Searching for reaction pathways describing rare events in large systems presents a long-standing challenge in chemistry and physics. Incorrectly computed reaction pathways result in the degeneracy of microscopic configurations and inability to sample hidden energy barriers. To this aim, we present a general enhanced sampling method to find multiple diverse reaction pathways of ligand unbinding through non-convex optimization of a loss function describing ligand-protein interactions. The method successfully overcomes large energy barriers using an adaptive bias potential, and constructs possible reaction pathways along transient tunnels without the initial guesses of intermediate or final states, requiring crystallographic information only. We examine the method on the T4 lysozyme L99A mutant which is often used as a model system to study ligand binding to proteins, provide a previously unknown reaction pathway, and show that using the bias potential and the tunnel widths it is possible to capture heterogeneity of the unbinding mechanisms between the found transient protein tunnels.
We here report on non-equilibrium targeted Molecular Dynamics simulations as tool for the estimation of protein-ligand unbinding kinetics. Correlating simulations with experimental data from SPR kinetics measurements and X-ray crystallography on two small molecule compound libraries bound to the N-terminal domain of the chaperone Hsp90, we show that the mean non-equilibrium work computed in an ensemble of trajectories of enforced ligand unbinding is a promising predictor for ligand unbinding rates. We furthermore investigate the molecular basis determining unbinding rates within the compound l…
Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multi-method approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obt…
Recent developments in enhanced sampling methods showed that it is possible to reconstruct ligand unbinding pathways with spatial and temporal resolution inaccessible to experiments. Ideally, such techniques should provide an atomistic definition of possibly many reaction pathways, because crude estimates may lead either to overestimating energy barriers, or inability to sample hidden energy barriers that are not captured by reaction pathway estimates. Here we provide an implementation of a new method [J. Rydzewski \& O. Valsson, J. Chem. Phys. {\bf 150}, 221101 (2019)] dedicated entirely to s…
A key factor influencing a drug's efficacy is its residence time in the binding pocket of the host protein. Using atomistic computer simulation to predict this residence time and the associated dissociation process is a desirable but extremely difficult task due to the long timescales involved. This gets further complicated by the presence of biophysical factors such as steric and solvation effects. In this work, we perform molecular dynamics (MD) simulations of the unbinding of a popular prototypical hydrophobic cavity-ligand system using a metadynamics based approach that allows direct asses…
We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) (Tiwary and Berne, Proc. Natl. Acad. Sci 2016, 113, 2839 (2016)), to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Usin…
The dissociation of ligands from proteins and other biomacromolecules occurs over a wide range of timescales. For most pharmaceutically relevant inhibitors, these timescales are far beyond those that are accessible by conventional molecular dynamics (MD) simulation. Consequently, to explore ligand egress mechanisms and compute dissociation rates, it is necessary to enhance the sampling of ligand unbinding. Random Acceleration MD (RAMD) is a simple method to enhance ligand egress from a macromolecular binding site, which enables the exploration of ligand egress routes without prior knowledge of…
The unbinding process of a protein-ligand complex of major biological interest was investigated by means of a computational approach at atomistic classical mechanical level. An energy minimisation-based technique was used to determine the dissociation paths of the system by probing only a relevant set of generalized coordinates. The complex problem was reduced to a low-dimensional scanning along a selected distance between the protein and the ligand. Orientational coordinates of the escaping fragment (the ligand) were also assessed in order to further characterise the unbinding. Solvent effect…
Determining the complete set of ligands' binding/unbinding pathways is important for drug discovery and to rationally interpret mutation data. Here we have developed a metadynamics-based technique that addressed this issue and allows estimating affinities in the presence of multiple escape pathways. Our approach is shown on a Lysozyme T4 variant in complex with the benzene molecule. The calculated binding free energy is in agreement with experimental data. Remarkably, not only we were able to find all the previously identified ligand binding pathways, but also we uncovered 3 new ones. This res…
The process of ligand-protein unbinding is crucial in biophysics. Water is an essential part of any biological system and yet, many aspects of its role remain elusive. Here, we simulate with state-of-the-art enhanced sampling techniques the binding of Benzamidine to Trypsin which is a much studied and paradigmatic ligand-protein system. We use machine learning methods to determine efficient collective coordinates for the complex non-local network of water. These coordinates are used to perform On-the-fly Probability Enhanced Sampling simulations, which we adapt to calculate also the ligand res…
