RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias.

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

Long-range allostery mediates the regulation of plasminogen activator inhibitor-1 by cell adhesion factor vitronectin.

The serpin plasminogen activator inhibitor 1 (PAI-1) spontaneously undergoes a massive structural change from a metastable and active conformation, with a solvent-accessible reactive center loop (RCL), to a stable, inactive, or latent conformation, with the RCL inserted into the central ß-sheet. Physiologically, conversion to the latent state is regulated by the binding of vitronectin, which hinders the latency transition rate approximately twofold. The molecular mechanisms leading to this rate change are unclear. Here, we investigated the effects of vitronectin on the PAI-1 latency transition using all-atom path sampling simulations in explicit solvent. In simulated latency transitions of free PAI-1, the RCL is quite mobile as is the gate, the region that impedes RCL access to the central ß-sheet. This mobility allows the formation of a transient salt bridge that facilitates the transition; this finding rationalizes existing mutagenesis results. Vitronectin binding reduces RCL and gate mobility by allosterically rigidifying structural elements over 40 Å away from the binding site, thus blocking transition to the latent conformation. The effects of vitronectin are propagated by a network of dynamically correlated residues including a number of conserved sites that were previously identified as important for PAI-1 stability. Simulations also revealed a transient pocket populated only in the vitronectin-bound state, corresponding to a cryptic drug-binding site identified by crystallography. Overall, these results shed new light on PAI-1 latency transition regulation by vitronectin and illustrate the potential of path sampling simulations for understanding functional protein conformational changes and for facilitating drug discovery.

Functional, pathogenic, and pharmacological roles of protein folding intermediates.

Protein expression and function in eukaryotic cells are tightly harmonized processes modulated by the combination of different layers of regulation, including transcription, processing, stability, and translation of messenger RNA, as well as assembly, maturation, sorting, recycling, and degradation of polypeptides. Integrating all these pathways and the protein quality control machinery, deputed to avoid the production and accumulation of aberrantly folded proteins, determines protein homeostasis. Over the last decade, the combined development of accurate time-resolved experimental techniques and efficient computer simulations has opened the possibility of investigating biological mechanisms at atomic resolution with physics-based models. A meaningful example is the reconstruction of protein folding pathways at atomic resolution, which has enabled the characterization of the folding kinetics of biologically relevant globular proteins consisting of a few hundred amino acids. Combining these innovative computational technologies with rigorous experimental approaches reveals the existence of non-native metastable states transiently appearing along the folding process of such proteins. Here, we review the primary evidence indicating that these protein folding intermediates could play roles in disparate biological processes, from the posttranslational regulation of protein expression to disease-relevant protein misfolding mechanisms. Finally, we discuss how the information encoded into protein folding pathways could be exploited to design an entirely new generation of pharmacological agents capable of promoting the selective degradation of protein targets.

Successes and challenges in simulating the folding of large proteins.

Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments, and to test the effects of mutations and small molecules on folding. However, whereas major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multidomain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization, and interactions with cellular chaperones remain poorly understood. Molecular dynamics based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates, and pathways. Further, increases in computational power and methodological advances have made folding simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Go and related structure-based models that can predict the effects of the native structure on folding to all-atom-based methods that include side-chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold, expanding our ability to predict and manipulate protein folding.

Full atomistic model of prion structure and conversion.

Prions are unusual protein assemblies that propagate their conformationally-encoded information in absence of nucleic acids. The first prion identified, the scrapie isoform (PrPSc) of the cellular prion protein (PrPC), caused epidemic and epizootic episodes [1]. Most aggregates of other misfolding-prone proteins are amyloids, often arranged in a Parallel-In-Register-ß-Sheet (PIRIBS) [2] or ß-solenoid conformations [3]. Similar folding models have also been proposed for PrPSc, although none of these have been confirmed experimentally. Recent cryo-electron microscopy (cryo-EM) and X-ray fiber-diffraction studies provided evidence that PrPSc is structured as a 4-rung ß-solenoid (4RßS) [4, 5]. Here, we combined different experimental data and computational techniques to build the first physically-plausible, atomic resolution model of mouse PrPSc, based on the 4RßS architecture. The stability of this new PrPSc model, as assessed by Molecular Dynamics (MD) simulations, was found to be comparable to that of the prion forming domain of Het-s, a naturally-occurring ß-solenoid. Importantly, the 4RßS arrangement allowed the first simulation of the sequence of events underlying PrPC conversion into PrPSc. This study provides the most updated, experimentally-driven and physically-coherent model of PrPSc, together with an unprecedented reconstruction of the mechanism underlying the self-catalytic propagation of prions.

