Deciphering plasmid replication dynamics: a computational approach to predict ColE1-like plasmid copy number

Abstract

Plasmids constitute a key tool in synthetic biology, providing a versatile framework for various research and industrial ventures. An essential determinant of plasmid functionality is its copy number, impacting both protein production rates and host cell metabolic burden. However, currently there is no model that can computationally predict the plasmid copy number from the sequence of its origin of replication (ORI). We present a novel software solution tailored to simplify plasmid copy number design, poised to redefine plasmid engineering workflows. At the heart of our tool lies a comprehensive machine learning model, informed by numerous features extracted from the ORI. This computational model emphasizes the importance of promoter strength and the RNA folding dynamics of regulatory elements within the ORI. Additionally, we detail a robust protocol for the efficient manipulation of plasmid ORIs used to validate our model’s predictive capabilities. This innovation represents a paradigm shift in plasmid-centric methodologies, offering unprecedented avenues for advancement in synthetic biology research and industrial applications. The software is available at: https://pcn-gradient.vercel.app/

1. Introduction

Plasmids are extrachromosomal DNA fragments commonly found residing in bacteria and can replicate independently of their host chromosome [1]. Plasmids are often used as vectors for the production of recombinant proteins or other substances [2]. Plasmid copy number (PCN) refers to the quantity of plasmid copies that can be found in a single cell.

Plasmids are integral in diverse applications in synthetic biology. For example, in the realm of metabolic engineering for biomanufacturing, plasmids are used to incorporate metabolic pathways within microorganisms [3–5]. This optimization is crucial for achieving maximum production efficiency and profitability. In the context of DNA vaccines, plasmids serve as carriers that introduce genetic material into cells, which trigger an immune response [6,7]. Maintaining an optimal PCN is critical for ensuring robust gene expression, efficient production of antigens and, ultimately, the effectiveness of the vaccine. Microbial biosensors, designed for applications in environmental monitoring, food quality assessment and biomedical contexts, rely on plasmid-driven genetic circuits [8–10]. Precise control over PCN is necessary to modulate the sensitivity and detection range of these biosensors. In the emerging field of computation within living cells, plasmids serve as essential components of synthetic gene circuits. Researchers design these circuits to perform complex computational operations within microorganisms [11,12]. Modulating the PCN of plasmids in these circuits allows for the fine-tuning of logical assessments and computations, providing higher degrees of freedom in the design of biological computing systems.

PCN is associated with gene expression, but the relationship is complex and depends on various factors. For example, overexpressing a gene can result in increased protein production; however, excessive expression may have toxic effects [13,14]. Therefore, controlling PCN is important for designing and optimizing biology systems to achieve the desired outcomes.

ColE1-like plasmids are the most popular vectors for recombinant protein expression in Escherichia coli. As a direct result, their respective plasmid replication regulation system is highly studied. ColE1 plasmid replication requires the formation of a primer that is complementary to the origin of replication (ORI). The plasmid codes for RNAp (also known as RNAII), a pre-primer complementary to the ORI. The 3′ end of RNAp forms a stable hybrid with the ORI, guided by complementary GC-rich stretches. This type of hybridization is known as an R-loop ([15]; see figure 1). The pre-primer matures into a primer when E. coli’s RNaseH processes the R-loop, creating a free 3'-OH terminus. DNA polymerase I can then extend this terminus, initiating leading-strand synthesis, which is the first step in the plasmid’s replication process [16,17]. RNA interference (RNAi, also known as RNAI) is complementary to RNAp, and together they form a complex known as a ‘kissing complex’ [18]. The kissing complex can be stabilized by interacting with the RNA one modulator (ROM), also known as the repressor of primer (Rop) protein dimer [19]. When bound together, this interaction interferes with the binding of RNAp to the ORI. Regulation is also affected by E. coli’s metabolic burden. RNAp and RNAi can interact with uncharged tRNA; such interactions prevent the formation of a kissing complex, thereby allowing RNAp to initiate plasmid replication [20]. By strategically manipulating these modulators, we gain the capability to fine-tune the replication dynamics of plasmids. A known change is the absence of the ROM gene and a single point mutation in the ORI region, both of which lead to the high copy number nature of plasmid pUC19 [21].

Figure 1.

(A) RNAp transcription forms a stable hybrid with the origin of replication creating a pre-primer. This pre-primer undergoes maturation into a primer through the host’s RNaseH cleavage, facilitating the recruitment of RNA polymerase to initiate plasmid replication. (B) The transcription of RNAi leads to its binding with RNAp, resulting in the formation of a kissing complex. This complex inhibits the primer creation and the initiation of plasmid replication.

Several predictive models simulate ColE1-like PCN dynamics. Brendel & Perelson [22] and Paulsson et al. [23] developed a kinetic model that includes the concentrations of RNAp, RNAi and the plasmid and the interactions between these variables. Goss & Peccoud [24] used a stochastic model to study plasmid distribution in bacterial populations based on the kinetic models mentioned above. A more recent kinetic model by Freudenau et al. [25] extended the previous models by adding the interactions of RNAp with uncharged tRNA.

Our goal was to develop computational models that can predict the way the PCN is encoded in the plasmid sequence and use the model as a tool to design the requested copy number. Thus, the approach enables us to understand, for the first time, the relevant ORI features that affect the PCN; additionally, the project has the potential to enhance the optimization of plasmid-related work in both academic and industrial settings. Additionally, we created a user-friendly Web tool that allows scientists and laboratory workers to easily obtain the modified plasmid sequence for their desired copy number.

