Bending rigidity of stiff polyelectrolyte chains: Single chain and a bundle of multichains

We study the bending rigidity of highly charged stiff polyelectrolytes, for both a single chain and many chains forming a bundle. A theory is developed to account for the interplay between competitive binding of counterions and charge correlations in softening the polyelectrolyte (PE) chains. The presence of even a small concentration of multivalent counterions leads to a dramatic reduction in the bending rigidity of the chains that are nominally stiffened by the repulsion between their backbone charges. The variation of the bending rigidity as a function of $f_{0}$, the fraction of charged monomers on the chain, does not exhibits simple scaling behavior; it grows with increasing $f_{0}$ below a critical value of $f_{0}$. Beyond the critical value, however, the chain becomes softer as $f_{0}$ increases. The bending rigidity also exhibits intriguing dependence on the concentration of multivalent counterion $n_{2}$; for highly charged PEs, the bending rigidity decreases as $n_2$ increases from zero, while it increases with increasing $n_{2}$ beyond a certain value of $n_{2}$. When polyelectrolyte chains form a $N$-loop condensate (e.g., a toroidal bundle formed by $N$ turns (winds) of the chain), the inter-loop coupling further softens the condensate, resulting in the bending free energy of the condensate that scales as $N$ for large $N$.Comment: 11 pages, 2 figure

Stretching Homopolymers

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {{sufficiently large}} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $\sim f$ for small $f$, and $\sim f^{{2/3}}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for \la Z\ra as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {{We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.Comment: 24 pages, 7 figure

Effects of molecular crowding and confinement on the spatial organization of a biopolymer

A chain molecule can be entropically collapsed in a crowded medium in a free or confined space. Here, we present a unified view of how molecular crowding collapses a flexible polymer in three distinct spaces: free, cylindrical, and (two-dimensional) slit-like. Despite their seeming disparities, a few general features characterize all these cases, even though the phi(c)-dependence of chain compaction differs between the two cases: a > a(c) and a a(c) (applicable to a coarse-grained model of bacterial chromosomes), chain size depends on the ratio a phi(c)/a(c), and "full'' compaction occurs universally at a phi(c)/a(c) approximate to 1; for a(c) > a (relevant for protein folding), it is controlled by phi(c) alone and crowding has a modest effect on chain size in a cellular environment (phi(c) approximate to 0.3). Also for a typical parameter range of biological relevance, molecular crowding can be viewed as effectively reducing the solvent quality, independent of confinement.NSERC (Canada)Korea Institute of Science and Technology Information (KISTI)Basic Science Research Program [2015R1D1A1A09057469]KIAS (Korea Institute for Advanced Study

How are molecular crowding and the spatial organization of a biopolymer interrelated

In a crowded cellular interior, dissolved biomolecules or crowders exert excluded volume effects on other biomolecules, which in turn control various processes including protein aggregation and chromosome organization. As a result of these effects, a long chain molecule can be phase-separated into a condensed state, redistributing the surrounding crowders. Using computer simulations and a theoretical approach, we study the interrelationship between molecular crowding and chain organization. In a parameter space of biological relevance, the distributions of monomers and crowders follow a simple relationship: the sum of their volume fractions rescaled by their size remains constant. Beyond a physical picture of molecular crowding it offers, this finding explains a few key features of what has been known about chromosome organization in an E. coli cell.NSERC (Canada)Korea Institute of Science and Technology Information (KISTI)Basic Science Research Program [2015R1D1A1A09057469]KIAS (Korea Institute for Advanced Study

Opposing effects of cationic antimicrobial peptides and divalent cations on bacterial lipopolysaccharides

© 2017 American Physical SocietyThe permeability of the bacterial outer membrane, enclosing Gram-negative bacteria, depends on the interactions of the outer, lipopolysaccharide (LPS) layer, with surrounding ions and molecules. We present a coarse-grained model for describing how cationic amphiphilic molecules (e.g., antimicrobial peptides) interact with and perturb the LPS layer in a biologically relevant medium, containing monovalent and divalent salt ions (e.g., Mg2+). In our approach, peptide binding is driven by electrostatic and hydrophobic interactions and is assumed to expand the LPS layer, eventually priming it for disruption. Our results suggest that in parameter ranges of biological relevance (e.g., at micromolar concentrations) the antimicrobial peptide magainin 2 effectively disrupts the LPS layer, even though it has to compete with Mg2+ for the layer. They also show how the integrity of LPS is restored with an increasing concentration of Mg2+. Using the approach, we make a number of predictions relevant for optimizing peptide parameters against Gram-negative bacteria and for understanding bacterial strategies to develop resistance against cationic peptides.Natural Sciences and Engineering Research Council (NSERC) of Canad