Polymer Physics by Quantum Computing.

Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. Here, we develop a formalism based on interacting binary tensors that allows for tackling this problem using quantum annealing machines. Our approach is general in that properties such as self-avoidance, branching, and looping can all be specified in terms of quadratic interactions of the tensors. Microstates' realizations of different lattice polymer ensembles are then seamlessly generated by solving suitable discrete energy-minimization problems. This approach enables us to capitalize on the strengths of quantum annealing machines, as we demonstrate by sampling polymer mixtures from low to high densities, using the D-Wave quantum annealer. Our systematic approach offers a promising avenue to harness the rapid development of quantum machines for sampling discrete models of filamentous soft-matter systems.

Target Search of Active Agents Crossing High Energy Barriers.

Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this nonequilibrium rare-event problem by developing an algorithm generalizing transition-path sampling to active Brownian dynamics. This method is exemplified and benchmarked for a paradigmatic two-dimensional potential with a high barrier. We find that even in such a simple landscape the structure and kinetics of the ensemble of transition paths changes drastically in the presence of activity. Indeed, active Brownian particles reach the target more frequently than passive Brownian particles, following longer and counterintuitive search patterns.

Dominant Reaction Pathways by Quantum Computing.

Characterizing thermally activated transitions in high-dimensional rugged energy surfaces is a very challenging task for classical computers. Here, we develop a quantum annealing scheme to solve this problem. First, the task of finding the most probable transition paths in configuration space is reduced to a shortest-path problem defined on a suitable weighted graph. Next, this optimization problem is mapped into finding the ground state of a generalized Ising model. A finite-size scaling analysis suggests this task may be solvable efficiently by a quantum annealing machine. Our approach leverages on the quantized nature of qubits to describe transitions between different system's configurations. Since it does not involve any lattice space discretization, it paves the way towards future biophysical applications of quantum computing based on realistic all-atom models.

All-atom simulation of the HET-s prion replication.

Prions are self-replicative protein particles lacking nucleic acids. Originally discovered for causing infectious neurodegenerative disorders, they have also been found to play several physiological roles in a variety of species. Functional and pathogenic prions share a common mechanism of replication, characterized by the ability of an amyloid conformer to propagate by inducing the conversion of its physiological, soluble counterpart. Since time-resolved biophysical experiments are currently unable to provide full reconstruction of the physico-chemical mechanisms responsible for prion replication, one must rely on computer simulations. In this work, we show that a recently developed algorithm called Self-Consistent Path Sampling (SCPS) overcomes the computational limitations of plain MD and provides a viable tool to investigate prion replication processes using state-of-the-art all-atom force fields in explicit solvent. First, we validate the reliability of SCPS simulations by characterizing the folding of a class of small proteins and comparing against the results of plain MD simulations. Next, we use SCPS to investigate the replication of the prion forming domain of HET-s, a physiological fungal prion for which high-resolution structural data are available. Our atomistic reconstruction shows remarkable similarities with a previously reported mechanism of mammalian PrPSc propagation obtained using a simpler and more approximate path sampling algorithm. Together, these results suggest that the propagation of prions generated by evolutionary distant proteins may share common features. In particular, in both these cases, prions propagate their conformation through a very similar templating mechanism.

Optimal navigation strategy of active Brownian particles in target-search problems.

We investigate exploration patterns of a microswimmer, modeled as an active Brownian particle, searching for a target region located in a well of an energy landscape and separated from the initial position of the particle by high barriers. We find that the microswimmer can enhance its success rate in finding the target by tuning its activity and its persistence in response to features of the environment. The target-search patterns of active Brownian particles are counterintuitive and display characteristics robust to changes in the energy landscape. On the contrary, the transition rates and transition-path times are sensitive to the details of the specific energy landscape. In striking contrast to the passive case, the presence of additional local minima does not significantly slow down the active-target-search dynamics.

Molecular Mechanisms of Activation in the Orange Carotenoid Protein Revealed by Molecular Dynamics.

