In this matter, other studies find important to make adjustments to their models to fit lag and stationary phase conjugation rates \cite{Philipsen_2010,Yurtsev_2013}.
There is another subtle discrepancy concerning interactions between conjugative and non-conjugative plasmids. In the work of \citep{Levin_1980} they conclude that maintenance of non-conjugative plasmids requires selection even when there is a mobilizing plasmid. In counterpart, \cite{Werisch_2017} states the opposite using a different approach in a almost the same case of study, the only difference is that in the latter the plasmids are incompatible. It is remarkable how this "little" difference can undergo really opposite conclusions.
*Considering conjugation lag times are important in spatially structured environments
Compensation
The mechanisms of plasmid cost amelioration could be due to changes in genes in expression of either in chromosomal or plasmid genes, changes in conjugation rates or the lost of plasmid genes \citep{Zwanzig_2019}. In this same work they explore the influence of compensatory mutations in the stability of plasmid, proving a fact that was often assumed, that those carried in plasmids has a greater effect due to horizontal propagation. But the relevance of considering compensatory mutations in modeling plasmid stability is very well exemplified in \citep{Millan_2014}, where the model failed to describe the stability unless compensatory mutation are addressed.
Compatibility
The most used scheme in modelling plasmid compatibility is surface exclusion through a state variable although some authors prefer to appeal to replication machinery competition to model uniqueness of a plasmid type within a cell or population \citep{Summers_1996}.
Stability
The majority of plasmid related model embrace plasmid stability, although many of them postulate a simple equations for the fraction of plasmid bearer population in very simplistic manner. More complex situations has been addressed.
In general, the studies regarding plasmid stability states that there is a trade-off between the segregation rate and the plasmid cost, strategies could be implemented such as selection against the plasmids, the use conjugative plasmids \citep{Werisch_2017}.
These strategies are relevant in the elucidation of the plasmid paradox which is major concert interest for many biologist. In the light of bioengineering, this strategies entails rather costs of production or production inefficiency. For this reason, finding easy implemented schemes that promotes plasmid stability are particularly relevant. The findings of \citep{Yuan_2010} propose a feasible strategy for the maintenance of non conjugative plasmids: controlling the substrate concentration by periodic pulses , dilution rate.
Although the work presented in \cite{Yurtsev_2013} disregarded the formation of plasmid free cells. It gave us a philosophical contribution to keep in mind when attempting to artificially stabilize a plasmid using inhibitors: the social aspect of the antibiotics and the importance of characterizing the social interactions such as cross-protection or any other public good.
The general three factors contributing to the maintenance of plasmids are horizontal gene transfer, selection against the trait carried by the a plasmid and compensatory mutations \citep{Millan_2014}.
PSK
PSK systems are per se mechanisms to ensure plasmid maintenance, and thus plasmid stability. Although this strategy is very effective, it is not often used in bioengineering because it is costly and reduces product efficiency.
We have analyzed \citep{Willms_2006}a model that explored the effects of the efficiency of the PSK with rather logic results, the efficiency increases plasmid persistence. But future applications of this model can be still explored. More over, we believe that there is still work to do in this matter, for example, study PSK in high copy number plasmids, particularly analyzing the dynamics of plasmid and toxin segregation at single-cell level. Or their affect on communities when the toxin is and exported bacteriocin.
approaches ...
Mass action models fit to expermial conditions specially to chemostat but realistic to communities
Populrity of ODEs models could be biased for the relative <> analytical solutions
Stochastic models pnciano -> describe plasmid dynamics better than deterministic models, which are mechanistically driven, from strategies incorporating noise directly from observed data. This gives the expectation that this kind of models are better fitted to study plasmids when not much of their biology is known.
As experimental techniques becomes more sophisticated, such as the using of reporter genes and imaging techniques, more in situ specific data can be taken into account for the study of plasmid dynamics in a more realistic way. The general assumption of mass action of population and stochastic models only works for well mixed environments. Which is not the case on spatially structure nature systems. In this scenarios, ecological interactions between populations could be better understood using individual-based models. \citep{S_rensen_2005}
This modeling framework can integrate individual specific characteristics and as the the number of processes involved increases so does the programming and computational complexity. Nonetheless, this approach becomes very useful in studying communities ecological interactions in spatially structured manner. The advantage of this models is that they can efficiently capture population dynamics from individuals interactions, that at the same time this interactions are driven by properties that could or not vary between individuals of the same type. Thus facilitating the incorporation of biological noise such as different cell cycle states or metabolic variations.
The scientists perception of plasmids, at the beginning they were treated as parasites, symbionts or even external control tools. Now days when a population carries a plasmid, it is considered as part of a system. This change of perspectives in addition with advances in technology and experimental approaches has increased the sophistication of the molecular mechanisms involved in plasmid dynamics modelling. Examples of this how the grade of complexity on replication and segregation mechanisms has been addressed over time.
Another relevant factor to consider is the computational power, some modelers often decide to ignore a particular process with the <> that it does not change qualitatively their results. This practice definitely simplify models, which make them easier to resolve analytically or compute. We believe that, at least computational problems should not be factor to be considered anymore. But of course, simplifications and generalizations, would be addressed depending on the objectives of the research investigation.