Nanxi
Lu†
^{a},
Arash
Massoudieh
*^{b},
Xiaomeng
Liang
^{b},
Tamir
Kamai
^{c},
Julie L.
Zilles
^{a},
Thanh H.
Nguyen
^{a} and
Timothy R.
Ginn
^{d}
^{a}Department of Civil and Environmental Engineering, University of Illinois, Urbana–Champaign, USA
^{b}Department of Civil Engineering, The Catholic University of America, Washington DC, USA. E-mail: arashmassoudieh@gmail.com
^{c}Institute of Soil, Water and Environmental Sciences, Agricultural Research Organization, Bet Dagan, Israel
^{d}Department of Civil and Environmental Engineering, University of California, Davis, USA

Received
28th January 2015
, Accepted 9th March 2015

First published on 12th March 2015

Horizontal gene transfer allows antibiotic resistance and other genetic traits to spread among bacteria in the aquatic environment. Despite this important role, quantitative models are lacking for one mechanism of horizontal gene transfer, which is natural transformation. The rates of horizontal gene transfer of a tetracycline resistance gene through natural transformation were experimentally determined for motile and non-motile strains of Azotobacter vinelandii. We developed a mathematical model adapted from the mass action law that successfully described the experimentally determined rates of natural transformation of a tetracycline resistance gene for motile and non-motile strains of Azotobacter vinelandii. Transformation rates showed a rapid initial increase, followed by a decrease in the first 30 minutes of the experiment, and then a constant rate was maintained at a given cell and DNA concentration. The proposed model also described the relationship between transformation frequency and varied DNA or cell concentrations. The modeling results revealed that under the given experimental conditions, the gene transformation rate was limited both by the abundance of the tetracycline resistance gene and by cellular activities associated with cell–DNA interactions. This work establishes a quantitative model of natural transformation, suggests a need to further investigate the cell properties affecting transformation rates, and provides a basis for development of comprehensive models of horizontal gene transfer and quantitative risk assessment of antibiotic resistance gene dissemination in the aquatic environment.

## Water impactAntibiotic resistance is an important water quality issue that is compounded by horizontal gene transfer among microorganisms. Among the known mechanisms of horizontal gene transfer, only natural transformation, the uptake and expression of extracellular DNA, lacks a quantitative model. This manuscript presents the first quantitative model of natural transformation, based on experimental data obtained with a tetracycline resistance gene and the model bacterium Azotobacter vinelandii. We found that only a small fraction of DNA participates in the transformation, and the rate is controlled by the abundance of the resistance gene. Our results contribute to the development of comprehensive models for horizontal gene transfer, providing a basis for understanding and ultimately risk assessment of antibiotic resistance dissemination in the aquatic environment. |

Natural transformation requires extracellular DNA and competent cells, both of which are present in sediments and soils.^{5–8} There is limited knowledge of natural transformation in aquatic systems, but aquatic biofilms and sediment microbial communities where conjugation is important also provide appropriate conditions for natural transformation.^{1} Despite being adsorbed on environmental surfaces,^{6,7,9} extracellular DNA is still accessible to microorganisms, as has been documented for Pseudomonas stutzeri,^{10}Bacillus subtilis,^{11} and Azotobacter vinelandii.^{12,13} The development of competence is typically regulated by bacteria, and hence the availability of competent cells depends on the growth conditions.^{5} In the current work, A. vinelandii was used as the model organism because it is environmentally relevant (native to soil), naturally competent/transformable, non-sequence-specific in its uptake of DNA,^{14} and motile due to its peritrichous flagella.^{15} For A. vinelandii, one condition that induces competence is iron limitation.^{16} Natural transformation rates also typically depend on the concentration of DNA, with the transformation frequency of A. vinelandii leveling off at around 0.1 μg of DNA per 10^{7} cells.^{17}

Because transformation requires contact between extracellular DNA and the cell, bacterial motility might also be expected to influence transformation rates. A connection between natural transformation and twitching motility, which is mediated by type IV pili and occurs on a surface, has been documented in multiple microorganisms. However, this connection appears to be due to an involvement of some of the components of the pilus in DNA uptake, rather than an effect of movement.^{18} Although flagellar motility affects bacterial transport and deposition,^{19–22} to our knowledge, the effect of flagellar motility on natural transformation frequencies or rates has not been examined previously.

