Implications of stressinduced genetic variation for minimizing multidrug resistance in bacteria
 Uri Obolski^{1} and
 Lilach Hadany^{1}Email author
DOI: 10.1186/174170151089
© Obolski and Hadany; licensee BioMed Central Ltd. 2012
Received: 27 February 2012
Accepted: 13 August 2012
Published: 13 August 2012
Abstract
Background
Antibiotic resistance in bacterial infections is a growing threat to public health. Recent evidence shows that when exposed to stressful conditions, some bacteria perform higher rates of horizontal gene transfer and mutation, and thus acquire antibiotic resistance more rapidly.
Methods
We incorporate this new notion into a mathematical model for the emergence of antibiotic multiresistance in a hospital setting.
Results
We show that when stress has a considerable effect on genetic variation, the emergence of antibiotic resistance is dramatically affected. A strategy in which patients receive a combination of antibiotics (combining) is expected to facilitate the emergence of multiresistant bacteria when genetic variation is stressinduced. The preference between a strategy in which one of two effective drugs is assigned randomly to each patient (mixing), and a strategy where only one drug is administered for a specific period of time (cycling) is determined by the resistance acquisition mechanisms. We discuss several features of the mechanisms by which stress affects variation and predict the conditions for success of different antibiotic treatment strategies.
Conclusions
These findings should encourage research on the mechanisms of stressinduced genetic variation and establish the importance of incorporating data about these mechanisms when considering antibiotic treatment strategies.
Keywords
stress induced mutagenesis HGT antibiotic resistance evolution mathematical modelBackground
Bacterial resistance to antibiotics has accompanied the introduction of new antibiotics since shortly after penicillin was first introduced [1] and is currently considered a major health issue [2, 3]. The implications of infection with antibioticresistant bacteria include increased mortality rates, prolonged hospitalization and higher cost of treatment [1, 4, 5]. A particularly dangerous prospect of the continued evolution of drug resistance in bacteria is the creation of new, multidrug resistant bacteria. Such bacterial strains are already present in several species of bacteria [3, 6] and treating them is more difficult and often accompanied by a period of ineffective treatment, resulting in increased patient mortality [6]. Moreover, the rate of new drug development is declining, leaving few treatment alternatives for treating the increasing burden of multiresistant bacteria [7, 8]. Since resistance is especially prevalent in hospitals [9], various treatment strategies have been suggested to facilitate better responses to resistant infections and minimize the emergence of new multiresistant bacteria.
Three prominent strategies of antibiotic treatment are cycling, mixing and combining. Under a cycling regime, all the patients are treated with the same antibiotic drug at a given time, and the drug used is periodically switched. The rationale behind cycling is that each time an alteration of drugs is administered, the pathogens resistant to the previously used drug are attacked and are hopefully susceptible to the new drug [10]. In the mixing strategy, each patient receives a randomly selected drug. This strategy can be viewed as the default antibiotic usage within a hospital unit, when there is no preference for any particular antibiotic. In such a case, if two relevant antibiotics exist, approximately half the patients receive each drug at any given time. Mixing has the advantage of creating a heterogeneous stress environment for the bacterial population [10]. At each transmission, a bacterium has a probability of half encountering a drug to which it has not recently been exposed, and hence to which it is unlikely to be resistant. Combining is the administration of several drugs to each patient. By applying several antibiotics at once, combining is designed to diminish the chance of evolving resistance by eradicating any bacteria resistant to just one type of antibiotics. As a result, more antibiotics are used in combining than in mixing or cycling. This could lead to higher antibioticrelated toxicity and increased treatment costs [11].
