Modeling Bacterial DNA: Simulation of Self-Avoiding Supercoiled Worm-Like Chains Including Structural Transitions of the Helix

Abstract

Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation bubbles and other alternative structures. Various polymer models have been developed to capture these properties, with Monte-Carlo (MC) approaches dedicated to the inference of thermodynamic properties. In this chapter, we explain how to perform such Monte-Carlo simulations, following two objectives. On one hand, we present the self-avoiding supercoiled Worm-Like Chain (ssWLC) model, which is known to capture the folding properties of supercoiled DNA, and provide a detailed explanation of a standard MC simulation method. On the other hand, we explain how to extend this ssWLC model to include structural transitions of the helix.

Intracellular Positioning Systems Limit the Entropic Eviction of Secondary Replicons Toward the Nucleoid Edges in Bacterial Cells

“…We simulated E. coli chromosomes using a worm-like chain (WLC) model, i.e. a flexible fiber model, of the bacterial chromosome (Junier et al, 2014;Lepage & Junier, 2017). One chromosomes and one plasmid were embedded in a volume whose dimensions corresponded to the nucleoid that is observed in vivo: a diameter equal to 800 nm and a length from 2.0 μm (G1 phase).…”

A polymer model of bacterial supercoiled DNA including structural transitions of the double helix

“…To demonstrate the ability of the 2sRLC model to capture the phenomenology of negatively supercoiled DNA, we performed Monte-Carlo simulations of long chains using the above effective energies. To this end, we have adapted the standard Monte-Carlo procedure used to simulate the equilibrium folding of the sRLC model [31] in order to include the possibility for mechanical parameters to change at any site of the chain, at any iteration of the simulation (see [66] for details). In practice, it involves a new transition type so that for any site i independently of the other sites, the value of the variable s i may change under the constraint of detailed balance.…”

“…More generally, length variation of a cylinder always requires an adjustment of the positions and orientations of the surrounding cylinders to preserve the continuity of the chain. As explained in [66], this is realised by performing specific random rotations that are constrained by the geometry of the chain.…”

“…DNA denaturation being expected to be the most likely alternative form at these forces and supercoiling densities [26,27], here we considered the situation where only B-DNA and D-DNA could form, with the following parameters leading to good agreement with experimental curves: a D = 0.45 nm, D = 15 nm, C D = 10 nm and γ D = 2k B T (see below for discussion of these values) -we intentionally used a D much larger than the 4 nm diameter of the chain because smaller values would lead, in any case, to larger effective persistence lengths [71]. We used J = 10k B T , in accord with previous analyses [69,26,52], and considered a discretization level of n = 10, leading to 3.3 cylinders per D and 15 cylinders per B (= 50 nm), a value that both offers reasonable computational times and ensures properties of B-DNA superstructuring to be insensitive to discretization procedures [42,66]. Finally, the quantitative reproduction of the buckling transition at σ > 0 (right part of the curves in Fig.…”

“…As a case study, we investigate a 1 kb long molecule with an alternative form characterized by X = 15 nm, a X = 0.54 nm, ψ X = 0, C X = 10 nm and γ X = 1.6kT , having in mind a form close to D-DNA; just as in the analysis of Fig. 2, the relatively high value of X compared to previous estimations for D-DNA (3 − 4 nm [33,25]) was chosen for practical purposes, that is, to avoid potential artifacts that may occur in the simulations when the persistence length is smaller or on the order of r e [66] and to avoid considering (longer) effective persistence lengths in our analytical approximations [71]. We also used a fine discretization level of n = 4 to get a large number of cylinders per D ( 7) so that to prevent any discrepancy coming from the discretization procedure of the rod-like chain.…”