A Study of the Morphology, Dynamics, and Folding Pathways of Ring Polymers with Supramolecular Topological Constraints Using Molecular Simulation and Nonlinear Manifold Learning

Abstract

Ring polymers are prevalent in natural and engineered systems, including circular bacterial DNA, crown ethers for cation chelation, and mechanical nanoswitches. The morphology and dynamics of ring polymers are governed by the chemistry and degree of polymerization of the ring, and intramolecular and supramolecular topological constraints such as knots or mechanically-interlocked rings. In this study, we perform molecular dynamics simulations of polyethylene ring polymers at two different degrees of polymerization and in different topological states, including a trefoil knot, catenane state (two interlocked rings), and Borromean state (three interlocked rings). We employ nonlinear manifold learning to extract the low-dimensional free energy surface to which the structure and dynamics of the polymer chain are effectively restrained. The free energy surfaces reveal how degree of polymerization and topological constraints affect the thermally accessible conformations, chiral symmetry breaking, and folding and collapse pathways of the rings, and present a means to rationally engineer ring size and topology to stabilize particular conformational states and folding pathways. We compute the rotational diffusion of the ring in these various states as a crucial property required for the design of engineered devices containing ring polymer components.2

Discovery of Self-Assembling π-Conjugated Peptides by Active Learning-Directed Coarse-Grained Molecular Simulation

“…We implement this formalism using the memory and compute efficient pivot diffusion map approach that reduces the scaling in the number of points N from to , where n ≪ N is the number of so-called “pivot points” employed . This approach enables the application of diffusion maps to large data sets by performing on-the-fly definition of the n pivot points defining an approximate spanning tree over the high-dimensional data and which are used to support interpolative embeddings of the remaining points.…”

“…where n << N is the number of so-called "pivot points" employed. 98 This approach enables the application of diffusion maps to large data sets by performing on-the-fly definition of the n pivot points defining an approximate spanning tree over the high-dimensional data and which are used to support interpolative embeddings of the remaining points.…”

Entropy-Induced Separation of Binary Semiflexible Ring Polymer Mixtures in Spherical Confinement

“…Every 10 4 steps are taken as a sample after ∆t 1 . The reduced temperature is T* = 1.0 in units of ε/k B by using a Nose-Hoover thermostat [53,54]. In order to avoid the system from being locally trapped, a slow reheat-annealing simulation is applied until the final equilibrium structure is obtained.…”

Topological Effects in Isolated Poly[n]catenanes: Molecular Dynamics Simulations and Rouse Mode Analysis

“…In recent decades, researchers have synthesized polymer architectures that incorporate mechanical (or topological) bonds, such as polyrotaxanes , and polycatenanes . These mechanically interlocking polymers (MIPs) possess distinct, well-defined topological interactions and, as a result, exhibit a variety of unique properties, which have been explored in experiments − and simulations. , For several decades, a highly sought-after MIP architecture has been the “poly­[ n ]­catenane” (Figure ), a linear chain of n mechanically interlocking ring molecules (macrocycles); this architecture was recently synthesized in our laboratory for the first time . These molecules are dominated by mechanical bonds, rather than traditional covalent linkages.…”