A systems biology approach to homeostasis in single cells exemplified by bacterial plasmids of Escherichia coli

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Random fluctuations in genetic and metabolic networks are inevitable as chemical reactions are probabilistic and many genes, mRNAs and proteins are present at low numbers per cell. Though such noise can sometimes be advantageous, it often poses a threat to fitness that organisms must carefully eliminate. The proposed project takes an interdisciplinary approach to noise suppression and single-cell homeostasis using mathematical theory, developing single-cell experimental methods, establishing single-cell phenotypes, and combining all these for in-depth analyses of the underlying regulatory networks. Replication control of bacterial plasmids (in Escherichia coli) is used as a model system, partly because plasmids rely on homeostatic control to avoid extinction, and partly because plasmids are among the best characterised control systems in the biosphere, rivalling or surpassing even the lac operon or lambda phage. The mathematical analyses combine Control Theory with Statistical Physics to analyse responses to external perturbations while simultaneously accounting for the fact that both the plant and the controller operate through probabilistic chemical reactions. In particular, I apply a recent reinterpretation of the Fluctuation-Dissipation Theorem to identify the guiding principles that govern chemical homeostasis. Preliminary results expose inherent fluctuation trade-offs (some of which, but not all, are related to Bode¿s Theorem) whereby suppressing one type of fluctuations automatically boosts another. I would also describe strongly nonlinear or non-Markovian strategies for breaking the trade-offs, and develop more detailed models of replication control. The experimental method development relies on two main principles: Molecules are counted as integers rather than quantified as continuities, and two independent methods are applied to the same cells for mutual validation. Counting involves suicide vectors, GFP synthesis rates, b-galactosidase activity, hybridisation and spatial PCR. Unperturbed growing cells would first be monitored and evaluated under the microscope, and then captured using microfluidics or Laser Capture Microdissection. Some methods could potentially generate time-series with single molecule resolution. Single cell copy numbers would be determined for unsynchronised distributions, as well as for selected unperturbed cells of a particular size or at a specific position in the cell cycle. The randomness of partitioning would be assessed by applying the method to both daughter cells immediately after septation. The different sources of fluctuations from replication control would be separated by repeating the measurements at different average copy numbers, and by subjecting the cells to fluctuating environments of different frequencies. Finally, the plasmids would be evaluated in terms of adjustments to steady state, growth rates and loss probabilities at cell division. Dissecting the regulatory networks would rely on mathematical analysis to identify experiments and to interpret data. Dynamic properties like lags and noisy signalling would be altered genetically. In the vein of Synthetic Biology, additional feedback loops would also be added to the system, to change the gains over the loop etc. Finally I would study accelerated control, whereby a homeostatic system can break the fluctuation trade-offs by responding insensitively around steady state, but turning on a second ultrasensitive response far from steady state. Most plasmids seem to use such systems, with CopB of plasmid R1 and Rom of plasmid CoIE1 as the best-studied candidates.