A Bayesian Approach for Parameterizing and Predicting Plasmid Conjugation Dynamics

A Bayesian Approach for Parameterizing and Predicting Plasmid Conjugation Dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Bayesian Approach for Parameterizing and Predicting Plasmid Conjugation Dynamics Sirinapa Kumsuwan, Chanon Jaichuen, Chakachon Jatura, Pakpoom Subsoontorn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4698773/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Mar, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Population dynamic models that explain and predict the spread of conjugative plasmids are pivotal for understanding microbial evolution and engineering microbiomes. However, prediction uncertainty of these models has rarely been assessed. We adopt a Bayesian approach, employing Markov Chain Monte Carlo (MCMC), to parameterize and model plasmid conjugation dynamics. This approach treats model parameters as random variables whose probability distributions informed by data on plasmid population dynamics. These distributions allow us to estimate confidence intervals of the model’s parameters and predictions. We validated this approach using synthetic population dynamic data with known parameter values and experimental population dynamic data of mini-RK2, a miniaturized counterpart of the well-characterized and widely used RK2 conjugation plasmids. Our methodology accurately estimated the parameters of synthetic data, and model predictions were robust across time scales and initial conditions. Incorporating long-term population dynamic data enhances the precision of parameter estimates related to plasmid loss and the accuracy of long-term population dynamic predictions. For experimental data, the model correctly explained and predicted most population dynamic trends, albeit with broader confidence intervals. Overall, our method allows for deeper investigation of plasmid population dynamics and could potentially be generalized to study population dynamics of other mobile genetic elements. Biological sciences/Microbiology/Bacteria/Bacterial genetics Biological sciences/Ecology/Ecological genetics Biological sciences/Ecology/Ecological modelling conjugation plasmid Bayesian Approach Markov Chain Monte Carlo Figures Figure 1 Figure 2 Figure 3 Introduction The study of mobile genetic elements (MGEs), such as phages and conjugative plasmids, is pivotal for understanding Horizontal Gene Transfer (HGT) in microbial communities. These elements are major drivers of microbial evolution, influencing the dissemination and persistence of critical traits, including virulence and antibiotic resistance (Frost et al., 2005 ; Ghaly et al, 2018; Haudiquet et al., 2022 ; Zhu et al, 2024 ). The ability to accurately predict the dynamics of MGEs spread in microbial populations is essential, not only for understanding microbial evolution but also for addressing public health concerns related to these evolutionary processes (Partridge et al., 2018 ; Leclerc et al., 2019 ). Furthermore, this predictive capability is crucial for devising strategies to either disseminate or eliminate specific genes in microbial population, thereby engineering microbiomes with desired features (Sheth et al., 2016 ; Bober et al., 2018 ; Marsh et al., 2023 ). The measurement and modelling of MGEs, particularly conjugative plasmids, within microbial populations have been by extensively explored (Hernández-Beltrán et al., 2021 ). A spectrum of modelling approaches, ranging from mass action kinetics to agent-based models, has been devised to explain and predict population dynamics of MGEs (Steward & Levin, 1977; Levin et al., 1979 ; Levin & Steward, 1980; Simonsen, 1990 ; Krone et al., 2007 ; Seoane et al., 2011 ; Zhong et al., 2012 ; Lopatkin et al., 2017 ; Malwade et al., 2017 ; Wang & You et al., 2022). These models hinge on accurately determining critical parameters, such as MGEs’ transfer and loss rates, alongside their influence on the fitness of host cells. Nonetheless, the simultaneous occurrence of MGE transfer, loss, and cell growth poses significant challenges to precise parameter quantification. Additionally, the sensitivity of parameter measurement techniques to experimental setups introduces further complexity. For instance, the quantification of MGE transfer rates can be influenced by variables such as cell density, growth rates, and plasmid (Huisman et al., 2022 ; Kosterlitz et al., 2023). Compounded by variability in population dynamics and the reproducibility of experimental outcomes, the assessment of parameter certainty and model predictions' reliability emerges as a crucial yet underexplored aspect. Despite its importance, previous research has often overlooked the reporting and analysis of uncertainty surrounding parameter estimates and model predictions. Parameter estimation from experimental data can fundamentally be tackled via two approaches: the frequentist and the Bayesian approaches (Linden et al, 2022 ). The frequentist approach conceptualizes parameter estimation as an optimization problem, seeking a singular set of parameters that most accurately fits given experimental data. This involves minimizing an error function that quantifies the discrepancy between the experimental observations and the model predictions derived from a specific parameter set. Conversely, the Bayesian approach focuses on estimating the probability distribution of parameters, known as the 'posterior distribution'. This distribution is computed from 'prior distributions', reflecting prior knowledge about the parameters, and the 'likelihood', which is the probability of observing the experimental data assuming that a given parameter set is correct. Despite its higher computational demands, the Bayesian approach offers the advantage of enabling a detailed assessment of the certainty associated with the estimated parameters and the ensuing model predictions. In practice, the posterior distribution can be determined using Markov Chain Monte Carlo (MCMC) techniques, methods that have been pivotal in Bayesian parameter inference across various scientific fields. Originating in the physical sciences, MCMC has expanded into biology, finding applications in the systems biology of gene regulatory networks, epidemiology of infectious diseases, and ecological population dynamics (Metropolis et al., 1953 ; Hasting, 1970; Tierney, 1994 ; Mathews et al., 2007 ; Keersmaekers et al., 2019 ; Valderrama-Bahamóndez & Frohlich, 2019; Linden et al., 2022 ; Rossini et al., 2023 ). In this study, we adopt a Bayesian approach to investigate the dynamics of MGE spread within microbial populations, with a particular focus on a simplified system consisting of both conjugative and non-mobilizable plasmids. We used mini-RK2 plasmid, a compact version of the extensively studied RK2 plasmid, to represent a conjugative plasmid (Aparicio et al., 2022). Known for its broad host range and efficacy in DNA transfer across a diverse spectrum of microbes, the RK2 plasmid and its derivatives have been widely used for gene delivery to undomesticated microbes or microbial community (Simon et al, 1983 ; Marsh et al., 2023 ). The mini-RK2 plasmid, with its relative simplicity and potential for significant applications, thus presents an ideal model for our investigation. We employ Markov Chain Monte Carlo (MCMC) techniques to derive posterior distributions of parameters governing conjugative transfer, plasmid loss, cell growth, and cell death, leveraging both “synthetic data”, with known parameters, and “real data” from our experiment involving the mini-RK2 plasmid, where the parameters are undetermined. Our findings not only confirm the utility of MCMC for accurate parameter estimation and dynamic modelling but also highlight the inherent limitations of this approach and the intricate challenges presented by conjugation systems that are not fully addressed by simplistic models. Results System Setup, Modelling and Analysis Workflow We used Escherichia coli DH5α strains as donors and recipients. The donor cells were equipped with a mini-RK2 conjugative plasmid, termed X61, which harbours genes for green fluorescent protein (GFP) and kanamycin resistance (Km R ). Conversely, the recipient cells contained a non-mobilizable plasmid, X13, with a red fluorescent protein gene (RFP) and chloramphenicol resistance (Cm R ). X61 can self-transfer from donors to recipients, resulting in transconjugants that carry both X61 and X13 plasmids (see Fig. 1A). We modelled this system with deterministic mass action kinetics, adapted from Lopatkin et al. ( 2017 ) (Fig. 1B, Fig S1 ). In our model, cell population comprises subpopulations of four distinct cell types: DH5α (DH5a), DH5α with X13 (DH5a-X13), DH5α with X61 (DH5a-X61), and DH5α with both X13 and X61 (DH5a-X13-X61). The dynamics of these subpopulations are governed by eight kinetic parameters (η, µ, µ13, µ61, µ1361, κ13, κ61, D, Nm), enabling the prediction of population trajectories for each cell type over time using ordinary differential equations (ODEs) (Fig S2 ). Our analysis workflow consists of two parts (Fig. 1C). The first part aims to assess the validity and limitations of our MCMC approach for estimating and analysing kinetic parameters from given data sets (Fig. 1C, top). This part starts with hypothetical “actual” parameter values, which we use for simulating population timecourses. We then add log-normal random noise to these population timecourses to generate "synthetic data," i.e., a collection of population measures of each cell type at various time points, mimicking the kind of data we typically get from experiments. We generate three synthetic data points for each time point to emulate triplicate experiment. Part of these synthetic data is designated as a "training set" while the rest is designated as "testing set." Next, we apply the Metropolis MCMC algorithm to the training set of synthetic data to obtain a "parameter ensemble," i.e., a collection of possible parameter sets that can explain the training set data (Fig S3 -S5). Finally, the parameter ensemble is used for simulating a collection of population timecourses (Fig S6). We can compare how well these simulated population timecourses fit the training and testing set of synthetic data. We can also explore distributions and correlations among parameters in the ensembles (Fig S7). These distributions estimate the posterior distribution of parameters. This information tells us how confident we can be in parameter estimation as well as how sensitive the population timecourses are to changes in parameter values. Moreover, we can compare the “actual” parameter value to the parameter ensemble to assess how accurate our parameter estimations are. The correlations imply possible relationships among parameters in producing observed dynamics. This second part of the analysis workflow (Fig. 1C, bottom) mirrors the first, with the key difference being the use of "experimental data" derived from actual population measurements in our laboratory conjugation experiment. We again divide the data into training and testing sets and employ the Metropolis MCMC algorithm to derive a parameter ensemble from training set. We then analyse population timecourses simulated with this ensemble, as well as the posterior distribution and correlation of parameters within the ensemble. Although the actual parameter values remain unknown in this scenario, the posterior distribution can still inform us about the confidence we can place in our estimated parameter values from the given training dataset. Furthermore, any unsuccessful attempts to predict population timecourses may indicate that critical mechanisms are missing from our simplified kinetic models. Synthetic Data, Parameter Estimation and Simulated Population Timecourses We generated synthetic data sets to emulate four conjugation experiments and growth rate measurements (Fig. 2A, data points). These experiments encompassed: (i) conjugation between DH5a-X61 and DH5a-X13 at a 1:1 ratio for 24 hours; (ii) conjugation between DH5a-X61 and DH5a-X13 at a 1:1 ratio for 14 days; (iii) conjugation between DH5a-X61 and DH5a-X13 at a 1:1000 ratio for 14 days; and (iv) conjugation between DH5a-X61 and DH5a at a 1:1000 ratio for 14 days. Additionally (v), we studied the growth curves by following the population timecourses of the four cell types (DH5a, DH5a-X13, DH5a-X61, DH5a-X13-X61), each cultured separately over five days. To accurately reflect the limitations of measurement in actual experiments, we assumed that not all subpopulations data were available for analysis. For