Molecular kinetics dictate population dynamics in CRISPR-based plasmid defense

Significance

Conjugative, or self-transmissible, plasmids are prolific vectors of horizontal gene transfer in bacteria, yet are frequently targeted for degradation by CRISPR (clustered regularly interspaced short palindromic repeats)-Cas adaptive immune systems. Further complicating this dynamic, individual cells often vary significantly in immunity levels, and spatial structures in bacterial populations can also affect conjugation rates. In this work, we develop a microscopy-based method to observe conjugation and CRISPR interference at both population and single cell levels. We quantify the effects of spatial structure and CRISPR variability on conjugation and plasmid clearance rates, and show that population-level dynamics can be predicted from these rates using an individual-based model. This research advances our understanding of plasmid spread in bacterial communities in medicine, synthetic biology, and microbial ecology.

Abstract

Understanding and manipulating the spread of mobile genetic elements represents a great challenge with potential benefits across synthetic biology, agriculture, and medicine. A key part of this challenge is the multiple scales in play, from the molecular kinetics of defense systems such as CRISPR-Cas, to single-cell variability in immunity levels, to spatial structure in bacterial populations. In this work, we use a time-lapse, imaging-based approach to characterize conjugative plasmid dynamics at the molecular, single-cell, and population levels. By fluorescently tagging the conjugative plasmid RP4 and CRISPR-Cascade complexes, we quantify population dynamics as a function of spacer target number, Cascade expression level, and the presence of plasmid addiction modules. Using single-cell tracking, we report conjugation rate per neighboring donor cell, estimate the latent period between plasmid uptake and subsequent onward transmission, and quantify the effect of Cascade expression variability on plasmid clearance kinetics. Finally, using a spatially resolved, agent-based model, we show that plasmid population dynamics can be successfully predicted using these single-cell biophysical parameters as inputs. This synthesis of population and single-cell measurements suggests that plasmids are the subject of a dynamic tug-of-war between defense expression, spacer distribution, neighboring cell identity, and plasmid cost–benefit tradeoffs. The imaging and analysis techniques used here will facilitate the disentanglement of how these factors coordinate to realize community-wide plasmid dynamics in diverse contexts.

Microbial communities are ubiquitous and extremely complex, taxonomically, spatially and functionally (1, 2). They possess an added level of complexity driven by their propensity to share genetic material (and associated functions) via horizontal gene transfer (HGT). Plasmid-mediated HGT, often transferred via Type IV secretion systems (T4SS) (3), can bestow beneficial functions on plasmid hosts. Plasmids can encode, for example, new metabolic functions (4, 5) or antibiotic resistance, with the latter is driving a burgeoning public health crisis (6). Despite their host-benefiting features, conjugative plasmids also impose a fitness cost (7–10). Bacteria have consequently evolved an array of defense systems against conjugative plasmids and other mobile genetic elements (MGEs) (11). Equally, those mobile elements have evolved strategies to evade such defense systems (12). Plasmid acquisition and maintenance cost must be balanced against defense cost and the current—or indeed potential future—benefit of the encoded functions.

CRISPR defense is widely recognized as a method for microbes to protect against invading genetic material (13, 14) with CRISPR systems present in around 75% of archeal isolates and around 36% of bacteria (15). Nonetheless, the evidence for CRISPR-Cas systems’ effectiveness is mixed (16, 17). In general, CRISPR appears to be used by bacteria to target plasmids for degradation, although perhaps less often than phages (18). Additionally, genetic studies have demonstrated a negative correlation between CRISPR defense, and plasmids, phages, and multidrug resistance (19, 20). Despite CRISPR’s apparent targeting of plasmids, experiments with Escherichia coli have demonstrated plasmids persisting over many cell generations while being targeted by CRISPR (21). By extension, mere CRISPR presence is not a panacea against plasmid invasion. CRISPR-based defense variation within populations could be a “bet-hedging” strategy to maintain low plasmid frequency. This has been discussed as a method for dealing with environmental uncertainty (22).

Wild-type E. coli K-12 harbors a Type I-E CRISPR-Cas system, comprised of the multiprotein Cascade complex for target search, which subsequently recruits Cas3 helicase-nuclease for degradation. E. coli K-12 generates very low levels of CRISPR-RNA, suggesting that this system is perhaps not active under known environmental conditions (23). Indeed, in the case of E. coli, CRISPR interference seems ineffective against mobile genetic elements (24). Nonetheless, the system’s components are fully functional (23), giving this model organism an important role in understanding CRISPR-MGE dynamics. E. coli studies artificially inducing CRISPR components show a clear relationship between Cascade expression and plasmid clearance and estimate a 90 min search time per Cascade complex (25). Single-cell Cascade expression stochasticity demonstrably affects CRISPR-targeting efficacy (26) but highly expressed CRISPR systems carry costs in terms of expression burden, DNA damage, and replication interference (27, 28). Furthermore, growth rate of cells in and of itself has been implicated in cells’ ability to degrade plasmids (26). Taken together, these studies indicate a complex interplay between defense expression, growth, clearance, and cost–benefit trade-offs at a single cell level, which play out to become population level changes.

Theoretical studies of plasmid conjugation and population dynamics often take the form of “mass action” ordinary differential equation (ODE) models which describe well-mixed bacteria in homogeneous environments (29–31). However, bacterial habitats are characterized by spatial constraints, physical inhomogeneity, small population sizes, and cell-to-cell variability not captured by ODEs. Confined environments can affect conjugation dynamics (32, 33) and cell-to-cell variability may have adaptive potential (26). Understanding such biophysical factors is, therefore, key to describing population dynamics.