Several models have been developed to describe rate-limited conjugation.^{23–26} Most of these models are based on the mass action relationship proposed by Levin et al.,^{23} where it is assumed that the gene transfer rate is proportional to the product of local donor and recipient cell number densities. Subsequent modifications have added plasmid transfer from newly formed transconjugants,^{27} growth and decay of donors, recipients and transconjugants,^{26} and consideration of mating pair formation, donor recovery, and transconjugant maturation times.^{28,29} In more recent modeling studies, the impacts of attachment to surfaces, biofilm formation, and heterogeneity on conjugation have been incorporated into models based on Levin's mass action transfer.^{25,30–33}

However, conjugation does not always follow Levin's mass action model (e.g.ref. 34); instead, a brief period of rapid conjugation may be observed after which no further increase in the number of transconjugants follows. Turner^{35} showed that the conjugation rate of plasmid pB15 in E. coli in poorly mixed environments was not linearly proportional to the recipient cell density. Ponciano et al.^{32} considered the conjugation rate to be not linearly dependent on the recipient density but via a Monod-type relationship, while Zhong et al.^{36} considered mating pair formation as an intermediate step and a rate limiting process in conjugative transfer. Kinetic models for transduction have also been developed.^{37,38}

The kinetics of horizontal gene transfer through natural transformation has not, to our knowledge, been modeled quantitatively. Also, although the impact of bacterial motility on the rate of conjugation has been recognized,^{34} to our knowledge, no studies have compared the natural transformation rates of motile vs. non-motile bacteria. These knowledge gaps limit our ability to understand and predict the fate and transport of genes in the environment, whether these genes encode beneficial or harmful traits. In this study, we developed a new kinetic model of transformation, built from models of conjugation but included dynamically changing available DNA, and applied the new model to transformation data collected under controlled laboratory conditions. This new model was used to test the hypothesis that DNA limitation is the controlling factor in the rate. Our experiments also used different strains of A. vinelandii to specifically investigate the effects of flagellar motility.

Three sets of natural transformation experiments with dissolved DNA were conducted to investigate the influence of cell concentration, DNA concentration, and transformation time. In the first set, the cell concentration was varied from 3.7 × 10^{7} to 9.8 × 10^{8} cells per mL and from 6.0 × 10^{7} to 8.7 × 10^{8} cells per mL for DJ and DJ77, respectively. The cell concentration range between 3.0 × 10^{7} to 1.0 × 10^{9} cells per mL allows transformant detection. The DNA concentration was held constant at 0.25 μg mL^{−1} and the transformation time was 30 min. The second set was carried out with varying DNA concentrations from 0.00025 to 2.5 μg mL^{−1} for both recipient strains. For these experiments, the cell concentration averaged 1.0 × 10^{7} ± 8.2 × 10^{6} cells per mL for DJ (± standard deviation, n = 20) and 7.8 × 10^{6} ± 3.3 × 10^{6} cells per mL for DJ77 (± standard deviation, n = 20). These biological replicates differed in their transformation time, 15 min and 30 min. The final set was conducted with transformation times ranging from 0 to 90 min and with 0.25 μg_{DNA} mL^{−1}. In the first biological replicates (panels a and c), the cell concentrations were 3.4 × 10^{7} ± 2.8 × 10^{7} cells per mL for DJ (± standard deviation, n = 20) and 4.6 × 10^{7} ± 8.6 × 10^{6} cells per mL for DJ77 (± standard deviation, n = 20). In the second replicates (panels b and d), the cell concentrations were 1.7 × 10^{8} ± 2.5 × 10^{7} cells per mL for DJ (± standard deviation, n = 12) and 1.7 × 10^{8} ± 3.7 × 10^{7} cells per mL for DJ77 (± standard deviation, n = 12).

Considering that only a fraction of genomic DNA fragments hold the tetracycline resistance gene required for detection of a transformation event in our assay, Levin's mass action model can be applied to express the temporal change in the concentration of transformants as:

(1) |

(2) |

The value of α is the fraction of the tetracycline resistance gene that was eventually expressed in the cells over the total DNA, and the value of β is the ratio of bacterial cells involved in transformation to the number of viable cells. The balance equations for D and C can be written as:

αD = αD_{0} − T | (3a) |

βC = βC_{0} − T | (3b) |

(4) |

The analytical solution to eqn (4) with the initial condition of T(t = 0) = 0 can be found as:

(5) |

If dimensionless quantities including dimensionless initial concentration of DNA, effective transformation frequency, and dimensionless time are defined respectively as D^{*}_{0} = αD_{0}/βC_{0}, T^{*} = T/βC_{0}, and t^{*} = λtβC_{0}, the dimensionless form of eqn (5) expressing the effective transformation frequency (transformation per unit competent and viable cell concentration) can be written as:

(6) |

Based on eqn (5) and (6), when βC_{0} ≫ αD_{0}, the ultimate concentration of transformed cells will be equal to αD_{0} and when βC_{0} ≪ αD_{0}, the ultimate number concentration will be equal to βC_{0}. Fig. 1 provides a graphical depiction of the variation of effective transformation frequency as a function of D^{*}_{0} and t^{*}. When D < 1, the limiting transformed cell concentration at t^{*} ≫ 1 approaches D^{*}_{0} which indicates DNA limitation and it approaches 1 (i.e. T = βC_{0}) when D^{*} > 1, representing cell limiting conditions.