instance, in conjugation experiments (i) through (iii), data for the DH5a subpopulation timecourse was unavailable, despite the potential presence of this cell type, due to the lack of a unique selection marker for colony forming unit assays. Similarly, during growth measurement of DH5a-X13, DH5a-X61, and DH5a-X13-X61, plasmids may be lost from certain cells, leading to the emergence of additional cell types such as DH5a; however, this data was not captured, as our quantification was limited to DH5a-X13, DH5a-X61, and DH5a-X13-X61. Therefore, we utilized only the available data (indicated by data points in Fig. 2A) to derive the parameter ensemble and conduct our analysis. For our selected parameter set, subpopulations harboring X61 (DH5a-X61 and DH5a-X13-X61) eventually dominated the population, even when only 1/1000 of the entire population carried this plasmid at the onset of the simulated conjugation experiments (Fig. 2A, (iii) – (iv)). Subpopulations carrying X13 (DH5a-X13 and DH5a-X13-X61) experienced a slight decrease over the course of the simulated conjugation experiments (Fig. 2A, (ii)-(iii)). Diverse experimental setups enable us to assess the predictive capability of our models. Specifically, we aim to utilize the parameter ensemble derived from timecourse data points in one setup (training set) to predict data points in other setups (testing set). To compile the parameter ensemble, we use either synthetic data from (i) + (v) or (i) + (ii) + (v) as the training set. (i) + (v) training set only has short-term conjugation data (e.g., 24 hours), whereas (i) + (ii) + (v) training set encompasses data on both short-term and long-term conjugation (e.g., 14 days). Previous research on conjugation dynamics often relies on short-term conjugation experiments (< 24 hours) to determine conjugative transfer rates and assess cell replication rates from growth curves of each strain (Lopatkin et al., 2017 ; Malwade et al., 2017 ). Therefore, in terms of the data content available for parameter estimation, these studies are akin to our use of the (i) + (v) training set. We hypothesize that incorporating data from long-term conjugation experiments, specifically (ii), could enhance the accuracy and precision of parameter estimation and model predictions. We used Meteropolis MCMC to obtain parameter ensembles that can explain training synthetic data sets (Fig S8). Parameter ensembles derived from training datasets were used to simulate collections of population timecourses for experiments (i) – (v). The geometric means and 95% confidence intervals of these population timecourses are depicted with colored lines and shaded areas, respectively, in Fig. 2A. When only short-term conjugation data (i) served as the training set, the geometric mean timecourses aligned closely with both the training (Fig. 2A i, v; left) and testing (Fig. 2A ii, iii, iv; left) synthetic data points. Consequently, this parameter ensemble could accurately explain and predict the synthetic data. However, the 95% confidence intervals for predictions became significantly wider at later time points, particularly for DH5a and DH5a-X13 (Fig. 2A ii, iii, iv; left), indicating a low predictive precision (i.e., low level of certainty about the predictions) from these parameter ensembles. This outcome was expected, considering the training data encompassed only short-term conjugation information. Conversely, when the training set included both short-term (i) and long-term (ii) conjugation data, the simulated population timecourses predicted the long-term testing dataset (iii)-(iv) with greater precision (Fig. 2A, right). Notably, the inclusion of long-term conjugation data in the training set resulted in much narrower 95% confidence intervals for the simulation timecourses compared to those without it (Fig. 2A, iii-iv, right compared to left). Posterior distributions of each parameter value illuminate the level of certainty we can attribute to estimated parameter values given specific training datasets. Narrow posterior distributions centred around the 'actual' parameter values used to generate synthetic data suggest a high degree of certainty about, and accuracy of, these estimated parameter values. When employing training sets from (i) + (v) or (i) + (ii) + (v), the estimated conjugative transfer parameters (η) and the growth parameters for all strains (µ, µ13, µ61, and µ1361) closely align with their actual values (Fig. 2B). The shapes and widths of their distributions exhibit minimal variance, regardless of the training set used. Therefore, incorporating additional data from a long-term conjugation experiment (ii) does not significantly enhance the accuracy or certainty of these estimated parameter values. On the contrary, with additional data from long-term conjugation experiment (ii), estimated plasmid loss parameters (κ 13 and κ 61 ) have narrower distribution and shift toward actual parameter values. This underscores the utility of long-term conjugation data in refining estimates for these specific parameters. Interestingly, the posterior distributions for the cell loss parameter D span six orders of magnitude and are not centred around the actual parameter value used for generating synthetic data, irrespective of the inclusion of long-term conjugation data (ii) in the training set. This phenomenon could be attributed to the D value in the synthetic data generation parameter set being so low that it has a negligible impact on the simulated timecourses, allowing any lower estimated D value to fit the training dataset adequately. For parameter ensembles derived from both (i) + (v) and (i) + (ii) + (v) training data, we observed similar correlation patterns among parameters. Overall, most parameters exhibited minimal correlation (Fig. 2C). Notably, there is a positive correlation between µ13 and µ61, which likely plays an important role in maintaining the population ratio between DH5a-X13 and DH5a-X61. Conversely, a negative correlation between η and µ61 could be essential for regulating the prevalence of X61 within the population. The incorporation of data from the long-term conjugation experiment (ii) alters the relationship between η and κ61, shifting from a weak negative correlation to a positive one. This change suggests that the impact of the X61 loss parameter, κ61, becomes more pronounced over extended periods. Therefore, adding long-term experimental data to the training set imposes a further balance between this parameter and the conjugative transfer rate parameter, η. Experimental Data, Parameter Estimation and Simulated Population Timecourses We gathered “experimental data” analogous to the “synthetic data” discussed in the previous section. Specifically, we conducted four distinct conjugation experiments, each under different initial conditions or time scales (Fig. 3A i-iv, data points). Additionally, we measured the growth kinetics of each strain (Fig. 3A v, data points). All four strains exhibited similar growth kinetics, with carrying capacities (the maximum total cell density in the system) approximately 1E + 9 CFU for all experiments. The non-mobilizable plasmid X13 was rapidly lost from the population. Notably, a decline in subpopulations carrying X13 (DH5a-X13 and DH5a-X13-X61) was observed within the first 24 hours without antibiotic selection (Fig. 3A, i). X13 was entirely absent from the population within a week, even when half of the population contained this plasmid at the beginning of the experiment (Fig. 3A, ii). Over an extended timeframe, we noted significant variability in the DH5a-X13 and DH5a-X13-X61 populations during growth experiments (Fig. 3A, v). This variability likely stems from the stochastic loss of X13 at the experiment's early stages, which, over time, may amplify into more pronounced variability. In contrast, X61 rapidly proliferated within the population in experiments (i) – (iv). Specifically, in experiments (i) and (ii), the proportion of cells containing X61 (DH5a-X61 and DH5a-X13-X61) increased from 50% to nearly 100% within 24 hours; in experiment (iii-iv), the proportion rose from 0.1% to nearly 100% within five days. To obtain parameter ensembles, we employed experimental data from either (i) + (v) or (i) + (ii) + (v) as the training dataset. We used Metropolis MCMC to obtain parameter ensembles that can explain training experimental data sets (Fig S9). These ensembles were then utilized to simulate the experimental outcomes (Fig. 3A, color lines and shaded areas). We observed that parameter ensembles could account for the training data from the short-term experiment (i). Specifically, the geometric means of the simulated timecourses closely matched the experimental data points, and the confidence intervals remained relatively narrow, regardless of whether we used (i) + (v) or (i) + (ii) + (v) as the training data. However, the predictive capability of these ensembles for the testing experimental data was less robust. Notable discrepancies arose between the geometric means of the simulated timecourses and the experimental data points when only short-term conjugation data served as the training dataset (Fig. 3A, ii-iv, left). The incorporation of long-term conjugation data into the training set improved the congruence between simulated and experimental timecourses (Fig. 3A, ii-iii, right), yet the confidence intervals of these predictions remained exceedingly wide (Fig. 3A, iii, right). Furthermore, the inclusion of long-term conjugation data appeared to widen the confidence intervals for the growth curves (Fig. 3A, v, right versus left). In essence, our simplistic model encountered difficulties in simultaneously explaining the short-term conjugation (i), the long-term conjugation (ii), and the growth kinetics (v). For the synthetic data discussed in the previous section, the posterior distributions of parameters typically approached unimodal distributions, except for the cell loss rate constant D (Fig. 2B). However, with the experimental data, we observed that posterior distributions were more prone to deviations from unimodal forms (Fig. 3B). For instance, the posterior distributions for the X61 transfer rate (η) and the X61 loss rate (κ61) appeared bimodal when using (i)+(v) and (i)+(ii)+(iv) as training sets, respectively. We hypothesize that this discrepancy arises from a more complex landscape of posterior values in the experimental data compared to the synthetic data, potentially leading to multiple pronounced local maxima that trap the MCMC random walks. Additionally, contrary to the synthetic data where the addition of long-term conjugation data scarcely influenced the posterior distribution of the cell loss parameter (D), the inclusion of long-term data in the experimental context significantly narrowed and shifted the distribution of D towards higher values. This shift indicates that a higher value of D is instrumental in elucidating the rapid decline of DH5a-X13 and DH5a-X13-X61 observed in long-term conjugation data (ii). Distinct differences were also evident in the parameter correlation patterns when long-term conjugation data were excluded versus included in the training dataset (Fig. 3C, left compared to right). In particular, a more pronounced positive correlation among parameters emerged with the inclusion of long-term data. The growth parameters for the subpopulation carrying X61 (µ61, and µ1361) and the cell loss parameter (D) became strongly correlated. We postulate that such correlations enable the model to sustain the level of X61 in the population while accelerating the attrition of the X13-carrying subpopulations, consistent with the trends suggested by the training data from the long-term conjugation experiment (ii). Discussion Our work presents the first comprehensive studies of mini-RK2 population dynamics. The mini-RK2 plasmid was derived from the widely utilized and well-studied RK2, renowned for its broad-host-range and extensive applications in gene delivery to microbial hosts and microbiomes (Marsh et al, 2023 ). Silbert et al. (2021) and Aparicio et al. (2022) miniaturized RK2 into mini-RK2, reducing its size from 60 kb to 25 kb by removing genetic components extraneous to DNA transfer. This streamlining potentially simplifies the understanding and engineering of this plasmid, opening doors to a multitude of applications in the fundamental science of IncP plasmid group and the field of genetic engineering. Although these studies quantified the conjugation efficiency and demonstrated the plasmid's ability to infiltrate and persist in complex microbial communities, they did not delve into the intricate