Here, we investigate the population and single-cell dynamics of plasmid conjugation and CRISPR interference in E. coli using microfluidics-coupled, time-lapse fluorescence microscopy. These methods facilitate measurement of key biophysical parameters in the conjugation–CRISPR dynamic. At the population level we find resistance to conjugative plasmid spread when CRISPR interference is high. This also has profound consequences for the population depending on the presence of a plasmid addiction system. With the help of single-cell tracking and classification, we are able to report conjugation rates per neighboring plasmid-containing cell and estimate the latent period between plasmid acquisition and subsequent onward transmission. We also find that cell-to-cell variability in CRISPR-Cascade expression significantly affects dynamics at the single-cell level. Finally, we use these experimental population-level measurements, together with single-cell biophysical measurements of conjugation and clearance, to build a spatially resolved agent-based model of plasmid population dynamics. The insights presented here advance our understanding of conjugation dynamics in natural and synthetic microbial communities and build toward potential future manipulation across medical, industrial, and agricultural applications.

Results

Population Dynamics Across CRISPR Interference Levels.

To visualize plasmid population dynamics we engineered “donor” and “recipient” E. coli cells such that donor cells displayed no fluorescent properties and did not express CRISPR-Cas proteins, while recipient cells displayed constitutive, homogeneous mCherry-ParB expression, and inducible Cas3 and Cascade operon expression (by IPTG and arabinose, respectively). The latter was achieved by replacing the wild-type Pcascade and Pcas3 promoters with the araBp8 and lacUV5 promoters, respectively (34), due to the lack of expression under native regulation (23). Cas8e, part of the Cascade complex, was translationally fused to sYFP2, and sYFP2-Cas8e was used as a proxy for Cascade concentration throughout this work (25). Transconjugant cells therefore also exhibit sYFP2-Cascade expression but form fluorescent mCherry foci from mCherry-ParB binding to parSMT1 sites on RP4 (Fig. 1A). We observed conjugation and Cascade expression dynamics in microfluidic chips (SI Appendix, Fig. S1) over 6 h with 6 RP4 plasmid variants; containing either 0, 1, or 18 spacer targets (the latter corresponding to all 12 and 6 spacers from the CRISPR1 and CRISPR2 arrays, respectively), each with and without parE toxin from RP4’s parDE toxin–antitoxin system. The stability of each of these plasmids in the absence of selective media was found to be high (SI Appendix, Tables S1 and S2). See Materials and Methods for more details on plasmids, strains, and stability tests.

Fig. 1.

(A) Donor cells harboring parSMT1-containing RP4 plasmids transfer plasmids via conjugation into fluorescently labeled recipient cells. Recipient cells contain mCherry-tagged ParB and sYFP2-tagged Cascade to allow tracking of conjugation and Cascade expression levels. (B) Corresponding phase contrast (Top), mCherry fluorescence (Middle), and classified segmented cell (Bottom) images for 0 target and 18 target RP4 variant experiments. (C and D) Mean fraction of the cell population classified as donor, recipient, or transconjugant across the course of microfluidic experiments with (C) RP4 ΔparE and (D) RP4 +parE plasmids. At least 8,000 individual cells were observed for each time point.

To start experiments, donor and recipient cells were cultured separately for 3 h in M9 glucose medium supplemented with IPTG and arabinose inducers, upon which a 50/50 mixed population was loaded into the microfluidic device and time-lapse imaging was performed in phase contrast, mCherry, and sYFP2 channels for 6 h. Observing the population fraction corresponding to each cell class (donor, recipient, or transconjugant) presents an overview of population dynamics over time for each CRISPR interference level (Fig. 1 C and D). For the nontargeted RP4-0-target variants, the recipient population was rapidly and comprehensively converted to transconjugants, reflecting RP4’s high conjugation rate. For the RP4-1-target variants, the transconjugant takeover was slowed and circa 40% of recipients remained plasmid-free. Finally, the RP4-18-target variants were efficiently targeted by CRISPR, with only a small proportion of the population succumbing to conjugation. All donor-recipient pairs were assayed at least twice on different days with similar results (SI Appendix, Fig. S2).

Here, the 1-target plasmid corresponds to the first (leader-adjacent) spacer present in the E. coli CRISPR I array (target_01). The final spacer target in the array (target_12) was also investigated using a separate 1-target plasmid. This target produced a much lower rate of clearance, only slightly higher than RP4-0-target variants (SI Appendix, Fig. S3). In the case of single target_01, the transconjugant fraction increased initially before slowly decreasing after 2.5 h. Over the course of the experiment, Cascade expression increased and the number of recipient–donor cell–cell contacts also decreased (SI Appendix, Fig. S4). These factors increase clearance rate and decrease conjugation rate, respectively, and could consequently produce such a dynamic.

The presence or absence of parE did not substantively alter population dynamics in this instance (Fig. 1), somewhat surprisingly as cleared cells should experience ParE toxicity. However, in these experiments Cascade induction took place prior to the experiment; conjugation is never allowed to proceed in the absence of CRISPR defense. We hypothesized that, under these conditions, the toxin may not have time to accumulate inside cells before clearance occurs.

Toxin–antitoxin systems can be effective counterdefense against CRISPR interference.

To assess the impact of plasmid establishment in cells before CRISPR interference is induced, RP4-18-target donor cells were loaded into microfluidic chips mixed with noninduced recipient cells. For the first hour of imaging, conjugation was allowed to proceed in the absence of CRISPR induction, at which point medium was switched to medium containing inducers (Fig. 2). Due to nonnative regulation employed here, this should be considered a hypothetical scenario where induction of the defense system occurs after the “infection” is underway (35). Around the 70 to 80 min time point the clearing of transconjugants is apparent in both the +parE (Right) and ΔparE (Left) experiments, as well as a concomitant increase in Cascade expression (Fig. 2B). Additionally in the case of +parE there is also a marked decrease in the fraction of the population made up of recipients (Fig. 2A). In Fig. 2C, we show representative images of segmented and classified cells at the end of the experiments. Experiments with parE present on RP4 show elongated, dying recipient (cleared transconjugant) cells whereas without parE the cells clear and remain healthy in appearance. Control experiments were also performed where the recipient cells had CRISPR arrays deleted. In these control experiments cells were never cleared of plasmids (SI Appendix, Fig. S5). These observations suggest that, depending on defense expression timing (35), CRISPR interference may be an ineffective mechanism to protect against unwanted conjugative plasmids that make use of parDE, and potentially other toxin–antitoxin, systems.

