How cooperatively folding are homopolymer molecular knots?

TL;DR

This study uses thermodynamic analysis and molecular dynamics simulations to understand the factors influencing the stable and cooperative folding of homopolymer molecular knots, revealing key parameters that control knot topology and folding cooperativity.

Contribution

It introduces a heat capacity decomposition framework and demonstrates how backbone stiffness and other parameters affect knot stability and folding cooperativity in coarse-grained models.

Findings

Stiff backbone bending angle is crucial for specific knot structures.

Tuning backbone torsion and side chains influences knot topology and stability.

Heat capacity peaks are mainly due to coil-to-globule transitions, not knotting itself.

Abstract

Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work we derive a heat capacity decomposition comprising contributions from each individual configurational state, which together sum to a baseline heat capacity, and contributions from each state-to-state transition. We apply this analysis framework to a series of replica exchange molecular dynamics simulations of linear and 1-1 coarse-grained homo-oligomer models which fold into stable, configurationally well-defined molecular knots, in order to better understand the parameters leading to stable and cooperative folding of these knots. We find that a stiff harmonic backbone bending angle potential is key to achieving knots with specific 3D structures. Tuning the backbone equilibrium angle in small increments yields a variety of knot topologies, including $3_1$, $5_1$, $7_1$, and $8_{19}$ types. Populations of different knotted states as functions of temperature can also be manipulated by tuning backbone torsion stiffness or by adding side chain beads. We find that sharp total heat capacity peaks for the homo-oligomer knots are largely due to a coil-to-globule transition, rather than a cooperative knotting step. However, in some cases the cooperativity of globule-to-knot and coil-to-globule transitions are comparable, suggesting that highly cooperative folding to knotted structures can be achieved by refining the model parameters or adding sequence specificity.