2. Results

2.1. Description of the research aims and flow

Our study is based on [26], which reports a method to experimentally adjust PCNs by physically altering the sequences of RNAp and RNAi, which are critical for regulating plasmid replication. They achieved this by generating a spectrum of 1194 ColE1-based plasmid variants, each with modified RNAp or RNAi sequences, and then measuring the resulting copy numbers across these variants, ranging from 1 to 800 copies per cell, for a subset of nine variants using ddPCR.

In contrast, our work introduces a novel computational tool that predicts PCNs based on the features of ORI sequences. We analyse the predictive features and provide novel insights related to the way copy number is encoded in the ORI.

Based on the model, we provide for the first time a user-friendly software for designing copy numbers in ColE1-based plasmid, enabling researchers to streamline the design process in synthetic biology with less experiments.

The research we performed in this study is summarized in the flowchart in figure 2. All the technical details of the methodology appear in the §4; here we will briefly review them. The study begins by collecting copy number measurements from Rouches et al. [26] (A) and genomic data (B) that will be used to train our model for PNC prediction. We also incorporated RNA folding predictors (D) and transcription models (F) for designing relevant features for our model. We extracted around 6000 features (J), including statistical features (H), sequence-related features (I), RNA folding features (E) and transcription features (G). This was followed by feature selection (K) to identify the most relevant aspects of ORI sequences affecting PCN. Various machine learning models, such as linear regression, neural networks, random forest and gradient boosting models (L), were evaluated, and their hyperparameters were optimized (M). The trained model was then used to predict PCN (N), and its results are analysed for interpretability (O) to ensure alignment with biological insights while also uncovering new ones. The study also included an experimental protocol for ORI replacement (P) to validate newly designed ORIs based on model predictions (Q). The copy number of these sequences was measured and used for comparison with the model predictions for further validation of the model’s predictions (R). Finally, a user-friendly Web tool (S) was developed, allowing researchers to modify plasmid sequences to achieve desired copy numbers.

Figure 2.

The flow diagram of the research (details in the text).

2.2. A computational model for predicting plasmid copy number from the origin of replication sequence

A model able to predict PCN from the ORI sequence will have practical applications, allowing researchers to design new plasmids with a specific copy number tailored to their individual needs. Creating it as an explainable model will also allow us to gain new insights into the biology of Col-E1-like plasmid replication, insights that can be capitalized upon in future research. We used a database of tagged ORI sequences (meaning different ORI variants, each with a corresponding copy number) that was recently published [26] as the foundation of our model. In the article, the authors created two libraries of ORI variants, one with mutations in the RNAp promoter region of the ORI and the other with changes in the RNAi promoter region. We therefore choose to create two separate models for each of the datasets. Setting out to build the framework for our model was first to extract sequence-related features from the literature, and second, to find the best fitting model for the task. In order to test different models, we split our data into training, test and validation sets (70%, 15% and 15%, respectively) and verified that all sets feature a copy number distribution similar to that of the entire dataset.

In order to use the promoter sequences for interpretable machine learning models, approximately 6000 features were engineered to represent transcription-related properties in prokaryotes. Raw sequences require preprocessing and feature extraction to transform them into numerical representations that capture relevant biological information, making them suitable as a model input. Each feature captures different aspects of biological interactions and molecular mechanisms that may influence PCNs.

These features include motif scores and p-values derived from known databases [27,28], calculated using the find individual motif occurrences (FIMO) module [29], a tool that scans DNA sequences for motif occurrences; position-specific scoring matrix (PSSM) scores based on nucleotide frequencies in high PCN sequences; promoter strength [30]; one hot encoding; nucleotide counts [31]; interaction and transcription rate measurements [32]; sequence entropy and de novo motif detection using HOMER [33]. Many of these features are computed at a resolution of a single nucleotide, allowing for the modelling of sequence-level determinants influencing the PCN. The features were selected to capture the complex biological factors that influence transcription in prokaryotic organisms, facilitating the development of predictive models (see the §4 for more details).

We trained eight different models, each for RNAp and RNAi, including neural network [34], linear regression models [35], random forest [36] and ensemble boosting learning models [37] such as CatBoost [38] and XGBoost [39]. Categorical boosting (CatBoost) is optimized for handling categorical features efficiently, while extreme gradient boosting (XGBoost) is designed for computational speed and model performance through advanced regularization techniques. We then tested their performance on the test set, and the results are shown in electronic supplementary material, figure S1. On the RNAp dataset, CatBoost and XGBoost performed best, with similar results (see more details about these models in the electronic supplementary material). In order to enhance performance and mitigate noise and overfitting, we utilized a voting model that combines both models, averaging their predictions (model performance shown in figure 3). On the RNAi set, CatBoost outperformed the rest of the models (results shown in figure 3). Both models were evaluated using Spearman and Pearson correlations, R² score, and mean absolute error (MAE). As can be seen, both models exhibited a strong correlation between their predictions and the test set (RNAp: Pearson’s correlation coefficient r = 0.959, p = 7.92 × 10⁻⁷⁰ and Spearman correlation coefficient ρ = 0.863, p = 1.30 × 10⁻³⁸ ; RNAi: Pearson’s correlation coefficient of r = 0.793, p = 5.13 × 10⁻¹³ and a Spearman correlation coefficient of ρ = 0.821, p = 1.62 × 10⁻¹⁴), demonstrating their ability to predict the PCN of plasmids that were not used for their training, based on the RNAp or RNAi promoter sequences alone. The relative error of predicted PCN in different ranges is displayed in electronic supplementary material, figure S3. On a standard personal computer, the model predicts the copy number from the input sequence in just a few seconds.

Figure 3.

