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\section*{Abstract}
The bacterial conjugation, despite of its importance, is poorly understood systemically. In this work we propose a
novel framework for the individual-based modeling which hinge on two main key points, namely the cell-cycle timing when conjugative is most likely to occur and the metabolic penalizations incurred by donor cells during the conjugative transfer and by the transconjugants cells once they have been infected and have to express the required gene products for the plasmid housekeeping. We have evaluated the model predictions using eight different plasmids on E. coli host.
\section*{Introduction}
{\bf [[TAG] CONTEXT]} The Domain Bacteria encompass one of most diverse and abundant form of life on earth. Part of this diversity is certainly in part a direct consequence of a succinct genome complemented by the existence of a feature rich supra-individual gene pool which is readily available for individuals in a population through different mechanisms. One of these mechanisms is the bacterial conjugation which is basically a form of horizontal gene transfer where cluster of genes are transferred from cell to cell in some population. The plasmids, which are the fundamental unit of horizontal gene transfer, are circular double stranded DNA and they are also autonomous replicons replicating independently of bacterial chromosome and having their own life-cycle.
Plasmids can also cross the domain boundaries and infect eukaryotic cells, as can be observed in genus Agrobacterium, responsible for causing plant diseases. That is the case of A. rhizogenes and A. tumefaciens and their associated plasmids which are termed Ri and Ti standing respectively for root inducer and tumor inducer plasmids. These plasmids are responsible for hairy root and crown gall plant diseases respectively. On the other hand the genus Rhizobium and its associated plasmids induce the nodule formation on plant roots acting as symbionts in the atmospheric nitrogen fixation process. These plasmids can also be harnessed for the insertion of T-DNA in plants to create transgenic cultivars. The bacterial gene pool is also used for genetic engineered plant cultivar creation such as herbicide resistant transgenic plants. That is the case of aroA gene coding the AprA enzymes which makes the plant show tolerance to glyphosate. Last but not least important, plasmids are deemed to be the main cause of spreading the multi-drug resistance associated with bacterial populations exposed to the antibiotic selective pressure. In fact this severely limits the arsenal of drugs available to fight against bacterial infections.
{\bf [[TAG] NEED]} Conjugative plasmids is beginning to seen as a viable tool as the {\it wiring protocol} for population wide computations, as the basic bricks for bacterial nano-networks and for more complex applications in synthetic biology but despite of the high relevance, there are either no dependable technique readily available yet, which have been thoroughly tested and systematically validated against the experimental data or simply an accepted standard to model the plasmid spread dynamics using single cell resolution. There is also more open question than answers on many points of the lateral gene transfer process with some opposing views about some specific aspects.
{\bf [[TAG] TASK]} We are primarily concerned, in this work, with providing a robust operational model for conjugation using an individual-based approach which can be easily adapted and used a standard modeling tool for simulating the kinetics of conjugative plasmids. In order to accomplish that goal we must bring to light some hidden aspects of conjugation which cannot be observed in whole population experimental setups and only can be detected at a single individual resolution. This approach has an added value because at the same time we produce a more dependable model we are providing useful hints about the local intra intracellular behavior of conjugation which certainly is useful to understand the process.
That is not an easy task because we have to make many assumptions and simplifications to provide a usable abstraction for the process. It has been used in other works as the operational abstraction for bacterial conjugation, a set of rules relying on parameters like some arbitrary probability value, the pilus scan speed, the action radius of conjugative pili\cite{citeulike:10283930} or even simply the number of infected individuals on the neighborhood\cite{citeulike:3567840}.
As general rule good initial assumptions for individual-based models are those which are biologically consistent and could be almost axiomatically accepted. The assumptions which fall in this category are fundamentally that most of processes inside of any cell are uphill which basically means that they have fight against an energy gradient, in other words they have a cost. The second assumption is that cellular processes are subjected to a precise set of timing constraints for all cellular activities and any deviation on these timers is disruptive for cellular activities.
In order to thoroughly understand how the plasmids are distributed and evolve in a bacterial population is necessary to separately identify the different aspects that affect the progression of cell to cell transmission and the invasion in the whole population. The final outcome of the process leading to the partial or total infection a bacterial colony can be seen as the sum of a set of contributions due to vertical and horizontal transfers as well as how much the metabolic burden contributes, as a negative feedback loop, to the pace of conjugative process.
{\bf [[TAG] OBJECT OF THE DOCUMENT]} In this work we introduce an individual-based model for bacterial conjugation constructed using a modular design which has been used to evaluate the better alternative for modeling and understand the conjugation systemically. Thereby, using this modular design we have plugged different approaches to model the conjugation with respect the time within cell cycle which produces the best and most natural fit to a complete and diverse experimental data.
