Using Small-Angle Scattering Data and Parametric Machine Learning to Optimize Force Field Parameters for Intrinsically Disordered Proteins

Predicting Conformational Ensembles of Intrinsically Disordered Proteins: From Molecular Dynamics to Machine Learning

Intrinsically disordered proteins and regions (IDP/IDRs) are ubiquitous across all domains of life. Characterized by a lack of a stable tertiary structure, IDP/IDRs populate a diverse set of transiently formed structural states that can promiscuously adapt upon binding with specific interaction partners and/or certain alterations in environmental conditions. This malleability is foundational for their role as tunable interaction hubs in core cellular processes such as signaling, transcription, and translation. Tracing the conformational ensemble of an IDP/IDR and its perturbation in response to regulatory cues is thus paramount for illuminating its function. However, the conformational heterogeneity of IDP/IDRs poses several challenges. Here, we review experimental and computational methods devised to disentangle the conformational landscape of IDP/IDRs, highlighting recent computational advances that permit proteome-wide scans of IDP/IDRs conformations. We briefly evaluate selected computational methods using the disordered N-terminal of the human copper transporter 1 as a test case and outline further challenges in IDP/IDRs ensemble prediction.

Toward a general neural network force field for protein simulations: Refining the intramolecular interaction in protein

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein-water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level.

Parameter inversion of a polydisperse system in small-angle scattering

An accurate and efficient method for model- and form-free inversion of a polydisperse small-angle scattering system is presented. It supports an arbitrary number of model parameters and both 1D and 2D intensity observations.

A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.

Optimization and inference of bin widths for histogramming inelastic neutron scattering spectra

A data-driven bin-width optimization for the histograms of measured data sets based on inhomogeneous Poisson processes was developed in a neurophysiology study [Shimazaki & Shinomoto (2007). Neural Comput. 19, 1503-1527], and a subsequent study [Muto, Sakamoto, Matsuura, Arima & Okada (2019). J. Phys. Soc. Jpn, 88, 044002] proposed its application to inelastic neutron scattering (INS) data. In the present study, the results of the method on experimental INS time-of-flight data collected under different measurement conditions from a copper single crystal are validated. The extrapolation of the statistics on a given data set to other data sets with different total counts precisely infers the optimal bin widths on the latter. The histograms with the optimized bin widths statistically verify two fine-spectral-feature examples in the energy and momentum transfer cross sections: (i) the existence of phonon band gaps; and (ii) the number of plural phonon branches located close to each other. This indicates that the applied method helps in the efficient and rigorous observation of spectral structures important in physics and materials science like novel forms of magnetic excitation and phonon states correlated to thermal conductivities.

A General Small-Angle X-ray Scattering-Based Screening Protocol for Studying Physical Stability of Protein Formulations

A fundamental step in developing a protein drug is the selection of a stable storage formulation that ensures efficacy of the drug and inhibits physiochemical degradation or aggregation. Here, we designed and evaluated a general workflow for screening of protein formulations based on small-angle X-ray scattering (SAXS). Our SAXS pipeline combines automated sample handling, temperature control, and fast data analysis and provides protein particle interaction information. SAXS, together with different methods including turbidity analysis, dynamic light scattering (DLS), and SDS-PAGE measurements, were used to obtain different parameters to provide high throughput screenings. Using a set of model proteins and biopharmaceuticals, we show that SAXS is complementary to dynamic light scattering (DLS), which is widely used in biopharmaceutical research and industry. We found that, compared to DLS, SAXS can provide a more sensitive measure for protein particle interactions, such as protein aggregation and repulsion. Moreover, we show that SAXS is compatible with a broader range of buffers, excipients, and protein concentrations and that in situ SAXS provides a sensitive measure for long-term protein stability. This workflow can enable future high-throughput analysis of proteins and biopharmaceuticals and can be integrated with well-established complementary physicochemical analysis pipelines in (biopharmaceutical) research and industry.

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales─picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure-function relationships require atomistic knowledge of the populated states in the ensemble. In this Perspective, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

When Order Meets Disorder: Modeling and Function of the Protein Interface in Fuzzy Complexes

The degree of proteins structural organization ranges from highly structured, compact folding to intrinsic disorder, where each degree of self-organization corresponds to specific functions: well-organized structural motifs in enzymes offer a proper environment for precisely positioned functional groups to participate in catalytic reactions; at the other end of the self-organization spectrum, intrinsically disordered proteins act as binding hubs via the formation of multiple, transient and often non-specific interactions. This review focusses on cases where structurally organized proteins or domains associate with highly disordered protein chains, leading to the formation of interfaces with varying degrees of fuzziness. We present a review of the computational methods developed to provide us with information on such fuzzy interfaces, and how they integrate experimental information. The discussion focusses on two specific cases, microtubules and homologous recombination nucleoprotein filaments, where a network of intrinsically disordered tails exerts regulatory function in recruiting partner macromolecules, proteins or DNA and tuning the atomic level association. Notably, we show how computational approaches such as molecular dynamics simulations can bring new knowledge to help bridging the gap between experimental analysis, that mostly concerns ensemble properties, and the behavior of individual disordered protein chains that contribute to regulation functions.