Attempts to compare the different treatment strategies and assess their relative efficiency have been made both in empirical studies [12–17] and using theoretical analysis [10, 18–20]. All in all, results obtained using both approaches have been inconclusive. It seems clear that current models do not capture all the aspects of the phenomenon, thus failing to properly distinguish between scenarios favoring different treatment strategies. We suggest that part of this shortcoming may result from the simplifying assumption that resistance is acquired at a constant rate, ignoring recent evidence to the effect of environmental stress on the mechanisms of resistance acquisition. The frequency of horizontal gene transfer (HGT) and mutation was shown to increase when bacteria are under various stressors, including nutritional deprivation, DNA damage, temperature shift, oxidative stress and exposure to antibiotics [21–24]. An environmental stressor especially relevant to our subject of inquiry is antibiotics. In Streptococcus uberis, acquisition of rifampin resistance through mutation was shown to increase more than 1,000fold under ciprofloxacin [25]. Interestingly, the rifampin resistant mutants showed no resistance for ciprofloxacin, which indicates that this was not merely the result of selection. It was also shown that Pseudomonas aeruginosa increases its mutation rate by up to 10^{5} in the presence of tetracycline antibiotics, and consequently obtains resistance to antibiotics [26]. Stressinduced mutation (SIM) might therefore have a substantial influence on the dynamics of antibiotic resistance acquisition [27–29]. In the context of HGT, Streptococcus pneumoniae was shown to increase the rate of chromosomal DNA uptake by transformation of a marker conferring resistance to streptomycin, when treated with either streptomycin or norfloxacin [30]. It was also shown that ciprofloxacin induces the transfer of the SXT integrating conjugative element, which is known to encode for antibiotic resistance genes, in SXTcontaining Escherichia coli and in Vibrio cholerae up to 300fold[31]. Phages were also observed to increase horizontal transfer of genetic material as a reaction to their host's antibioticinduced SOS response[32], a process which might lead to an increased rate of antibiotic resistance acquisition [33]. Theoretical work also supports stressinduced genetic variation as a successful evolutionary strategy [34–36] so this phenomenon might be even more widespread then we currently know. Our goal is to explore the impact of genetic variation induced by antibiotic stress on the spread of antibiotic multiresistance in a hospital unit. We use a classical modeling approach (first described in [37]), modified to describe SIM and stressinduced HGT. Our model is used to evaluate the efficacy of each treatment strategy under different assumptions regarding the effect of stress on genetic variation. We find that stressinduced variation can indeed alter the preferred treatment strategy.
Methods
Our mathematical model describes the dynamics of bacterial infections in a hospital unit. The bacterial pathogens in question are assumed to accompany other ailments and not be the main reason for hospitalization. We consider two different antibiotic drugs, denoted antibiotic 1 and antibiotic 2. The frequencies of patients infected with bacteria resistant to antibiotics 1 and 2 are R _{1} and R _{2} , respectively, and the frequency of patients infected by susceptible bacteria is S. The frequency of uninfected patients is X . Clearance due to antibiotic usage occurs at rate τ , and χ_{ i } determines the fraction of patients receiving antibiotic i. Resistance is assumed to be complete, so that a patient infected by a bacterial strain resistant to drug 1 will not be affected at all by treatment with that drug. Conversely, if treated with drug 2, the patient becomes uninfected ( X ) at rate τ . γ is the rate of spontaneous clearance due to the response of the patient's immune system, β is the rate of bacterial transmissions resulting in infection (for simplicity, superinfection is neglected), and m is the rate of patient turnover (so that the mean patient hospitalization time is $\frac{1}{m}$ days). Since we assume the bacterial infection is not the main reason for hospitalization, patients leave the hospital or die at a rate proportional to their frequency. The proportion of infected patients entering the hospital is determined by ${\lambda}_{{R}_{1}},\phantom{\rule{2.77695pt}{0ex}}{\lambda}_{{R}_{2}},\phantom{\rule{2.77695pt}{0ex}}{\lambda}_{S}$ for patients carrying bacteria resistant to antibiotic 1, to antibiotic 2, or to none, respectively. Uninfected patients enter the hospital at rate $m\left(1\left({\lambda}_{{R}_{1}}+\phantom{\rule{2.77695pt}{0ex}}{\lambda}_{{R}_{2}}+\phantom{\rule{2.77695pt}{0ex}}{\lambda}_{S}\right)\right)$, so hospital occupancy is kept constant. All of the parameters representing rates are given in units of day^{1}. We assume there are no doubleresistant bacteria in the hospital initially, and that their frequency in the general population is negligible. This scenario may reflect situations where newly developed antimicrobial agents have been recently introduced, or were kept as the last resort, so that double resistance is still scant.
Equations E1 were solved analytically [See Additional file 1, section 3], and by numerical integration using Matlab^{®} R2009a.
