Maximum Compaction Density of Folded Semiflexible Polymers

Abstract

We study the dynamics of polymer chain collapse into a globular state in poor solvent, as a function of chain flexibility. We examine the compactness of the folded globule assessing the direct contact and a larger length-scale structural characteristics at various persistence lengths l p. We discover that semiflexible polymer chains with a specific stiffness (l p ≈ 8 monomers) form the most densely folded structures, independently of the chain length, a phenomenon due to nematic-like hairpin formation and stacking of hairpin segments in the most compact state. Even in this most compactly folded state, the number of contacts between monomers (accounting for covalent bonds as well as noncovalent physical interactions) is still low, and the globule is only just above the marginal stability threshold. We identify morphological changes associated with the dynamics of semiflexible chain collapse: flexible chains fold into globules, less flexible form rod-like structures, followed by toroidal structures of different geni, and finally, even stiffer chains form highly elongated rods. We also study the time of collapse as a function of persistence length, which shows that stiff chains take much longer to reach their elongated lowest energy state. We propose that polymer chain stiffness, as a regulator of both local and global chain compactness, is highly important in biological systems and in the dynamics of DNA and protein folding.

Organization of Associating or Crosslinked Actin Filaments in Confinement

“…However, in this case the filament length also starts to become comparable to the actin persistence length and disorganized metastable arrangements (loops, collapsed, etc) can also occur. Prior models have described the formation of looped metastable minima structures for single self-attractive filaments [Ou andMuthukumar, 2005, Lappala andTerentjev, 2013]. Here we show how confinement leads to a shift from a kinetically-determined bulk network to rings and irregular loop structures.…”

“…The configurations of filaments in "open bundle", ring, and irregular looped structures (that resemble the lollipop shapes of individual self-associating filaments [Lau et al, 2009] or unequal double rings) occur in the region of phase space where filament sliding along bundles can occur more easily (r atr ≥ 0.08µm). This reflects the existence of multiple topologically-different free energy minima in the system (as can also occur in the collapse of single self-attractive filaments [Ou andMuthukumar, 2005, Lappala andTerentjev, 2013]). Confinement enables the system to explore and evolve towards these minima as follows.…”

Simulating the Entropic Collapse of Coarse-Grained Chromosomes

“…Significantly longer structural monomer chains with narrower good solvent regimes could be simulated to verify that scaling with contour length changes throughout the coil-globular collapse. By further including rigidity, we expect that simulations of this nature will observe a discontinuous phase transition from a swollen state to a collapsed globule that passes through metastable states similar to those observed in more traditional solvents [78][79][80][81][82][83]. In addition, implicit-depletants simulations would have the ability to consider confinement conditions, such as those experienced by intracellular chromosomes and it has been shown that confinement can play a significant role in the collapse of semiflexible chains [84].…”

Going beyond the classical amphiphilicity paradigm: the self-assembly of completely hydrophobic polymers into free-standing sheets and hollow nanostructures in solvents of variable quality

“…49,50 In fact, these morphologies in simulations have been captured by microscopic imaging during the collapse transitions of semiflexible biopolymers such as DNA and xanthan-chitosan complexes. 49,50 In fact, these morphologies in simulations have been captured by microscopic imaging during the collapse transitions of semiflexible biopolymers such as DNA and xanthan-chitosan complexes.…”

“…Combining the above theoretical analysis [34][35][36]49,50 together with the previous [44][45][46][47][48]51,52 and present experimental results achieved with the tunable solvent quality, we inferred that the formation of free-standing sheets of PPA-1 and PPA-2 was attributed to a delicate balance of two ''opposing interactions'': van der Waals attractive and entropic repulsive forces generated between the segments within a single chain, between two chains, and among more chains in the toluene/methanol solvents. It should be highlighted that in the present case, both intra-and intermolecular van der Waals attractions should be cooperatively anisotropic in the free-standing sheets obtained under these solvent conditions, which presumably originated from the bending stiffness of the semiflexible polymers.…”