Modelling

Before starting the work in the wet lab, we wanted to make sure that our theorized copy number control mechanism using RNA I expression modulation is viable. It was crucial for us, because if model results were any different, we might have turned to another approach to reach our framework goals.

Our main objective was to investigate how different RNA I concentrations affect plasmid copy number, in order to know if this approach is applicable in the wet lab. We have mostly relied on Brendel et al. (1992), Tomizawa (1981), Brendel and Perelson (1993) as our literature sources. The modelling was performed using Matlab software suite.

Overview and scheme of the model

RNA II in the ColE1 system initiates plasmid replication by forming a RNA-DNA primer on the plasmid. RNA I is a counter transcript of RNA II and can inhibit the primer formation by forming a secondary three-stem-loop structure, which pairs these two molecules

First, RNA II forms an early complex with a plasmid. Early complex means that the RNA II transcript is not longer than 360 nucleotides and until it reaches that length it can be inhibited by RNA I. After reaching the critical length, pDNA-RNA II merges into a stable complex and then can proceed to forming a primer for replication initiation. If early RNA I bounds RNA II molecule in the initial transcript stage it can inhibit the replication by forming a duplex with RNA II. At first, early and unstable RNA I-RNA II complex is formed. After some time it becomes stable and RNA I-RNA II complex detaches from the plasmid, leaving that replication cycle inhibited.

Species and initial concentrations

*We have assumed that our simulation begins with half of the maximum expected wild type ColE1 plasmid concentration, because when parent cell divides, plasmid concentration reduces by 2 times.

ODE system

$$A/dt = -k1*A + k3*B*RNAI - k4*A - k10*A +k11*H - µ*A\quad (1)$$ $$B/dt = -k3*B*RNAI + k4*A - k5*B + k9*G - k15*B - µ*B\quad (2)$$ $$RNAI/dt = -k3*B*RNAI + k4*A + k14*G - k16*RNAI - µ*RNAI\quad (3)$$ $$D/dt = k5*B - k6*D - k8*D - µ*D\quad (4)$$ $$E/dt = k6*D - k7*E - µ*E\quad (5)$$ $$F/dt = k7*E + k8*D - µ*F\quad (6)$$ $$G/dt = 2*k7*E + k8*D - k9*G + k12*H - k17*G - µ*G\quad (7)$$ $$H/dt = k10*A - k11*H - k12*H - µ*H\quad (8)$$ $$RNAII/dt = -k9*G - k14*RNAII + k15*G - k17*RNAII - k18*RNAI*RNAII - µ*RNAII\quad (9)$$ $$J/dt = k18*RNAI*RNAII - µ*J\quad (10)$$