Noise in a minimal regulatory network: plasmid copy number control

Abstract

1. Introduction 22. Plasmid biology 32.1 What are plasmids? 32.2 Evolution of CNC: cost and benefit 42.3 Plasmids are semi-complete regulatory networks 62.4 The molecular mechanisms of CNC for plasmids ColE1 and R1 62.4.1 ColE1 72.4.2 R1 72.5 General simplifying assumptions and values of rate constants 93. Macroscopic analysis 113.1 Regulatory logic of inhibitor-dilution CNC 113.2 Sensitivity amplification 123.3 Plasmid control curves 133.4 Multistep control of plasmid ColE1: exponential control curves 143.5 Multistep control of plasmid R1: hyperbolic control curves 163.6 Time-delays, oscillations and critical damping 184. Mesoscopic analysis 204.1 The master equation approach 204.2 A random walker in a potential well 234.3 CNC as a stochastic process 244.4 Sensitivity amplification 264.4.1 Single-step hyperbolic control 264.4.2 ColE1 multistep control can eliminate plasmid copy number variation 284.4.3 Replication backup systems – the Rom protein of ColE1 and CopB of R1 294.5 Time-delays 304.5.1 Limited rate of inhibitor degradation 304.5.2 Precise delays – does unlimited sensitivity amplification always reduce plasmid losses? 324.6 Order and disorder in CNC 334.6.1 Disordered CNC 344.6.2 Ordered CNC: R1 multistep control gives narrowly distributed interreplication times 344.7 Noisy signalling – disorder and sensitivity amplification 374.7.1 Eliminating a fast but noisy variable 384.7.2 Conditional inhibitor distribution: Poisson 394.7.3 Increasing inhibitor variation I: transcription in bursts 404.7.4 Increasing inhibitor variation II: duplex formation 414.7.5 Exploiting fluctuations for sensitivity amplification: stochastic focusing 444.7.6 A kinetic uncertainty principle 454.7.7 Disorder and stochastic focusing 464.7.8 Do plasmids really use stochastic focusing? 474.8 Metabolic burdens and values of in vivo rate constants 485. Previous models of copy number control 495.1 General models of CNC 495.2 Modelling plasmid ColE1 CNC 495.3 Modelling plasmid R1 CNC 526. Summary and outlook: the plasmid paradigm 537. Acknowledgements 568. References 56This work is a theoretical analysis of random fluctuations and regulatory efficiency in genetic networks. As a model system we use inhibitor-dilution copy number control (CNC) of the bacterial plasmids ColE1 and R1. We chose these systems because they are simple and well-characterised but also because plasmids seem to be under an evolutionary pressure to reduce both average copy numbers and statistical copy number variation: internal noise.