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Unbalanced growth environments give rise to rich perturbations. A. A typical growth curve of MG1655z1 bacterial strain. Grey crosses represent original data. The black line represents the denoised growth curve using the “wden” function in Matlab with a Daubechies (db4) wavelet, a soft universal threshold and no rescaling. B. Wavelet transform of the raw growth curve (a) using a Daubechies (db4) wavelet. The heat map shows the amplitudes at each specific period and time-point. The black box indicates the range of periods that did not generate tight clusters of bacterial strains (Figure S2C). C. Classification of bacterial strains using the corresponding wavelet transforms. All bacterial strains were classified correctly. mg = MG1655z1, dpro = DH5αPro, pao = PAO1, mds = MDS42, bpro = BL21Pro, etec = ETEC, jm109 = JM109, top 10 = Top10. All data was classified using the standard hierarchical clustering algorithm in Matlab with the average Euclidean distance as the metric. D. Classification of bacterial strains using the raw growth curves. One strain was classified incorrectly, as indicated by the red arrow.
Source publication
Fluctuations in the growth rate of a bacterial culture during unbalanced growth are generally considered undesirable in quantitative studies of bacterial physiology. Under well-controlled experimental conditions, however, these fluctuations are not random but instead reflect the interplay between intra-cellular networks underlying bacterial growth...
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... growth rates were calculated using the central differences of optical densities at each time point. For each growth curve, the specific growth rates fluctuated drastically over time ( Figure 3A & Figure S2A). For comparison, we first calculated several conventional metrics, including maximal growth rates, final OD, and summa- tion of differences (Table S2). ...
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... next transformed each time course of growth rates into the time-frequency domain, which was unique for each strain ( Figure 3B & Figure S2B). All wavelet transform was performed using the Daubechies (db4) wavelet unless otherwise noted. ...
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... Davies-Bouldin score calculates the tightness of a cluster by comparing the scattering of data within a cluster versus the distance between centroids of two clusters: the smaller the score, the more distinct are the clusters. We found that many wavelet frequencies with small Davies-Bouldin scores ( Figure S2C, score ,0.4) gave rise to clusters that correctly classify growth curves according to bacterial strains ( Figure 3C, period = 24.6 h). This result suggests that the wavelet transform could filter and focus the data on informative frequencies by suppressing random fluctua- tions. ...
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... result suggests that the wavelet transform could filter and focus the data on informative frequencies by suppressing random fluctua- tions. We note that the use of raw growth curves resulted in the mis-identification of one strain ( Figure 3D & Figure S2D). In addition, a bootstrap analysis shows that the wavelet-based method produces fewer numbers of misclassified strains when compared to using raw data ( Figure S2E & F). ...
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... we hypothesized that strain classification can be enhanced by combining data measured in the presence of well-defined perturbations ( Figure S3 & Text S1). Specifically, we perturbed bacterial growth by decreasing temperature, introducing a metabolic burden using a plasmid [35], or decreasing the nutrient concentration ( Figure S3A & B, & Table S3). ...
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... we hypothesized that strain classification can be enhanced by combining data measured in the presence of well-defined perturbations ( Figure S3 & Text S1). Specifically, we perturbed bacterial growth by decreasing temperature, introducing a metabolic burden using a plasmid [35], or decreasing the nutrient concentration ( Figure S3A & B, & Table S3). We concatenated growth curves of each bacterial strain into one time series ( Figure S3C), which was used for strain identification. ...
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... we perturbed bacterial growth by decreasing temperature, introducing a metabolic burden using a plasmid [35], or decreasing the nutrient concentration ( Figure S3A & B, & Table S3). We concatenated growth curves of each bacterial strain into one time series ( Figure S3C), which was used for strain identification. Indeed, the combination of the perturbation results improved strain identifi- cation by increasing the separation between clusters of MG1655z1 and BL21pro strains ( Figure S3D). ...
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... concatenated growth curves of each bacterial strain into one time series ( Figure S3C), which was used for strain identification. Indeed, the combination of the perturbation results improved strain identifi- cation by increasing the separation between clusters of MG1655z1 and BL21pro strains ( Figure S3D). These analyses demonstrate that unbalanced growth environments can indeed improve the classification of bacterial strains. ...
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... plasmid load was simulated by increasing k 4 to 1.2 (Equation 2-5 & Table S4) and a lower growth temperature was simulated by reducing all of the kinetic constants by 30%. The perturbed model gave rise to results ( Figure S5) that agree with the qualitative trends of our experimental results ( Figure S3A). With plasmid load, the maximum growth rate is decreased and the entry time to stationary phase is maintained. ...