Fig. 2.

(A) Mean fraction of the cell population classified as donor, recipient, or transconjugant across the course of microfluidic experiments with delayed Cascade induction with 18-target RP4 plasmids, with and without parE. (B) Median Cascade copy number per cell across the course of the experiment. Inducers were added to the medium at 60 min, indicated with // on axis. In the case of +parE, copy number estimation beyond around 4 h becomes unreliable as dying cells become very bright in the sYFP2 channel. (C) Representative segmented, classified cell images at the end of +parE (Right) and ΔparE (Left) experiments. At least 5,000 individual cells were observed for each time point.

Single-Cell Characterization of Conjugation Kinetics.

Conjugation from neighboring cells is independent and additive.

The population dynamics shown in Figs. 1 and 2 reflect the interplay of the opposing forces of conjugation and CRISPR interference. Next, we sought to characterize each of these processes separately at the single-cell level, focusing first on conjugation. In Fig. 3, we examine how quickly recipient cells are “converted” to transconjugants as a function of how many donor neighbors they have. In particular, in Fig. 3A, we plot the relative transconjugant fraction $T/(T+R)$ for experiments shown in Fig. 1, where T is the number of transconjugants and R is the number of recipients. This quantity represents the fraction of recipients that have been converted to transconjugants. We plot this fraction for different subsets of the population based on how many donor neighbors each recipient or transconjugant has (Image Analysis). Recipients with more donor neighbors are conjugated more rapidly than recipients with fewer donor neighbors.

Fig. 3.

Single-cell characterization of conjugation dynamics. (A) Relative transconjugant fraction $T/(T+R)$ as a function of time, donor plasmid (color), and number of donor neighbors (line thicknesses). T and R denote numbers of transconjugants and recipients, respectively. Black-outlined lines are averages across all donor-neighbor counts. CRISPR targeting makes recipients much less likely to become transconjugants, but cells with more donor neighbors are more likely to become transconjugants. At least 2,184 cells were analyzed for each donor and timepoint (3,182 cells on average). 1-target plasmids omitted for figure clarity. (B) Dependence of conjugation rate on number of donor neighbors. Conjugation rates were determined by fitting exponential functions (Eq. 1) to the 0 target donor curves shown in (A) for nonzero donor neighbors. The conjugation rate is directly proportional to the number of donor neighbors, highlighting the effects of local spatial inhomogeneities. The dotted line is a guide to the eye. (C) Latent period for conjugation, defined as the length of time from when a recipient becomes a transconjugant until the new transconjugant itself performs conjugation (see text).

To isolate the dynamics of conjugation, we further analyzed RP4-0-target donors which are not targeted for CRISPR interference. For each of the curves with one or more donor neighbors, we fit an exponential function of the form

$$\begin{array}{c}\hfill \frac{T}{T+R}=1-e^{-k_{\mathit{conj}}t},\end{array}$$ [1]

where $k_{\mathit{conj}}$ represent the conjugation rate for a given number of donor neighbors. In Fig. 3B, we plot $k_{\mathit{conj}}$ for donor neighbor counts from 1 to 5 and find that conjugation rate is linearly proportional to donor neighbor count. Thus, conjugation from donor neighbors appears to be independent and additive. For single donor neighbors, we obtained a value of $k_{\mathit{conj}}=2.4 {\mathrm{h}}^{-1}$, which implies that recipients with a single donor neighbor will be conjugated after $1/2.4 {\mathrm{h}}^{-1}\approx 0.42 \mathrm{h}$ or 25 min on average. The mean numbers of donor neighbors during the first hour of the experiment were 2.0 and 1.9 for $+parE$ and $\mathrm{\Delta }parE$ RP4-0-target donors, respectively.

New transconjugants experience a 40 to 50 min long latent period before performing conjugation.

In Fig. 3A, we also plotted $T/(T+R)$ for cells with zero donor neighbors. These curves generally start to rise after a delay of approximately 30 min from $t=0$. We surmised that this delay reflects the latent period required for newly conjugated transconjugants to produce conjugation machinery and become able to perform conjugation themselves. However, as these plots are based on the number of donor-neighbors in a particular frame only, some of these cells may have transiently come into contact with donors in previous frames, meaning that 30 min should be considered a lower bound for the latent period.

To more accurately characterize the latent period, we turned to lineage-based analysis based on tracking individual cells and their daughters over time (36). We sought to identify lineages of recipient cells in which conjugation is performed by newly conjugated transconjugant cells rather than donor cells (see Materials and Methods for details) In Fig. 3C, we plot the times from the first appearance of a transconjugant neighbor until the recipient is conjugated and find a mean latent period of approximately 40 to 50 min, consistent with the picture in Fig. 3A.

Cell-to-cell variability in Cascade expression determines clearance rates.

To investigate the function of expression stochasticity in potential bet-hedging strategies we now turn to analyzing the variability in Cascade expression between single cells (Fig. 4A). In Fig. 4B, we plot a histogram of Cascade copy number per cell for recipients and transconjugants, combined from all experiments and donor strains in Fig. 1. Cell-to-cell variability is an inescapable feature of gene expression; however, expression variability under native regulation may differ from that seen here. With single-cell Cascade copy number estimations in hand, we evaluated the extent to which Cascade expression is costly for cell growth, and found that growth rate is largely constant with respect to Cascade expression, with at most a slight downward trend (Fig. 4B, blue dots; see Right y-axis). Evidently, in this relatively rich growth medium, Cascade expression does not unduly burden cells.