Prediction of protein-ligand binding affinity is a major goal in drug discovery. Generally, free energy gap is calculated between two states (e.g., ligand binding and unbinding). The energy gap implicitly includes the effects of changes in protein dynamics induced by the binding ligand. However, the relationship between protein dynamics and binding affinity remains unclear. Here, we propose a novel method that represents protein behavioral change upon ligand binding with a simple feature that can be used to predict protein-ligand affinity. From unbiased molecular simulation data, an unsupervis…
We consider the recently developed weighted ensemble milestoning (WEM) scheme [J. Chem. Phys. 152, 234114 (2020)], and test its capability of simulating ligand-receptor dissociation dynamics. We performed WEM simulations on the following host-guest systems: Na$^+$/Cl$^-$ ion pair and 4-hydroxy-2-butanone (BUT) ligand with FK506 binding protein (FKBP). As proof or principle, we show that the WEM formalism reproduces the Na$^+$/Cl$^-$ ion pair dissociation timescale and the free energy profile obtained from long conventional MD simulation. To increase accuracy of WEM calculations applied to kine…
Using explicit-water molecular dynamics (MD) simulations of a generic pocket-ligand model we investigate how chemical and shape anisotropy of small ligands influences the affinities, kinetic rates and pathways for their association to hydrophobic binding sites. In particular, we investigate aromatic compounds, all of similar molecular size, but distinct by various hydrophilic or hydrophobic residues. We demonstrate that the most hydrophobic sections are in general desolvated primarily upon binding to the cavity, suggesting that specific hydration of the different chemical units can steer the o…
Ligand diffusion through proteins is a fundamental process governing biological signaling and enzymatic catalysis. The complex topology of protein tunnels results in difficulties with computing ligand escape pathways by standard molecular dynamics (MD) simulations. Here, two novel methods for searching of ligand exit pathways and cavity exploration are proposed: memory random acceleration MD (mRAMD), and memetic algorithms (MA). In mRAMD, finding exit pathways is based on a non-Markovian biasing that is introduced to optimize the unbinding force. In MA, hybrid learning protocols are exploited …
Accelerated descriptor-free path sampling for protein-ligand binding kinetics
Goethe University Frankfurt（法兰克福歌德大学）；Institute for Computer Science, Goethe University Frankfurt（法兰克福歌德大学计算机研究所）；Frankfurt Institute for Advanced Studies (FIAS), Goethe University Frankfurt（法兰克福高等研究院）
A new computational scheme to analyze electron transfer (ET) pathways in large biomolecules is presented with applications to ETs in bacterial photosynthetic reaction center. It consists of a linear combination of fragment molecular orbitals and an electron tunneling current analysis, which enables an efficient first-principles analysis of ET pathways in large biomolecules. The scheme has been applied to the ET from menaquinone to ubiquinone via nonheme iron complex in bacterial photosynthetic reaction center. It has revealed that not only the central Fe$^{2+}$ ion but also particular histidin…
Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using a variety of atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on the already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent theoretical and experimental work has indicated that cycling will be…
We have investigated photoinduced intramolecular electron transfer dynamics following metal-to-ligand charge-transfer (MLCT) excitation of [Fe(CN)$_4$(2,2'-bipyridine)]$^{2-}$ (1), [Fe(CN)$_4$(2,3-bis(2-pyridyl)pyrazine)]$^{2-}$ (2) and [Fe(CN)$_4$(2,2'-bipyrimidine)]$^{2-}$ (3) complexes in various solvents with static and time-resolved UV-visible absorption spectroscopy and Fe 2p3d resonant inelastic X-ray scattering. We observe $^3$MLCT lifetimes from 180 fs to 67 ps over a wide range of MLCT energies in different solvents by utilizing the strong solvatochromism of the complexes. Intramolec…
The response of proteins to chemical reactions or impulsive excitation that occurs within the molecule has fascinated chemists for decades. In recent years ultrafast X-ray studies have provided ever more detailed information about the evolution of protein structural change following ligand photolysis, and time-resolved IR and Raman techniques, e.g., have provided detailed pictures of the nature and rate of energy transport in peptides and proteins, including recent advances in identifying transport through individual amino acids of several heme proteins. Computational tools to locate energy tr…
The Alchemical Transfer Method (ATM) for the calculation of standard binding free energies of non-covalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk, and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of ATM is as straightforward as for physical pathway methods of binding. The method is applicable in princi…
