A Specific Set of Heterogeneous Native Interactions Yields Efficient Knotting in Protein Folding

Abstract

Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study, we ask if non-native interactions are strictly necessary to tangle a protein or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous (i.e., having distinct energies), interactions. In order to address this problem, we conducted extensive Monte Carlo simulations of lattice models of proteinlike sequences designed to fold into a preselected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en route to the native structure. Our results thus show thatat least in the context of the adopted modelnon-native interactions are not necessary to knot a protein. However, when they are taken into account in protein energetics, it is possible to find specific, nonlocal non-native interactions that operate as a scaffold that assists the knotting step.

In silico method for identifying the key residues in a knotted protein: with MJ0366 as an example

“…Different from the folding process where the native contacts are dominant, the non-native contacts may also play an important role in the unfolding process. 28,29 Hence, we perform the AMD simulations in both the coarse-grained “Go”-like model and all-atom model with a realistic force field, respectively. The “Go”-like model only contains the native contacts, while the all-atom model includes both native and non-native contacts.…”

“…19 The protein MJ0366 from Methanocaldococcus jannaschii (PDBID: 2EFV) 20,21 is a typical example with a very shallow trefoil knot (i.e., the knot will be untangled if just a few residues are removed from one of the termini), 22 and hence has been a hot spot for studying the knotted proteins. [23][24][25][26][27][28][29] There are two popular methods used in the previous research on the folding problem of the knotted protein, known as the plain MD simulation with the structure-based model (such as the ''Go''-like Model) and the restrained MD (rMD) simulation with realistic force fields. For example, Noel et al obtained the folding landscape of protein MJ0366 using the structure-based model and found two different knotting pathways known as threading and slipknot.…”

“…carefully explored the relative role of the native and non-native interactions in knotted proteins and identified that the native interactions are critical for knotting. 28,29 Recently, Paissoni et al studied the transition states and key residues for knotting through genetic mutations and rMD based on f-values obtained from experiments. 24 In this paper, we present a simple in silico method to predict the key residues for knotting and unknotting a knotted protein, with the trefoil protein MJ0366 as an example.…”

“…25 In addition, Faisca et al carefully explored the relative role of the native and non-native interactions in knotted proteins and identified that the native interactions are critical for knotting. 28,29 Recently, Paissoni et al studied the transition states and key residues for knotting through genetic mutations and rMD based on ϕ -values obtained from experiments. 24…”

A Note on the Effects of Linear Topology Preservation in Monte Carlo Simulations of Knotted Proteins

“…The effects of knot deepness have also been investigated [13] as deep knots are expected to complicate the folding process. Monte Carlo (MC) methods and Molecular Dynamics simulations, often combined with parallel tempering (or replica-exchange) schemes [14,15], have been used to sample the conformational space of knotted model systems spanning different levels of resolution, from simple cubic lattices [16][17][18] and C-alpha models [19][20][21][22][23][24] to full atomistic representations [25][26][27]. Due to its lower computational cost, replica-exchange MC (RE-MC) is perhaps the most efficient method to sample canonically distributed conformational states across different temperatures and evaluate equilibrium properties [15].…”