Optimizing reaction coordinate by flux maximization in the transition path ensemble

Transition path ensemble is a collection of reactive trajectories, all of which largely keep going forward along the transition channel from the reactant state to the product one, and is believed to possess the information necessary for the identification of reaction coordinate. Previously, the full coordinates (both position and momentum) of the snapshots in the transition path ensemble were utilized to obtain the reaction coordinate (J. Chem. Phys. 2016, 144, 114103; J. Chem. Phys. 2018, 148, 084105). Here, with the conformational (or position) coordinates alone, it is demonstrated that the reaction coordinate can be optimized by maximizing the flux of a given coordinate in the transition path ensemble. In the application to alanine dipeptide in vacuum, dihderal angles ϕ and θ were identified to be the two best reaction coordinates, which was consistent with the results in existing studies. A linear combination of these two coordinates gave a better reaction coordinate, which is highly correlated with committor. Most importantly, the method obtained a linear combination of pairwise distances between heavy atoms, which was highly correlated with committor as well. The standard deviation of committor at the transition region defined by the optimized reaction coordinate is as small as 0.08. In addition, the effects of practical factors, such as the choice of transition path sub-ensembles and saving interval between frames in transition paths, on reaction coordinate optimization were also considered.

A Mechanism for the Rare Fluctuation that Powers Protein Conformational Change

Most functional processes of biomolecules are rare events. Key to a rare event is the rare fluctuation that enables the energy activation process, which powers the system across the activation barrier. But the physical nature of this rare fluctuation and how it enables barrier crossing are unknown. With the help of a novel metric, the reaction capacity pC, that rigorously defines the beginning and parameterizes the progress of energy activation, the rare fluctuation was identified as a special phase-space condition that is necessary and sufficient for initiating systematic energy flow from the non-reaction coordinates into the reaction coordinates. The energy activation of a prototype biomolecular isomerization reaction is dominated by kinetic energy transferring into and accumulating in the reaction coordinates, administered by inertial forces alone. The two major reaction coordinates move in precise synergy, with one acting as a gating mechanism on the other. This mechanism is enabled by the structural features of biomolecules and may the cause of their unique functions that are not possible in small molecules.

Comparing state-of-the-art approaches to back-calculate SAXS spectra from atomistic molecular dynamics simulations

Small-angle X-ray scattering (SAXS) experiments are arising as an effective instrument in the structural characterization of biomolecules in solution. However, they suffer from limited resolution, and complementing them with molecular dynamics (MD) simulations can be a successful strategy to obtain information at a finer scale. To this end, tools that allow computing SAXS spectra from MD-sampled structures have been designed over the years, mainly differing in how the solvent contribution is accounted for. In this context, RNA molecules represent a particularly challenging case, as they can have a remarkable effect on the surrounding solvent. Herein, we provide a comparison of SAXS spectra computed through different available software packages for a prototypical RNA system. RNA conformational dynamics is intentionally neglected so as to focus on solvent effects. The results highlight that solvent effects are important also at relatively low scattering vector, suggesting that approaches explicitly modeling solvent contribution are advisable when comparing with experimental data, while more efficient implicit-solvent methods can be a better choice as reaction coordinates to improve MD sampling on-the-fly. Graphic abstract

Predicting the Conformational Variability of Oncogenic GTP-bound G12D Mutated KRas-4B Proteins at Cell Membranes

KRas proteins are the largest family of mutated Ras isoforms, participating in a wide variety of cancers. Due to their importance, large effort is being carried out on drug development by small-molecule inhibitors. However, understanding protein conformational variability remains a challenge in drug discovery. In the case of the Ras family, their multiple conformational states can affect the binding of potential drug inhibitors. To overcome this challenge, we propose a computational framework based on combined all-atom Molecular Dynamics and Metadynamics simulations able to accurately access conformational variants of the target protein. We tested the methodology using a G12D mutated GTP bound oncogenic KRas-4B protein located at the interface of a DOPC/DOPS/cholesterol model anionic cell membrane. Two main orientations of KRas-4B at the anionic membrane have been obtained and explored. The corresponding angles have been taken as reliable reaction coordinates so that free-energy landscapes have been obtained by well-tempered metadynamics simulations, revealing the local and global minima of KRas-4B binding to the cell membrane, unvealing reactive paths of the system between the two preferential orientations and highlighting opportunities for targeting the unique metastable states through the identification of druggable pockets.

