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Register a new userCharacterizing the Interplay between Polymer Solvation and Conformation
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Conformational transitions of flexible molecules, especially those driven by hydrophobic effects, tend to be hindered by desolvation barriers. For such transitions, it is thus important to characterize and understand the interplay between solvation and conformation. Using specialized molecular simulations, here we perform such a characterization for a hydrophobic polymer solvated in water. We find that an external potential, which unfavorably perturbs the polymer hydration waters, can trigger a coil-to-globule or collapse transition, and that the relative stabilities of the collapsed and extended states can be quantified by the strength of the requisite potential. Our results also provide mechanistic insights into the collapse transition, highlighting that polymer collapse proceeds through the formation of a sufficiently large non-polar cluster, and that collective water density fluctuations play an important role in stabilizing such a cluster. We also study the collapse of the hydrophobic polymer in octane, a non-polar solvent, and interestingly, we find that the mechanistic details of the transition are qualitatively similar to that in water.
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Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation through a nanochannel embedded in two dimensions under an applied external field. We examine the translocation time for various ratio of the channel length $L$ to the polymer length $N$. For short channels $Lll N$, the translocation time $tau sim N^{1+ u}$ under weak driving force $F$, while $tausim F^{-1}L$ for long channels $Lgg N$, independent of the chain length $N$. Moreover, we observe a minimum of translocation time as a function of $L/N$ for different driving forces and channel widths. These results are interpreted by the waiting time of a single segment.
In this paper we derive the general equilibrium equations of a polymer chain with a noncircular cross section by the variation of the free energy functional. From the equilibrium equation of the elastic ribbon we derive analytically the equilibrium conformations both of the helical ribbons and the twisted ribbons. We find that the pitch angle of the helical ribbons depends on the ratio of the torsional rigidity to the bending one. For the twisted ribbons, the rotation rate depends on the spontaneous torsion, which is determined by the elastic properties of the polymers. Our results for helical and twisted ribbons strongly indicate that the formation of these structures is determined by their elastic properties.
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling. The probability distributions of block length $k$, which are analogous to the first-passage probabilities, are calculated analytically and determined from the computer simulations. In any domain, the probability distribution can be described by the asymptote $~k^{-3/2}$ at moderate values of $k$ if the spatial size of the block is less than the smallest characteristic size of the domain. For large blocks, the exponential asymptote $exp(-const , k a^2/d_{as}^2)$ is valid, $d_{as}$ being the asymptotic domain length (a is the monomer unit size). The number average block lengths and their dispersities change linearly with the block length for lamellae, cylinders, and balls, when the domain is characterized by a single characteristic size. If the domain is described by more than one size, the number average block length can grow nonlinearly with the domain sizes and the length das can depend on all of them.
We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that the adsorption threshold is the same for systems with quenched and annealed disorder. The results are discussed with respect to their implications for the physics of molecular recognition.
Finding the dense regions in a graph is an important problem in network analysis. Core decomposition and truss decomposition address this problem from two different perspectives. The former is a vertex-driven approach that assigns density indicators for vertices whereas the latter is an edge-driven technique that put density quantifiers on edges. Despite the algorithmic similarity between these two approaches, it is not clear how core and truss decompositions in a network are related. In this work, we introduce the vertex interplay (VI) and edge interplay (EI) plots to characterize the interplay between core and truss decompositions. Based on our observations, we devise CORE-TRUSSDD, an anomaly detection algorithm to identify the discrepancies between core and truss decompositions. We analyze a large and diverse set of real-world networks, and demonstrate how our approaches can be effective tools to characterize the patterns and anomalies in the networks. Through VI and EI plots, we observe distinct behaviors for graphs from different domains, and identify two anomalous behaviors driven by specific real-world structures. Our algorithm provides an efficient solution to retrieve the outliers in the networks, which correspond to the two anomalous behaviors. We believe that investigating the interplay between core and truss decompositions is important and can yield surprising insights regarding the dense subgraph structure of real-world networks.
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