details of the plasmid's propagation, loss, and impact on host fitness. Our investigation bridges this knowledge gap by scrutinizing both the short-term and long-term dynamics of the plasmid under varied initial conditions, extracting key parameters, and rigorously testing our model's predictive power. Such in-depth analyses of conjugative plasmid behaviors are scarce in the literature, even for well-characterized plasmids like the original RK2, F, and R388 (Hernández-Beltrán et al, 2023). The second aspect of novelty in this research lies in the methodological approach to modeling plasmid conjugation dynamics over time. While modeling efforts date back to the 1970s, previous studies have predominantly aimed at predicting the steady-state outcomes of conjugative plasmid populations, such as their persistence or extinction (Steward & Levin, 1977; Levin et al, 1979 ; Levin & Steward 1980; Lopatkin, et al 2017; Wang et al, 2020). Our study advances beyond this traditional objective by seeking to chart the temporal dynamics of subpopulations carrying the plasmid. We used distinct training and testing datasets to assess predictive power of the model, eschewing the common practice of merely adjusting model to fit the data. While a study by Malwade et al. ( 2017 ) present the prediction of short-term dynamics over a five-hour window, it did not extend to the long-term dynamics that are central to our analysis. Our work, therefore, showcases the model's predictive strength, successfully predicting the behavior of the conjugation system under various initial conditions and timescales that diverge from the scenarios presented in the training datasets. The third and perhaps most significant novelty of this study is the adoption of MCMC and Bayesian approach for estimating and employing parameters in modeling plasmid conjugation dynamics. Historically, parameters were measured individually, often without quantifying the level of confidence, and models that used these parameters seldom reported the certainty of their predictions. The use of MCMC and Bayesian inference allows for simultaneous extraction of parameters from experimental data along with a quantifiable degree of certainty (Linden et al, 2022 ). This method introduces greater flexibility in experimental design, allowing any timecourse data to inform the determination of parameter posterior distributions. Furthermore, the parameter distribution data informs the selection of the most informative experimental setups for parameter estimation and model prediction. To our knowledge, this is the first application of MCMC to implement a Bayesian approach for studying plasmid population dynamics. Our approach's ability to concurrently estimate the distribution of all parameters and make predictions from any given dataset increases the versatility in experimental design and data utilization. For instance, it could facilitate parameter estimation from in situ conjugation data where researchers might have limited control over the experimental conditions. Understanding the interplay between raw data and parameter estimation also reveals the system's robustness to parametric variations, indicating that even substantial fluctuations in parameters like plasmid and cell loss rates may have minimal impact on the observable dynamics of subpopulations. Thus, we may conclude that the system exhibits resilience to changes in certain parameter values, suggesting that microscopic alterations, such as mutations affecting plasmid conjugation, might exert negligible effects on the broader subpopulation dynamics. In this study, we leveraged synthetic data to investigate the relationship between the choice of training datasets and our capability to determine parameter distributions and to make predictions. We created synthetic data and asked whether our method can correctly produce ensemble parameter that can be used for explaining and predicting these data. Our methodology can estimate most parameters with both accuracy and precision. Notably, the incorporation of long-term conjugation data in the training data set was found to be critical for enhancing the estimation of specific parameters, like plasmid loss rates, which are slow to manifest yet pivotal for accurate long-term dynamic predictions. This insight is particularly significant as many studies to date have focused solely on short-term conjugation data, which may not suffice for precise predictions across varying experimental conditions and time scales (Hernández-Beltrán et al., 2021 ). Additionally, we observed that some parameters, such as the cell loss rate (D) in synthetic data sets, proved challenging to pinpoint due to their diminished relevance in conjugation dynamics. The analysis of posterior parameter distributions also shed light on parameter sensitivity; for instance, the conjugative transfer parameter in our synthetic data spanned nearly two orders of magnitude. This indicates that substantial variations in this parameter—due to genetic mutations or environmental factors—may not necessarily translate to noticeable changes in the overall plasmid population dynamics. Our study revealed some unexpected findings that we have yet to fully elucidate. The models performed sub-optimally when applied to experimental data in comparison to synthetic data, suggesting that there are essential mechanisms not captured by the current model. The estimated posterior distributions from the training datasets did not have normal shapes, indicating multiple local maxima and hinting at the complexity of the underlying biological processes. The misalignment of the geometric means of the model's time course with experimental results, along with broader 95% confidence intervals, further underscores this point. Differences between experimental and synthetic data were noted: notably, the experimental data showed a quicker and more variable loss of the DH5a-X13 and DH5a-X13-X61 populations. It is possible that at such a low donor-to-recipient ratio as in some of our experiments, traditional mass-action kinetics may be insufficient for elucidating the mechanisms of solid-phase conjugation on agar surfaces (Simonsen, 1990 ; Zhong et al, 2012 ). Future studies should aim to refine and expand upon the methodologies applied in this research. First, MCMC algorithm can further be improved. For example, by running MCMC for a greater number of steps and employing more advanced algorithms, we can minimize the risk of becoming trapped in local maxima (Ballnus et al, 2017 ). Additionally, integrating prior distributions from existing literature or new molecular studies could improve the calculation of posterior distributions (Sheppard et al, 2020 ). A weighted error function could also be utilized to prioritize data. For example, short term conjugation may contain more information than long-term dynamics where there subpopulation barely change after the first few days and the algorithms merely try to fit a constant lines. Second, there should be an in-depth exploration of the relationship between the training dataset and the MCMC's ability to determine posterior distribution of parameters. For example, one could investigate how the number of repeats, standard deviation across repeats, and the numbers and duration of time points influence the quality of posterior distribution estimation and prediction capabilities. Third, we should identify the hidden mechanisms causing discrepancies between experimental results and model predictions. For example, we currently assume that donor remain active all the time and conjugative transfer remain constant. We know that this is not always the case. Growth phase and microenvionment around cells can affect conjugative transfer (Sysoeva et al, 2020 , Sheppard et al, 2020 ; Hunter et al, 2008 ). The question is to what extend this effect has impact on overall plasmid population dynamics. Fourth, we should attempt to bridge the macroscopic population dynamic model with a microscopic model at the level of gene regulatory networks. The exploration of parameter correlations could be expanded to understand how plasmid population dynamics can be linked to the dynamic behaviors of genetic elements and gene networks. We could attempt to estimate the posterior parameter distribution of gene expression and then apply this to fit the macroscopic experimental data on cell population dynamics. Such insights would not only enrich our comprehension of multi-scale phenomena—from genetics to the evolution and ecology of microbes—but also inform our experimental design and data collection strategies (Hernandez-Beltran et al, 2021; Sheppard et al 2021 ; Bethke et al, 2023 ). This would enable the development of more robust predictive models for applications such as microbiome engineering and strategies to combat antibiotic resistance related to horizontal gene transfer (HGT). Conclusion We have introduced and applied a novel approach for the extraction and analysis of parameters governing plasmid spread dynamics within cell populations. Utilizing the Markov Chain Monte Carlo (MCMC) method, we were able to simultaneously derive a set of parameters from experimental observations. This innovative approach enabled us to evaluate the precision of our parameter estimations and the reliability of our predictions. Our findings underscore the necessity of long-term experiments for adequately constraining parameters, thus enabling accurate predictions concerning long-term dynamics. This underscores the importance of conducting mating experiments over varied timescales. This study also represents the first to document the short and long-term dynamics of the mini-RK2 plasmid in a simple E. coli population across varied initial donor-recipient ratios and timescales. The adoption of this new parameter estimation and analysis methodology has provided deeper insight into the certainties and limitations inherent in our current experimental setups and analytical techniques. Future research will necessitate broader experimental setups to sufficiently constrain the model for enhanced explanation and prediction capabilities. Furthermore, employing a simplified and standardized conjugation system like mini-RK2 could facilitate the exploration of the function of each genetic element within the system and its relationship to the overall observed plasmid population dynamics. This approach holds potential for application to other conjugation systems, mobile genetic elements (MGEs), or infection models, offering a promising avenue for advancing our understanding of microbial dynamics and antibiotic resistance spread. Material & Methods Bacteria, plasmids and growth media E. coli DH5α and plasmids used in this study are listed in Table 1 . Plasmid X61 and X13 were transferred to E. coli DH5α via CCMB80 chemical transformation to be used as donor and recipient host cells, respectively. Selection was carried out on Luria-Bertani (LB) agar supplemented with the appropriate antibiotics: kanamycin (Km R : 50 mg/mL) and chloramphenicol (Cm R : 25 mg/mL). Mating Assay Overnight cultures of donor and recipient strains were re-grown for 2–3 hours in a 200 rpm shaking incubator at 37°C. Following incubation, the cultures were washed three times with 1 mL of PBS to eliminate residual antibiotics. After removing the supernatant, the cellular pellet was resuspended and adjusted to an OD600 of 0.3 using PBS. Donors and recipients were combined at ratios of 1:1 or 1:1000 as indicated. Ten microliters of the mixture were applied to a 3x3 mm nitrocellulose membrane placed on LB agar plates. Subsequently, the plates were incubated at 37°C for the specified durations. Following filter mating, the nitrocellulose membrane was resuspended in 1 ml of PBS through gentle pipetting or vortexing. For long term conjugation experimenting lasting for multiple days, we refreshed media every 24 hr. Specifically, once a day, mating samples were resuspended from nitrocellulose membrane in 1 ml PBS. Then, ten microliters of resuspended sample were dropped on a new nitrocellulose membrane on fresh LB agar. Cell Quantification For each experiment, all mixtures were serially diluted, and subsequently, ten microliters of the mixtures was dropped on selective agar plates to quantify the numbers of donors (D), recipients (R), and transconjugants (TC). Plasmid transfer frequency (𝑓) was determined by counting colonies and calculated using the formula 𝑓 = 𝑇C/𝑅 Computational Model and Parameter Estimation Mass action kinetic model of plasmid conjugation and Metropolis Monte Carlo algorithm were implemented in python on google colab platform (see detail and codes in supplementary). Data visualisation and analysis were performed using Matplotlib and Seaborn package in python. Generative AI (ChatGPT) was used for guiding python programming and revising manuscript. Declarations Competing Interests The authors declare no competing interests. Author Contribution S. K., C. J., C. J. conducted experimental work; S. K. and C. J. (Jaichuen) analyzed data. C. J (Jaichuen) and P. S. wrote the manuscript. All authors reviewed the manuscript. Acknowledgement This study is financially supported by the Air Force Office of Scientific Research, USA, under award number FA2386-23-1-4017 and Ministry of Higher Education, Science, Research and Innovation, Thailand, under award number RGNS 63-131. We would like to thank Dr. Sudarat Chadsuthi from the Department of Physics, Faculty of Science, Naresuan University, for her valuable comment on the manuscript. We would also like to thank Faculty of Medical Science, Naresuan University for supporting all facilities. Data Availability The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials. References Ballnus, B. et al. Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems. BMC Syst. Biol. 11, 1–18 (2017). Bethke, J. H. et al. Vertical and horizontal gene transfer tradeoffs direct plasmid fitness. Mol. Syst. Biol. 19, 1–10 (2023). Bober, J. R., Beisei, C. L. & Nair, N. U. Synthetic Biology Approaches to Engineer Probiotics and Members of the Human Microbiota for Biomedical Applications. Annu. Rev. Biomed. Eng (2018). doi: 10.1016/j.physbeh.2017.03.040 De Gelder, L., Ponciano, J. M., Joyce, P. & Top, E. M. Stability of a promiscuous plasmid in different hosts: No guarantee for a long-term relationship. Microbiology 153, 452–463 (2007). De Gelder, L., Williams, J. J., Ponciano, J. M., Sota, M. & Top, E. M. Adaptive plasmid evolution results in host-range expansion of a broad-host-range plasmid. Genetics 178, 2179–2190 (2008). De La Cruz, F. Horizontal Gene Transfer . Brenner’s Encyclopedia of Genetics: Second Edition (2020). doi: https://doi.org/10.1007/978-1-4939-9877-7 Frost, L. S., Leplae, R., Summers, A. O. & Toussaint, A. Mobile genetic elements: The agents of open source evolution. Nature Reviews Microbiology 3, 722–732 (2005). Ghaly, T. M. & Gillings, M. R. Mobile DNAs as Ecologically and Evolutionarily Independent Units of Life. 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R. & Stewart, F. M. The population biology of bacterial plasmids: a priori conditions for the existence of mobilizable nonconjugative factors. Genetics (1980). Levin, B. R., Stewart, F. M. & Rice, V. A. The kinetics of conjugative plasmid transmission: Fit of a simple mass action model. Plasmid 2, 247–260 (1979). Linden, N. J., Kramer, B. & Rangamani, P. Bayesian parameter estimation for dynamical models in systems biology . PLoS Computational Biology 18, (2022). Loftie-Eaton, W. et al. Compensatory mutations improve general permissiveness to antibiotic resistance plasmids. Nat. Ecol. Evol. 1, 1354–1363 (2017). Loftie-Eaton, W. et al. Evolutionary paths that expand plasmid host-range: Implications for spread of antibiotic resistance. Mol. Biol. Evol. 33, 885–897 (2016). Lopatkin, A. J. et al. Persistence and reversal of plasmid-mediated antibiotic resistance. Nat. Commun. 8, (2017). Malwade, A., Nguyen, A., Sadat-Mousavi, P. & Ingalls, B. P. Predictive modeling of a batch filter mating process. Front. Microbiol. 8, 1–11 (2017). Marsh, J. W., Kirk, C. & Ley, R. E. Toward Microbiome Engineering: Expanding the Repertoire of Genetically Tractable Members of the Human Gut Microbiome. Annu. Rev. Microbiol. 77, 427–449 (2023). Mathews, J. D., McCaw, C. T., McVernon, J., McBryda, E. S. & McCaw, J. M. A biological model for influenza transmission: Pandemic planning implications of asymptomatic infection and immunity. PLoS One 2, (2007). Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 21, 1087–1092 (1953). Partridge, S. R., Kwong, S. M., Firth, N. & Jensen, S. O. Mobile genetic elements associated with antimicrobial resistance. Clin. Microbiol. Rev. 31, (2018). Rossini, L., Bruzzone, O. A., Speranza, S. & Delfino, I. Estimation and analysis of insect population dynamics parameters via physiologically based models and hybrid genetic algorithm MCMC methods. Ecol. Inform. 77, 102232 (2023). Seoane, J. et al. An individual-based approach to explain plasmid invasion in bacterial populations. FEMS Microbiol. Ecol. 75, 17–27 (2011). Sheppard, R. J., Barraclough, T. G. & Jansen, V. A. A. The evolution of plasmid transfer rate in bacteria and its effect on plasmid persistence. Am. Nat. 198, 473–488 (2021). Sheppard, R. J., Beddis, A. E. & Barraclough, T. G. The role of hosts, plasmids and environment in determining plasmid transfer rates: A meta-analysis. Plasmid 108, 102489 (2020). Sheth, R. U., Cabral, V., Chen, S. P. & Wang, H. H. Manipulating Bacterial Communities by in situ Microbiome Engineering. Trends in Genetics 32, 189–200 (2016). Simon, R., Priefer, U. & Puhler, A. A Broad Host Range Mobilization System for In Vivo Genetic Engineering: Transposon Mutagenesis in Gram Negative Bacteria. Nat. Biotechnol. 1, 784–791 (1983). Simonsen, L., Gordon, D. M., Art^, F. M. S. & In^, B. R. L. Estimating the rate of plasmid transfer: an end-point method. J. Gen. Microbiol. 136, 2319–2325 (1990). Simonsen, L. Dynamics of plasmid transfer on surfaces. J. Gen. Microbiol. 136, 0–1 (1990). Stewart, F. M. & Levin, B. R. The Population Biology of Bacterial Plasmids: A PRIORI Conditions for the Existence of Conjugationally Transmitted Factors. Genetics 87, 209–28 (1977). Sysoeva, T. A., Kim, Y., Rodriguez, J., Lopatkin, A. J. & You, L. Growth-stage-dependent regulation of conjugation. AIChE J. 66, 1–10 (2020). Tierney, L. Markov Chains for Exploring Posterior Distributions. Annu. Stat. 22, 1701–1762 (1994). Valderrama-Bahamóndez, G. I. & Fröhlich, H. MCMC Techniques for Parameter Estimation of ODE Based Models in Systems Biology. Front. Appl. Math. Stat. 5, 1–10 (2019). Wang, T. et al. Horizontal gene transfer enables programmable gene stability in synthetic microbiota. Nat. Chem. Biol. (2022). doi: 10.1038/s41589-022-01114-3 Wang, T. & You, L. The persistence potential of transferable plasmids. Nat. Commun. 11, 1–10 (2020). Zhong, X., Droesch, J., Fox, R., Top, E. M. & Krone, S. M. On the meaning and estimation of plasmid transfer rates for surface-associated and well-mixed bacterial populations. J. Theor. Biol. (2012). doi: 10.1016/j.jtbi.2011.10.034 Zhu, S., Hong, J. & Wang, T. Horizontal gene transfer is predicted to overcome the diversity limit of competing microbial species. Nat. Commun. 15, 1–9 (2024). Tables Table 1 Bacterial strains and plasmids used for the conjugation in this study. Strains/Plasmids Relevant characteristics Source/Reference E. coli strains DH5α (Donor and recipient cells) hsdR17(rK – mK þ) F– mcr1 Δ(mrr-hsrRMS-mcrBC) 80(lacZΔM15) ΔlaX74 recA1 endA1 araD139 Δ(ara, leu)7697 galU galK rpsL nupG Thermo Fisher Scientific Plasmid X013 p1008, Ori ColE1, Cm r provided by Dr. Drew Endy, Endy lab X061 pMATINGα-msfGFP, PEM7 → msfGFP, Ori RK2, Tra1 and Tra2 gene, Km r Aparicio et al., 2022 Additional Declarations No competing interests reported. Supplementary Files ms020SUPP070724SciRepFinal.docx ms020supplementaryRawData300424.xlsx ms020supplementaryScript300424.ipynbColab.pdf Cite Share Download PDF Status: Published Journal Publication published 03 Mar, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 15 Oct, 2024 Reviews received at journal 15 Oct, 2024 Reviews received at journal 14 Oct, 2024 Reviewers agreed at journal 30 Sep, 2024 Reviewers agreed at journal 27 Sep, 2024 Reviewers invited by journal 27 Sep, 2024 Editor assigned by journal 26 Sep, 2024 Editor invited by journal 12 Jul, 2024 Submission checks completed at journal 09 Jul, 2024 First submitted to journal 07 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4698773","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":334164942,"identity":"1593d3ce-cd77-432c-8f95-558f5559c2a4","order_by":0,"name":"Sirinapa Kumsuwan","email":"","orcid":"","institution":"Naresuan University","correspondingAuthor":false,"prefix":"","firstName":"Sirinapa","middleName":"","lastName":"Kumsuwan","suffix":""},{"id":334164943,"identity":"e4191bfa-28ac-4ff0-ac5c-9355ae79fdd3","order_by":1,"name":"Chanon Jaichuen","email":"","orcid":"","institution":"Naresuan University","correspondingAuthor":false,"prefix":"","firstName":"Chanon","middleName":"","lastName":"Jaichuen","suffix":""},{"id":334164944,"identity":"5f04435c-1213-4daa-80fe-126b48192819","order_by":2,"name":"Chakachon Jatura","email":"","orcid":"","institution":"Naresuan University","correspondingAuthor":false,"prefix":"","firstName":"Chakachon","middleName":"","lastName":"Jatura","suffix":""},{"id":334164945,"identity":"476df533-758a-414c-84be-f245fb0a3b59","order_by":3,"name":"Pakpoom Subsoontorn","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYFACNijN3gBlSBCthecAlCZei0QCkVrM2Y+lPfhQsc3e4ObbYxIMNXYM9tIN+LVY9qQdN5xx5nbihtt5aRIMx5IZeGQO4NdicCC9TZq37XaCwe0cMwkGtgNAhyUQ0HL+OVgL0GFngFr+EaPlRtoxkBbGDTd4zCQY24jQYjnjWTrYLzPP5BhbJPYl8/DcIKDFnD/NDBhit+35jp8xvPHhm50c+wxCDkNEDBAAFfPgV4+hZRSMglEwCkYBNgAAxIlARTgxpI4AAAAASUVORK5CYII=","orcid":"","institution":"Naresuan University","correspondingAuthor":true,"prefix":"","firstName":"Pakpoom","middleName":"","lastName":"Subsoontorn","suffix":""}],"badges":[],"createdAt":"2024-07-07 04:59:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4698773/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4698773/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-82799-5","type":"published","date":"2025-03-03T15:56:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":61592038,"identity":"fff61c07-0368-421d-99fd-5dc5dc3a2067","added_by":"auto","created_at":"2024-08-01 15:42:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":352906,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConjugative transfer system and parameter analysis workflow.\u003c/strong\u003e \u003cstrong\u003e(A)\u003c/strong\u003e A diagram showing conjugative transfer of a plasmid from a donor cell to a recipient cell. \u003cstrong\u003e(B) \u003c/strong\u003eModelling population dynamics. Each cell type (DH5a, DH5a-X13, DH5a-X61, and DH5a-X13-X61) could have different growth rate (μ, μ\u003csub\u003e13\u003c/sub\u003e, μ\u003csub\u003e61\u003c/sub\u003e, and μ\u003csub\u003e1361\u003c/sub\u003e, respectively) but have the same cell loss rate due to death and dilution (D). The total population (all cell types combined) is limited to a fixed carry capacity (N\u003csub\u003em\u003c/sub\u003e, not shown in the figure). Plasmid X13 and X61 can be lost from a cell at different rate (κ\u003csub\u003e13\u003c/sub\u003e and κ\u003csub\u003e61\u003c/sub\u003e, respectively). Plasmid X61 can be transferred from DH5a-X61 or DH5a-X13-X61 to a cell DH5a or DH5a-X13 at rate η. \u003cstrong\u003e(C)\u003c/strong\u003e parameter analysis workflows and key questions to answer in this study using synthetic data (top) or experimental data (bottom). \u0026nbsp;\u003c/p\u003e","description":"","filename":"Fig1ms020sciRep.png","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/c00421f2235dd86b985683bb.png"},{"id":61592040,"identity":"14931c11-6997-41e6-80dc-6a302442d3a8","added_by":"auto","created_at":"2024-08-01 15:42:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":587335,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eUtilizing and analysing of parameter ensembles from synthetic data.\u003c/strong\u003e \u003cstrong\u003e(A)\u003c/strong\u003e Synthetic data and simulated population timecourses using parameter ensembles. Points are synthetic data; curves and shade areas show geometric mean and 95% confidence interval, respectively, of simulated ensemble of population timecourses. DH5a, DH5a-X13, DH5a-X61 and DH5a-X13-X61 population levels, measured as Colony Forming Unit (CFU), are shown in black, red, green and yellow, respectively. (i)- (iv) show timecourse population changes of conjugation experiment, i.e., cells are all together in the same environment at various time scales and initial conditions. (v) shows growth curve of individual cell type cultured in separated environment. Left and right column show the same synthetic data point but different simulated timecourses that uses different parameter ensembles from (i)+(v) and (i)+(ii)+(v) data as training set, respectively. \u003cstrong\u003e(B)\u003c/strong\u003e Distribution of each parameter in parameter ensembles derived from synthetic data. Red lines show the actual values of parameters used for generating synthetic data \u003cstrong\u003e(C)\u003c/strong\u003eCorrelation among parameters in parameter ensemble derived from synthetic data.