Fig. 4.

Cell-to-cell variability in CRISPR interference. (A) Representative fluorescence image acquired in the Venus channel. The image has been rescaled so that the colormap indicates the corresponding Cascade copy number in an average-sized cell. Dark areas correspond to donor cells, which do not express sYFP2-Cas8e. (B and C). Estimated Cascade copy number per cell and dependence of growth rate on (binned) Cascade copy number for recipient and transconjugant cells from $\mathrm{\Delta }parE$ experiments in Fig. 1. To accurately compare growth rates across different experiments, growth rates are normalized to donor cell growth rates within each experiment. Error bars represent SEM. (Nonnormalized growth rates are presented in SI Appendix, Fig. S6.) (D) Time-lapse images in mCherry-ParB channel showing a recipient cell (green outline) that receives a plasmid (dot outlined in red) at $t=235$ min before clearing the plasmid at $t=255$ min. (E and F). Fraction of cell lineages that acquired and subsequently cleared the plasmid as a function of time and CRISPR target number (color). Initial plasmid acquisition is defined as $t=0$ in these plots. More CRISPR targets and higher Cascade expression generally yield faster clearance. At least 1,189 unique plasmid infection events were analyzed for each donor. (G) Plasmid clearance rate for all plasmid variants as a function of Cascade expression. Clearance rate increases for 18-target plasmid before saturating at high Cascade concentration. Lower clearance observed for 1-target plasmid. See text and SI Appendix, Supporting Information Text for calculation of clearance rate.

Next, we turned our attention to the dynamics of CRISPR interference. We performed cell tracking to build a database of “infection events”–i.e. intervals of a cell lineage during which plasmids are present, illustrated in Fig. 4D. By summing over infection events, we can compute the fraction of lineages that have cleared the plasmid as a function of the elapsed time since initial conjugation. Note that this can involve multiple generations of cells along a lineage. This clearance fraction is shown in Fig. 4 E and F for +parE and ΔparE plasmid variants, respectively. Considering plasmid variants first, we find rapid and complete clearance for RP4-18-target variants, medium levels of clearance for RP4-1-target variants, and low albeit nonzero clearance for RP4-0-target variants. The latter should have essentially zero clearance and is therefore representative of a false negative dot-detection rate (plasmid loss due to cell division may also contribute). After about 30 min, the RP4-0-target clearance curves plateau around 0.2, indicating that plasmid copy number has built up sufficiently that the probability of false negatives is small.

Considering Cascade expression variability, we binned “infection events” into quintiles according to mean Cascade expression during the infection. We then estimated the plasmid clearance rates for each plasmid variant and Cascade expression bin. To do so, we used the clearance fraction at $t=5$ min after initial infection. Assuming that plasmid replication time is greater than 5 min, this allows us to avoid the confounding effects of plasmid replication after conjugation. We further corrected for false negative plasmid measurements and the possibility of additional conjugation events during the 5 min interval; see SI Appendix, Supporting Information Text for a complete derivation. The estimated clearance rates are shown in Fig. 4G as a function of Cascade copy number, and are also reproduced in SI Appendix, Table S3. The clearance rates for 0-target plasmids are close to zero, for 1-target plasmids, slightly higher, while 18-target clearance rates increase with Cascade before plateauing around 50 to 100 Cascade/cell. For $\mathrm{\Delta }parE$ RP4-18-target, the estimated clearance rate was 20.8 ${\text{h}}^{-1}$ for the 35.4 Cascade/cell bin, yielding a per-Cascade clearance time of ${(20.8 {\text{h}}^{-1})}^{-1}\times 35.4=1.7 \text{h}$, or 1.5 h averaged over the first two bins. In Discussion, we compare these rates to previous biophysical measurements and find good agreement (25).

Toxin–Antitoxin Distribution Relative to CRISPR Spacers.

Given our earlier finding that, in the absence of preinduction of Cascade, parE-containing plasmids are able to effectively counter CRISPR clearance and cause cell death, we hypothesized that spacers against parE-containing plasmids should be underrepresented in CRISPR arrays found in bacterial populations. Effective CRISPR targeting and parE should be evolutionarily incompatible. A negative correlation between the presence of parE and CRISPR targets in available sequence databases would provide strong evidence for the applicability of this mechanism in wider bacterial ecology.

We searched 72556 plasmid sequences (37) for spacers and parE using 11767782 predicted spacer sequences (38) and E. coli RP4 parE (XCD26522.1). Consequently we identified 42728 plasmids with spacer target sequences, 502 plasmid sequences containing parE-like sequences, and 106 sequences with both parE and CRISPR spacer targets. We further refined this analysis by considering the genome assemblies from which spacers were predicted, under the assumption that spacers predicted from the same assembly likely originate from the same CRISPR array. For each plasmid we assessed the number of targets per genome assembly from which the spacers were predicted, yielding a given number of targets per plasmid–genome assembly pairing. We found 9.84 million pairings with at least 1 target, of which 7.43 million had 1 spacer target. This drops sharply to 1.09 million for 2 targets and continues to drop at higher target numbers (SI Appendix, Fig. S7). The mean and median numbers of targets per pairing was 1.6 and 1 respectively (excluding pairings with zero targets). Naïvely, the global fraction of spacer-targeted plasmids 42728/72556 (59%) compared to the fraction of spacer-targeted, parE-containing plasmids 106/502 (21%), is an underrepresentation of spacer targeting in parE-containing plasmids.