(A) RNAp results showing actual copy number versus predicted copy number, with a Pearson correlation of 0.959 (p = 7.92 × 10⁻⁷⁰) and a Spearman correlation of 0.863 (p = 1.3 × 10⁻³⁸). (B) RNAi results showing actual copy number versus predicted copy number, with a Pearson correlation of 0.79 (p = 5.13 × 10⁻¹³) and a Spearman correlation of 0.82 (p = 1.62 × 10⁻¹⁴). (C) A table of the results.

2.3. Model explainability

By identifying which features of the ORI sequence are most influential in determining the PCN, we could uncover new aspects of the sequence or structural elements that are critical for the replication process, gaining insights into the biological mechanisms that regulate ColE1 replication. To do so, we evaluate the feature distributions and their relationship to PCN, examine the impact of individual features on model predictions and, finally, use these insights to interpret the mechanisms of the ColE1 replication system. Electronic supplementary material, table S2 includes the definitions of the key features.

2.4. Feature distributions and their relation to copy number

The model was trained using engineered features stated earlier, which represent key transcriptional and sequence-related properties. A full description of all extracted features can be found in the §4. After feature selection, the RNAp model is based on 18 features, and the RNAi model is based on 20 features. To evaluate the contribution of different features to PCN prediction, we examined feature importance scores from XGBoost and CatBoost models (figure 4A–C). The most important feature for RNAp was dG_total for CatBoost and rpoD16_score for XGBoost; both features are related to the efficiency of the RNAp’s promoter: dG_total quantifies the change in Gibbs free energy associated with the binding of RNA polymerase to a promoter, a critical determinant of transcription initiation. In the context of [30], the dG_total is directly linked to the RNAp promoter strength, which in turn influences the transcriptional activity of a plasmid. A lower dG_total indicates a more energetically favourable binding and typically correlates with higher transcriptional activity. Since PCN is partly regulated by the efficiency of its transcription initiation, dG_total serves as a predictive indicator for the potential PCN in a cellular environment. This connection allows us to infer that promoters with optimized dG_total values could be engineered to achieve desired copy numbers, enhancing both plasmid stability and gene expression efficiency. The rpoD16_score feature reflects the presence and strength of the rpoD16 motif, known for its role in recruiting a sigma factor, which is essential for initiating transcription at specific promoters. Higher scores indicate a greater probability of successful biosynthesis.

Figure 4.

(A) Priming RNA feature importance for the CatBoost model, the higher the feature importance score, the higher the feature contribution to the predicted copy number. (B) Priming RNA feature importance for the XGBoost model, the higher the feature importance score, the higher the feature contribution to the predicted copy number. (C) Inhibitory RNA feature importance for the CatBoost model, the higher the feature importance score, the higher the feature contribution to the predicted copy number. (D) The absolute mean Shapley additive explanations (SHAP) value for each feature chosen during the feature selection process in the model based on the RNAp model. (E) The absolute mean SHAP value for each feature chosen during the feature selection process in the model based on the RNAi model. More information about the features appearing in the figure are given in the electronic supplementary material.

For the RNAi CatBoost model, the most important features were seq_end_400_375_385 and TGCGCGTTTAAT_denovo_high, which are defined here: RNAfold [40] provides the probability of each nucleotide pairing with a nearby nucleotide. The feature seq_end_400_375_385 indicates that the first 400 bases of the RNA sequences were analysed, specifically checking the probability of the nucleotide in index 375 to pair with the nucleotide in index 385. The sequence TGCGCGTTTAAT is a de novo motif that appears at higher rates in groups of promoters that have a high copy number compared with a reference group of promoters with a low copy number. Thus, this motif is probably related to the transcription rate of the RNAi that maximizes PCN.

Figure 5 displays the selected features along with their respective copy numbers and the distribution patterns for these features. In the RNAp-related features distribution graph, rpoD16_score exhibits a pronounced peak, indicating a strong effect of a specific score on the copy number. The second peak at 0 in the rpoD16 score distribution represents promoter sequences, where the motif was not detected. This suggests that a subset of promoters in our dataset does not rely on the rpoD16 motif for transcription initiation, potentially utilizing alternative sigma factors or regulatory elements. Additionally, figure 6 shows a spread of values of the feature dG_total, with most data points concentrated around −3.4 to −2.7, suggesting a stability region that could be critical for high copy numbers: it is possible that when dG_total is too high (i.e. a weak binding of RNA polymerase to a promoter) the RNA polymers will start transcription with low rate and this will correspond to a low PCN. However, it is possible that when dG_total is too low (i.e. a strong binding of RNA polymerase to a promoter), too many plasmids are generated and this is toxic to the host cell.

Figure 5.

(A) Feature distributions corresponding to their copy number for the common features of XGBoost and CatBoost in the voting model for RNAp. (B) Feature distributions corresponding to their copy number for the two most important features of CatBoost in the RNAi model.

Figure 6.

(A) SHAP value for each value of the feature dG_total. There is a specific range of dG_total values with positive SHAP values. (B) Copy number as a function of the feature dG_total. It can be seen that high copy number sequences are in the same dG_total range as observed in A, and we validated this conclusion statistically by enrichment p-value and found that it was significant.

For RNAi-related features, the scatter plot for seq_end_400_375_385 in figure 5 shows a dense accumulation of points at the lower end of the scale, which may indicate a significant negative correlation (Pearson’s correlation coefficient r = −0.15, p = 0.006; Spearman correlation coefficient ρ = −0.16, p = 0.0045) with increased copy numbers; however, the relation seems more complex than a simple monotonic relation. Conversely, the feature TGGCGGTTTAAT_denovo_HIGH, which is a de novo motif of the high PCN, displays a spread of data points, with notable bars extending towards moderate values, hinting at the possibility of complex interactions of this feature and other features to affect the copy number.

