Characterizing the asymmetry in hardness between synthesis and destruction of heteropolymers

TL;DR

This paper introduces a simple model to analyze the asymmetric difficulty in synthesizing versus destroying heteropolymers, revealing exponential time requirements for synthesis and linear for decomposition, highlighting fundamental operational asymmetries.

Contribution

The paper provides a theoretical proof demonstrating the exponential asymmetry in synthesis and linearity in destruction times for heteropolymers, advancing understanding of operational hardness.

Findings

Synthesis time grows exponentially with the number of $A$-$B$ connections.

Decomposition time scales linearly with chain length.

Exponential asymmetry occurs when $d$ is proportional to $n$.

Abstract

We present a simple model describing the assembly and disassembly of heteropolymers consisting of two types of monomers $A$ and $B$. We prove that no matter how we manipulate the concentrations of $A$ and $B$, it takes longer than the exponential function of $d$ to synthesize a fixed amount of the desired heteropolymer, where $d$ is the number of $A$-$B$ connections. We also prove the decomposition time is linear for chain length $n$. When $d$ is proportional to $n$, synthesis and destruction have an exponential asymmetry. Our findings may facilitate research on the more general asymmetry of operational hardness.