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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.

Fluorescence spectroscopy offers particularly sensitive tools for the investigation of physical properties of macromolecules in solution. Differences in molecular structure under varying experimental conditions are often reflected in quantum yield and lifetime of natural or synthetically inserted fluorescent probes. inserted fluorescent probes. Energy transfer between fluorescent groups at known places of a primary sequence can be used to measure distances between the label sites (Eisinger, 1976) as well as to investigate their relative motion, e.g. measurements of the kinetics of variations in the end to end distance of a polymer (E. Haas & I. Steinberg, personal communication).

Spectroscopic probes have become powerful tools in analysing the correlation between structure and function of biological macromolecules. Though these spectral methods cannot give as circumstantial information about the anatomy of a biological structure as, for example, X-ray diffraction they can provide information on physical properties at defined loci in a macromolecule which are not accessible by other techniques. Most important, spectroscopic studies have provided means to study the dynamics of structural changes and interactions in time domains spanning from nanoseconds and less up to infinite time.

From the results of X-ray crystallography a wealth of information is now available concerning the detailed molecular structure of proteins, nucleic acids, and membrane components. This has made it possible to apply successfully various spectroscopie techniques for time resolved studies as well as theoretical simulations of internal molecular dynamics in the biological macromolecules and molecular aggregates. We were particularly pleased to see professor Ivar Waller among the participants of the workshop since new use of the wellknown Debye–Waller factor has greatly contributed to this development. A molecular picture is presently emerging including the dimension of time which ultimately will give us a detailed understanding of the functional interactions between biomolecules in general, and in particular enzyme catalysis, nucleic acid functions, and transport of matter and information through membranes.

A quantitative relationship between polarization properties of fluorescence light and molecular rotational diffusion was first derived by Perrin (1926). His results, which concerned spherical particles, have later been refined to the more complex rotational motion of asymmetric bodies (Memming, 1961; Chuang & Eisenthal, 1972; Ehrenberg & Rigler, 1972; Belford, Belford & Weber, 1972).

A bacterium incorporates amino acids into protein with an error frequency close to one in three thousand (Edelman & Gallant, 1977). Nevertheless, the structural differences between related amino acids are so small that it is difficult to see how they can be distinguished from each other with such accuracy (see, for example, Pauling, 1958).Indeed, the selection of amino acids during protein synthesis is carried out twice: first by the aminoacyl-tRNA synthetases and then by the codon-programmed ribosome. Each of these substrate selections is in fact a double selection. In the case of the synthetase both a particular amino acid and a corresponding cognate tRNA must be chosen to form the aminoacyl-tRNA. On the ribosome, the aminoacyl-tRNA must be matched with a cognate codon, and then the mRNA must be advanced by exactly one codon length to position the next codon in the appropriate ribosome site so that it too can be translated.