2.5. Impact of individual features on model predictions using Shapley additive explanations and their biological interpretation

Shapley additive explanations (SHAP) [41] is a tool used to interpret machine learning models by assigning each feature an importance score for a particular prediction. It is based on Shapley values from game theory, which allocate fair payoffs to players based on their contribution to the total payout. SHAP helps identify which features most strongly influence the model’s predictions, revealing their impact on the predicted outcome. This insight allows us to identify the most significant features in determining the PCN, providing a deeper understanding of the underlying plasmid replication system. The SHAP analysis provided a quantitative measure of each feature’s influence on the model’s predictions, highlighting those with high absolute Shapley values across both RNAp and RNAi models. Figure 4D,E shows the SHAP values for each feature chosen to train the models during the feature selection process. In the RNAp model, dG_total emerged as the most influential feature, leading to significant positive impacts on predicted copy numbers. The strong positive influence of dG_total was particularly striking in contrast to more moderate effects of other features, positioning dG_total as a potentially critical determinant in the RNAp model’s decision-making process. Within the RNAi model, TGCGGTTTAAT_denovo_HIGH was identified as having the highest mean absolute SHAP value, signifying its substantial role in the model’s output.

2.6. Interpretation of the ColE1 replication system’s mechanisms

Since dG_total appeared to be significant in our analysis, we continue to analyse it using a SHAP force plot. This plot, shown in figure 6A, visualizes the cumulative effect of features on the model’s prediction and accumulates the SHAP values in a sorted manner to illustrate the sequential impact of each feature on the model’s output. It highlights which values of the feature are driving the model towards a higher or lower copy number prediction, and can illustrate how dG_total contributes to the behaviour of the colE1 replication system.

The dG_total feature represents the overall change in free energy (Gibbs free energy) associated with the plasmid replication process. A lower dG_total value indicates a more thermodynamically favourable biosynthesis reaction.

The analysis of the ColE1 replication system mechanisms, particularly through the lens of the effect of the dG_total feature on the copy number, offers valuable insights into the plasmid replication process. The dG_total, as depicted in figure 6, plays a critical role in the replication efficiency, with a specific range appearing to be optimal. This optimal range, located between −3.4 and −2.7, corresponds to a more thermodynamically favourable reaction for plasmid replication, thereby indicating a threshold effect where certain energy levels are conducive to higher copy numbers. The presence of clustering within this range suggests a stable and efficient replication process, with dG_total values outside this range potentially leading to less favourable replication outcomes. This range represents the reaction’s thermodynamic ‘sweet spot’—a state of maximum favourability characterized by the stable interaction of molecular complexes, efficient regulatory mechanisms, environmental adaptation and optimal resource utilization. In the context of the ColE1 replication system, understanding this optimal dG_total range is crucial for enhancing the efficiency and predictability of plasmid replication processes, which is of significant interest in genetic engineering and biotechnology applications.

2.7. Plasmid copy number measurements and correlation to the model predictions

We were successfully able to replace the origins of replications of a pUC19 plasmid with new modified sequences taken from the literature or generated by our model. This innovative approach allowed us to construct a library of plasmid sequences, which played a crucial role in the verification and improvement of our model. This library is available in the electronic supplementary material. This procedure, as illustrated in figure 7A, involves the following steps: a pUC19 plasmid is amplified using polymerase chain reaction (PCR) to introduce new flanking regions around the ORI. Next, a restriction enzyme is employed to specifically target a cut site in the original pUC19 sequence. A modified ORI, synthesized from tool-generated data, is then integrated into the pUC19 backbone via homologous recombination and then verifying the modified plasmids after transformation into E. coli using Sanger sequencing, confirming the presence of the intended mutations within the RNAp and RNAi promoters (see more details in figure 7A and in §4). Following the successful verification of mutations, we proceeded to calculate the copy numbers of the newly constructed plasmids. To minimize potential errors stemming from DNA isolation procedures, we adopted a colony qPCR approach to measure the PCNs for the various constructs within our library. The results of this copy number analysis provided valuable insights into the replication dynamics of these engineered plasmids. Based on these findings, as anticipated, it is evident that substituting the promoter sequences at the ORI has an impact on the PCN.

Figure 7.

(A) A modified origin of replication is synthesized from tool-generated data, followed by PCR amplification of pUC19 to incorporate new flanking regions around the ORI. Subsequently, a restriction enzyme is utilized to target a specific cut site in the original pUC19 sequence. The modified ORI is integrated into the pUC19 backbone via homologous joining, resulting in successful transformation of the modified pUC19 vectors. (B) Predicted copy number by the improved model (see §4.9) versus ddPCR or qPCR measurements. Pearson correlation of 0.652, p = 0.028.

We used ddPCR measurements by Rouches et al. [26], in addition to our qPCR measurements to improve our model. As done by Rouches et al., we also performed a mathematical transformation to the copy number data used to train our model for improving the model performance (see more details in the §4).

We achieved a high correlation on both the test set and our biological results (Pearson correlation of 0.652, p = 0.028), as seen in figure 7B, which presents a linear fit between the predicted copy number and the ddPCR/qPCR measurements. Of the nine available ddPCR measurements from Rouches et al. [26], only three are shown here as they were part of the held-out test set following our training/validation split. This further verifies the reliability of our model and the success of introducing a machine learning model for copy number engineering and prediction.