To test this relationship statistically we constrained our analysis to ten host species where parE-containing plasmid presence was most likely and constructed a phylogeny-weighted random permutation test, plasmid phylogenies were constructed using gene presence–absence (Materials and Methods). Qualitatively, we can see that the presence of both parE and CRISPR is not restricted to any one species or phylogenetic lineage but bias is apparent (Fig. 5). Co-occurrence of parE and CRISPR targets is observed less frequently than expected by chance, when accounting for phylogeny (Fig. 5 and SI Appendix, Table S7). We repeated the method for eight other known toxin genes. We found that relE, vapC and ccdB actually showed more co-occurrence than expected by chance (SI Appendix, Table S7). Inferring causal relationships using such bioinformatic analysis is challenging given the many challenges and uncertainties associated with fully annotating both CRISPR targets and TA systems. Furthermore, such interaction is likely highly context-dependent and therefore general conclusions should be considered cautiously.

Fig. 5.

Genetic co-occurrence of parE and CRISPR spacers. Phylogenetic tree depicting clustering of sampled plasmid sequences for species analyzed based on gene presence–absence. Color-coded rings around the tree indicate source species, CRISPR target presence/absence, parE predicted presence/absence and predicted plasmid mobility for each plasmid included.

An Agent-Based Model Predicts Population Dynamics from Biophysical Parameters.

Finally, we sought to synthesize our single-cell (Figs. 3 and 4) and population-level (Figs. 1 and 2) measurements into a biophysical model and assess its ability to explain the observed population dynamics. In order to incorporate spatial and single-cell variability effects, we built a CellModeller-based (39) agent-based model, where each cell is an “agent” whose internal state and interactions with other cells evolve according to defined rules. These rules are encoded in two modules: first, a physics module governing the spatial distribution of cells and, second, a biochemistry module dealing with molecular events such as plasmid conjugation, replication, and degradation (Fig. 6A and SI Appendix, Fig. S8). This biochemistry module is a custom implementation of the Gillespie algorithm (40) (SI Appendix, Supporting Information Text).

Fig. 6.

Agent-based model of plasmid population dynamics. (A) Schematic of plasmid dynamics. Plasmids replicate at rate $k_{\mathit{rep}}$, are degraded at rate $k_{\mathit{clear}}$, and conjugate at rate $k_{\mathit{conj}}$. Rates are taken from experimental measurements (Figs. 3 and 4). (B) Initial conditions from $t=0$ timepoints in experiments are used as starting point for simulation runs. (C) For all detected cells, individual cells or “agents” are initialized with identical cell class [donor (D), recipient (R), transconjugant (T)], Cascade concentration, number of plasmids, and spatial positions as corresponding experimentally detected cells. Three such “agents” are shown here for illustrative purposes. (D) Simulations are then run as described from initial conditions. (E) For 0-target plasmids, conjugation is faster in simulations (dashed lines) than in experiments in the absence of a latent period for conjugation. (F) The implementation of a 1 h latent period yields excellent agreement between simulation and experiment. (G) Simulation vs. experiment for 18 target plasmid, showing good agreement when $k_{\mathit{clear}}=1.2{\text{h}}^{-1}$. A complete list of parameters is found in SI Appendix, Table S6. (H) Simulated relative transconjugant ratio T/(T+R) for varying numbers of targets from 0 to 18, assuming equal expression of all spacers in CRISPR array. The effectiveness of CRISPR defense exhibits diminishing returns with increasing target number. (I) Similar to H, but here the conjugation rate is also allowed to vary in addition to number of targets. Simulations were run for 240 min and the mean value of T/(T+R) after 210 min is displayed in the heat map for each combination of conjugation rate and target number. The same diminishing returns with respect to target number are visible, while conjugation rate has a modest impact. (J) For plasmids targeted by CRISPR spacers, how many spacers in a given CRISPR array target the plasmid? Using sequence databases we find that the majority of targeted plasmids are targeted by one spacer. The underlying data are the same as in SI Appendix, Fig S7.

We initialized simulation runs by mirroring exactly experimental data at $t=0$ (Fig. 6 B and C) and simulated according to the defined rules. Using measured conjugation rates (Fig. 3), and in the absence of a latent period for onward transmission by new transconjugants, the simulated dynamics (dashed lines) initially match the experiment for $\mathrm{\Delta }parE$ RP4-0-target, but the transconjugant fraction soon exceeds the experimentally observed fraction (Fig. 6E). Altering $k_{\mathit{conj}}$ could not capture observed dynamics (SI Appendix, Fig. S9A). Including our estimated latent period (Fig. 3C), produced excellent agreement between simulation and experiment (Fig. 6F), highlighting the importance of spatial factors for population dynamics.

Ideally, for CRISPR-targeted plasmids, another “zero parameter fit” could be achieved by simply incorporating the observed per-Cascade $k_{\mathit{clear}}=0.66 {\text{h}}^{-1}$ and single-cell Cascade copy numbers. Simulating the $\mathrm{\Delta }parE$ 18-target case, where interference is strong, yielded a transconjugant fraction about 5 % greater than experimental observations (SI Appendix, Fig. S9B). To determine which $k_{\mathit{clear}}$ values are consistent with experimental data, we applied Approximate Bayesian Computation (ABC) (41). ABC performs many simulations with different parameter values, and accepts or rejects them depending on how well simulation and observed data agree (SI Appendix, Fig. S9 C and D and Supporting Information Text). Here, we used the relative transconjugant fraction $T/(T+R)$ to compare the two. We found that accepted simulation runs had a mean ± SD of $k_{\mathit{clear}}=1.5\pm 0.3 {\text{h}}^{-1}$ per Cascade (SI Appendix, Fig. S9E) and good agreement with experimental results was found using $k_{\mathit{clear}}=1.2 {\text{h}}^{-1}$ (Fig. 6G). A complete list of parameter values is found in SI Appendix, Table S6. Taken together, these results show that population dynamics can successfully be predicted by spatially explicit agent-based models based on measured biophysical parameters.