Moving average calculation: We used the numerical solutions of equations E1 and the analytical computations of double resistance emergence [See Additional file 1, sections 1 and 2] to calculate values of a moving average. First, the different sets of parameters are ordered according to the parameter plotted on the × axis. Each point in the plot presents the average double resistance emergence over 201 equally weighted parameter sets: the one corresponding to the point itself, the 100 nearest parameter sets with lower values of $\tau \left(\frac{{\lambda}_{{R}_{1}}}{{\lambda}_{{R}_{2}}}\right)$, and the 100 nearest parameter sets with higher values of$\tau \left(\frac{{\lambda}_{{R}_{1}}}{{\lambda}_{{R}_{2}}}\right)$. The same 201 data sets are used to calculate double resistance emergence for a given value of $\tau \left(\frac{{\lambda}_{{R}_{1}}}{{\lambda}_{{R}_{2}}}\right)$ under each of the three strategies, resulting in a correlation between the three values, and a similarity in the shape of the three moving average curves (since the three means are taken over the same parameter sets).
Results
Stressinduced mutation
Intuitively, inequality C1 is satisfied due to either abundance of single resistance in the population outside the hospital, causing high entrance rates of single resistant bacteria, or abundance inside the hospital due to infection and selection.
An important feature of antibiotic resistance is its persistence within a host without direct selective forces for long periods of time [38]. Direct selection occurs when a patient is treated with a certain antibiotic, say antibiotic 1, and a new bacterium resistant to antibiotic 1 arises within the host, by mutation or HGT. Thus, due to strong selection for antibiotic resistance, it has a high probability of taking over the entire infecting population and turning the host to R _{1}. When the host is not treated with antibiotic 1, resistance to antibiotic 1 might not confer any direct fitness advantage. Thus, we assume that the probability of a bacterium to take over the infection in the second scenario is σ times the chance in the first scenario, where 0 < σ < 1 represents the relative persistence of antibiotic resistance when there is no direct antibiotic usage. Under condition C1, we can consider σ only when computing withinhost dynamics of double resistant bacteria.
The exact value of σ is hard to measure, but is likely to be nonzero, as evidence suggests that patients who have not been treated with antibiotics for periods of up to three years still carry antibiotic resistant bacteria [6] . One reason for high persistence of resistant bacteria in ambulatory patients and medical staff might be residuals of antibiotics that are found in the environment at amounts sufficient to change the fitness of sensitive bacteria. This might often be the case in hospitals, as it was shown that even very low concentrations of antibiotics can select for antibiotic resistant bacteria [39] and that even ambulatory patients who have not received antibiotics for long periods of time harbor high frequencies of antibiotic resistant bacteria [40].
For cycling we have a more complex expression. We will divide time into segments in which only one antibiotic is applied. In each of these segments only one strain of resistant bacteria is under antibiotic stress. Thus,
In addition to the parameters pertaining to the stress induction mechanisms and withinhost selection, the parameters determining E _{ SIM } also play an important role in the emergence of double resistance. To test the robustness of our model to changes in these parameters we study the emergence of double resistance for 10^{4} random sets of parameters. The values of m were chosen from a generalized extreme value distribution fitted to the length of patients' stay in observed data [41]. Antibiotic clearance rates, $\frac{1}{\tau}$, were chosen from a uniform distribution on [2, 14] (deduced from optimal treatment estimations in [42]). Spontaneous clearance, γ, is then chosen from a uniform distribution on [0,τ] , and Infection rates, β, were chosen from a log uniform distribution on [0.001,1] [10]. Four more values were chosen from the uniform distribution on 0[1], and then normalized to determine the entrance frequencies ${\lambda}_{s},{\lambda}_{{R}_{1}},{\lambda}_{{R}_{2}},1{\lambda}_{s}{\lambda}_{{R}_{1}}{\lambda}_{{R}_{2}}$.
The clearance rate due to antibiotic usage,τ, mildly decreases both infection (Figure 4) and resistance emergence (Figure 3). As the clearance rate increases, bacteria are eliminated more efficiently, thus the window of opportunity for infecting bacteria to acquire double resistance narrows.
Stressinduced horizontal gene transfer
For the rate of encounters between bacteria of different resistant strains we multiply E _{ HGT } (U) by a constant C, which denotes the rate of bacterial transmission from one patient to another (by hospital staff, direct contact, and so on). We denote by d the probability that bacteria will donate genetic material, and by r the probability that bacteria will receive genetic material, given that a bacterial transmission event has occurred. The probability of successful HGT between bacteria, given bacterial transmission, is thus r · d . However, when stressinduced HGT is considered, r and d are no longer constant, as different treatment strategies create varying levels of stress for different bacteria. We will define r _{ r } , d _{ r } to be the probabilities of receiving and donating genetic material for bacteria which are not under antibiotic stress. Similarly, r _{ s } and d _{ s } will be the probabilities of receiving and donating genetic material for bacteria which are under antibiotic stress. For example, if all patients are treated with the same drug, bacteria resistant to that drug would perform HGT with probabilities r _{ r } and d _{ r } , while bacteria sensitive to it would perform HGT with probabilities r _{ s } and d _{ s } . Stressinduced HGT will be expressed by the conditions r _{ s } > r _{ r } and d _{ s } > d _{ r } .