\u003c/p\u003e","description":"","filename":"Fig2ms020sciRep.png","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/a550e30ba803b76743c626ac.png"},{"id":61592039,"identity":"b2e2765b-6a6a-4bae-b715-3e022cb62b30","added_by":"auto","created_at":"2024-08-01 15:42:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":588193,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eUtilizing and analysing of parameters from experimental data.\u003c/strong\u003e \u003cstrong\u003e(A)\u003c/strong\u003e Experimental data and simulated population timecourses using extracted parameter ensembles. Points are experimental data; curves and shade areas show geometric mean and 95% confidence interval, respectively. DH5a, DH5a-X13, DH5a-X61 and DH5a-X13-X61 population levels, measured as Colony Forming Unit (CFU), are shown in black, red, green and yellow, respectively. (i)- (iv) show time-course population changes of conjugation experiment, i.e., cells are all together in the same environment at various time scales and initial conditions. (v) shows growth curve of individual cell type cultured in separated environment. Note that for experiment (iv), it is difficult to determine the population level of DH5a when this population level is much lower than that of DH5a-X61. This is because we do not have any selection marker for isolating DH5a from DH5a-X61. After day 5 of this experiment, we found that CFU on LB agar are within same order of magnitude as CFU on LB agar with kanamycin (selector for X61). This could imply that most cells have received X61 plasmid. \u003cstrong\u003e(B)\u003c/strong\u003e Distribution of each parameter in parameter ensembles derived from experimental data. \u003cstrong\u003e(C)\u003c/strong\u003e Correlation among parameters in parameter ensemble derived from experimental data.\u003c/p\u003e","description":"","filename":"Fig3ms020sciRep.png","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/b9a04dc931703344f5e058de.png"},{"id":78181456,"identity":"a481b67e-82fb-4e7a-a018-72b0b46de6dd","added_by":"auto","created_at":"2025-03-10 17:46:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2012967,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/e1862708-5bcd-4353-a4b6-15e4a5db5239.pdf"},{"id":61592042,"identity":"e7224070-90c8-406d-a810-abf4ebfc42c2","added_by":"auto","created_at":"2024-08-01 15:42:13","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2623238,"visible":true,"origin":"","legend":"","description":"","filename":"ms020SUPP070724SciRepFinal.docx","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/d305dacb04484dd15d207d46.docx"},{"id":61592037,"identity":"ad734dca-e4c4-4a25-b6c6-dee6676ae6a0","added_by":"auto","created_at":"2024-08-01 15:42:12","extension":"xlsx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":21873,"visible":true,"origin":"","legend":"","description":"","filename":"ms020supplementaryRawData300424.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/d9f04c899ae8a6acd0c92189.xlsx"},{"id":61592041,"identity":"816f8506-f825-422c-af22-d29dc6be06f5","added_by":"auto","created_at":"2024-08-01 15:42:13","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":2583439,"visible":true,"origin":"","legend":"","description":"","filename":"ms020supplementaryScript300424.ipynbColab.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4698773/v1/6ced521b693c3a919030205d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Bayesian Approach for Parameterizing and Predicting Plasmid Conjugation Dynamics","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe study of mobile genetic elements (MGEs), such as phages and conjugative plasmids, is pivotal for understanding Horizontal Gene Transfer (HGT) in microbial communities. These elements are major drivers of microbial evolution, influencing the dissemination and persistence of critical traits, including virulence and antibiotic resistance (Frost et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Ghaly et al, 2018; Haudiquet et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhu et al, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The ability to accurately predict the dynamics of MGEs spread in microbial populations is essential, not only for understanding microbial evolution but also for addressing public health concerns related to these evolutionary processes (Partridge et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Leclerc et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Furthermore, this predictive capability is crucial for devising strategies to either disseminate or eliminate specific genes in microbial population, thereby engineering microbiomes with desired features (Sheth et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Bober et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Marsh et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe measurement and modelling of MGEs, particularly conjugative plasmids, within microbial populations have been by extensively explored (Hern\u0026aacute;ndez-Beltr\u0026aacute;n et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). A spectrum of modelling approaches, ranging from mass action kinetics to agent-based models, has been devised to explain and predict population dynamics of MGEs (Steward \u0026amp; Levin, 1977; Levin et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1979\u003c/span\u003e; Levin \u0026amp; Steward, 1980; Simonsen, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Krone et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Seoane et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Zhong et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Lopatkin et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Malwade et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Wang \u0026amp; You et al., 2022). These models hinge on accurately determining critical parameters, such as MGEs\u0026rsquo; transfer and loss rates, alongside their influence on the fitness of host cells. Nonetheless, the simultaneous occurrence of MGE transfer, loss, and cell growth poses significant challenges to precise parameter quantification. Additionally, the sensitivity of parameter measurement techniques to experimental setups introduces further complexity. For instance, the quantification of MGE transfer rates can be influenced by variables such as cell density, growth rates, and plasmid (Huisman et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Kosterlitz et al., 2023). Compounded by variability in population dynamics and the reproducibility of experimental outcomes, the assessment of parameter certainty and model predictions' reliability emerges as a crucial yet underexplored aspect. Despite its importance, previous research has often overlooked the reporting and analysis of uncertainty surrounding parameter estimates and model predictions.\u003c/p\u003e \u003cp\u003eParameter estimation from experimental data can fundamentally be tackled via two approaches: the frequentist and the Bayesian approaches (Linden et al, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The frequentist approach conceptualizes parameter estimation as an optimization problem, seeking a singular set of parameters that most accurately fits given experimental data. This involves minimizing an error function that quantifies the discrepancy between the experimental observations and the model predictions derived from a specific parameter set. Conversely, the Bayesian approach focuses on estimating the probability distribution of parameters, known as the 'posterior distribution'. This distribution is computed from 'prior distributions', reflecting prior knowledge about the parameters, and the 'likelihood', which is the probability of observing the experimental data assuming that a given parameter set is correct. Despite its higher computational demands, the Bayesian approach offers the advantage of enabling a detailed assessment of the certainty associated with the estimated parameters and the ensuing model predictions. In practice, the posterior distribution can be determined using Markov Chain Monte Carlo (MCMC) techniques, methods that have been pivotal in Bayesian parameter inference across various scientific fields. Originating in the physical sciences, MCMC has expanded into biology, finding applications in the systems biology of gene regulatory networks, epidemiology of infectious diseases, and ecological population dynamics (Metropolis et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1953\u003c/span\u003e; Hasting, 1970; Tierney, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Mathews et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Keersmaekers et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Valderrama-Baham\u0026oacute;ndez \u0026amp; Frohlich, 2019; Linden et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Rossini et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn this study, we adopt a Bayesian approach to investigate the dynamics of MGE spread within microbial populations, with a particular focus on a simplified system consisting of both conjugative and non-mobilizable plasmids. We used mini-RK2 plasmid, a compact version of the extensively studied RK2 plasmid, to represent a conjugative plasmid (Aparicio et al., 2022). Known for its broad host range and efficacy in DNA transfer across a diverse spectrum of microbes, the RK2 plasmid and its derivatives have been widely used for gene delivery to undomesticated microbes or microbial community (Simon et al, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1983\u003c/span\u003e; Marsh et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The mini-RK2 plasmid, with its relative simplicity and potential for significant applications, thus presents an ideal model for our investigation. We employ Markov Chain Monte Carlo (MCMC) techniques to derive posterior distributions of parameters governing conjugative transfer, plasmid loss, cell growth, and cell death, leveraging both \u0026ldquo;synthetic data\u0026rdquo;, with known parameters, and \u0026ldquo;real data\u0026rdquo; from our experiment involving the mini-RK2 plasmid, where the parameters are undetermined. Our findings not only confirm the utility of MCMC for accurate parameter estimation and dynamic modelling but also highlight the inherent limitations of this approach and the intricate challenges presented by conjugation systems that are not fully addressed by simplistic models.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eSystem Setup, Modelling and Analysis Workflow\u003c/h2\u003e\n \u003cp\u003eWe used \u003cem\u003eEscherichia coli\u003c/em\u003e DH5\u0026alpha; strains as donors and recipients. The donor cells were equipped with a mini-RK2 conjugative plasmid, termed X61, which harbours genes for green fluorescent protein (GFP) and kanamycin resistance (Km\u003csup\u003eR\u003c/sup\u003e). Conversely, the recipient cells contained a non-mobilizable plasmid, X13, with a red fluorescent protein gene (RFP) and chloramphenicol resistance (Cm\u003csup\u003eR\u003c/sup\u003e). X61 can self-transfer from donors to recipients, resulting in transconjugants that carry both X61 and X13 plasmids (see Fig.\u0026nbsp;1A). We modelled this system with deterministic mass action kinetics, adapted from Lopatkin et al. (\u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e) (Fig. 1B, Fig \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e). In our model, cell population comprises subpopulations of four distinct cell types: DH5\u0026alpha; (DH5a), DH5\u0026alpha; with X13 (DH5a-X13), DH5\u0026alpha; with X61 (DH5a-X61), and DH5\u0026alpha; with both X13 and X61 (DH5a-X13-X61). The dynamics of these subpopulations are governed by eight kinetic parameters (\u0026eta;, \u0026micro;, \u0026micro;13, \u0026micro;61, \u0026micro;1361, \u0026kappa;13, \u0026kappa;61, D, Nm), enabling the prediction of population trajectories for each cell type over time using ordinary differential equations (ODEs) (Fig \u003cspan class=\"InternalRef\"\u003eS2\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eOur analysis workflow consists of two parts (Fig. 1C). The first part aims to assess the validity and limitations of our MCMC approach for estimating and analysing kinetic parameters from given data sets (Fig. 1C, top). This part starts with hypothetical \u0026ldquo;actual\u0026rdquo; parameter values, which we use for simulating population timecourses. We then add log-normal random noise to these population timecourses to generate \u0026quot;synthetic data,\u0026quot; i.e., a collection of population measures of each cell type at various time points, mimicking the kind of data we typically get from experiments. We generate three synthetic data points for each time point to emulate triplicate experiment. Part of these synthetic data is designated as a \u0026quot;training set\u0026quot; while the rest is designated as \u0026quot;testing set.