Self-consistent calculation of protein folding pathways

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.

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 PrP^Sc 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.

Prions are proteins capable of replicating in absence of nucleic acids. By propagating the information encoded in their conformation, prions exemplify the phenomenon of protein-based inheritance. These peculiar agents are associated with neurodegenerative pathologies in mammals, but also involved in a wide variety of physiological processes occurring in various biological contexts along the evolutionary scale. In this work, we apply a recently developed computational method to study the propagation mechanism of the fungal prion HET-s, using a realistic all-atom model. We find that the replication of HET-s shares fundamental features with the templated conversion of the mammalian prion PrP^Sc.

Understanding prion structure and conversion

Since their original identification, prions have represented enigmatic agents that defy the classical concept of genetic inheritance. For almost four decades, the high-resolution structure of PrP^Sc, the infectious and misfolded counterpart of the cellular prion protein (PrP^C), has remained elusive, mostly due to technical challenges posed by its high insolubility and aggregation propensity. As a result, such a lack of information has critically hampered the search for an effective therapy against prion diseases. Nevertheless, multiple attempts to get insights into the structure of PrP^Sc have provided important experimental constraints that, despite being at limited resolution, are paving the way for the application of computer-aided technologies to model the three-dimensional architecture of prions and their templated replication mechanism. Here, we review the most relevant studies carried out so far to elucidate the conformation of infectious PrP^Sc and offer an overview of the most advanced molecular models to explain prion structure and conversion.

Chemical Langevin equation: A path-integral view of Gillespie's derivation

In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation (CME). In this work, we construct an original path-integral description of the CME and show how applying Gillespie's two conditions to it directly leads to a path-integral equivalent to the CLE. We compare this approach to the path-integral equivalent of a large system size derivation and show that they are qualitatively different. In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems and are readily generalizable.

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 Gō 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.

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.

Allostery in Its Many Disguises: From Theory to Applications

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

All-atom calculation of protein free-energy profiles

The Bias Functional (BF) approach is a variational method which enables one to efficiently generate ensembles of reactive trajectories for complex biomolecular transitions, using ordinary computer clusters. For example, this scheme was applied to simulate in atomistic detail the folding of proteins consisting of several hundreds of amino acids and with experimental folding time of several minutes. A drawback of the BF approach is that it produces trajectories which do not satisfy microscopic reversibility. Consequently, this method cannot be used to directly compute equilibrium observables, such as free energy landscapes or equilibrium constants. In this work, we develop a statistical analysis which permits us to compute the potential of mean-force (PMF) along an arbitrary collective coordinate, by exploiting the information contained in the reactive trajectories calculated with the BF approach. We assess the accuracy and computational efficiency of this scheme by comparing its results with the PMF obtained for a small protein by means of plain molecular dynamics.