Light-harvesting in photosynthesis is accompanied by photoprotective processes. In cyanobacteria, the photoprotective role is played by a specialized complex, the orange carotenoid protein, which is activated by strong blue-green light. This photoactivation involves a unique series of structural changes which terminate with an opening of the complex into two separate domains, one of which acts as a quencher for the light-harvesting complexes. Many experimental studies have tried to reveal the molecular mechanisms through which the energy absorbed by the carotenoid finally leads to the large conformational change of the complex. Here, for the first time, these mechanisms are revealed by simulating at the atomistic level the whole dynamics of the complex through an effective combination of enhanced sampling techniques. On the basis of our findings, we can conclude that the carotenoid does not act as a spring that, releasing its internal strain, induces the dissociation, as was previously proposed, but as a "latch" locking together the two domains. The photochemically triggered displacement of the carotenoid breaks this balance, allowing the complex to dissociate.

Microscopic calculation of absorption spectra of macromolecules: An analytic approach.

We develop a cross-disciplinary approach to analytically compute optical response functions of open macromolecular systems by exploiting the mathematical formalism of quantum field theory (QFT). Indeed, the entries of the density matrix for the electronic excitations interacting with their open dissipative environment are mapped into vacuum-to-vacuum Green's functions in a fictitious relativistic closed quantum system. We show that by re-summing appropriate self-energy diagrams in this dual QFT, it is possible to obtain analytic expressions for the response functions in Mukamel's theory. This yields physical insight into the structure and dynamics of vibronic resonances, since their frequency and width is related to fundamental physical constants and microscopic model parameters. For illustration, we apply this scheme to compute the linear absorption spectrum of the Fenna-Matthews-Olson light harvesting complex, comparing analytic calculations, numerical Monte Carlo simulations, and experimental data.

All-Atom Simulations Reveal How Single-Point Mutations Promote Serpin Misfolding.

Protein misfolding is implicated in many diseases, including serpinopathies. For the canonical inhibitory serpin α1-antitrypsin, mutations can result in protein deficiencies leading to lung disease, and misfolded mutants can accumulate in hepatocytes, leading to liver disease. Using all-atom simulations based on the recently developed bias functional algorithm, we elucidate how wild-type α1-antitrypsin folds and how the disease-associated S (Glu264Val) and Z (Glu342Lys) mutations lead to misfolding. The deleterious Z mutation disrupts folding at an early stage, whereas the relatively benign S mutant shows late-stage minor misfolding. A number of suppressor mutations ameliorate the effects of the Z mutation, and simulations on these mutants help to elucidate the relative roles of steric clashes and electrostatic interactions in Z misfolding. These results demonstrate a striking correlation between atomistic events and disease severity and shine light on the mechanisms driving chains away from their correct folding routes.

Atomic Detail of Protein Folding Revealed by an Ab Initio Reappraisal of Circular Dichroism.

Circular dichroism (CD) is known to be an excellent tool for the determination of protein secondary structure due to fingerprint signatures of α and ß domains. However, CD spectra are also sensitive to the 3D arrangement of the chain as a result of the excitonic nature of additional signals due to the aromatic residues. This double sensitivity, when extended to time-resolved experiments, should allow protein folding to be monitored with high spatial resolution. To date, the exploitation of this very appealing idea has been limited, due to the difficulty in relating the observed spectral evolution to specific configurations of the chain. Here, we demonstrate that the combination of atomistic molecular dynamics simulations of the folding pathways with a quantum chemical evaluation of the excitonic spectra provides the missing key. This is exemplified for the folding of canine milk lysozyme protein.

Serpin latency transition at atomic resolution.

Protease inhibition by serpins requires a large conformational transition from an active, metastable state to an inactive, stable state. Similar reactions can also occur in the absence of proteases, and these latency transitions take hours, making their time scales many orders of magnitude larger than are currently accessible using conventional molecular dynamics simulations. Using a variational path sampling algorithm, we simulated the entire serpin active-to-latent transition in all-atom detail with a physically realistic force field using a standard computing cluster. These simulations provide a unifying picture explaining existing experimental data for the latency transition of the serpin plasminogen activator inhibitor-1 (PAI-1). They predict a long-lived intermediate that resembles a previously proposed, partially loop-inserted, prelatent state; correctly predict the effects of PAI-1 mutations on the kinetics; and provide a potential means to identify ligands able to accelerate the latency transition. Interestingly, although all of the simulated PAI-1 variants readily access the prelatent intermediate, this conformation is not populated in the active-to-latent transition of another serpin, α1-antitrypsin, which does not readily go latent. Thus, these simulations also help elucidate why some inhibitory serpin families are more conformationally labile than others.