2.8. Web tool for predicting plasmid copy number

We used our machine learning model results and developed a software tool (available at: https://pcn-gradient.vercel.app/) that enables researchers to design and predict PCNs simply and efficiently. The model’s high performance allows our tool to accurately predict the copy number of ColE1-type plasmids, based on their sequence. The tool offers several key features to enhance plasmid sequence manipulation and customization. As demonstrated in figure 8, users can input a plasmid sequence (FASTA or GenBank files) along with the desired copy number, and the tool generates a modified sequence with ORI adjustments to achieve the specified copy number. Its versatility extends to both modifying existing plasmids for a desired copy number and creating plasmids from scratch with the designated copy number. For tailored adjustments, the tool efficiently generates FASTA files, ensuring precision in achieving the desired copy number. Additionally, users can request multiple copy numbers simultaneously, receiving dedicated sequences for each. The tool’s output includes clear and concise plasmid maps, seamlessly integrated with annotations within the sequence, providing comprehensive information. Accessible on both computers and mobile devices, the tool caters to diverse user needs. Furthermore, developers can seamlessly integrate the tool into their projects using the provided API, enhancing its adaptability and accessibility.

Figure 8.

Ctrl-C Web tool. (A) Choose between (i) using the provided plasmids (currently supporting pUC19 and pBR322), (ii) uploading your own plasmid’s FASTA file or (iii) providing the plasmid’s sequence as text. Choose your desired copy number. If you want a grid (range) of copy numbers, first click on the ‘grid’ option, then enter five values of your desired grid of copy numbers. Choose whether to visualize the annotated plasmid map or not. Click ‘Get Modified Plasmid’ and wait for the results to appear on the screen. (B) If ‘visualize the plasmid map’ checkbox was marked, clicking on the different site of the plasmid’s map illustration will refer the user to the site sequence. Click ‘Download Modified Sequence’ to download the plasmid modified sequence as a FASTA file.

This accomplishment contributes to the field of synthetic biology in a notable way. For the first time, a model has been successfully developed to predict PCN, solely based on the ORI sequence. This is particularly important because it addresses a critical challenge in genetic engineering, and researchers can now more accurately engineer plasmids for desired traits, since plasmids are essential tools in gene cloning, recombinant protein synthesis, genetic editing, complex genetic circuits and many more applications.

3. Discussion

Controlling the expression levels of genes is crucial in the fields of synthetic biology and biotechnology because it influences the yield of protein production and the metabolic burden related to the heterologous genes introduced into the engineered organisms. Currently, most of the researchers in the field either ignore this issue or try to modulate the production level via choosing among a small number of promoters and/or plasmids.

In this study, we suggest a novel approach for dealing with this challenge: accurate model-based fine-tuning of the PCN. Our approach can be used to modulate the exact protein levels in the cell: a high copy number can enhance the protein yield but may also lead to metabolic burden and instability, whereas a low copy number may result in insufficient product formation.

In recent years, advancements in synthetic biology have been markedly accelerated by the integration of computational models. These models have facilitated a deeper understanding of biological processes, enabling researchers to design biological systems more efficiently. By simulating complex biological systems, scientists can predict how these systems will behave in real life, thereby reducing the need for extensive trial and error in the laboratory.

Specifically, computational models have already played a crucial role in the field of plasmid engineering, enhancing our understanding and capabilities in genetic manipulation and biotechnological applications. For instance, the use of machine learning techniques such as artificial neural networks and random forests in plasmid classification has been demonstrated by the MetaPCbin tool [42], which distinguishes plasmids from chromosomes in DNA sequences.

Here, we suggest for the first time a model that can predict PCN based on the ORI sequence. Using the computational model, a library of plasmid sequences was constructed, and a colony qPCR method was used to measure copy numbers, validating the model’s predictions and allowing for improvements.

Our model can be used both for understanding the regulation of PCN and for engineering it.

The observed correlation between the model predictions and qPCR measurements is significant (r = 0.652, p = 0.028). We believe that the correlation is not higher due to intra-population heterogeneity and stochasticity of the PCN in the population. Future studies should take this into consideration both from the experimental and computational points of view: experimental techniques for measuring the PCN distribution will provide an estimation of the nature of this stochasticity and can be used to infer stochastic models of PCN.

We developed two separate machine learning models to predict the copy number from RNAp and RNAi promoter sequences using a database of tagged ORI sequences. The models demonstrated a high correlation in predicting PCNs not used for training the model. We found that the sequence features related to transcription regulation of the RNA genes encoded in the ORI (e.g. dG_total and rpoD16_score) are the most important features in our models. These features represent aspects related to transcription efficiency such as the free energy of promoter binding and the strength of sigma factor recognition sites. Based on the feature analyses, insights into the ColE1 replication system were gained: there is a specific range of ‘dG_total’ values that will optimize the copy number, where a too high or too low copy number will result in lower copy numbers. Lower efficiency of interaction may be related to lower levels of RNAp and thus less replication and fewer plasmids; on the other hand, it is possible that very high levels of RNAp due to very high interaction efficiency are too toxic.

Interestingly, our analysis suggests that the interactions between RNAp and RNAi within the ColE1 plasmid family, particularly in the pUC19 model, through their respective secondary structures, play a pivotal role in the regulation of PCN. Specifically, the inclusion of secondary structure features into our computational model has significantly enhanced its predictive accuracy. This result supports previous studies in the field about the importance of the RNA–RNA interaction of RNAp and RNAi [43,44]. Future experimental studies can help understanding the top features in our models (e.g. motifs such as TGCGCGTTTAAT); for example, this can be done by designing for each such feature a library that will modulate the feature values (while trying not to effect other features) to better understand the nature of the effect of the feature on PCN.

In the current study, we were able to quantify how mutations in the RNAi promoter impact the RNAp secondary structure, which is critical for designing strategies to optimize plasmid stability and efficiency in synthetic biology applications.

