Unzipping of two random heteropolymers: Ground state energy and finite size effects

TL;DR

This paper investigates the ground state energy and unzipping force of two random heteropolymers with quenched sequences, analyzing finite size effects and the influence of monomer interaction ratios at low temperatures.

Contribution

It provides a detailed analysis of the ground state energy dependence on chain length and interaction ratios, deriving unzipping forces for heteropolymer pairs.

Findings

Ground state energy per monomer depends on chain length and interaction ratio.

Derived unzipping force as a function of chain separation and sequence randomness.

Finite size effects significantly influence the energy and unzipping behavior.

Abstract

We have analyzed the dependence of average ground state energy per monomer, $e$, of the complex of two random heteropolymers with quenched sequences, on chain length, $n$, in the ensemble of chains with uniform distribution of primary sequences. Every chain monomer is randomly and independently chosen with the uniform probability distribution $p=1/c$ from a set of $c$ different types A, B, C, D, .... Monomers of the first chain could form saturating reversible bonds with monomers of the second chain. The bonds between similar monomer types (like A--A, B--B, C--C, etc.) have the attraction energy $u$, while the bonds between different monomer types (like A--B, A--D, B--D, etc.) have the attraction energy $v$. The main attention is paid to the computation of the normalized free energy $e(n)$ for intermediate chain lengths, $n$, and different ratios $a=\frac{v}{u}$ at sufficiently low temperatures when the entropic contribution of the loop formation is negligible compared to direct energetic interactions between chain monomers and the partition function of the chains is dominated by the ground state. The performed analysis allows one to derive the force, $f$, which is necessary to apply for unzipping of two random heteropolymer chains of equal lengths whose ends are separated by the distance $x$, averaged over all equally distributed primary structures at low temperatures for fixed values $a$ and $c$.