Topological constraints (TCs) between polymers determine the behavior of complex fluids such as creams, oils, and plastics. Most of the polymer solutions used in everyday life employ linear chains; their behavior is accurately captured by the reptation and tube theories which connect microscopic TCs to macroscopic viscoelasticity. On the other hand, polymers with nontrivial topology, such as rings, hold great promise for new technology but pose a challenging problem as they do not obey standard theories; additionally, topological invariance, i.e., the fact that rings must remain unknotted and unlinked if prepared so, precludes any serious analytical treatment. Here we propose an unambiguous, parameter-free algorithm to characterize TCs in polymeric solutions and show its power in characterizing TCs of entangled rings. We analyze large-scale molecular dynamics simulations via persistent homology, a key mathematical tool to extract robust topological information from large datasets. This method allows us to identify ring-specific TCs which we call "homological threadings" (H-threadings) and to connect them to polymer behavior. It also allows us to identify, in a physically appealing and unambiguous way, scale-dependent loops which have eluded precise quantification so far. We discover that while threaded neighbors slowly grow with ring length, the ensuing TCs are extensive also in the asymptotic limit. Our proposed method is not restricted to ring polymers and can find broader applications for the study of TCs in generic polymeric materials.
Damage to the DNA backbone occurs from natural sources, and with exceedingly large density during radiotherapy, as typically used for cancer treatment. Here, we focus on the molecular-scale dynamics of the events immediately following the production of single- and double-strand breaks, since this early-stage evolution of the damage is crucial to determine the subsequent fate of the DNA fragment. While multiple cleavage of phosphodiester bonds is the first step, however the remaining hydrogen-bond and π-stacking interactions maintain a considerable DNA cohesion, and determine further defect evolution. We use all-atom molecular dynamics to simulate the force spectra and thermal stability of different single- and multiple-defect configurations, in a random 31 bp DNA sequence. Simulations reveal a complex dynamical behaviour of the defects, where collective bond-rearrangement phenomena dominate with respect to simple bond cleavage. Defects are stable against thermal disruption, unless very closely spaced. We establish the necessary conditions for the events ultimately leading to DNA fragmentation. Such findings impact the early stages of damage recognition and signalling by specialised proteins, also implying that the identification and counting of DSBs by different experimental methods is non-unique.
Double strand breaks (DSB) in the DNA backbone are the most lethal type of defect induced in the cell nucleus by chemical and radiation treatments of cancer. However, little is known about the outcomes of damage in nucleosomal DNA, and on its effects on damage repair. We performed microsecond-long molecular dynamics computer simulations of nucleosomes including a DSB at various sites, to characterize the early stages of the evolution of this DNA lesion. The damaged structures are studied by the essential dynamics of DNA and histones, and compared to the intact nucleosome, thus exposing key features of the interactions. All DSB configurations tend to remain compact, with only the terminal bases interacting with histone proteins. Umbrella sampling calculations show that broken DNA ends at the DSB must overcome a free-energy barrier to detach from the nucleosome core. Finally, by calculating the covariant mechanical stress, we demonstrate that the coupled bending and torsional stress can force the DSB free ends to open up straight, thus making it accessible to damage signalling proteins.
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