Using data from contact maps of the DNA-polymer of E. Coli (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. By suitable Monte Carlo Simulations, we show that the presence of these cross-links leads to a particular architecture and organization of the chain at large (micron) length scales of the DNA. We also investigate the structure of a ring polymer with an equal number of cross-links at random positions along the chain. We find that though the polymer does get organized at the large length scales, the nature of the organization is quite different from the organization observed with cross-links at specific biologically determined positions. We used the contact map of E. Coli bacteria which has around 4.6 million base pairs in a single circular chromosome. In our coarse-grained flexible ring polymer model, we used 4642 monomer beads and observed that around 80 cross-links are enough to induce the large-scale organization of the molecule accounting for statistical fluctuations caused by thermal energy. The length of a DNA chain of an even simple bacterial cell such as E. Coli is much longer than typical proteins, hence we avoided methods used to tackle protein folding problems. We define new suitable quantities to identify large scale structure of a polymer chain with a few cross-links.

In-vivo DNA organization at large length scales (∼ 100nm) is highly debated and polymer modelshave proved useful to understand the principle of DNA-organization. Here, we show that < 2% cross-links at specific points in a ring polymer can lead to a distinct spatial organization of the polymer. The specific pairs of cross-linked monomers were extracted from contact maps of bacterial DNA.We are able to predict the structure of 2 DNAs using Monte Carlo simulations of the beadspring polymer with cross-links at these special positions. Simulations with cross-links at random positions along the chain show that the organization of the polymer is different in nature from the previous case.PACS numbers: 87.15.ak,82.35.Lr,82.35.Pq,87.16.Sr,61.25.hp It is established that DNA-polymer is not a random coil in either bacterial cells [1][2][3] or in eukaryotic cells [4][5][6][7]. Experimental methods such as CCC (chromosomal conformation capture) which was then further developed as 5C and then Hi-C have consistently shown the presence of topologically associated domains (TADs) in the contact maps (C-maps) of DNA-chains [8][9][10]. The Hi-C technique gives us the C-map which is the map of frequencies that a segment of the DNA chain (say i) is found in spatial proximity to another segment (say j) for all combinations i, j of segments along the contour length of the DNA-polymer. TADs are patches in Cmaps which indicate that some segments of the chain (at 1 mega-base pair(BP) to 1 kilo-BP resolution), are found spatially close to other particular segments with higher frequencies compared to the rest of the segments.The ds-DNA is stiff at length scales of 1nm but can be considered to be a flexible chain at length scales beyond 100nm [11] . The persistence length ℓ p of a naked DNA is 150 Base Pairs (BP) ≡ 50 nm [12] and the value of ℓ p in vivo is debated [13]. Since, the resolution of Hi-C experiments are well above this length scale [1,4], there has a focussed attempts in the last few years trying to understand the DNA organization and in particular origin of formation of TADs from the principles of polymer physics [14][15][16][17][18]. A series of studies indicate that TADs in eukaryotic cells are indicative of fractal globule organization of the polymer (as opposed to equilibrium globule) [4,19]. Recently, more detailed polymer models with either different lengths of loops or with many distinct (coarse-grained) diffusing binder molecules which cross-link different segments of the chain have reproduced TADs of sections of a particular eukaryotic DNA by performing optimizations in multi-parameter space. Distinct kinds of binder molecules link correspondingly distinct monomers (DNA-segments) along the chain, and the optimization parameters include the number of distinct kind of binders/monomers as well as the position and number of distinct monomers as well as diffusing cross-links along the contour [16,[20][21][22].We propose a much simpler model for shorter bacterial DNAs and ask a more general question: Does fixed cross-links...

We showed in our previous studies that just 3% cross-links, at special points along the contour of the bacterial DNA help the DNA-polymer to get organized at micron length scales [1,2]. In this work, we investigate how does the release of topological constraints help in the organization of the DNA-polymer. Furthermore, we show that the chain compaction induced by the crowded environment in the bacterial cytoplasm contributes to the organization of the DNA-polymer. We model the DNA chain as a flexible bead-spring ring polymer, where each bead represents 1000 base pairs. The specific positions of the cross-links have been taken from the experimental contact maps of the bacteria C. crescentus and E. coli. We introduce different extents of topological constraints in our model by systematically changing the diameter of the monomer bead. It varies from the value where the chain crossing can occur freely to the value where the chain crossing is disallowed. We also study the role of molecular crowders by introducing an effective Lennard Jones attraction between the monomers. Using Monte-Carlo simulations, we show that the release of topological constraints and the crowding environment play a crucial role to obtain a unique organization of the polymer.

Using a bead-spring model of bacterial DNA polymers of C. crescentus and E. coli we show that just 33 and 38 effective cross-links at special positions along the chain contour of the DNA can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the 33 cross-links along the chain contour are chosen from the contact map data of C. crescentus. We represent 1000 base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA. Thus a 4017 beads on a flexible ring polymer represents the C. crescentus DNA with 4017 kilo-base pairs. Choosing suitable parameters from our preceding study, we also incorporate the role of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the C. crescentus with available experimental contact map data and also give a prediction of the approximate positions of different segments within the cell in 3D. For the E. coli chromosome with 4.6 million base pairs, we need around 38 effective cross-links with cylindrical confinement to organize the chromosome. We also predict the 3D organization of the E. coli chromosome segments within the cylinder which represents the cell wall.