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Many cell functions require a concerted effort from multiple membrane proteins, for example, for signaling, cell division, and endocytosis. One contribution to their successful self-organization stems from the membrane deformations that these proteins induce. While the pairwise interaction potential of two membrane deforming spheres has recently been measured, membrane-deformation induced interactions have been predicted to be non-additive and hence their collective behavior cannot be deduced from this measurement. We here employ a colloidal model system consisting of adhesive spheres and giant unilamellar vesicles to test these predictions by measuring the interaction potential of the simplest case of three membrane-deforming spherical particles. We quantify their interactions and arrangements and for the first time experimentally confirm and quantify the non-additive nature of membrane-deformation induced interactions. We furthermore conclude that there exist two favorable configurations on the membrane: (1) a linear, and (2) a triangular arrangement of the three spheres. Using Monte Carlo simulations we corroborate the experimentally observed energy minima and identify a lowering of the membrane deformation as the cause for the observed configurations. The high symmetry of the preferred arrangements for three particles suggests that arrangements of many membrane-deforming objects might follow simple rules.

Populations of genetically identical cells generally show a large variability in cell phenotypes, which is typically associated with the stochastic nature of gene expression processes. It is widely believed that a significant source of such randomness is transcriptional bursting, which is when periods of active production of RNA molecules alternate with periods of RNA degradation. However, the molecular mechanisms of such strong fluctuations remain unclear. Recent studies suggest that DNA supercoiling, which happens during transcription, might be directly related to the bursting behavior. Stimulated by these observations, we developed a stochastic mechanochemical model of supercoiling-induced transcriptional bursting in which the RNA synthesis leads to the buildup of torsion in DNA. This slows down the RNA production until it is bound by the enzyme gyrase to DNA, which releases the stress and allows for the RNA synthesis to restart with the original rate. Using a thermodynamically consistent coupling between mechanical and chemical processes, the dynamic properties of transcription are explicitly evaluated. In addition, a first-passage method to evaluate the dynamics of transcription is developed. Theoretical analysis shows that transcriptional bursting is observed when both the supercoiling and the mechanical stress release due to gyrase are present in the system. It is also found that the overall RNA production rate is not constant and depends on the number of previously synthesized RNA molecules. A comparison with experimental data on bacteria allows us to evaluate the energetic cost of supercoiling during transcription. It is argued that the relatively weak mechanochemical coupling might allow transcription to be regulated most effectively.