Study of population dynamic for a recombinant bacterium during continuous cultures: Appliction of data filtering and smoothing

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Abstract
A numerical method to process experimental data concerning plasmid stability of a recombinant bacteria during continuous cultures with nonselective media is proposed here. This method differs from previous ones in that it uses the derivatve form of the state equation of the Imanaka‐Aiba model for recombinant cultures. The methodology proposed here allows one to estimate values for the two model parameters without forcing them to be constant. Until now, this could not be done using classical analytical techniques because these parameters have been considered invariable because of the integration used in the evaluation of the model. These parameters are (1) the difference in the specific growth rates between plasmid‐carrying cells and plasmid‐free cells (δμ), and (2) the probability of plasmid loss by plasmid‐containing cells (ρr μ+). The derivative technique used here is completed by mathematical treatments involving data filtering and smoothing. The values of the two parameters are in agreement with those already publised. The current technique does not impose preconditions and permit us to further study related phenomena.