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Topological Enhancement of Protein Kinetic Stability

João NC Especial, Patrícia FN Faísca

Abstract

Knotted proteins embed a physical (i.e., open) knot within their native structures. For decades, significant effort has been devoted to elucidating the functional role of knots in proteins, yet no consensus has been reached. Here, using extensive Monte Carlo off-lattice simulations of a simple structure-based model, we isolate the effect of topology by comparing simulations that preserve the linear topology of the chain with simulations that allow chain crossings. This controlled framework enables us to isolate topological effects from sequence, structure and energetic contributions. We show that protein kinetic stability, defined as resistance to unfolding at a fixed temperature, is higher in knotted proteins. Additionally, kinetic stability increases significantly with knot depth, whereas foldability (or folding efficiency) is comparatively less affected. By considering a simple model of protein evolution in which amino-acid alphabet size is used as a proxy for evolutionary time, we find that increasing primary-sequence complexity through the addition of biotic amino acids predominantly enhances kinetic stability. Taken together, these results indicate that kinetic stability is a functional advantage conferred by protein knots and suggest that evolutionary pressure for kinetic stability could contribute to the persistence of knotted proteins.

Topological Enhancement of Protein Kinetic Stability

Abstract

Knotted proteins embed a physical (i.e., open) knot within their native structures. For decades, significant effort has been devoted to elucidating the functional role of knots in proteins, yet no consensus has been reached. Here, using extensive Monte Carlo off-lattice simulations of a simple structure-based model, we isolate the effect of topology by comparing simulations that preserve the linear topology of the chain with simulations that allow chain crossings. This controlled framework enables us to isolate topological effects from sequence, structure and energetic contributions. We show that protein kinetic stability, defined as resistance to unfolding at a fixed temperature, is higher in knotted proteins. Additionally, kinetic stability increases significantly with knot depth, whereas foldability (or folding efficiency) is comparatively less affected. By considering a simple model of protein evolution in which amino-acid alphabet size is used as a proxy for evolutionary time, we find that increasing primary-sequence complexity through the addition of biotic amino acids predominantly enhances kinetic stability. Taken together, these results indicate that kinetic stability is a functional advantage conferred by protein knots and suggest that evolutionary pressure for kinetic stability could contribute to the persistence of knotted proteins.
Paper Structure (8 sections, 3 equations, 4 figures)

This paper contains 8 sections, 3 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Model and Methods
  3. The C$_\alpha$ Gō model
  4. Monte Carlo simulations
  5. Results and discussion
  6. Model systems
  7. Author contributions
  8. Declaration of interests

Figures (4)

  • Figure 1: Native structures of the model systems: (A) FNIII (PDB 1TEN, unknotted), (B) MJ0366 (PDB 2EFV, shallow trefoil knot), and (C) YibK (PDB 1J85, chain A, deep trefoil knot). Cartoon (left) and C$_\alpha$ bead representations (right) are shown. The knotted core is depicted in gray; N- and C-terminal tails are colored blue and red, respectively. The sizes of the knotted core and tails (in number of beads) are indicated.
  • Figure 2: Folding and unfolding transitions per million Monte Carlo steps (MMCs) as a function of temperature for (A) FNIII, (B) MJ0366, and (C) YibK. Solid lines correspond to topology-preserving (LTyP) simulations; dashed lines correspond to topology-breaking (non-LTyP) simulations. Blue and red shaded regions indicate folding ($T<T_m$) and unfolding ($T>T_m$) regimes, respectively. Green (fold) and purple (unfold) curves show the transition count ratios (LTyP/non-LTyP).
  • Figure 3: Effect of increasing knot depth in MJ0366. (A) Native structures of MJ0366 and variants with extended terminal tails. (B,C) Folding ($T<T_m$) and unfolding ($T>T_m$) transitions per MMCs for MJ0366+5 and MJ0366+25 variants, respectively, obtained from LTyP (solid) and non-LTyP (dashed) simulations. (D) Folding transition ratios (LTyP/non-LTyP) at $T<T_m$ as a function of tail extension. (E) Unfolding transition ratios at $T>T_m$.
  • Figure 4: Effect of amino acid alphabet size on YibK kinetics. (A) Schematic of the reverse evolution (revol) procedure reducing the amino acid alphabet from 20 to 10 letters; representative native structures for alphabet sizes 20 and 10 are shown. (B) Folding transition ratios (LTyP/non-LTyP) in the folding regime ($T<T_m$). (C) Unfolding transition ratios in the unfolding regime ($T>T_m$).