Challenges and limitations in the studies of glycoproteins: A computational chemist's perspective

Experimenters face challenges and limitations while analyzing glycoproteins due to their high flexibility, stereochemistry, anisotropic effects, and hydration phenomena. Computational studies complement experiments and have been used in characterization of the structural properties of glycoproteins. However, recent investigations revealed that computational studies face significant challenges as well. Here, we introduce and discuss some of these challenges and weaknesses in the investigations of glycoproteins. We also present requirements of future developments in computational biochemistry and computational biology areas that could be necessary for providing more accurate structural property analyses of glycoproteins using computational tools. Further theoretical strategies that need to be and can be developed are discussed herein.

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.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

Interpretable, calibrated neural networks for analysis and understanding of inelastic neutron scattering data

Deep neural networks (NNs) provide flexible frameworks for learning data representations and functions relating data to other properties and are often claimed to achieve 'super-human' performance in inferring relationships between input data and desired property. In the context of inelastic neutron scattering experiments, however, as in many other scientific scenarios, a number of issues arise: (i) scarcity of labelled experimental data, (ii) lack of uncertainty quantification on results, and (iii) lack of interpretability of the deep NNs. In this work we examine approaches to all three issues. We use simulated data to train a deep NN to distinguish between two possible magnetic exchange models of a half-doped manganite. We apply the recently developed deterministic uncertainty quantification method to provide error estimates for the classification, demonstrating in the process how important realistic representations of instrument resolution in the training data are for reliable estimates on experimental data. Finally we use class activation maps to determine which regions of the spectra are most important for the final classification result reached by the network.

Full structural ensembles of intrinsically disordered proteins from unbiased molecular dynamics simulations

Molecular dynamics (MD) simulation is widely used to complement ensemble-averaged experiments of intrinsically disordered proteins (IDPs). However, MD often suffers from limitations of inaccuracy. Here, we show that enhancing the sampling using Hamiltonian replica-exchange MD (HREMD) led to unbiased and accurate ensembles, reproducing small-angle scattering and NMR chemical shift experiments, for three IDPs of varying sequence properties using two recently optimized force fields, indicating the general applicability of HREMD for IDPs. We further demonstrate that, unlike HREMD, standard MD can reproduce experimental NMR chemical shifts, but not small-angle scattering data, suggesting chemical shifts are insufficient for testing the validity of IDP ensembles. Surprisingly, we reveal that despite differences in their sequence, the inter-chain statistics of all three IDPs are similar for short contour lengths (< 10 residues). The results suggest that the major hurdle of generating an accurate unbiased ensemble for IDPs has now been largely overcome.

Recent Force Field Strategies for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are widely distributed across eukaryotic cells, playing important roles in molecular recognition, molecular assembly, post-translational modification, and other biological processes. IDPs are also associated with many diseases such as cancers, cardiovascular diseases, and neurodegenerative diseases. Due to their structural flexibility, conventional experimental methods cannot reliably capture their heterogeneous structures. Molecular dynamics simulation becomes an important complementary tool to quantify IDP structures. This review covers recent force field strategies proposed for more accurate molecular dynamics simulations of IDPs. The strategies include adjusting dihedral parameters, adding grid-based energy correction map (CMAP) parameters, refining protein-water interactions, and others. Different force fields were found to perform well on specific observables of specific IDPs but also are limited in reproducing all available experimental observables consistently for all tested IDPs. We conclude the review with perspective areas for improvements for future force fields for IDPs.

Artificial intelligence techniques for integrative structural biology of intrinsically disordered proteins

We outline recent developments in artificial intelligence (AI) and machine learning (ML) techniques for integrative structural biology of intrinsically disordered proteins (IDP) ensembles. IDPs challenge the traditional protein structure-function paradigm by adapting their conformations in response to specific binding partners leading them to mediate diverse, and often complex cellular functions such as biological signaling, self-organization and compartmentalization. Obtaining mechanistic insights into their function can therefore be challenging for traditional structural determination techniques. Often, scientists have to rely on piecemeal evidence drawn from diverse experimental techniques to characterize their functional mechanisms. Multiscale simulations can help bridge critical knowledge gaps about IDP structure-function relationships-however, these techniques also face challenges in resolving emergent phenomena within IDP conformational ensembles. We posit that scalable statistical inference techniques can effectively integrate information gleaned from multiple experimental techniques as well as from simulations, thus providing access to atomistic details of these emergent phenomena.

Molecular simulations of IDPs: From ensemble generation to IDP interactions leading to disorder-to-order transitions

Intrinsically disordered proteins (IDPs) lack a well-defined three-dimensional structure but do exhibit some dynamical and structural ordering. The structural plasticity of IDPs indicates that entropy-driven motions are crucial for their function. Many IDPs undergo function-related disorder-to-order transitions upon by their interaction with specific binding partners. Approaches that are based on both experimental and theoretical tools enable the biophysical characterization of IDPs. Molecular simulations provide insights into IDP structural ensembles and disorder-to-order transition mechanisms. However, such studies depend strongly on the chosen force field parameters and simulation techniques. In this chapter, we provide an overview of IDP characteristics, review all-atom force fields recently developed for IDPs, and present molecular dynamics-based simulation methods that allow IDP ensemble generation as well as the characterization of disorder-to-order transitions. In particular, we introduce metadynamics, replica exchange molecular dynamics simulations, and also kinetic models resulting from Markov State modeling, and provide various examples for the successful application of these simulation methods to IDPs.