The physical nature of the bacterial chromosome has important implications for its function. Using high-resolution dynamic tracking, we observe the existence of rare but ubiquitous 'rapid movements' of chromosomal loci exhibiting near-ballistic dynamics. This suggests that these movements are either driven by an active machinery or part of stress-relaxation mechanisms. Comparison with a null physical model for subdiffusive chromosomal dynamics shows that rapid movements are excursions from a basal subdiffusive dynamics, likely due to driven and/or stress-relaxation motion. Additionally, rapid movements are in some cases coupled with known transitions of chromosomal segregation. They do not co-occur strictly with replication, their frequency varies with growth condition and chromosomal coordinate, and they show a preference for longitudinal motion. These findings support an emerging picture of the bacterial chromosome as off-equilibrium active matter and help developing a correct physical model of its in vivo dynamic structure.

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Recent experimental and theoretical approaches have attempted to quantify the physical organization (compaction and geometry) of the bacterial chromosome with its complement of proteins (the nucleoid). The genomic DNA exists in a complex and dynamic protein-rich state, which is highly organised at various length scales.This has implications for modulating (when not directly enabling) the core biological processes of replication, transcription, segregation. We overview the progress in this area, driven in the last few years by new scientific ideas and new interdisciplinary experimental techniques, ranging from high space-and time-resolution microscopy to high-throughput genomics employing sequencing to map different aspects of the nucleoid-related interactome. The aim of this review is to present the wide spectrum of experimental and theoretical findings coherently, from a physics viewpoint. In particular, we highlight the role that statistical and soft condensed matter physics play in describing this system of fundamental biological importance, specifically reviewing classic and more modern tools from the theory of polymers.We also discuss some attempts towards unifying interpretations of the current results, pointing to possible directions for future investigation.

In this paper, we present numerical calculations of the band spectrum of periodic approximants of the octagonal quasiperiodic tiling. We have studied a one-parameter family of Hamiltonians, including the pure hopping case, the Laplacian, and a regime in which atomic potentials prevail. We have found a parameter range over which the spectrum consists of only one band. Moreover, the Lebesgue measure is finite except maybe in a small domain of the parameter range. We have also studied the statistics of the levels. We have obtained a transition between a regime of level repulsion (quantum chaos) and another of level clustering (Cantor spectrum).