Entropic force of cone-tethered polymers interacting with a planar surface

Abstract

Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched-Rosenbluth-method (PERM) Monte Carlo simulations are used to calculate the variation of the conformational free energy, F , of a hard-sphere polymer with respect to cone-tip-to-surface distance, h, from which the variation of the entropic force, f ≡ |dF/dh|, with h is determined. We consider the following cases: (1) a single freelyjointed tethered chain, (2) a single semiflexible tethered chain, and (3) several freely-jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi et al. (EPL, 96, 66002(2011); Phys. Rev. E 86, 061801 (2012)) that f ∝ (γ ∞ − γ 0 )h −1 , where γ 0 and γ ∞ are universal scaling exponents for the partition function of the tethered polymer for h = 0 and h = ∞, respectively. The measured functions f (h) are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.

Structural preferences shape the entropic force of disordered protein ensembles

“…The homopolymeric GS-repeat entropic force was fitted to an exponential decay function, indicating it is solely determined by the sequence length 6 . In agreement with Kuel et al’s observations, UGDH-derived sequences of different lengths also fell on the same line as the GS-repeats ( Fig.…”

“…1B ). For homopolymers, the strength of this entropic force is determined by the polymer’s length and the geometry of the constraining surface 5 as shown both theoretically and experimentally 6,7 .…”

“…1B). For homopolymers, the strength of this entropic force is determined by the polymer's length and the geometry of the constraining surface 5 as shown both theoretically and experimentally 6,7 . This tethering scenario may seem rare when considering naturally occurring proteins, but it is actually rather common: in eukaryotes, IDRs are often tethered to a more rigid surface that constrains the chain's conformational entropy, and this tethering results in measurable effects.…”

Structural Preferences Shape the Entropic Force of Disordered Protein Ensembles

“…As a result, upon tethering, an IDR will try to maximize its conformational entropy by producing an effective force that pulls up and away from the point of tethering, gaining entropy by increasing its number of accessible conformations generating an entropic force (Figure 1B). 5,6 This tethering scenario may seem rare when considering naturally occurring proteins, but it is rather common: in eukaryotes, IDRs are often tethered to a more rigid surface that constrains the chain's conformational entropy, and this tethering results in measurable effects. For example, IDRs tethered to a cell membrane can sense the curvature of the membrane and help to facilitate the endocytosis process through entropic force.…”

“…Beyond the steric and chemical features of the monomers, these studies have implicated the length and the geometry of the constraining surface as major factors affecting polymer entropic force strength. 5,6,22 Thus, previous entropic force studies of IDRs also focused on the role of sequence length and the geometry of the constraining surface. 9,11,13 IDR length is indeed a critical factor in determining entropic force magnitude 8,13 since the longer the chain, the higher the number of conformations available.…”