Current protein structure predictors do not produce meaningful folding pathways

Protein structure prediction has long been considered a gateway problem for understanding protein folding. Recent advances in deep learning have achieved unprecedented success at predicting a protein's crystal structure, but whether this achievement relates to a better modelling of the folding process remains an open question. In this work, we compare the pathways generated by state-of-the-art protein structure prediction methods to experimental folding data. The methods considered were AlphaFold 2, RoseTTAFold, trRosetta, RaptorX, DMPfold, EVfold, SAINT2 and Rosetta. We find evidence that their simulated dynamics capture some information about the folding pathwhay, but their predictive ability is worse than a trivial classifier using sequence-agnostic features like chain length. The folding trajectories produced are also uncorrelated with parameters such as intermediate structures and the folding rate constant. These results suggest that recent advances in protein structure prediction do not yet provide an enhanced understanding of the principles underpinning protein folding.

Dissecting Multiple Pathways in the Relaxation Dynamics of Helix Coil Transitions with Optimum Dimensionality Reduction

Fast kinetic experiments with dramatically improved time resolution have contributed significantly to understanding the fundamental processes in protein folding pathways involving the formation of a-helices and b-hairpin, contact formation, and overall collapse of the peptide chain. Interpretation of experimental results through application of a simple statistical mechanical model was key to this understanding. Atomistic description of all events observed in the experimental findings was challenging. Recent advancements in theory, more sophisticated algorithms, and a true long-term trajectory made way for an atomically detailed description of kinetics, examining folding pathways, validating experimental results, and reporting new findings for a wide range of molecular processes in biophysical chemistry. This review describes how optimum dimensionality reduction theory can construct a simplified coarse-grained model with low dimensionality involving a kinetic matrix that captures novel insights into folding pathways. A set of metastable states derived from molecular dynamics analysis generate an optimally reduced dimensionality rate matrix following transition pathway analysis. Analysis of the actual long-term simulation trajectory extracts a relaxation time directly comparable to the experimental results and confirms the validity of the combined approach. The application of the theory is discussed and illustrated using several examples of helix <==> coil transition pathways. This paper focuses primarily on a combined approach of time-resolved experiments and long-term molecular dynamics simulation from our ongoing work.

A Topological Selection of Folding Pathways from Native States of Knotted Proteins

Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.

Chaperonin Abundance Enhances Bacterial Fitness

The ability of chaperonins to buffer mutations that affect protein folding pathways suggests that their abundance should be evolutionarily advantageous. Here, we investigate the effect of chaperonin overproduction on cellular fitness in Escherichia coli. We demonstrate that chaperonin abundance confers 1) an ability to tolerate higher temperatures, 2) improved cellular fitness, and 3) enhanced folding of metabolic enzymes, which is expected to lead to enhanced energy harvesting potential.

Comparative Assessment of NMR Probes for the Experimental Description of Protein Folding Pathways with High-Pressure NMR

Multidimensional NMR intrinsically provides multiple probes that can be used for deciphering the folding pathways of proteins: NH amide and CH groups are strategically located on the backbone of the protein, while CH3 groups, on the side-chain of methylated residues, are involved in important stabilizing interactions in the hydrophobic core. Combined with high hydrostatic pressure, these observables provide a powerful tool to explore the conformational landscapes of proteins. In the present study, we made a comparative assessment of the NH, CH, and CH3 groups for analyzing the unfolding pathway of ∆+PHS Staphylococcal Nuclease. These probes yield a similar description of the folding pathway, with virtually identical thermodynamic parameters for the unfolding reaction, despite some notable differences. Thus, if partial unfolding begins at identical pressure for these observables (especially in the case of backbone probes) and concerns similar regions of the molecule, the residues involved in contact losses are not necessarily the same. In addition, an unexpected slight shift toward higher pressure was observed in the sequence of the scenario of unfolding with CH when compared to amide groups.

RAFFT: Efficient prediction of RNA folding pathways using the fast Fourier transform

We propose a novel heuristic to predict RNA secondary structures. The algorithm is inspired by the kinetic partitioning mechanism, by which molecules follow alternative folding pathways to their native structure, some much faster than others. Similarly, our algorithm RAFFT generates an ensemble of concurrent folding pathways ending in multiple metastable structures for each given sequence; this is in contrast with traditional thermodynamic approaches, which are based on aim to find single structures with minimal free energies. When analyzing 50 predicted folds per sequence, we found near-native predictions (79% PPV and 81% sensitivity) for RNAs of length < 200 nucleotides, matching the performance of recent deep-learning-based structure prediction methods. Our algorithm also acts as a folding kinetic ansatz, which we tested on two RNAs: the coronavirus frameshifting stimulation element (CFSE) and a classic bi-stable sequence. For the CFSE, an ensemble of 68 distinct structures computed by RAFFT allowed us to produce complete folding kinetic trajectories, whereas known methods require evaluating millions of sub-optimal structures to achieve this result. For the second application, only 46 distinct structures were required to reproduce the kinetics, whereas known methods required a sample of 20,000 structures. Thanks to the efficiency of the fast Fourier transform on which RAFFT is based, these computations are efficient, with complexity O(L^2 log L).

Linear Bounds on the Size of Conformations in Greedy Deterministic Oritatami

Oritatami is a computational model of RNA cotranscriptional folding, in which an RNA transcript is folding upon itself while being synthesized from its template DNA. This model is known to be Turing universal. Under the restriction on its parameters delay and arity both being 1, however, any deterministically foldable conformation is known to be at most ten times as large as its initial conformation (seed), and hence, the model becomes weaker. In this paper, we shall improve the size upper bound from [Formula: see text] down to [Formula: see text] and also provide a system that can fold into a conformation of size [Formula: see text]. These tighter bounds result from a novel graph representation of deterministic oritatami folding pathways. We shall also study the case in which a transcript is trapped in a region closed by a seed and show that under this confinement, the upper bound is further improved to [Formula: see text].

Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface

The three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30 nm fiber.

Double Mutant Cycles as a Tool to Address Folding, Binding, and Allostery

Quantitative measurement of intramolecular and intermolecular interactions in protein structure is an elusive task, not easy to address experimentally. The phenomenon denoted ‘energetic coupling’ describes short- and long-range interactions between two residues in a protein system. A powerful method to identify and quantitatively characterize long-range interactions and allosteric networks in proteins or protein–ligand complexes is called double-mutant cycles analysis. In this review we describe the thermodynamic principles and basic equations that underlie the double mutant cycle methodology, its fields of application and latest employments, and caveats and pitfalls that the experimentalists must consider. In particular, we show how double mutant cycles can be a powerful tool to investigate allosteric mechanisms in protein binding reactions as well as elusive states in protein folding pathways.