Given the success of our model, we elected to explore scenarios not covered by experiments, starting with varying spacer targets from 0 to 18. We assumed that all spacers are equally represented in the pool of Cascade complexes; thus, given that $k_{\mathit{clear}}=1.2 {\text{h}}^{-1}$ in Fig. 6G, the effective $k_{\mathit{clear}}$ for 1 target is $\frac{1}{18}\times 1.2 {\text{h}}^{-1}$, and so on. In Fig. 6H, we plot the relative transconjugant fraction $T/(T+R)$ for all target numbers from 0 to 18, showing decreasing marginal benefit to increasing targets beyond 2 to 3. As leader-adjacent spacers are overrepresented compared to leader-distal spacers in the CRISPR array, this effect is likely even more pronounced in reality. In Fig. 6I, we extend this analysis to vary conjugation rate as well. For each combination of conjugation rate and target site number, we ran the simulation for 240 min.; in Fig. 6I, we display the “steady-state” value of $T/(T+R)$ as the mean value of this parameter between 210 and 240 min. We observe the same diminishing returns with respect to target sites and a relatively modest effect of conjugation rate. Finally, in Fig. 6J, we highlight a subset of the data presented in SI Appendix, Fig. S7, showing that for plasmids targeted by a CRISPR array, the majority are targeted by a single spacer, and essentially none are targeted by more than a few spacers. This is consistent with the diminishing returns to increased target number seen in Fig. 6 H and I.

Discussion

Here, we have explored plasmid population dynamics at both the population and single-cell level, describing the role of spacer target number, Cascade expression and search time, conjugation rates, plasmid transmission latency, and toxin–antitoxin (TA) system presence. Together, these comprise a synthesis of multiscale measurements describing the ability of CRISPR to nudge plasmid conjugation dynamics and impact overall population dynamics.

Plasmids, on average, have low spacer target numbers (42) and our bioinformatic analysis corroborates this. In addition, the wild-type level of CRISPR-RNA production in E. coli is very low under known growth conditions (23, 43). Nonetheless, the wild-type Cascade constituents are capable of providing CRISPR defense when expressed (23, 43). Similarly, we observed moderate RP4 clearance when target number or expression level were low, but highly efficient interference when the plasmid was targeted by all spacers and Cascade was induced, holding the percentage of transconjugants at less than 10% of recipients. Acquiring more spacer targets for any single plasmid increases the clearance capability without increasing expression burden but also effectively dilutes the effect of other spacers present in the genome. This increases the expression burden required to clear MGEs targeted by other spacers in the genome. This concept has been explored previously in modeling viral attack, predicting optimal spacer number (44).

Apparent difference between the efficiency of defense provided by specific targets raises further questions about the mechanism behind such differences. It has been shown previously that different spacers are present at different abundances in cells (43) and that spacers appearing later in an array may act less strongly (45). Research has shown that the standard behavior of bacteria to integrate new spacers into the 5’ end of the spacer array provides better protection than erroneous integration into the middle of the array (46), which agrees with our finding. Modifying spacer number may provide fine-tuning of the “nudging” capability of CRISPR interference based on ecological niche requirements. Such fine-tuning can be achieved in response to phage in days (14). The relationship between interference and target number and identity is also valuable knowledge for the development of simulation models and synthetic biology applications. Such applications include e.g. safeguarding against plasmid uptake and acquisition and spread of antibiotic resistance (47).

In some circumstances, highly effective clearance proved a pyrrhic victory. RP4 encodes the parDE plasmid addiction mechanism which targets gyrase and ultimately decreases cell viability (48, 49). Transconjugant cells, with established plasmids, which subsequently cleared exhibited elongated phenotypes typical of DNA damage, ultimately reducing the combined transconjugant/recipient/cleared transconjugant population. Such selective pressure against CRISPR-spacer TA co-occurrence has been noted previously (50). Given the potential cost of expressing CRISPR defense (51–53), it is likely unrealistic that CRISPR defense is constitutively strongly expressed in wild populations. It is more likely that expression is initiated as required or that expression stochasticity allows populations to capitalize on a few cells with high expression. Such an assumption that most cells have low CRISPR expression most of the time makes toxin accumulation before plasmid clearance more likely, increasing the countering capabilities of TA systems. Indeed, our bioinformatic assessment suggests that CRISPR targeting is less prevalent for parE-containing plasmids but is clearly far from redundant in countering TA defense given its prevalence in plasmids with other toxins.

Cell-to-cell variability and its effect on population dynamics has aroused interest in recent works (21, 22, 26, 54). The incomplete plasmid clearance observed here at “wildtype-like” levels (one spacer target, ≈100 Cascade/cell) raises questions about CRISPR efficacy against plasmids—only high target numbers could completely clear cells. This can be countered by higher Cascade expression levels but such expression may be costly; studies have highlighted the potential costs associated with CRISPR immunity (51, 52). Equally, the absence of immunity is a way for bacteria to obtain new genetic material (55). In our study, Cascade expression level had little effect on growth rate. Many reports study CRISPR dynamics in vitro with relatively high resource availability (7, 21, 25, 26), which would mask potential plasmid maintenance and CRISPR interference costs. Other studies take a genetic outlook (17–20, 24) and are thus blind to environmental factors. Nonetheless, experimental (7) and theoretical (56) work has shown and explored the importance of plasmid maintenance and acquisition cost. Cascade expression stochasticity, again, may allow CRISPR to always maintain a few cells with and without plasmids, consequently upholding the ability to nudge the population toward clearance or maintenance depending on cost and benefit.

