M19 | radiation increases intraspecific competition, but no radiation effect on cell proliferation | – |
26.86 | 0.000 |
M20 | no radiation effect on cell proliferation | – |
33.28 | 0.000 |
Direct cell killing by radiation (parameter
There was little support for quadratic terms for radiation effects on cell killing (models M6, M16,
There was some support for effects of radiation and/or dilution rate on intraspecific competition: the sum of Akaike weights [
The parameter values for the best-supported model M1 were quite robust to random modification of the data set:
Combined predictions from all models generated by MMI were numerically very similar to those of the best-supported model M1. Consequently, both model M1 and MMI suggested the following conclusions:
The critical dose rate decreased rapidly and non-linearly with increasing dilution rate (
Details of the methods used are provided in
The critical dose rate was sensitive to radiation-induced cell killing (parameter
When one parameter was increased, all others were held constant at best-fit values. The
Taken together, the results of our analysis of three diverse data sets by descriptive and mechanistic mathematical modeling approaches demonstrate that microbial population responses to radioactive contamination can be strongly influenced by additional stressors. These stressors, such as chemical toxicants, should be taken into consideration when predicting radionuclide effects on the environment [
Specifically, analysis of data set one revealed that the nuclear waste at Hanford had strong toxic effects on soil bacteria. However, much of these effects were caused by chemical contaminants (e.g. NO2) rather than by radionuclides. Radiation from radionuclides (e.g. 137Cs) probably provided a competitive advantage for taxa with the highest resistance to radiation and oxidative stress (e.g.
The results for data set two suggest that chronic irradiation can potentially produce non-monotonic dose response shapes: the probability to detect some (or even most) fungal species within the Chernobyl reactor buildings was predicted to increase (rather than decrease) with increasing radiation dose rate (within the range of dose rates represented in this data set). These findings are consistent with previously reported stimulation of directional growth and/or proliferation of some fungi by chronic irradiation [
Mutation rates in fungi within reactor buildings were probably elevated [
Analysis of data set three showed that the presence of additional stressors, such as a high cell mortality (removal) rate due to factors other than radiation, lowers by several-fold the critical radiation dose rate, which precipitates population extinction. In addition, reproduction suppression by radiation can be more important for determining the critical dose rate, than radiation-induced cell mortality.
The conclusions drawn from analyzing these three data sets quantitatively support the following generalizations, which could be useful for environmental protection and radionuclide bioremediation [
First, the most severe effects (e.g. extinction) on microbial populations may occur when unfavorable environmental conditions (e.g. fluctuations of temperature and/or nutrient levels) coincide with radioactive contamination. For example, certain microbial species may persist in contaminated areas for some time, but become extinct when conditions become harsher due to seasonal and/or random factors. Consequently, to predict the long-term responses of such communities to radioactive contamination, it may be insufficient to measure radiation toxicity to the target organisms under laboratory conditions, or even under typical field conditions–measurements under the worst expected conditions (i.e. when non-radiation stressors attain maximal values) may be needed.
Second, to identify promising candidates for microbial bioremediation of radioactive wastes, it may be insufficient to screen only for radioresistance and/or efficiency in remediating certain chemicals–robustness against multiple stressors may be required to carry out bioremediation in the field. For example, many organisms which can grow in rich laboratory media with high radionuclide concentrations [
The strengths of the present study include rigorous quantitative analysis intended to identify parsimonious explanations for how radiation and other stressors affected bacterial and fungal taxa under both field and laboratory conditions. State of the art descriptive and mechanistic methods, which incorporate elements of machine learning [
The limitations of this study result from the properties of the data sets. For example, in data set one only a single contaminated site was sampled and, therefore, there is no guarantee that this site is representative. In data set two, many potentially relevant environmental variables (e.g. spatial locations of samples, temperature, pH) were not reported. In data set three, sample size was limited and results of replicate experiments at each stressor combination were not reported.
The limitations of the data sets resulted in unavoidable limitations of the methodology used to analyze them. In particular, the large number of taxa and/or stressors in data sets one and two prevented mechanistic modeling and we therefore relied on descriptive approaches, although in principle we believe that mechanistic models provide advantages over statistical ones [
Despite these limitations, we believe that our analysis of three diverse data sets provides useful insight into the important role of chemical and environmental stressors in determining the responses of microbial populations to radioactive contamination and might help to select the best microbial candidates for use in bioremediation.
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We are very grateful to Dr. Halim E. Lehtihet for instructive comments on the manuscript.