Configurational Entropy of Folded Proteins and Its Importance for Intrinsically Disordered Proteins

Computational Methods to Investigate Intrinsically Disordered Proteins and their Complexes

In 1999 Wright and Dyson highlighted the fact that large sections of the proteome of all organisms are comprised of protein sequences that lack globular folded structures under physiological conditions. Since then the biophysics community has made significant strides in unraveling the intricate structural and dynamic characteristics of intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs). Unlike crystallographic beamlines and their role in streamlining acquisition of structures for folded proteins, an integrated experimental and computational approach aimed at IDPs/IDRs has emerged. In this Perspective we aim to provide a robust overview of current computational tools for IDPs and IDRs, and most recently their complexes and phase separated states, including statistical models, physics-based approaches, and machine learning methods that permit structural ensemble generation and validation against many solution experimental data types.

The Energetic Origins of Pi-Pi Contacts in Proteins

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

Learning to evolve structural ensembles of unfolded and disordered proteins using experimental solution data

The structural characterization of proteins with a disorder requires a computational approach backed by experiments to model their diverse and dynamic structural ensembles. The selection of conformational ensembles consistent with solution experiments of disordered proteins highly depends on the initial pool of conformers, with currently available tools limited by conformational sampling. We have developed a Generative Recurrent Neural Network (GRNN) that uses supervised learning to bias the probability distributions of torsions to take advantage of experimental data types such as nuclear magnetic resonance J-couplings, nuclear Overhauser effects, and paramagnetic resonance enhancements. We show that updating the generative model parameters according to the reward feedback on the basis of the agreement between experimental data and probabilistic selection of torsions from learned distributions provides an alternative to existing approaches that simply reweight conformers of a static structural pool for disordered proteins. Instead, the biased GRNN, DynamICE, learns to physically change the conformations of the underlying pool of the disordered protein to those that better agree with experiments.

Targeting disordered-structured domain interactions in Galectin-3 based on NMR and enhanced MD

Intrinsically disordered regions (IDRs) are common and important functional domains in many proteins. However, IDRs are difficult to target for drug development due to the lack of defined structures that would facilitate the identification of possible drug-binding pockets. Galectin-3 is a carbohydrate-binding protein of which overexpression has been implicated in a wide variety of disorders, including cancer and inflammation. Apart from its carbohydrate-recognition/binding domain (CRD), Galectin-3 also contains a functionally important disordered N-terminal domain (NTD) that contacts the C-terminal domain (CTD) and could be a target for drug development. To overcome challenges involved in inhibitor design due to lack of structure and the highly dynamic nature of the NTD, we used a protocol combining nuclear magnetic resonance data from recombinant Galectin-3 with accelerated molecular dynamics (MD) simulations. This approach identified a pocket in the CTD with which the NTD makes frequent contact. In accordance with this model, mutation of residues L131 and L203 in this pocket caused loss of Galectin-3 agglutination ability, signifying the functional relevance of the cavity. In silico screening was used to design candidate inhibitory peptides targeting the newly discovered cavity, and experimental testing of only three of these yielded one peptide that inhibits the agglutination promoted by wild-type Galectin-3. NMR experiments further confirmed that this peptide indeed binds to a cavity in the CTD, not within the actual CRD. Our results show that it is possible to apply a combination of MD simulations and NMR experiments to precisely predict the binding interface of a disordered domain with a structured domain, and furthermore use this predicted interface for designing inhibitors. This procedure can potentially be extended to many other targets in which similar IDR interactions play a vital functional role.

Absolute binding free energies of mucroporin and its analog mucroporin-M1 with the heptad repeat 1 domain and RNA-dependent RNA polymerase of SARS-CoV-2

The peptide Mucroporin and its analog Mucroporin-M1 were studied using the molecular docking and molecular dynamics simulation of their complexation with two protein targets, the Heptad Repeat 1 (HR1) domain and RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. The molecular docking of the peptide-protein complexes was performed using the glowworm swarm optimization algorithm. The lowest energy poses were submitted to molecular dynamics simulation. Then, the binding free energies of Mucroporin and its analog Mucroporin-M1 with these two protein targets were calculated using the Multistate Bennett Acceptance Ratio (MBAR) method. It was verified that the peptides/HR1 domain complex showed stability in the interaction site determined by molecular docking. It was also found that Mucroporin-M1 has a much higher affinity than Mucroporin to the HR1 protein target. The peptides showed similar stability and affinity at the NTP binding site in the RdRp protein. Additional experimental studies are needed to confirm the antiviral activity of Mucroporin-M1 and a possible mechanism of action against SARS-CoV-2. However, here we indicate that Mucroporin-M1 may have potential antiviral activity against the HR1 domain with the possibility for further peptide optimization.Communicated by Ramaswamy H. Sarma.