By leveraging single-cell tracking and neighbor analysis, we were able to measure key biophysical parameters: namely, Cascade search time, conjugation rate per neighboring donor cell, and transconjugant latent period. Our estimate of Cascade search time is 90 min, in agreement with other research (25). Conjugation rate was measured at 2.4 conjugations per hour per donor neighbor. Conjugation rate curves are well fit by an exponential function, implying that conjugation rate is limited by a single rate-limiting step: plausibly, the conjugative pilus’ search for recipient cells (57). We also found the latent period between plasmid acquisition and subsequent transfer to be 50 min; much slower than conjugation. As exemplified by our agent-based model, the estimation of such single-cell, spatially aware parameters is key for the understanding, accurate prediction, and potential manipulation of population level plasmid dynamics.

Taken together, our results suggest that individual cells are the subject of a delicate trade-off between plasmid cost, plasmid benefit, defense expression, the cost of plasmid clearance, spacer acquisition, and spatial considerations i.e. neighboring cells that can influence the rate of plasmid acquisition. If CRISPR defense is expressed too little, there is limited interference. With moderate expression, and sufficient spacers, interference can be efficient. For fewer targets, expression must be higher to obtain interference, but the burden of expression may become relevant in certain environments. Furthermore, the ability of plasmids to fight back with toxin–antitoxin systems means that plasmid acquisition may be especially risky when the cost of clearance is greater than the burden of defense expression or plasmid maintenance. Maintaining a range of Cascade expression levels, coupled with varied spacer acquisition may maintain cells at all points along this continuum and subsequently ensure their preparedness for all eventualities.

Materials and Methods

Cloning and Strain Construction.

Strains and plasmids were constructed using lambda red recombineering and other standard cloning techniques. Please see SI Appendix, Supporting Information Text for details.

Plasmid Stability Tests.

To test the stability of plasmid retention in the absence of antibiotic selection plasmid-containing cells were first cultured overnight in LB medium containing 12.5 μg/mL chloramphenicol. These cells were diluted 1:500 into 10mL M9 RPMI 0.4% glucose with no antibiotic selection and cultured overnight at 37 ^°C with shaking 200rpm. The resulting suspensions were standardized to an OD₆₀₀ of $1\times {10}^{-6}$ and 100 μL μL plated on LB with and without 12.5 μg/mL chloramphenicol. Plates were incubated at 37 ^°C overnight and colonies counted. Alternatively, 1 μL suspension was spotted onto 1.5% PBS agarose pads and imaged; subsequently images were segmented and dot detection performed as for microfluidic assays.

Microfluidic Assays.

Strains were grown overnight in LB broth (tryptone 10 g/L, yeast extract 5 g/L, NaCl 10 g/L) from single colony with appropriate antibiotic addition (spectinomycin 15 μg/L for recipient strains or chloramphenicol 12.5 μg/L for donor strains) shaking 200 rpm at 37 ^°C. Overnight cultures were diluted 20 μL into 10 mL M9 medium in 50 mL falcon tubes. Final M9 medium composition is as follows [Na₂HPO₄ 12.8 g/L, KH₂PO₄ 3 g/L, NaCl 0.5 g/L, NH₄Cl 1 g/L, CaCl₂ 100 μM, MgSO₄ 2 mM, x1 RPMI 1640 amino acid solution 1640 (Sigma R7513), glucose 0.4%, pluronic F-127 85 mg/L (Sigma-Aldrich P2443)]; where inducers were included in the media these are final concentration (IPTG (isopropyl β-D-1-thiogalactopyranoside) 1 mM, arabinose 0.2%). Diluted cells were returned to shaking incubation for three hours; at this point cells were mixed 1:1 (donor:recipient) by volume and loaded into microfluidic chips for imaging. The device used has two parallel row of traps separated by a central barrier. This allows loading of two different strain combinations in each experiment. For most experiments $+parE$ and $-parE$ variants of the same donor strain were run concurrently. For experiments with delayed induction, the $+/-$ CRISPR array-containing recipient strains were run concurrently with one donor strain.

The microfluidic device used here is a modified version of the device used in ref. 58 with a 1,000 μm channel height and large rectangular cell traps measuring 48 μm × 60 μm. Cells were loaded into these traps immediately after mixing under 0.4 to 0.6 bar pressure. After cells were loaded, fresh M9 medium was flowed into the device at 0.2 bar and continued for the duration of each experiment. Imaging set-up was composed of a Nikon Ti2 equipped with Teledyne Kinetix camera, 100× Ph3 objective (CFI Plan Apo lambda 100X/1.45 oil. MRD01905), 1.5× internal magnification selected (for a total magnification of 150×), Lumencore SPECTRA light engine and filters configured for mCherry (no excitation filter, Chroma ET645/75M emission filter and Chroma ZT594rdc dichroic mirror) and SYFP2 (Chroma Z514/10 excitation filter, Semrock FF01-542/27M emission filter and Semrock BrightLine Di02/R514 dichroic mirror) fluorescence imaging. The microscope stage was encased in Okolab H201-ENCLOSURE hood and H201-T-UNIT-BL temperature control unit to maintain a constant 30 ^°C throughout the experiments. Cells were imaged in phase contrast (100 ms exposure), mCherry fluorescence (200 ms), SYFP2 fluorescence (100 ms) channels over a period of 6 h. Phase, mCherry, and SYFP2 images were taken at 1.25, 5, and 30 min intervals, respectively.

Image Analysis.

The image analysis performed in this work is based on the following basic steps: segmentation, cell tracking, dot (i.e., plasmid) detection, and cell classification. These steps are followed by downstream analyses such as plasmid clearance rates, latent period calculations, etc. All steps were integrated into a custom image analysis pipeline based on the pipeline described in ref. 59.

