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\  where $|B^t|t_i$ and $|B^t|t_{i-1}$ are respectively the counting of $B^t$ cells at $t_i$ and $t_{i-1}$ and $\Delta_t = t_i - t_{i-1}$. The The intercept $\alpha$ is zero since at $t_0$ the number of $|B^t|$ cells are also zero. The choice of $|B^t|$ as the indicator of network flooding is just for the sake of generality but the same principles will also hold if instead of it the value of $T/(T+R)$ were used.  \subsection*{Cost of Conjugation}  The global effect of conjugation and the plasmid infection on their hosts is an increment in the duration of cellular cycle meaning an overall reduction in the nominal growth rate. This is known generically as the plasmid metabolic burden or the plasmid penalization. The knowledge about the process is scarce as well as de common values for this metabolic penalty which range from values little as one percent up to more than 30\% of increment in the doubling time of infected cells. These figures are taken from population wide measurements and it is surely hard to use it for individual-based models. There is also no suitable explanatory theory for explaining the effect of plasmid infection on their hosts and the experimental studies fail to provide useful data for constructing a bottom-up theory of conjugation cost.  In order to circumvent that limitation we propose a simple theory to understand the cost of plasmid infection. Thus the metabolic burden of conjugative process expressed as a cost function is summarized the Equation ~\eqref{eq:cost}  \  \begin{equation}  \label{eq:cost}  \phi = P_r + P_{cn} + P_{genes}  \end{equation}  \  where r is the plasmid replication cost, c the cost of maintenance of plasmid copy number and g the cost of genes which are being expressed by the plasmid during the cell life cycle. The energy driven cellular process are carried out hydrolyzing ATP molecules which could be seen as the currency for our cost system. The number of ATP required for the most of plasmid processes can be determined based on the plasmid structural properties. Hence, on average approximately 12 ATP are required for replicating every base pair\cite{citeulike:13778825}\cite{citeulike:13778820}, of course it is a rough approximation and the actual value depends on the kind of nucleotide is being replicated.  \subsection*{Plasmids}  In order to fully validate the outcomes of our model and the quality of fitting for the different alternatives to represent computationally the conjugation we have checked the simulation outputs against a complete set of experimental results, for a combination of plasmids and initial donor to recipient ratio. Thus we have simulated eight different plasmids, namely the pAR109, pAR111, pAR113, pAR115, pAR118, pAR120, pSU2007 and a MOB R388 construction, each of them with their own distinctive features. All plasmids are constitutively expressing the genes required for conjugation with exception of pAR113 and pAR118 plasmids.   The plasmid {\it pAR113} designates a version of plasmid {\it pLG272} with the {\it yfp} tag controlled by the inducible lac promoter. The original plasmid belongs to the incompatibility group {\it IncI\textalpha} being a descendant of naturally occurring {\it ColIb-P9} plasmid\cite{citeulike:13777224}.