In eukaryotes, many stable and heritable phenotypes arise from the same DNA sequence, owing to epigenetic regulatory mechanisms relying on the molecular cooperativity of ‘reader–writer’ enzymes. In this work, we focus on the fundamental, generic mechanisms behind the epigenome memory encoded by post-translational modifications of histone tails. Based on experimental knowledge, we introduce a unified modeling framework, the painter model, describing the mechanistic interplay between sequence-specific recruitment of chromatin regulators, chromatin-state-specific reader–writer processes and long-range spreading mechanisms. A systematic analysis of the model building blocks highlights the crucial impact of tridimensional chromatin organization and state-specific recruitment of enzymes on the stability of epigenomic domains and on gene expression. In particular, we show that enhanced 3D compaction of the genome and enzyme limitation facilitate the formation of ultra-stable, confined chromatin domains. The model also captures how chromatin state dynamics impact the intrinsic transcriptional properties of the region, slower kinetics leading to noisier expression. We finally apply our framework to analyze experimental data, from the propagation of γH2AX around DNA breaks in human cells to the maintenance of heterochromatin in fission yeast, illustrating how the painter model can be used to extract quantitative information on epigenomic molecular processes.

In a classic paper, Edward Purcell analysed the dynamics of flagellated bacterial swimmers and derived a geometrical relationship which optimizes the propulsion efficiency. Experimental measurements for wild-type bacterial species E. coli have revealed that they closely satisfy this geometric optimality. However, the dependence of the flagellar motor speed on the load and more generally the role of the torque-speed characteristics of the flagellar motor is not considered in Purcell's original analysis. Here we derive a tuned condition representing a match between the flagella geometry and the torque-speed characteristics of the flagellar motor to maximize the bacterial swimming speed for a given load. This condition is independent of the geometric optimality condition derived by Purcell and interestingly this condition is not satisfied by wild-type E. coli which swim 2-3 times slower than the maximum possible speed given the amount of available motor torque. Our analysis also reveals the existence of an anomalous propulsion regime, where the swim-speed increases with increasing load (drag). Finally, we present experimental data which supports our analysis.Here, A, D are the translational and rotational drag coefficients and V, ω are the translation and angular speed of the flagella. The constant, B, couples the rotational motion of helical flagella to the translation motion of bacterium.Purcell in his landmark paper on helical swimming considered the optimal geometry of the flagella which will maximize the propulsion efficiency η, defined as η =where Ω is the rotational speed of the flagellar motor, for a given size of cell body. Purcell showed that η is maximised when the translational drag coefficient of the flagella is matched to that of the cell body, i.e. A = A 0 . The propulsion matrix elements in Eq. (1) and (2) have been explicitly measured for the bacterial species E. coli and A and A 0 are found to be quite close to each other (1.48 × 10 −8 N. s. m −1 and 1.4 × 10 −8 N. s. m −1 respectively) [5] in agreement with Purcell's result. Equations (1) and (2) can be solved to obtain the swim-speed V and the torque τ produced by the flagellar motor in terms of the flagellar motor speed Ω m = Ω + ω (see Sec. 1 of the Supplemental Material (SM)) for the detailed derivation).

Burgeoning interest in the area of bacteria-powered micro robotic systems prompted us to study the dynamics of cargo transport by single bacteria. In this paper, we have studied the swimming...

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