Analysis of ξ _{ HGT } for each strategy shows that high enough values of min $\left\{\frac{{d}_{s}}{{d}_{r}},\frac{{r}_{s}}{{r}_{r}}\right\}$will cause the ratio $\frac{{\xi}_{HGT}\left(cycling\right)}{{\xi}_{HGT}\left(combining\right)}$ to be arbitrarily close to zero [See Additional file 1, section 1.1, equation (6)]. In other words, the more HGT becomes affected by stress in both the donor and the recipient ends, the more efficient cycling becomes relative to combining. This occurs due to the fact that when cycling is applied only one type of resistant bacteria is stressed at any given time. For double resistant bacteria to emerge through HGT, a donor and a recipient of different resistance types are needed, but under cycling they will never be simultaneously under stress. In contrast, when the combining strategy is applied all bacteria are stressed, including potential donors and recipients alike.
The efficiency of the mixing strategy depends on ϕ. This results from the fact that under mixing, different patients are treated with different drugs. When ϕ is low, bacteria transported from one patient to another change their HGT probabilities according to the drug taken by the new host. Therefore, for both mixing and cycling, bacterial HGT events which produce double resistance will rarely occur when both donor and recipient are stressed. In contrast, when ϕ is high, bacteria transported from one patient to another retain HGT probabilities complying to the antibiotic treatment of their former host, allowing the emergence of double resistance through HGT in which both donor and recipient are stressed.
When exploring the effects of stress induced HGT we take $\frac{{d}_{s}}{{d}_{r}}=\frac{{r}_{s}}{{r}_{r}}$, since we have shown that min $\left\{\frac{{d}_{s}}{{d}_{r}},\frac{{r}_{s}}{{r}_{r}}\right\}$ is the dominant factor in the dynamics [See Additional file 1, section 1.1 equations 46], and in order to avoid assumptions about the role of donor and recipient in the dynamics. For ease of notation we define $\theta :=\frac{{d}_{s}}{{d}_{r}}=\frac{{r}_{s}}{{r}_{r}}=\text{min}\left\{\frac{{d}_{s}}{{d}_{r}},\frac{{r}_{s}}{{r}_{r}}\right\}$.
As we mentioned above, combining always outperforms cycling and mixing in terms of minimizing overall infected patients, but the benefit is of only a few percent (Figure 4 and Additional file 1, table S1). When antibiotic resistance persistence,σ, is low, even without stress induction, emergence of double resistance under combining is higher by 30% than under other strategies [See Additional file 1, table S1]. When stress induction is significant, double resistance emergence under combining is more than tenfold higher than under cycling, and more than 30% higher than under mixing (Figure 6 and Additional file 1, table S1).
Discussion
Several conclusions can be derived from our mathematical model. We have shown that stressinduced genetic variation can have a drastic influence on the emergence of double resistance, and should be considered when deciding on a hospital wide strategy of antibiotic usage. Although always slightly more efficient than other strategies in decreasing the incidence of single resistant infections, the strategy of combining performs very poorly in inhibiting double resistance emergence when genetic variation is stressinduced. This holds true despite the fact that under the combining strategy all patients receive effective treatment, and even though we disregard the toxic effects of combining antibiotics for the patient and the economic burden it carries for the population [11, 44].
Cycling is the preferred strategy with respect to the acquisition of resistance through SIM. Low persistence of antibiotic resistance (σ) further amplifies the effects of SIM and increases the relative efficiency of cycling. In the presence of stressinduced HGT, cycling and mixing are the favored strategies, and the preference between them is determined by how fast the bacteria respond to environmental changes (the parameter ϕ in our model). If changes in HGT frequencies in response to antibiotic stress are rapid, mixing is the preferred strategy, whereas slow response to stress would tilt the scales in favor of cycling. We should note that our predictions hold even for a very mild increase of HGT and mutation rates under antibiotic stress (Figures 3 and 6) in comparison with those described in the literature [25, 26, 30, 31]. Higher dependence of variation on stress leads to results which are more robust to changes in other parameter values.