The performances of the RNAp model are significantly better than the performances of the RNAi. We suggest biological and technical explanations related to this discrepancy: as mentioned, the RNAi and RNAp promoters regulate plasmid replication through different mechanisms. The RNAi system involves more complex regulatory interactions that might not be fully captured by the current features, such as the formation of a ‘kissing complex’ with RNAp that is stabilized by the ROM protein dimer ([18,19]; see details in §1). Conversely, the RNAp model benefits from more straightforward dynamics between the promoter sequences and plasmid replication rates, which are easier to model with available features.

Additionally, the RNAi model is based on fewer data points compared with the RNAp model (336 versus 833). This difference in dataset size contributes to the variance in model performance.

Finally, we suggest a Web-based software tool that offers a user-friendly platform for researchers to efficiently design, predict and modify plasmid sequences, thereby streamlining research workflows and enhancing the precision of genetic manipulations. We believe that our tool will be helpful for researchers in academia and the biotechnology industry.

While our work has marked a significant advance in the field of synthetic biology by enabling the prediction and design of PCNs using computational models, it does present certain limitations. As mentioned above, a fundamental problem in heterologous gene expression is the fine-tuning of the exact protein expression such that it will be as high as possible without too strong an effect on the growth of the host cell. Thus, our tools should be used together with models that can predict the exact protein levels and their effect on cell fitness. While some aspects of these models have been developed (for example, models with all the ribosomes and mRNA in the cell [45]), others will be developed in the future. In addition, performing copy number measurements of various ORI sequences in different conditions will enable us to fit the model to various conditions.

Moreover, maintaining the stability of these plasmids within the host over time, especially under varying environmental and selective conditions, is another concept that needs to be addressed; this can be done with additional computational tools (for example [46]); however, in this frontier also additional research is needed.

Finally, we show that the predictions of our model with experimental results are high and significant; however, they are, of course (as in the case of any systems biology model), not perfect. We believe that the model can be improved if more high-quality experimental data are generated for training the model; such data will probably help detect additional relevant features. It is also important to emphasize the fact that our tool is relevant for ColE1-type plasmids in E. coli. These are widely used plasmids but there are additional plasmid systems that are used in the biotech industry for E. coli and for other organisms; with relevant large-scale measurements of copy numbers of plasmids with different ORI, the approach developed here can be applied to additional plasmid types and organisms.

4. Material and methods

4.1. RNAp and RNAi promoter variants library

We analysed the pUC19 plasmid library given in [26], consisting of distinct promoter variants for RNAp or RNAi. The mutations are specifically confined to the promoter regions of RNAp or RNAi. The data contain 366 RNAi promoter variants and 833 RNAp promoter variants with their corresponding copy number.

The models were trained separately on RNAp and RNAi datasets, allowing each model to learn distinct patterns related to PCN. The features were selected via a feature selection process (details below) to make sure that there will be no overfitting. The number of features is also affected by the size of the dataset and the details of the biological mechanism. When there are more measurements, it is usually possible to infer more complex models (with more features). Thus, among others, fewer features were selected for the RNAi model as we had fewer measurements related to the RNAp model.

The variants were edited at positions (−33,−30), (−11,−8) and +1 for RNAp and (−33,−30), (−10,−7) and +1 for RNAi (figure 9F). We divided the data into three sets, 15% test set, 15% validation set and 70% train set. During this process, we ensured that the copy number distribution in each set remained consistent with the original dataset.

Figure 9.

(A) The PSSM of RNA priming; the top figure is for high copy number, and the lower figure for low copy number. (B) The PSSM of RNA inhibitor; the top figure is for high copy number, and the lower figure for low copy number (see more details about PSSM calculation in the §4.2). (C) The interaction strengths between RNA polymerase and the subunit of RNA polymerase σ70 factor and promoter DNA (see more details in the §4.3 or in [47]). (D) RNA polymerase binding energy matrix. Colours indicate the contribution of each base pair to the total binding energy (see more details in the §4.2 or in [30]. (E) Model training and evaluation workflow. (F) A few examples of RNAp variants and their corresponding copy number. All the variants are mutated in positions −33 to −30, −8 to −11 and +1.

Additionally, we adjusted all negative copy number values to zero to ensure biological relevance and avoid generating nonsensical results.

4.2. Sequence features for machine learning

The promoter’s sequences cannot be used directly as input for the models, so approximately 6000 features were engineered to represent the sequence properties that correspond to transcriptions in prokaryotes. The features and their description are given in the electronic supplementary material; see also figure 9A–D.

The analysed features were:

• —Motifs. Motif files were downloaded from the DPINTERACT database [28] and the SwissRegulon E. coli database [27]. The score and p-value of each motif were calculated with the FIMO module [29], and sequences with no matching motif were replaced with a 0 score and a p-value of 1 (330 features).
• —PSSM score. The position-specific scoring matrix (PSSM) score of each sequence is calculated based on the 20% high copy number matrix, as follows:
  $${\displaystyle {\displaystyle [\mathrm{P}\mathrm{S}\mathrm{S}\mathrm{M}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}]={\log }_2\left(\frac{1}{N}\sum _{i=1}^{N}I\left(X_{i,j}=k\right)\right),}}$$

  where ${\displaystyle i\in \left(1,\dots ,N\right)\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}N\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h},j\in \left(A,C,T,G\right)}$ and $I(a=k)$ is an indicator function, where $I(a=k)$ is 1 if $a=k$ and 0 otherwise (one feature).