\u0026quot; Next, we apply the Metropolis MCMC algorithm to the training set of synthetic data to obtain a \u0026quot;parameter ensemble,\u0026quot; i.e., a collection of possible parameter sets that can explain the training set data (Fig \u003cspan class=\"InternalRef\"\u003eS3\u003c/span\u003e-S5). Finally, the parameter ensemble is used for simulating a collection of population timecourses (Fig S6). We can compare how well these simulated population timecourses fit the training and testing set of synthetic data. We can also explore distributions and correlations among parameters in the ensembles (Fig S7). These distributions estimate the posterior distribution of parameters. This information tells us how confident we can be in parameter estimation as well as how sensitive the population timecourses are to changes in parameter values. Moreover, we can compare the \u0026ldquo;actual\u0026rdquo; parameter value to the parameter ensemble to assess how accurate our parameter estimations are. The correlations imply possible relationships among parameters in producing observed dynamics.\u003c/p\u003e\n \u003cp\u003eThis second part of the analysis workflow (Fig.\u0026nbsp;1C, bottom) mirrors the first, with the key difference being the use of \u0026quot;experimental data\u0026quot; derived from actual population measurements in our laboratory conjugation experiment. We again divide the data into training and testing sets and employ the Metropolis MCMC algorithm to derive a parameter ensemble from training set. We then analyse population timecourses simulated with this ensemble, as well as the posterior distribution and correlation of parameters within the ensemble. Although the actual parameter values remain unknown in this scenario, the posterior distribution can still inform us about the confidence we can place in our estimated parameter values from the given training dataset. Furthermore, any unsuccessful attempts to predict population timecourses may indicate that critical mechanisms are missing from our simplified kinetic models.\u003c/p\u003e\n \u003ch2\u003eSynthetic Data, Parameter Estimation and Simulated Population Timecourses\u003c/h2\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003cp\u003eWe generated synthetic data sets to emulate four conjugation experiments and growth rate measurements (Fig.\u0026nbsp;2A, data points). These experiments encompassed: (i) conjugation between DH5a-X61 and DH5a-X13 at a 1:1 ratio for 24 hours; (ii) conjugation between DH5a-X61 and DH5a-X13 at a 1:1 ratio for 14 days; (iii) conjugation between DH5a-X61 and DH5a-X13 at a 1:1000 ratio for 14 days; and (iv) conjugation between DH5a-X61 and DH5a at a 1:1000 ratio for 14 days. Additionally (v), we studied the growth curves by following the population timecourses of the four cell types (DH5a, DH5a-X13, DH5a-X61, DH5a-X13-X61), each cultured separately over five days. To accurately reflect the limitations of measurement in actual experiments, we assumed that not all subpopulations data were available for analysis. For instance, in conjugation experiments (i) through (iii), data for the DH5a subpopulation timecourse was unavailable, despite the potential presence of this cell type, due to the lack of a unique selection marker for colony forming unit assays. Similarly, during growth measurement of DH5a-X13, DH5a-X61, and DH5a-X13-X61, plasmids may be lost from certain cells, leading to the emergence of additional cell types such as DH5a; however, this data was not captured, as our quantification was limited to DH5a-X13, DH5a-X61, and DH5a-X13-X61. Therefore, we utilized only the available data (indicated by data points in Fig.\u0026nbsp;2A) to derive the parameter ensemble and conduct our analysis. For our selected parameter set, subpopulations harboring X61 (DH5a-X61 and DH5a-X13-X61) eventually dominated the population, even when only 1/1000 of the entire population carried this plasmid at the onset of the simulated conjugation experiments (Fig.\u0026nbsp;2A, (iii) \u0026ndash; (iv)). Subpopulations carrying X13 (DH5a-X13 and DH5a-X13-X61) experienced a slight decrease over the course of the simulated conjugation experiments (Fig.\u0026nbsp;2A, (ii)-(iii)).\u003c/p\u003e\n \u003cp\u003eDiverse experimental setups enable us to assess the predictive capability of our models. Specifically, we aim to utilize the parameter ensemble derived from timecourse data points in one setup (training set) to predict data points in other setups (testing set). To compile the parameter ensemble, we use either synthetic data from (i) + (v) or (i) + (ii) + (v) as the training set. (i) + (v) training set only has short-term conjugation data (e.g., 24 hours), whereas (i) + (ii) + (v) training set encompasses data on both short-term and long-term conjugation (e.g., 14 days). Previous research on conjugation dynamics often relies on short-term conjugation experiments (\u0026lt;\u0026thinsp;24 hours) to determine conjugative transfer rates and assess cell replication rates from growth curves of each strain (Lopatkin et al., \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e; Malwade et al., \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e). Therefore, in terms of the data content available for parameter estimation, these studies are akin to our use of the (i) + (v) training set. We hypothesize that incorporating data from long-term conjugation experiments, specifically (ii), could enhance the accuracy and precision of parameter estimation and model predictions.\u003c/p\u003e\n \u003cp\u003eWe used Meteropolis MCMC to obtain parameter ensembles that can explain training synthetic data sets (Fig S8). Parameter ensembles derived from training datasets were used to simulate collections of population timecourses for experiments (i) \u0026ndash; (v). The geometric means and 95% confidence intervals of these population timecourses are depicted with colored lines and shaded areas, respectively, in Fig.\u0026nbsp;2A. When only short-term conjugation data (i) served as the training set, the geometric mean timecourses aligned closely with both the training (Fig.\u0026nbsp;2A i, v; left) and testing (Fig.\u0026nbsp;2A ii, iii, iv; left) synthetic data points. Consequently, this parameter ensemble could accurately explain and predict the synthetic data. However, the 95% confidence intervals for predictions became significantly wider at later time points, particularly for DH5a and DH5a-X13 (Fig.\u0026nbsp;2A ii, iii, iv; left), indicating a low predictive precision (i.e., low level of certainty about the predictions) from these parameter ensembles. This outcome was expected, considering the training data encompassed only short-term conjugation information. Conversely, when the training set included both short-term (i) and long-term (ii) conjugation data, the simulated population timecourses predicted the long-term testing dataset (iii)-(iv) with greater precision (Fig.\u0026nbsp;2A, right). Notably, the inclusion of long-term conjugation data in the training set resulted in much narrower 95% confidence intervals for the simulation timecourses compared to those without it (Fig.\u0026nbsp;2A, iii-iv, right compared to left).\u003c/p\u003e\n \u003cp\u003ePosterior distributions of each parameter value illuminate the level of certainty we can attribute to estimated parameter values given specific training datasets. Narrow posterior distributions centred around the \u0026apos;actual\u0026apos; parameter values used to generate synthetic data suggest a high degree of certainty about, and accuracy of, these estimated parameter values. When employing training sets from (i) + (v) or (i) + (ii) + (v), the estimated conjugative transfer parameters (\u0026eta;) and the growth parameters for all strains (\u0026micro;, \u0026micro;13, \u0026micro;61, and \u0026micro;1361) closely align with their actual values (Fig.\u0026nbsp;2B). The shapes and widths of their distributions exhibit minimal variance, regardless of the training set used. Therefore, incorporating additional data from a long-term conjugation experiment (ii) does not significantly enhance the accuracy or certainty of these estimated parameter values. On the contrary, with additional data from long-term conjugation experiment (ii), estimated plasmid loss parameters (\u0026kappa;\u003csub\u003e13\u003c/sub\u003e and \u0026kappa;\u003csub\u003e61\u003c/sub\u003e) have narrower distribution and shift toward actual parameter values. This underscores the utility of long-term conjugation data in refining estimates for these specific parameters. Interestingly, the posterior distributions for the cell loss parameter D span six orders of magnitude and are not centred around the actual parameter value used for generating synthetic data, irrespective of the inclusion of long-term conjugation data (ii) in the training set. This phenomenon could be attributed to the D value in the synthetic data generation parameter set being so low that it has a negligible impact on the simulated timecourses, allowing any lower estimated D value to fit the training dataset adequately.\u003c/p\u003e\n \u003cp\u003eFor parameter ensembles derived from both (i) + (v) and (i) + (ii) + (v) training data, we observed similar correlation patterns among parameters. Overall, most parameters exhibited minimal correlation (Fig.\u0026nbsp;2C). Notably, there is a positive correlation between \u0026micro;13 and \u0026micro;61, which likely plays an important role in maintaining the population ratio between DH5a-X13 and DH5a-X61. Conversely, a negative correlation between \u0026eta; and \u0026micro;61 could be essential for regulating the prevalence of X61 within the population. The incorporation of data from the long-term conjugation experiment (ii) alters the relationship between \u0026eta; and \u0026kappa;61, shifting from a weak negative correlation to a positive one. This change suggests that the impact of the X61 loss parameter, \u0026kappa;61, becomes more pronounced over extended periods. Therefore, adding long-term experimental data to the training set imposes a further balance between this parameter and the conjugative transfer rate parameter, \u0026eta;.\u003c/p\u003e\n \u003ch2\u003eExperimental Data, Parameter Estimation and Simulated Population Timecourses\u003c/h2\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003cp\u003eWe gathered \u0026ldquo;experimental data\u0026rdquo; analogous to the \u0026ldquo;synthetic data\u0026rdquo; discussed in the previous section. Specifically, we conducted four distinct conjugation experiments, each under different initial conditions or time scales (Fig.\u0026nbsp;3A i-iv, data points). Additionally, we measured the growth kinetics of each strain (Fig.\u0026nbsp;3A v, data points). All four strains exhibited similar growth kinetics, with carrying capacities (the maximum total cell density in the system) approximately 1E\u0026thinsp;+\u0026thinsp;9 CFU for all experiments. The non-mobilizable plasmid X13 was rapidly lost from the population. Notably, a decline in subpopulations carrying X13 (DH5a-X13 and DH5a-X13-X61) was observed within the first 24 hours without antibiotic selection (Fig.\u0026nbsp;3A, i). X13 was entirely absent from the population within a week, even when half of the population contained this plasmid at the beginning of the experiment (Fig.\u0026nbsp;3A, ii). Over an extended timeframe, we noted significant variability in the DH5a-X13 and DH5a-X13-X61 populations during growth experiments (Fig.\u0026nbsp;3A, v). This variability likely stems from the stochastic loss of X13 at the experiment\u0026apos;s early stages, which, over time, may amplify into more pronounced variability. In contrast, X61 rapidly proliferated within the population in experiments (i) \u0026ndash; (iv). Specifically, in experiments (i) and (ii), the proportion of cells containing X61 (DH5a-X61 and DH5a-X13-X61) increased from 50% to nearly 100% within 24 hours; in experiment (iii-iv), the proportion rose from 0.1% to nearly 100% within five days.