There are several criteria which are used to evaluate the efficiency of an antibiotic strategy: reduction of total infection burden; single resistance minimization; and inhibition of multiple resistance emergence [10, 19, 20, 43, 45, 46]. We compared two measures of treatment efficiency: proportion of infected patients and emergence of double resistance. The latter is of interest mainly in a population where double resistance bacteria are still at a low frequency, thus we focused on that scenario. There is rarely a strategy which is ideal for both infection and emergence of double resistance at the same time. A strategy that is successful at reducing infection applies more accurate treatment, and this has two effects on emergence: on the one hand, eliminating infection and thus minimizing the bacteria that would become resistant. On the other hand, treatment creates selective pressure and potentially stress induced variation  two factors that might lead to a faster generation of resistance. We find that combining always outperforms mixing and cycling by a small amount, when it comes to minimizing infection. When considering double resistance emergence, both mixing and cycling outperform combining substantially when variation is stressinduced. This contrast should be taken into account when deciding on a treatment strategy.
We make several assumptions that should be discussed explicitly. First, we did not consider the possible fitness cost of antibiotic resistance. This is consistent with recent evidence suggesting that compensatory mechanisms reduce such cost to a low level [27, 47, 48]. Additionally, for stressinduced HGT to have substantial influence on the dynamics we require that both donor and recipient probabilities of HGT would increase with stress. It was shown in [30] that acquisition of resistance through transformation increases with the recipient's stress. The amount of genetic material available for transformation in the environment is influenced by the death of bacteria, and is therefore dependent on the stress that the donor bacteria experience. This is particularly true when phages cause lysis of their host when the host is stressed [32, 33]. Similarly, donation and acquisition of conjugative elements were each, separately, shown to increase under stress [31, 49, 50]. Another issue we did not address is the influence of stochastic events on the dynamics. The population size within a hospital unit might be small enough for stochastic events such as epidemic outbursts of bacteria and extinction of rare bacterial strains for long periods of time, to be very influential [45]. Human errors in the form of dosage errors, lack of compliance to hospital guidelines and so on can be another source of stochastic noise that might shift the dynamics from the deterministic expectation described here.
Furthermore, the values of certain parameters might be different for different patients. For instance, elderly patients might be more susceptible to bacterial infections than other patients [51, 52]. This could be expressed by modeling compartments of patients with different parameter values (in this example, higher β values) in accordance with the epidemiological data. Finally, the relative efficiency of the different drugs was assumed to be equal, and no drug interactions were considered  two factors that may further affect the evolution of resistance [53]. Future work could address these matters explicitly.
Our model points to several directions in which empirical data can guide the planning of efficient treatment strategies. First, it is important to understand whether a pathogen acquires resistance primarily through mutation or through HGT. Second, it is important to estimate the persistence of antibiotic resistant bacteria within hosts not currently treated with antibiotics effective against those bacteria (the parameter σ in our model). Finally, we would like to directly assess the degree to which stress, and in particular antibiotic stress, increases the rates of bacterial mutation and HGT. Obtaining such data would be an important step in the ongoing struggle against multidrug resistance. We believe that obtaining such precise data will help to decrease the prevalence of multiple resistance strains in bacterial pathogens which have already shown to increase genetic variation under stress, such as P. aeruginosa, S. pneumoniae, E. coli and V. cholerae [26, 30, 31].
Conclusions
In conclusion, our work presents an important factor thus far overlooked when planning antibiotic treatment strategies, namely the effect of stress on genetic variation. We show that considering the effects of stressinduced genetic variation alters the results of existing theoretical models: specifically, combining antibiotics may result in an increased rate of emergence of double resistant bacteria, whereas cycling antibiotics can be more effective than previously thought. Applying our predictions to specific pathogens would require better empirical evaluation of a few key parameters that affect the dynamics of double resistance emergence. We make specific predictions regarding the parameter values that would favor particular treatment strategies, suggesting that further investigation of stressinduced variation and its mechanisms might have crucial importance for combating multiple antibiotic resistance.
Abbreviations
 HGT:

horizontal gene transfer
 SIM:

stressinduced mutation.
Declarations
Acknowledgements
We wish to thank Tuvik Beker, Eran Even Tov, Ariel Gueijman, Michael Fishman, Yoav Ram, and Eytan Ruppin for many helpful comments on the manuscript. This study was supported by grant 840/08 from the Israel Science Foundation (to LH), and Marie Curie grant 2007224866 (to LH).
Authors’ Affiliations
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