Interplays of electron and nuclear motions along CO dissociation trajectory in myoglobin revealed by ultrafast X-rays and quantum dynamics calculations

Ultrafast structural dynamics with different spatial and temporal scales were investigated during photodissociation of carbon monoxide (CO) from iron(II)–heme in bovine myoglobin during the first 3 ps following laser excitation. We used simultaneous X-ray transient absorption (XTA) spectroscopy and X-ray transient solution scattering (XSS) at an X-ray free electron laser source with a time resolution of 80 fs. Kinetic traces at different characteristic X-ray energies were collected to give a global picture of the multistep pathway in the photodissociation of CO from heme. In order to extract the reaction coordinates along different directions of the CO departure, XTA data were collected with parallel and perpendicular relative polarizations of the laser pump and X-ray probe pulse to isolate the contributions of electronic spin state transition, bond breaking, and heme macrocycle nuclear relaxation. The time evolution of the iron K-edge X-ray absorption near edge structure (XANES) features along the two major photochemical reaction coordinates, i.e., the iron(II)–CO bond elongation and the heme macrocycle doming relaxation were modeled by time-dependent density functional theory calculations. Combined results from the experiments and computations reveal insight into interplays between the nuclear and electronic structural dynamics along the CO photodissociation trajectory. Time-resolved small-angle X-ray scattering data during the same process are also simultaneously collected, which show that the local CO dissociation causes a protein quake propagating on different spatial and temporal scales. These studies are important for understanding gas transport and protein deligation processes and shed light on the interplay of active site conformational changes and large-scale protein reorganization.

Exploring Energy Landscapes of Intrinsically Disordered Proteins: Insights into Functional Mechanisms

Intrinsically disordered proteins (IDPs) lack a rigid 3D structure and populate a polymorphic ensemble of conformations. Because of the lack of a reference conformation, their energy landscape representation in terms of reaction coordinates presents a daunting challenge. Here, our newly developed Energy Landscape Visualization Method (ELViM), a reaction coordinate-free approach, shows its prime application to explore frustrated energy landscapes of an intrinsically disordered protein, Prostate-Associated Gene 4 (PAGE4). PAGE4 is a transcriptional coactivator that potentiates the oncogene c-Jun. Two kinases, namely HIPK1 and CLK2, phosphorylate PAGE4 generating variants phosphorylated at different serine/threonine residues (HIPK1-PAGE4 and CLK2-PAGE4, respectively) with opposing functions. While HIPK1-PAGE4 predominantly phosphorylates Thr51 and potentiates c-Jun, CLK2-PAGE4 hyper-phosphorylates PAGE4 and attenuates transactivation. To understand the underlying mechanisms of conformational diversity among different phosphoforms, we have analyzed their atomistic trajectories simulated using AWSEM forcefield and the energy landscapes were elucidated using ELViM. This method allows us to identify and compare the population distributions of different conformational ensembles of PAGE4 phosphoforms using the same effective phase space. The results reveal a predominant conformational ensemble with an extended C-terminal segment of WT PAGE4, which exposes a functional residue Thr51, implying its potential of undertaking a fly-casting mechanism while binding to its cognate partner. In contrast, for HIPK1-PAGE4, a compact conformational ensemble enhances its population sequestering phosphorylated-Thr51. This clearly explains the experimentally observed weaker affinity of HIPK1-PAGE4 for c-Jun. ELViM appears as a powerful tool especially to analyze the highly-frustrated energy landscape representation of IDPs where appropriate reaction coordinates are hard to apprehend.