Fig. 1 Typical variation of transformation frequency as a function of dimensionless transferable DNA number concentration and dimensionless time. |

Due to the uncertainties associated with the measured viable cell and transformed cell concentrations, there are also uncertainties associated with the maximum likelihood estimates of the model parameters. To assess these uncertainties, a Bayesian inference using the Markov Chain Monte Carlo (MCMC) approach was employed to find the joint probability distributions of the model parameters. Assuming conditional independence of observed transformant concentrations, non-informative priors for the parameters, and log-normal and multiplicative error structures, the posterior distribution of the model parameters can be written as:^{44}

(7) |

The Metropolis–Hastings MCMC algorithm^{45} was used to sample from the posterior distribution. The algorithm draws a large number of samples from the posterior distribution (eqn (5)).

The plot of transformation frequency versus time shows that the transformation frequencies increased rapidly at the beginning, and then the increase slowed down, stabilizing after about 30 minutes for both biological replicates of both strains (Fig. 4). The plateau in transformation frequency versus time occurred at a lower transformation frequency than expected; several hypotheses were investigated to explain this observation. One hypothesis was that this lower plateau was due to the loss of competence. This hypothesis was tested by incubating competent cells under the reaction conditions but without DNA for varying times before being used in a transformation experiment. Under these conditions, the cells maintained both viability and competence for 48 h, well beyond the duration of the experiments described here, disproving this hypothesis. In another hypothesis, we tested the possibility that mixing limitations affected the transformation kinetics. In our standard transformation assay, the transformation reactions were only mixed once, at the beginning of the transformation period. An additional transformation experiment was therefore conducted where a second round of mixing and 30 minute incubation was performed after the initial mixing and incubation. The transformation rate for this case was compared with that for a case where the second set had 30 minutes of incubation without mixing. No statistically significant difference was observed. This rejects the mixing limitation hypothesis. We then considered the hypothesis that the secretion of nucleases from Azotobacter vinelandii competent cells damaged the transforming DNA. Secretion of nucleases was not directly tested here, but a previous report suggests that A. vinelandii does not produce extracellular nucleases during natural transformation.^{46} Considering this information, we hypothesize that the temporal decrease in the transformation rate was a result of depletion of the transforming gene pool. The concave relationship between transformation frequency and time suggested that the transforming genes were consumed given enough time; this result was consistent with the results of the experiments varying either DNA or cell concentrations.

The transformation frequencies were lower for both strains in the second replicate because the viable cell concentrations in the second replicate were higher than those in the first replicate (4.9 and 3.8 times higher for DJ and DJ77, respectively). As observed in the previous cell concentration experiments, the transformation frequency was lower at higher cell concentrations.

Fig. 5 shows the 95% credible intervals (C.I.) and medians of the parameters obtained from the posterior distributions of the model parameters α and λ. The range of values of α was consistent for the experiments with the motile and non-motile strains. This observation agrees with our definition of α as reflecting the fraction of DNA producing detectable transformation events in our assay, which should not be dependent on motility. The highest value of α was around 10^{−6}. Since A. vinelandii possesses a chromosome size of 5365 kb (ref. 47) and that of the tetracycline resistance gene is 1.2 kb, 2 × 10^{−4} genomic DNA would be expected to contain the tetracycline resistance gene. The fact that α was even lower than 2 × 10^{−4} suggests that either not all copies of the genome contain the tetracycline resistance gene or other characteristics of the cells limit the ultimate expression of the tetracycline resistance gene. These characteristics could affect DNA uptake or its subsequent incorporation into the recipient cell genome and the expression for assay detection. The 95% intervals of λ and β are wide, indicating equifinality (i.e., the non-unique combination of the two parameters can result in equally good agreement between modeled and measured values). For the experimental results shown here, a model without β could explain the data, but considering the broader range of cell concentrations in the environment, a cell concentration parameter was included for versatility. As shown in Fig. 5c, the 95% interval value of β varied between almost zero to 0.93 for DJ77 and zero to 0.92 for DJ, with expected average values of ~0.2 and ~0.1, respectively.