Spectroscopic Fingerprints of Cavity Formation and Solute Insertion as a Measure of Hydration Entropic Loss and Enthalpic Gain

Hydration free energies are dictated by a subtle balance of hydrophobic and hydrophilic interactions. We present here a spectroscopic approach, which gives direct access to the two main contributions: Using THz-spectroscopy to probe the frequency range of the intermolecular stretch (150-200 cm-1 ) and the hindered rotations (450-600 cm-1 ), the local contributions due to cavity formation and hydrophilic interactions can be traced back. We show that via THz calorimetry these fingerprints can be correlated 1 : 1 with the group specific solvation entropy and enthalpy. This allows to deduce separately the hydrophobic (i.e. cavity formation) and hydrophilic contributions to thermodynamics, as shown for hydrated alcohols as a case study. Accompanying molecular dynamics simulations quantitatively support our experimental results. In the future our approach will allow to dissect hydration contributions in inhomogeneous mixtures and under non-equilibrium conditions.

Protein Dynamics to Define and Refine Disordered Protein Ensembles

Intrinsically disordered proteins and unfolded proteins have fluctuating conformational ensembles that are fundamental to their biological function and impact protein folding, stability, and misfolding. Despite the importance of protein dynamics and conformational sampling, time-dependent data types are not fully exploited when defining and refining disordered protein ensembles. Here we introduce a computational framework using an elastic network model and normal-mode displacements to generate a dynamic disordered ensemble consistent with NMR-derived dynamics parameters, including transverse R₂ relaxation rates and Lipari-Szabo order parameters (S² values). We illustrate our approach using the unfolded state of the drkN SH3 domain to show that the dynamical ensembles give better agreement than a static ensemble for a wide range of experimental validation data including NMR chemical shifts, J-couplings, nuclear Overhauser effects, paramagnetic relaxation enhancements, residual dipolar couplings, hydrodynamic radii, single-molecule fluorescence Förster resonance energy transfer, and small-angle X-ray scattering.

Origin of Increased Solvent Accessibility of Peptide Bonds in Mutual Synergetic Folding Proteins

Mutual Synergetic Folding (MSF) proteins belong to a recently discovered class of proteins. These proteins are disordered in their monomeric but ordered in their oligomeric forms. Their amino acid composition is more similar to globular proteins than to disordered ones. Our preceding work shed light on important structural aspects of the structural organization of these proteins, but the background of this behavior is still unknown. We suggest that solvent accessibility is an important factor, especially solvent accessibility of the peptide bonds can be accounted for this phenomenon. The side chains of the amino acids which form a peptide bond have a high local contribution to the shielding of the peptide bond from the solvent. During the oligomerization step, other non-local residues contribute to the shielding. We investigated these local and non-local effects of shielding based on Shannon information entropy calculations. We found that MSF and globular homodimeric proteins have different local contributions resulting from different amino acid pair frequencies. Their non-local distribution is also different because of distinctive inter-subunit contacts.

Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins

Finding optimal parameters for force fields used in molecular simulation is a challenging and time-consuming task, partly due to the difficulty of tuning multiple parameters at once. Automatic differentiation presents a general solution: run a simulation, obtain gradients of a loss function with respect to all the parameters, and use these to improve the force field. This approach takes advantage of the deep learning revolution whilst retaining the interpretability and efficiency of existing force fields. We demonstrate that this is possible by parameterising a simple coarse-grained force field for proteins, based on training simulations of up to 2,000 steps learning to keep the native structure stable. The learned potential matches chemical knowledge and PDB data, can fold and reproduce the dynamics of small proteins, and shows ability in protein design and model scoring applications. Problems in applying differentiable molecular simulation to all-atom models of proteins are discussed along with possible solutions and the variety of available loss functions. The learned potential, simulation scripts and training code are made available at https://github.com/psipred/cgdms.