\u003c/p\u003e\n \u003cp\u003eTo obtain parameter ensembles, we employed experimental data from either (i) + (v) or (i) + (ii) + (v) as the training dataset. We used Metropolis MCMC to obtain parameter ensembles that can explain training experimental data sets (Fig S9). These ensembles were then utilized to simulate the experimental outcomes (Fig.\u0026nbsp;3A, color lines and shaded areas). We observed that parameter ensembles could account for the training data from the short-term experiment (i). Specifically, the geometric means of the simulated timecourses closely matched the experimental data points, and the confidence intervals remained relatively narrow, regardless of whether we used (i) + (v) or (i) + (ii) + (v) as the training data. However, the predictive capability of these ensembles for the testing experimental data was less robust. Notable discrepancies arose between the geometric means of the simulated timecourses and the experimental data points when only short-term conjugation data served as the training dataset (Fig.\u0026nbsp;3A, ii-iv, left). The incorporation of long-term conjugation data into the training set improved the congruence between simulated and experimental timecourses (Fig.\u0026nbsp;3A, ii-iii, right), yet the confidence intervals of these predictions remained exceedingly wide (Fig.\u0026nbsp;3A, iii, right). Furthermore, the inclusion of long-term conjugation data appeared to widen the confidence intervals for the growth curves (Fig.\u0026nbsp;3A, v, right versus left). In essence, our simplistic model encountered difficulties in simultaneously explaining the short-term conjugation (i), the long-term conjugation (ii), and the growth kinetics (v).\u003c/p\u003e\n \u003cp\u003eFor the synthetic data discussed in the previous section, the posterior distributions of parameters typically approached unimodal distributions, except for the cell loss rate constant D (Fig.\u0026nbsp;2B). However, with the experimental data, we observed that posterior distributions were more prone to deviations from unimodal forms (Fig.\u0026nbsp;3B). For instance, the posterior distributions for the X61 transfer rate (\u0026eta;) and the X61 loss rate (\u0026kappa;61) appeared bimodal when using (i)+(v) and (i)+(ii)+(iv) as training sets, respectively. We hypothesize that this discrepancy arises from a more complex landscape of posterior values in the experimental data compared to the synthetic data, potentially leading to multiple pronounced local maxima that trap the MCMC random walks. Additionally, contrary to the synthetic data where the addition of long-term conjugation data scarcely influenced the posterior distribution of the cell loss parameter (D), the inclusion of long-term data in the experimental context significantly narrowed and shifted the distribution of D towards higher values. This shift indicates that a higher value of D is instrumental in elucidating the rapid decline of DH5a-X13 and DH5a-X13-X61 observed in long-term conjugation data (ii). Distinct differences were also evident in the parameter correlation patterns when long-term conjugation data were excluded versus included in the training dataset (Fig.\u0026nbsp;3C, left compared to right). In particular, a more pronounced positive correlation among parameters emerged with the inclusion of long-term data. The growth parameters for the subpopulation carrying X61 (\u0026micro;61, and \u0026micro;1361) and the cell loss parameter (D) became strongly correlated. We postulate that such correlations enable the model to sustain the level of X61 in the population while accelerating the attrition of the X13-carrying subpopulations, consistent with the trends suggested by the training data from the long-term conjugation experiment (ii).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eOur work presents the first comprehensive studies of mini-RK2 population dynamics. The mini-RK2 plasmid was derived from the widely utilized and well-studied RK2, renowned for its broad-host-range and extensive applications in gene delivery to microbial hosts and microbiomes (Marsh et al, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Silbert et al. (2021) and Aparicio et al. (2022) miniaturized RK2 into mini-RK2, reducing its size from 60 kb to 25 kb by removing genetic components extraneous to DNA transfer. This streamlining potentially simplifies the understanding and engineering of this plasmid, opening doors to a multitude of applications in the fundamental science of IncP plasmid group and the field of genetic engineering. Although these studies quantified the conjugation efficiency and demonstrated the plasmid's ability to infiltrate and persist in complex microbial communities, they did not delve into the intricate details of the plasmid's propagation, loss, and impact on host fitness. Our investigation bridges this knowledge gap by scrutinizing both the short-term and long-term dynamics of the plasmid under varied initial conditions, extracting key parameters, and rigorously testing our model's predictive power. Such in-depth analyses of conjugative plasmid behaviors are scarce in the literature, even for well-characterized plasmids like the original RK2, F, and R388 (Hern\u0026aacute;ndez-Beltr\u0026aacute;n et al, 2023).\u003c/p\u003e \u003cp\u003eThe second aspect of novelty in this research lies in the methodological approach to modeling plasmid conjugation dynamics over time. While modeling efforts date back to the 1970s, previous studies have predominantly aimed at predicting the steady-state outcomes of conjugative plasmid populations, such as their persistence or extinction (Steward \u0026amp; Levin, 1977; Levin et al, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1979\u003c/span\u003e; Levin \u0026amp; Steward 1980; Lopatkin, et al 2017; Wang et al, 2020). Our study advances beyond this traditional objective by seeking to chart the temporal dynamics of subpopulations carrying the plasmid. We used distinct training and testing datasets to assess predictive power of the model, eschewing the common practice of merely adjusting model to fit the data. While a study by Malwade et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2017\u003c/span\u003e ) present the prediction of short-term dynamics over a five-hour window, it did not extend to the long-term dynamics that are central to our analysis. Our work, therefore, showcases the model's predictive strength, successfully predicting the behavior of the conjugation system under various initial conditions and timescales that diverge from the scenarios presented in the training datasets.\u003c/p\u003e \u003cp\u003eThe third and perhaps most significant novelty of this study is the adoption of MCMC and Bayesian approach for estimating and employing parameters in modeling plasmid conjugation dynamics. Historically, parameters were measured individually, often without quantifying the level of confidence, and models that used these parameters seldom reported the certainty of their predictions. The use of MCMC and Bayesian inference allows for simultaneous extraction of parameters from experimental data along with a quantifiable degree of certainty (Linden et al, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This method introduces greater flexibility in experimental design, allowing any timecourse data to inform the determination of parameter posterior distributions. Furthermore, the parameter distribution data informs the selection of the most informative experimental setups for parameter estimation and model prediction. To our knowledge, this is the first application of MCMC to implement a Bayesian approach for studying plasmid population dynamics. Our approach's ability to concurrently estimate the distribution of all parameters and make predictions from any given dataset increases the versatility in experimental design and data utilization. For instance, it could facilitate parameter estimation from \u003cem\u003ein situ\u003c/em\u003e conjugation data where researchers might have limited control over the experimental conditions. Understanding the interplay between raw data and parameter estimation also reveals the system's robustness to parametric variations, indicating that even substantial fluctuations in parameters like plasmid and cell loss rates may have minimal impact on the observable dynamics of subpopulations. Thus, we may conclude that the system exhibits resilience to changes in certain parameter values, suggesting that microscopic alterations, such as mutations affecting plasmid conjugation, might exert negligible effects on the broader subpopulation dynamics.\u003c/p\u003e \u003cp\u003eIn this study, we leveraged synthetic data to investigate the relationship between the choice of training datasets and our capability to determine parameter distributions and to make predictions. We created synthetic data and asked whether our method can correctly produce ensemble parameter that can be used for explaining and predicting these data. Our methodology can estimate most parameters with both accuracy and precision. Notably, the incorporation of long-term conjugation data in the training data set was found to be critical for enhancing the estimation of specific parameters, like plasmid loss rates, which are slow to manifest yet pivotal for accurate long-term dynamic predictions. This insight is particularly significant as many studies to date have focused solely on short-term conjugation data, which may not suffice for precise predictions across varying experimental conditions and time scales (Hern\u0026aacute;ndez-Beltr\u0026aacute;n et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Additionally, we observed that some parameters, such as the cell loss rate (D) in synthetic data sets, proved challenging to pinpoint due to their diminished relevance in conjugation dynamics. The analysis of posterior parameter distributions also shed light on parameter sensitivity; for instance, the conjugative transfer parameter in our synthetic data spanned nearly two orders of magnitude. This indicates that substantial variations in this parameter\u0026mdash;due to genetic mutations or environmental factors\u0026mdash;may not necessarily translate to noticeable changes in the overall plasmid population dynamics.\u003c/p\u003e \u003cp\u003eOur study revealed some unexpected findings that we have yet to fully elucidate. The models performed sub-optimally when applied to experimental data in comparison to synthetic data, suggesting that there are essential mechanisms not captured by the current model. The estimated posterior distributions from the training datasets did not have normal shapes, indicating multiple local maxima and hinting at the complexity of the underlying biological processes. The misalignment of the geometric means of the model's time course with experimental results, along with broader 95% confidence intervals, further underscores this point. Differences between experimental and synthetic data were noted: notably, the experimental data showed a quicker and more variable loss of the DH5a-X13 and DH5a-X13-X61 populations. It is possible that at such a low donor-to-recipient ratio as in some of our experiments, traditional mass-action kinetics may be insufficient for elucidating the mechanisms of solid-phase conjugation on agar surfaces (Simonsen, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Zhong et al, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFuture studies should aim to refine and expand upon the methodologies applied in this research. First, MCMC algorithm can further be improved. For example, by running MCMC for a greater number of steps and employing more advanced algorithms, we can minimize the risk of becoming trapped in local maxima (Ballnus et al, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Additionally, integrating prior distributions from existing literature or new molecular studies could improve the calculation of posterior distributions (Sheppard et al, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). A weighted error function could also be utilized to prioritize data. For example, short term conjugation may contain more information than long-term dynamics where there subpopulation barely change after the first few days and the algorithms merely try to fit a constant lines. Second, there should be an in-depth exploration of the relationship between the training dataset and the MCMC's ability to determine posterior distribution of parameters. For example, one could investigate how the number of repeats, standard deviation across repeats, and the numbers and duration of time points influence the quality of posterior distribution estimation and prediction capabilities. Third, we should identify the hidden mechanisms causing discrepancies between experimental results and model predictions. For example, we currently assume that donor remain active all the time and conjugative transfer remain constant. We know that this is not always the case. Growth phase and microenvionment around cells can affect conjugative transfer (Sysoeva et al, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, Sheppard et al, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Hunter et al, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). The question is to what extend this effect has impact on overall plasmid population dynamics. Fourth, we should attempt to bridge the macroscopic population dynamic model with a microscopic model at the level of gene regulatory networks. The exploration of parameter correlations could be expanded to understand how plasmid population dynamics can be linked to the dynamic behaviors of genetic elements and gene networks. We could attempt to estimate the posterior parameter distribution of gene expression and then apply this to fit the macroscopic experimental data on cell population dynamics. Such insights would not only enrich our comprehension of multi-scale phenomena\u0026mdash;from genetics to the evolution and ecology of microbes\u0026mdash;but also inform our experimental design and data collection strategies (Hernandez-Beltran et al, 2021; Sheppard et al \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Bethke et al, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This would enable the development of more robust predictive models for applications such as microbiome engineering and strategies to combat antibiotic resistance related to horizontal gene transfer (HGT).