In the posterior distributions, β and λ were correlated, which means that a decrease in β and a proportional increase in λ resulted in the same numbers of transformation events. This correlation is due to the fact that the concentration of competent cells did not control the ultimate transformed cell concentrations in these experiments. Fig. 6a shows the 95% confidence interval of the quantity βλ (referred to as the effective transformation rate constant).

Fig. 6b shows the possibility space of β and λ obtained using the outcome of the MCMC analysis and a strong correlation between the posterior distributions of the logarithms of the two parameters is evident. The 95% brackets for the product of the two parameters are much narrower than that for λ, indicating its better identifiability. Theoretically, a narrower confidence interval could be obtained regarding β by conducting the experiments either with a much larger DNA concentration or with a much smaller cell concentration, so that viable and competent cells become the limiting factor of the ultimate transformation frequency. However, this solution was not feasible due to the amount of DNA required and the detection limits in the transformation assay. The βλ value for the two strains overlapped, with the expected average value of βλ for DJ77 roughly two times larger. The p-value for the hypothesis that the βλ for DJ77 is larger than that for DJ (i.e. the probability that the βλ for DJ is larger) was 0.00751. We attribute this difference to the difference in motility between the two strains, rather than to DJ77's Nif^{−} phenotype, because fixed nitrogen was provided throughout the experiment. A motility defect could affect transformation by allowing a longer contact time between the cells and extracellular DNA. However, this difference was not substantial enough to lead to a distinctive model structure.

The modeled transformation frequencies were compared to the experimental results using all measured data (Fig. 7) as well as data from the transformation experiments featuring only cell concentrations (Fig. 2), DNA concentrations (Fig. 3), or transformation kinetics (Fig. 4). The R^{2} values reported in Fig. 7 were calculated based on the log-transformed transformed cell concentrations. Using all of the measured data (Fig. 7), the predicted values are the likeliest parameter sets obtained through minimization of the squared error between measured and modeled data. R^{2} values of 0.92 (DJ) and 0.96 (DJ77) were obtained using the log-transformed modeled and measured transformed cell concentrations. In addition to the proposed model, we tested alternative models including Levin's mass action model without considering the reduction of DNA as well as a few other models where the relationship between the transformation rate and D and C was considered non-linear through power law relationships. The proposed model was able to reproduce the observed data significantly better, as evaluated using R^{2} and the Bayesian information criterion.

Next, we explore the transformation kinetics. Fig. 4 shows modeled and observed transformation kinetics. Since the cell concentrations showed some variation around the target concentrations, each of the points in Fig. 4 is from a different cell concentration. Therefore, we present two modeled transformation frequency curves, one based on the minimum experimental viable cell concentration (the solid curve) and the other one based on the maximum experimental viable cell concentration (the dashed curve). The values of α, β and λ used to generate these plots are the likeliest values obtained through deterministic maximization of the likelihood function.

Considering the effect of cell concentration, in one set of experiments for each strain (DJ and DJ77), the cell concentration was varied by less than one order of magnitude (Fig. 2, panels a and c), while in the second set of experiments (Fig. 2, panels b and d), the cell concentration was varied by about two orders of magnitude from 3.7 × 10^{7} to 9.8 × 10^{8} cells per mL. For both strains, the model describes the decreasing trend in transformation frequency as a result of an increase in the cell concentration well.

Fig. 3 shows modeled vs. measured transformation frequencies in the experiment where the DNA concentrations were varied by four orders of magnitude. Similar to Fig. 7, the model predictions based on the largest and the smallest cell concentrations in each experiment are presented. The sensitivity towards cell concentration is small compared to that towards DNA concentration, indicating DNA limitation. The almost linear (slightly convex) relationship between transformation frequency and DNA concentration is captured by the model.

In aquatic environments, HGT can contribute to the dissemination of antibiotic resistance genes, virulence genes, and new biodegradation capabilities. In particular, the dissemination of antibiotic resistance genes in aquatic environments presents a current and pressing public health concern for which risk assessment and identification of appropriate control measures require an understanding of horizontal gene transfer and the parameters that control it. The quantitative model of natural transformation presented in this work provides a basis for identifying the parameters controlling natural transformation rates in the environment. In combination with existing models of conjugation and transduction, this model will allow the development of a comprehensive predictive model of horizontal gene transfer.

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## Footnote |

† The first and the second authors equally contributed to this work. |

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