Dominant folding pathways of a WW domain.

We investigate the folding mechanism of the WW domain Fip35 using a realistic atomistic force field by applying the Dominant Reaction Pathways approach. We find evidence for the existence of two folding pathways, which differ by the order of formation of the two hairpins. This result is consistent with the analysis of the experimental data on the folding kinetics of WW domains and with the results obtained from large-scale molecular dynamics simulations of this system. Free-energy calculations performed in two coarse-grained models support the robustness of our results and suggest that the qualitative structure of the dominant paths are mostly shaped by the native interactions. Computing a folding trajectory in atomistic detail only required about one hour on 48 Central Processing Units. The gain in computational efficiency opens the door to a systematic investigation of the folding pathways of a large number of globular proteins.

Folding pathways of a knotted protein with a realistic atomistic force field.

We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native [Formula: see text]-sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting.

Sampling a Rare Protein Transition Using Quantum Annealing.

Simulating spontaneous structural rearrangements in macromolecules with classical molecular dynamics is an outstanding challenge. Conventional supercomputers can access time intervals of up to tens of µs, while many key events occur on exponentially longer time scales. Path sampling techniques have the advantage of focusing the computational power on barrier-crossing trajectories, but generating uncorrelated transition paths that explore diverse conformational regions remains a problem. We employ a hybrid path-sampling paradigm that addresses this issue by generating trial transition paths using a quantum annealing (QA) machine. We first employ a classical computer to perform an uncharted exploration of the conformational space. The data set generated in this exploration is then postprocessed using a path integral-based method to yield a coarse-grained network representation of the reactive kinetics. By resorting to a quantum annealer, quantum superposition can be exploited to encode all of the transition pathways in the initial quantum state, thus potentially solving the path exploration problem. Furthermore, each QA cycle yields a completely uncorrelated trial trajectory. We previously validated this scheme on a prototypically simple transition, which could be extensively characterized on a desktop computer. Here, we scale up in complexity and perform an all-atom simulation of a protein conformational transition that occurs on the millisecond time scale, obtaining results that match those of the Anton special-purpose supercomputer. Despite limitations due to the available quantum annealers, our study highlights how realistic biomolecular simulations provide potentially impactful new ground for applying, testing, and advancing quantum technologies.

The role of non-native interactions in the folding of knotted proteins.

Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a natively-knotted N-acetylornithine carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase (OTCase). In addition, two different sets of pairwise amino acid interactions are considered: one promoting exclusively native interactions, and the other additionally including non-native quasi-chemical and electrostatic interactions. With the former model neither protein shows a propensity to form knots. With the additional non-native interactions, knotting propensity remains negligible for the natively-unknotted OTCase while for AOTCase it is much enhanced. Analysis of the trajectories suggests that the different entanglement of the two transcarbamylases follows from the tendency of the C-terminal to point away from (for OTCase) or approach and eventually thread (for AOTCase) other regions of partly-folded protein. The analysis of the OTCase/AOTCase pair clarifies that natively-knotted proteins can spontaneously knot during early folding stages and that non-native sequence-dependent interactions are important for promoting and disfavouring early knotting events.

Quantum-inspired encoding enhances stochastic sampling of soft matter systems.

Quantum advantage in solving physical problems is still hard to assess due to hardware limitations. However, algorithms designed for quantum computers may engender transformative frameworks for modeling and simulating paradigmatically hard systems. Here, we show that the quadratic unconstrained binary optimization encoding enables tackling classical many-body systems that are challenging for conventional Monte Carlo. Specifically, in self-assembled melts of rigid lattice ring polymers, the combination of high density, chain stiffness, and topological constraints results in divergent autocorrelation times for real-space Monte Carlo. Our quantum-inspired encoding overcomes this problem and enables sampling melts of lattice rings with fixed curvature and compactness, unveiling counterintuitive topological effects. Tackling the same problems with the D-Wave quantum annealer leads to substantial performance improvements and advantageous scaling of sampling computational cost with the size of the self-assembled ring melts.