ColE1-Plasmid Production in Escherichia coli: Mathematical Simulation and Experimental Validation

Abstract

Plasmids have become very important as pharmaceutical gene vectors in the fields of gene therapy and genetic vaccination in the past years. In this study, we present a dynamic model to simulate the ColE1-like plasmid replication control, once for a DH5α-strain carrying a low copy plasmid (DH5α-pSUP 201-3) and once for a DH5α-strain carrying a high copy plasmid (DH5α-pCMV-lacZ) by using ordinary differential equations and the MATLAB software. The model includes the plasmid replication control by two regulatory RNA molecules (RNAI and RNAII) as well as the replication control by uncharged tRNA molecules. To validate the model, experimental data like RNAI- and RNAII concentration, plasmid copy number (PCN), and growth rate for three different time points in the exponential phase were determined. Depending on the sampled time point, the measured RNAI- and RNAII concentrations for DH5α-pSUP 201-3 reside between 6 ± 0.7 and 34 ± 7 RNAI molecules per cell and 0.44 ± 0.1 and 3 ± 0.9 RNAII molecules per cell. The determined PCNs averaged between 46 ± 26 and 48 ± 30 plasmids per cell. The experimentally determined data for DH5α-pCMV-lacZ reside between 345 ± 203 and 1086 ± 298 RNAI molecules per cell and 22 ± 2 and 75 ± 10 RNAII molecules per cell with an averaged PCN of 1514 ± 1301 and 5806 ± 4828 depending on the measured time point. As the model was shown to be consistent with the experimentally determined data, measured at three different time points within the growth of the same strain, we performed predictive simulations concerning the effect of uncharged tRNA molecules on the ColE1-like plasmid replication control. The hypothesis is that these tRNA molecules would have an enhancing effect on the plasmid production. The in silico analysis predicts that uncharged tRNA molecules would indeed increase the plasmid DNA production.

Keywords: biotechnology; high copy plasmid; modeling; ordinary differential equations; plasmid replication; small RNA; uncharged tRNA.

Figure 1

Growth curve for E. coli DH5α-pSUP 201-3. The growth curve based on OD₆₀₀ measurements are marked by black circles and the appropriate best-fit curve is indicated in blue. The harvesting time points T₁, T₂, and T₃ are presented as bold big points. The minimum–maximum area, within which the measurement values have to reside, is bordered by the red curve (minimal measured OD₆₀₀ values) and the green curve (maximal measured OD₆₀₀ values).

Figure 2

Growth curve for E. coli DH5α-pCMV-lacZ. The growth curve based on OD₆₀₀ measurements is marked by small black circles and the appropriate best-fit curve is indicated in blue. The harvesting time points T₁, T₂, and T₃ are presented as bold big points. The minimum–maximum area, within which the measurement values have to reside, is bordered by the red curve (minimal measured OD₆₀₀ value) and the green curve (maximal measured OD₆₀₀ value).

Figure 3

Structural model of ColE1-like plasmid replication control for low and high copy plasmids as outlined by the CellDesigner software. The structural model represents an extension of the model proposed by Brendel and Perelson (1993) for ColE1-like plasmid replication control (the corresponding reactions are surrounded by the blue box). The difference between the description of the replication control for a low copy plasmid and for a high copy plasmid is three additional reactions (shown in the red box). These reactions describe the control by the Rom protein and are not active in a high copy plasmid. The reactions outside of the blue box were added within this work and describe the replication control by uncharged tRNA molecules.

Figure 4

Simulation of the plasmid replication control for E. coli DH5α-placZ, beginning at time point T₃, for the following three different growth conditions: blue, growth with normal nutrient conditions; green, growth with amino acid starvation conditions, red, growth with modified tRNA gene without amino acid starvation conditions.