• —Promoter strength. The promoter strength was calculated as described in Brewster et al. [30] (three features).
• —One hot encoding features. Each promoter sequence was split into 144 (= 36 × 4) columns so that each column represents the index and nucleotide combination, and the value is set to 1 if it matches the current sequence and 0 otherwise (144 features).
• —Nucleotide count features. Nucleotide count features from an article by Muhammod et al. [31] (5945 features).
• —dG total and TX rate. These features represent the interactions between the promoter sequence and RNA polymerase with or without sigma factor and the transcription rate, as described in LaFleur et al. [32] (three features).
• —Entropy. The promoter sequence entropy was calculated as follows:
  $${\displaystyle {\displaystyle \mathit{S}=-\frac{\sum _{i=0}^n{p}_{\mathrm{i}}{\log }_2\left(p_{\mathrm{i}}\right)}{2},}}$$

  where $p_i$ is the probability of each nucleotide to appear in each index i (one feature).

• —De novo motif detection. Motifs that appear with higher rates in groups of promoters that have high copy number against a reference group of promoters with low copy number, and vice versa, were detected using hypergeometric optimization of motif enrichment (HOMER) [33] (29 features).

4.3. Secondary structure features for RNAi model

The model based on RNAi promoters, using the above features, produced less successful results than the model based on RNAp promoters. To improve this, we added features describing the RNAp secondary structure, considering the complementarity between RNAi sequences and RNAp promoters. Mutations in RNAi’s promoter can impact RNAp’s structure, leading to alterations in its secondary structure. Some of these structures are presented in electronic supplementary material, figure S2.

We investigated the replication mechanism of the ColE1 plasmid family, specifically pUC19, where RNAp’s persistence on the DNA template is vital for initiating replication. A key interaction involves a G-rich loop in the RNAp transcript binding to a C-rich stretch on the DNA, affecting RNAp conformations and the formation of RNA–DNA hybrids necessary for DNA synthesis [47].

RNAp contains three binding sites: alpha, beta and gamma. The RNAp transcript undergoes structural changes during transcription, forming three stem-loop domains and later an extended stem-loop. This folding is influenced by the pairing of alpha–beta or beta–gamma sequences, which determines the transcript’s ability to form the hybrid for DNA synthesis.

RNAi’s structure, with three stem loops and an unpaired region, binds to RNAp, influencing its folding and favouring beta–gamma pairing. This interaction affects primer formation, essential for replication [47].

Our study used RNAi and RNAp sequences from the pUC19 plasmid, analysing RNAi promoter mutations. We focused on nine specific mutation positions in the RNAi promoter, corresponding to key points in the RNAp sequence. We employed the ViennaRNA package [40], particularly RNAfold and RNAeval, to calculate RNAp’s secondary structure, considering the impact of RNAi promoter mutations. This approach allowed us to generate features describing RNAp’s secondary structure at different transcription stages, enhancing our RNAi-based model’s accuracy.

The features (additional approx. 25 000 features to the features detailed above) are calculated for a range of lengths of RNAp in order to describe its structure during transcription. See electronic supplementary material, table S1 for a description of the features.

4.4. Model training and evaluation

We explored various models, including neural networks [34], linear regression models [35], random forest [36] and ensemble learning models [37], while tuning their hyperparameters with Optuna [48] (more details below). We assessed the Spearman and Pearson correlations on both the training and validation sets. Notably, XGBoost [39], CatBoost [38], LightGBM [49] and random forest [36] demonstrated superior performance. Consequently, we advanced to the subsequent stages, feature selection and hyperparameter optimization, with these selected models.

For hyperparameter optimization, the best set of hyperparameters that fit the data and the model were selected using Optuna [48]. Optuna automates the search for optimal hyperparameter configurations using Bayesian optimization, where each trial employs a different set of hyperparameter values and evaluates an evaluation score on the validation set.

The feature selection was performed in two steps:

• (1) Mutual information based feature selection. We calculated the mutual information (MI) between each feature and the copy number, selecting those with MI values greater than the mean MI as potential candidates. Subsequently, we assessed the MI between the remaining features, identifying pairs of features exhibiting strong correlations within the top percentile. For each pair of correlated features, we chose the one displaying a higher MI with the copy number, ensuring the retention of the most informative attributes.

• (2) Boruta–SHAP based feature selection. Boruta–SHAP is a feature selection algorithm that combines the Boruta algorithm with SHAP values to select important features.

  • (a) Boruta [50] is a tree-based feature selection algorithm that works by creating random shadow features (noise) and comparing the importance of the original features with the importance of the shadow features. Features that are more important than the shadow features are kept, while features that are not more important than the shadow features are removed.

  • (b) SHAP [41] values are a way to measure the individual impact of each feature on the prediction of a model. SHAP values are calculated by considering all possible combinations of features and their impact on the prediction.

    Using Boruta–SHAP works by using SHAP values to rank the importance of the features and the shallow features.

Ultimately, the CatBoost model was employed for predicting the final outcomes of the test set in the case of RNAi. In the context of RNAp, a voting model was adopted, wherein the final prediction is determined by averaging the predictions from the ensemble learning model, CatBoost and XGBoost. This voting model approach not only enhances performance but also mitigates noise and overfitting.

The model performance was evaluated using Pearson and Spearman correlations, R² score and MAE.

The model development workflow is demonstrated in figure 9E.

4.5. Model explainability

The most important features of each model were analysed and visualized to summarize their main characteristics. XGBoost employs a distinct method for assessing feature importance, known as ‘gain’. This method calculates the contribution of each feature to the model by considering the improvement in accuracy brought about by splitting on that feature, averaged over all trees. The gain is a measure of the average contribution of a feature to the model’s prediction performance: the higher the gain, the more important the feature. On the other hand, the CatBoost model uses a combination of the SHAP values and internal algorithms to rank features, providing a measure of the impact each feature has on the variation in the predicted outcome. This model-agnostic approach is beneficial as it offers a consistent way to interpret feature importance across different types of models.