Segmentation was performed on phase contrast images using the Omnipose software package (60), which uses a U-net-based neural net architecture to perform morphology-independent cell segmentation. Custom neural nets were trained for this project using manually curated segmentation of cells grown in microfluidic devices as ground truth. Cell tracking was performed using the Baxter algorithm (36). Dot detection was performed using the radial symmetry algorithm; detected dots were subsequently refined by fitting a Gaussian to each detected dot.

To classify cells as donors, recipients, and transconjugants, a two-step process was used. Recipients and transconjugants express ParB-mCherry, whereas donors have no signal in the mCherry channel. Cells were first classified as “mCherry positive” or “mCherry negative” by thresholding, where the threshold was chosen to minimize the SD of fluorescence signal intensity within the respective “mCherry positive” and “mCherry negative” groups. “mCherry negative” cells can then immediately be identified as donors. “mCherry positive” cells containing detected mCherry dots (corresponding to ParB-mCherry-tagged RP4 plasmids) are classified as transconjugants, whereas “mCherry positive” cells not containing detected mCherry dots are classified as recipients. For analyses involving cell tracking across multiple frames, transconjugant cells must have two consecutive frames without detected dots in order to revert to recipient status.

Cell neighbors were determined using morphological operations on segmentation masks. For each segmented cell, the segmentation mask was cropped to the bounding box of the cell plus 15 pixels in each dimension. (Pixel size is $6.5 \mathrm{\mu }\text{m}/150\approx 0.043 \mathrm{\mu }\text{m}$ per pixel). The cell of interest was dilated by six pixels, and the other cells within the cropped region were subsequently dilated by six pixels, one at a time. When the central cell’s dilated mask overlapped by 40 pixels or more with another cell’s dilated mask, the cells were determined to be neighbors. We experimented with different thresholds and found empirically that 40 pixels was a reasonable threshold to match our judgments by eye of which cells were neighbors.

Latent period lineage selection.

For conjugation latent period calculations, we selected recipient cell lineages based on the following criteria: 1. no donor neighbors prior to conjugation 2. no transconjugant neighbors for at least the first 10 min of the lineage (to ensure that conjugation is performed by “new” transconjugants undergoing the latent period) 3. starting from the first frame with a transconjugant neighbor, a transconjugant neighbor must be present in at least 80% of frames until conjugation.

Cascade Copy Number Calculations.

E. coli strain EL4269 was used as a basis for the calculation of Cascade copy number. This strain expresses a LacI-SYFP2 fusion at low copy number (ca. 3-5) and contains a single genomic Osym LacI-binding site. The strain was cultured under the same conditions as cells used in experiments. After growth to exponential growth cells were mounted on agarose pads (1.5% agarose, M9 + inducers as described above). Cells were imaged on the same microscope set-up as described above but with varying exposure times and light intensity settings (1,000 ms, 10% intensity and 500 ms 40% intensity). Circular ROIs were drawn around visible dots within cells (representative of a single bound LacI-SYFP2 molecule) and a background measurement taken inside the same cell away from the dot position with the same size and shape ROI. By averaging background subtracted measurements over biological and technical repetitions we obtained a value of 6,382 and 2,222 fluorescence units per Cascade molecule under (1,000 ms and 500 ms) imaging conditions, respectively. Next we used constitutively SYFP2-expressing strain EL2788 imaged under the same conditions as the LacI fusion strain. Manual cell counting, automated masking with Fiji autothreshold function and intensity measurements allowed us to calculate the copy number as approximately 23 SYFP2 copies per cell across all replicates. We then imaged strain EL2788 in microfluidic traps under experimental imaging conditions. Given the known copy number per cell we were able to calculate 526 total arbitrary fluorescence units per SYFP2 molecule under experimental imaging conditions. This value was then used to calculate SFYP2-Cas8e copy number (used as a proxy for Cascade copy number) from background subtracted fluorescence values in experiments.

Bioinformatics Analysis.

CRISPR spacer sequences (http://crispr.genome.ulaval.ca/) and parE sequences (XCD26522.1) were used to search plasmid sequences (37) using local blastn and tblastn respectively. For spacer sequence hits those with 100% sequence identity over 90% of the sequence length were retained. For parE sequences, hits with evalue < 1 were retained and considered parE-like sequences for our analysis.

We constrained our analysis to plasmid host species in which there was evidence of parE presence. We calculated the predicted proportion of plasmids having a parE hit for each species and selected the top 10. The predicted proportion of plasmids was estimated using an empirical Bayes approach by applying a beta prior to the proportion for species i, where β and α are parE-containing and parE-free plasmids across the global dataset and n and x are the total and parE-containing, respectively, number of plasmids.

$$\begin{array}{c}\hfill {\widehat{p}}_i=\frac{\alpha +x_i}{\alpha +\beta +n_i}\end{array}$$ [2]

To account for plasmid phylogenetic relatedness we used a gene clustering and co-occurrence method. We first took all the amino acid sequences for annotated genes in selected plasmids and applied pairwise sequence alignment and clustering using MMseq2 (61), 70% sequence identity over 80% of sequence length, to create clusters of likely gene orthologs. After this step, plasmid collections were randomly subsampled to a maximum depth of 100 plasmids for each species-mobility combination; giving a maximum of 300 plasmids per species. Cluster assignments were then used to calculate pairwise Jaccard distances between all plasmids selected and construct phylogenetic relationships, similar to the method described in ref. 62. Phylogenetic distances derived from the constructed tree were used as probability weightings to perform phylogenetic permutations [as described previously (63)] to test the significance of the relationship between toxin presence and CRISPR target presence. The methods described above were repeated for 8 additional known toxin genes: relE, vapC, pemK, mazF, txe, doc, CcdB, and higB.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All experimental data and analysis code are available in the SciLIfeLab Data Repository at DOI: 10.17044/scilifelab.31017391 (64).