\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe have introduced and applied a novel approach for the extraction and analysis of parameters governing plasmid spread dynamics within cell populations. Utilizing the Markov Chain Monte Carlo (MCMC) method, we were able to simultaneously derive a set of parameters from experimental observations. This innovative approach enabled us to evaluate the precision of our parameter estimations and the reliability of our predictions. Our findings underscore the necessity of long-term experiments for adequately constraining parameters, thus enabling accurate predictions concerning long-term dynamics. This underscores the importance of conducting mating experiments over varied timescales. This study also represents the first to document the short and long-term dynamics of the mini-RK2 plasmid in a simple \u003cem\u003eE. coli\u003c/em\u003e population across varied initial donor-recipient ratios and timescales. The adoption of this new parameter estimation and analysis methodology has provided deeper insight into the certainties and limitations inherent in our current experimental setups and analytical techniques. Future research will necessitate broader experimental setups to sufficiently constrain the model for enhanced explanation and prediction capabilities. Furthermore, employing a simplified and standardized conjugation system like mini-RK2 could facilitate the exploration of the function of each genetic element within the system and its relationship to the overall observed plasmid population dynamics. This approach holds potential for application to other conjugation systems, mobile genetic elements (MGEs), or infection models, offering a promising avenue for advancing our understanding of microbial dynamics and antibiotic resistance spread.\u003c/p\u003e "},{"header":"Material \u0026 Methods","content":"\u003ch2\u003eBacteria, plasmids and growth media\u003c/h2\u003e\u003cp\u003e \u003cem\u003eE. coli\u003c/em\u003e DH5α and plasmids used in this study are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Plasmid X61 and X13 were transferred to \u003cem\u003eE. coli\u003c/em\u003e DH5α via CCMB80 chemical transformation to be used as donor and recipient host cells, respectively. Selection was carried out on Luria-Bertani (LB) agar supplemented with the appropriate antibiotics: kanamycin (Km\u003csup\u003eR\u003c/sup\u003e: 50 mg/mL) and chloramphenicol (Cm\u003csup\u003eR\u003c/sup\u003e: 25 mg/mL).\u003c/p\u003e\u003ch3\u003eMating Assay\u003c/h3\u003e\u003cp\u003eOvernight cultures of donor and recipient strains were re-grown for 2–3 hours in a 200 rpm shaking incubator at 37°C. Following incubation, the cultures were washed three times with 1 mL of PBS to eliminate residual antibiotics. After removing the supernatant, the cellular pellet was resuspended and adjusted to an OD600 of 0.3 using PBS. Donors and recipients were combined at ratios of 1:1 or 1:1000 as indicated. Ten microliters of the mixture were applied to a 3x3 mm nitrocellulose membrane placed on LB agar plates. Subsequently, the plates were incubated at 37°C for the specified durations. Following filter mating, the nitrocellulose membrane was resuspended in 1 ml of PBS through gentle pipetting or vortexing. For long term conjugation experimenting lasting for multiple days, we refreshed media every 24 hr. Specifically, once a day, mating samples were resuspended from nitrocellulose membrane in 1 ml PBS. Then, ten microliters of resuspended sample were dropped on a new nitrocellulose membrane on fresh LB agar.\u003c/p\u003e\u003ch3\u003eCell Quantification\u003c/h3\u003e\u003cp\u003eFor each experiment, all mixtures were serially diluted, and subsequently, ten microliters of the mixtures was dropped on selective agar plates to quantify the numbers of donors (D), recipients (R), and transconjugants (TC). Plasmid transfer frequency (𝑓) was determined by counting colonies and calculated using the formula 𝑓 = 𝑇C/𝑅\u003c/p\u003e\u003ch2\u003eComputational Model and Parameter Estimation\u003c/h2\u003e\u003cp\u003eMass action kinetic model of plasmid conjugation and Metropolis Monte Carlo algorithm were implemented in python on google colab platform (see detail and codes in supplementary). Data visualisation and analysis were performed using Matplotlib and Seaborn package in python. Generative AI (ChatGPT) was used for guiding python programming and revising manuscript.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eS. K., C. J., C. J. conducted experimental work; S. K. and C. J. (Jaichuen) analyzed data. C. J (Jaichuen) and P. S. wrote the manuscript. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis study is financially supported by the Air Force Office of Scientific Research, USA, under award number FA2386-23-1-4017 and Ministry of Higher Education, Science, Research and Innovation, Thailand, under award number RGNS 63-131. We would like to thank Dr. Sudarat Chadsuthi from the Department of Physics, Faculty of Science, Naresuan University, for her valuable comment on the manuscript. We would also like to thank Faculty of Medical Science, Naresuan University for supporting all facilities.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBallnus, B. \u003cem\u003eet al.\u003c/em\u003e Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems. BMC Syst. Biol. 11, 1\u0026ndash;18 (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBethke, J. H. \u003cem\u003eet al.\u003c/em\u003e Vertical and horizontal gene transfer tradeoffs direct plasmid fitness. Mol. Syst. Biol. 19, 1\u0026ndash;10 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBober, J. R., Beisei, C. L. \u0026amp; Nair, N. U. 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Commun. 15, 1\u0026ndash;9 (2024).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBacterial strains and plasmids used for the conjugation in this study.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStrains/Plasmids\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelevant characteristics\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSource/Reference\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eE. coli\u003c/em\u003e strains\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDH5α (Donor and recipient cells)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ehsdR17(rK – mK þ) F– mcr1 Δ(mrr-hsrRMS-mcrBC) 80(lacZΔM15) ΔlaX74 recA1 endA1 araD139 Δ(ara, leu)7697 galU galK rpsL nupG\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThermo Fisher Scientific\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003ePlasmid\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eX013\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ep1008, Ori ColE1, Cm\u003csup\u003er\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eprovided by Dr. Drew Endy, Endy lab\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eX061\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003epMATINGα-msfGFP, PEM7 → msfGFP, Ori RK2, Tra1 and Tra2 gene, Km\u003csup\u003er\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAparicio et al., 2022\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"conjugation, plasmid, Bayesian Approach, Markov Chain Monte Carlo","lastPublishedDoi":"10.21203/rs.3.rs-4698773/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4698773/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePopulation dynamic models that explain and predict the spread of conjugative plasmids are pivotal for understanding microbial evolution and engineering microbiomes. However, prediction uncertainty of these models has rarely been assessed. We adopt a Bayesian approach, employing Markov Chain Monte Carlo (MCMC), to parameterize and model plasmid conjugation dynamics. This approach treats model parameters as random variables whose probability distributions informed by data on plasmid population dynamics. These distributions allow us to estimate confidence intervals of the model\u0026rsquo;s parameters and predictions. We validated this approach using synthetic population dynamic data with known parameter values and experimental population dynamic data of mini-RK2, a miniaturized counterpart of the well-characterized and widely used RK2 conjugation plasmids. Our methodology accurately estimated the parameters of synthetic data, and model predictions were robust across time scales and initial conditions. Incorporating long-term population dynamic data enhances the precision of parameter estimates related to plasmid loss and the accuracy of long-term population dynamic predictions. For experimental data, the model correctly explained and predicted most population dynamic trends, albeit with broader confidence intervals. Overall, our method allows for deeper investigation of plasmid population dynamics and could potentially be generalized to study population dynamics of other mobile genetic elements.\u003c/p\u003e","manuscriptTitle":"A Bayesian Approach for Parameterizing and Predicting Plasmid Conjugation Dynamics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-01 15:42:08","doi":"10.21203/rs.3.rs-4698773/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-15T17:30:58+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-15T07:25:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-14T21:27:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"244422348960321581921577796449764076246","date":"2024-09-30T10:49:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"94518829616696269886568117821712987690","date":"2024-09-27T16:10:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-27T15:11:25+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-09-26T12:10:52+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-12T14:46:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-09T04:22:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-07-07T04:57:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"38bec725-dd75-450c-8da8-7ca52d90463c","owner":[],"postedDate":"August 1st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35387093,"name":"Biological sciences/Microbiology/Bacteria/Bacterial genetics"},{"id":35387094,"name":"Biological sciences/Ecology/Ecological genetics"},{"id":35387095,"name":"Biological sciences/Ecology/Ecological modelling"}],"tags":[],"updatedAt":"2025-03-10T17:09:22+00:00","versionOfRecord":{"articleIdentity":"rs-4698773","link":"https://doi.org/10.1038/s41598-024-82799-5","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-03-03 15:56:55","publishedOnDateReadable":"March 3rd, 2025"},"versionCreatedAt":"2024-08-01 15:42:08","video":"","vorDoi":"10.1038/s41598-024-82799-5","vorDoiUrl":"https://doi.org/10.1038/s41598-024-82799-5","workflowStages":[]},"version":"v1","identity":"rs-4698773","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4698773","identity":"rs-4698773","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}