SHAP [41], an interpretable AI approach leveraging Shapley values, is a model-agnostic technique designed to elucidate the impact of individual features on model predictions. This method assigns a Shapley value to each feature, providing a quantitative measure of its contribution to the model’s output for a specific instance. Features with high absolute Shapley values are indicative of having a substantial influence on predictions.

In our analysis, we employed SHAP to examine the selected features and assess their influence on the decision-making process of the models. This approach allows us to identify the critical features and understand how specific values of each feature contribute to the prediction of a high copy number. This interpretability framework was particularly valuable as we sought to enhance our comprehension of the ColE1 replication system’s mechanisms. By delving into the model structure and leveraging SHAP, we aimed to unravel the intricate dynamics underlying the replication system and glean insights into its functional intricacies.

4.6. Origin of replication replacement

The modified ORIs were synthesized based on sequences generated by our computational tool. To introduce the modified ORIs into the pUC19 plasmid, we first amplified the plasmid using PCR with primers designed to flank the ORI region. The PCR amplicons included homologous sequences necessary for downstream assembly.

Next, a restriction enzyme was used to create a specific cut at the original ORI site, facilitating its removal. The modified ORI sequences were synthesized as double-stranded DNA fragments and introduced into the linearized plasmid using homologous recombination. This assembly was performed with the NEBuilder^® HiFi DNA Assembly kit following the manufacturer’s instructions to ensure seamless integration.

Following recombination, the newly constructed plasmids were chemically transformed into competent E. coli DH5α cells using a standard heat-shock protocol. Transformants were selected on LB-agar plates containing ampicillin. To verify successful insertion of the modified ORIs, plasmid DNA was extracted from several colonies and analysed by Sanger sequencing. Specifically, sequencing primers were designed to cover the ORI region and flanking sequences to confirm correct integration and the presence of intended mutations in the RNAp and RNAi promoter regions. The full workflow is depicted in figure 7A.

4.7. Real-time qPCR using SYBR Green

All qPCR reactions were performed in technical replicates on an Applied Biosystems real-time PCR detection instrument using the following cycling conditions for all reactions: 95°C for 10 min, and 40 cycles of 3 s at 95°C and 30 s at 60°C. Primers were designed for the plasmid and the bacteria and were tested with a melt curve (detailed in table 1 below).

Table 1.

Properties of the promers we used.

target	primer sequence	position	length	melting temperature
plasmid F’′	cgtgtcgcccttattccctt	ampicillin resistance	20 bp	56.5°C
plasmid R’′	cccaactgatcttcagca	ampicillin resistance	18 bp	50.9°C
chromosome F’′	cgagaaactggcgatcctta	E. coli dxs gene	20 bp	60°C
chromosome R’′	cttcatcaagcggtttacac	E. coli dxs gene	20 bp	60°C

To perform the qPCR, a colony was picked and mixed in DDW into a dilution of 10⁻⁶. A reaction mix was prepared with: 10 µl fast SYBR Green Master Mix, 2 µl of each primer and 5 µl DDW. A volume of 19 μl of the reaction mix was transferred into the qPCR plate, and 1 μl of the colony sample was added. The PCR plate went through a spin down for 1 min at 800 r.p.m. prior to its loading in the instrument.

4.8. Plasmid copy number determination

A standard curve was created for the quantification of the targeted DNA of the plasmid and the bacteria. By finding the amplification efficiency (E), the PCN was calculated using the equation: PCN = (Ec)^Ctc/(Ep)^Ctp [51].

4.9. Plasmid copy number transformation

The biological measurements in [26] represented a relative copy number based on growth parameters. These measurements showed a high correlation with their model’s predictions of actual copy numbers. The conversion between a relative copy number and the actual copy number was achieved by performing a polynomial fit based on ddPCR measurements in order to convert the relative copy number into the actual copy number. Building on this approach and incorporating additional qPCR biological copy number measurements, we applied a mathematical transformation to our data to improve model performance.

Starting with the relative copy number, we enhanced the data fitting process to align with the measured copy number. To achieve this, we increased the data points for fitting by 30% while reserving an equal number of data points for validation. Our analysis revealed a power-law relationship between the measured and relative copy numbers. Therefore, we performed a logarithmic transformation on the relative copy number data and then applied linear regression to these logarithmic values. This transformation allowed us to estimate the actual copy numbers more accurately from the relative copy number data.

Ethics

This work did not require ethical approval from a human subject or animal welfare committee.

Data accessibility

The original article by Rouches et al. [26] provides the two libraries of promoter sequences and their copy numbers. In the spirit of reproducible research, our code is available at [52]. This repository includes a notebook with an example of how to use the API. Our library of promotor sequences is available in the electronic supplementary material.

Supplementary material is available online [53].

Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors’ contributions

R.S.: conceptualization, data curation, investigation, methodology, software, visualization, writing—original draft, writing—review and editing; O.T.: conceptualization, investigation, methodology, validation, writing—original draft, writing—review and editing; D.H.: conceptualization, data curation, investigation, methodology, software, visualization, writing—original draft, writing—review and editing; Y.T.: data curation, investigation, visualization, writing—original draft, writing—review and editing; M.A.: conceptualization, investigation, methodology, validation, writing—original draft, writing—review and editing; T.T.: conceptualization, data curation, funding acquisition, investigation, methodology, resources, software, supervision, validation, visualization, writing—original draft, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We submitted a patent related to this study.

Funding

The study was partially supported by Safra center of bioinformatics at Tel Aviv university and by a donation from Lonza as it competed in the iGEM competition.