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... lower score indicates better separation of clusters. D. Classification of growth rate curves into respective groups using the results from Figure 3C & D. The top panels show the classification results using raw growth data and the bottom panels show the classification results using wavelet transform. Red labels indicate growth curves that were mis-classified into the wrong groups. ...
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... clustering analysis classified all strains correctly in only one instance of the bootstrap samples. (TIFF) Figure S3 Time series multiplexing for enhanced iden- tification of bacterial strains. A. Growth rates of MG1655z1 over time. ...
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... closer to rpoH, as well as those with high ChIP-on-chip scores, had a consensus sequence that was more similar to the functional consensus sequence than those that clustered farther away (and those with lower ChIP-on-chip scores). (TIFF) Figure S5 Perturbation of the estimated growth model. Predicted growth rates using the estimated model (Fig. 3B). To test the predictive power of the estimated growth model, we emulated either plasmid load or a lower growth temperature by modifying system parameters (Equation 2-5). To emulate plasmid load, k 4 was increased to 1.2 (Equation 2-5 & Table S4). To emulate a lower growth temperature, all kinetic constants were reduced by 30%. The ...
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... model, we emulated either plasmid load or a lower growth temperature by modifying system parameters (Equation 2-5). To emulate plasmid load, k 4 was increased to 1.2 (Equation 2-5 & Table S4). To emulate a lower growth temperature, all kinetic constants were reduced by 30%. The predicted results agree qualitatively with our experi- mental results (Fig. S3A). Specifically, with plasmid load, maximum growth rates decrease, but the overall growth rate profile is similar between unperturbed and perturbed cells. With a lower growth temperature, maximum growth rates decrease and perturbed cells reach stationary phase later than the unperturbed cells. (TIFF) Table S1 Genotypes of bacteria used ...
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... a lower growth temperature, maximum growth rates decrease and perturbed cells reach stationary phase later than the unperturbed cells. (TIFF) Table S1 Genotypes of bacteria used in this study (Figure 3 & Figure S2). The detailed genotypes and sources of bacterial strains used in the study. ...
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... S2 Growth metrics extracted from bacterial growth curves (Figure 3). We extracted three growth metrics from growth curves: maximum growth rate, final optical density (OD), and summation of differences. ...
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Significance
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Significance
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Author Summary
Antibiotic resistance is a growing problem that the World Health Organization describes as “one of the top three threats to global health.” To date, bacteria have developed resistance to all antibiotics used in clinical settings. Unfortunately, the evolution of antibiotic resistant bacteria is accelerating, as antibiotics continue to be misused and overused. As the antibiotic pipeline is drying up, it becomes increasingly critical to utilize the antibiotics already on the market more effectively. The key to designing better regimens lies in the ability to predict how bacteria will respond to a particular antibiotic treatment. Because of this, we need a simple metric that characterizes this pathogen-antibiotic interaction that can be easily measured and used to design dosing protocols that will effectively clear an infection. To help guide the design of effective protocols, we use quantitative modeling to develop a metric that is easy to measure and quantifies the pathogen-antibiotic interaction. Through optimized antibiotic regimens, our strategy could extend the use of first-line antibiotics, improve treatment outcome, and preserve last-resort antibiotics.
Plasmids are a major type of mobile genetic elements (MGEs) that mediate horizontal gene transfer. The stable maintenance of plasmids plays a critical role in the functions and survival for microbial populations. However, predicting and controlling plasmid persistence and abundance in complex microbial communities remain challenging. Computationally, this challenge arises from the combinatorial explosion associated with the conventional modeling framework. Recently, a plasmid-centric framework (PCF) has been developed to overcome this computational bottleneck. This framework enables the derivation of a simple metric, the persistence potential, to predict plasmid persistence and abundance. Here, we discuss how PCF can be extended to account for plasmid interactions. We also discuss how such model-guided predictions of plasmid fates can benefit from the development of new experimental tools and data-driven computational methods.
Antibiotic resistance is one of the biggest threats to public health. The rapid emergence of resistant bacterial pathogens endangers the efficacy of current antibiotics and has led to increasing mortality and economic burden. This crisis calls for more rapid and accurate diagnosis to detect and identify pathogens, as well as to characterize their response to antibiotics. Building on this foundation, treatment options also need to be improved to use current antibiotics more effectively and develop alternative strategies that complement the use of antibiotics. We here review recent developments in diagnosis and treatment of bacterial pathogens with a focus on quantitative biology and synthetic biology approaches.
