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Ojha AA, Votapka LW, Amaro RE. QMrebind: incorporating quantum mechanical force field reparameterization at the ligand binding site for improved drug-target kinetics through milestoning simulations. Chem Sci 2023; 14:13159-13175. [PMID: 38023523 PMCID: PMC10664576 DOI: 10.1039/d3sc04195f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/22/2023] [Indexed: 12/01/2023] Open
Abstract
Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.
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Affiliation(s)
- Anupam Anand Ojha
- Department of Chemistry and Biochemistry, University of California San Diego La Jolla California 92093 USA
| | - Lane William Votapka
- Department of Chemistry and Biochemistry, University of California San Diego La Jolla California 92093 USA
| | - Rommie Elizabeth Amaro
- Department of Molecular Biology, University of California San Diego La Jolla California 92093 USA
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2
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Chipot C. Predictions from First-Principles of Membrane Permeability to Small Molecules: How Useful Are They in Practice? J Chem Inf Model 2023; 63:4533-4544. [PMID: 37449868 DOI: 10.1021/acs.jcim.3c00686] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/18/2023]
Abstract
Predicting from first-principles the rate of passive permeation of small molecules across the biological membrane represents a promising strategy for screening lead compounds upstream in the drug-discovery and development pipeline. One popular avenue for the estimation of permeation rates rests on computer simulations in conjunction with the inhomogeneous solubility-diffusion model, which requires the determination of the free-energy change and position-dependent diffusivity of the substrate along the translocation pathway through the lipid bilayer. In this Perspective, we will clarify the physical meaning of the membrane permeability inferred from such computer simulations, and how theoretical predictions actually relate to what is commonly measured experimentally. We will also examine why these calculations remain both technically challenging and overly computationally expensive, which has hitherto precluded their routine use in nonacademic settings. We finally synopsize possible research directions to meet these challenges, increase the predictive power of physics-based rates of passive permeation, and, by ricochet, improve their practical usefulness.
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Affiliation(s)
- Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n◦7019, Université de Lorraine, 54500 Vandœuvre-lès-Nancy cedex, France
- Beckman Institute for Advanced Science and Technology, and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61820, United States
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637, United States
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3
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Ray D, Stone SE, Andricioaei I. Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories. J Chem Theory Comput 2021; 18:79-95. [PMID: 34910499 DOI: 10.1021/acs.jctc.1c00803] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.
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Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States
| | - Sharon Emily Stone
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States.,Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, United States
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4
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The time-fractional kinetic equation for the non-equilibrium processes. Sci Rep 2021; 11:20625. [PMID: 34663836 PMCID: PMC8523695 DOI: 10.1038/s41598-021-00135-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 09/29/2021] [Indexed: 11/12/2022] Open
Abstract
In this study, we consider the non-Markovian dynamics of the generic non-equilibrium kinetic process. We summarize the generalized master equation, the continuous and discrete forms of the time-fractional diffusion equation. Using path integral formulation, we generalized the solutions of the Markovian system to the non-Markovian for the non-equilibrium kinetic processes. Then, we obtain the time-fractional kinetic equation for the non-equilibrium systems in terms of free energy. Finally, we introduce a time-fractional equation to analyse time evolution of the open probability for the deformed voltage-gated ion-channel system as an example.
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5
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Abstract
Every protein has a story-how it folds, what it binds, its biological actions, and how it misbehaves in aging or disease. Stories are often inferred from a protein's shape (i.e., its structure). But increasingly, stories are told using computational molecular physics (CMP). CMP is rooted in the principled physics of driving forces and reveals granular detail of conformational populations in space and time. Recent advances are accessing longer time scales, larger actions, and blind testing, enabling more of biology's stories to be told in the language of atomistic physics.
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Affiliation(s)
- Emiliano Brini
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA
| | - Carlos Simmerling
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA.,Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, USA
| | - Ken Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA. .,Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, USA.,Department of Physics and Astronomy, Stony Brook University, Stony Brook, New NY 11794, USA
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Elber R, Fathizadeh A, Ma P, Wang H. Modeling molecular kinetics with Milestoning. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1512] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Ron Elber
- Department of Chemistry, The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Arman Fathizadeh
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Piao Ma
- Department of Chemistry University of Texas at Austin Austin Texas USA
| | - Hao Wang
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
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Ray D, Gokey T, Mobley DL, Andricioaei I. Kinetics and free energy of ligand dissociation using weighted ensemble milestoning. J Chem Phys 2020; 153:154117. [PMID: 33092382 DOI: 10.1063/5.0021953] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the recently developed weighted ensemble milestoning (WEM) scheme [D. Ray and I. Andricioaei, 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 ligand with FK506 binding protein. As a proof of 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 the accuracy of WEM calculations applied to kinetics and thermodynamics in protein-ligand binding, we introduced a modified WEM scheme called weighted ensemble milestoning with restraint release (WEM-RR), which can increase the number of starting points per milestone without adding additional computational cost. WEM-RR calculations obtained a ligand residence time and binding free energy in agreement with experimental and previous computational results. Moreover, using the milestoning framework, the binding time and rate constants, dissociation constants, and committor probabilities could also be calculated at a low computational cost. We also present an analytical approach for estimating the association rate constant (kon) when binding is primarily diffusion driven. We show that the WEM method can efficiently calculate multiple experimental observables describing ligand-receptor binding/unbinding and is a promising candidate for computer-aided inhibitor design.
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Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Trevor Gokey
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - David L Mobley
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
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Krämer A, Ghysels A, Wang E, Venable RM, Klauda JB, Brooks BR, Pastor RW. Membrane permeability of small molecules from unbiased molecular dynamics simulations. J Chem Phys 2020; 153:124107. [PMID: 33003739 PMCID: PMC7519415 DOI: 10.1063/5.0013429] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 08/31/2020] [Indexed: 12/26/2022] Open
Abstract
Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé-Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé-Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations.
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Affiliation(s)
- Andreas Krämer
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - An Ghysels
- IBiTech - BioMMeda, Ghent University, Corneel Heymanslaan 10, Block B - Entrance 36, 9000 Gent, Belgium
| | - Eric Wang
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20740, USA
| | - Richard M. Venable
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jeffery B. Klauda
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20740, USA
| | - Bernard R. Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Richard W. Pastor
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
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Ray D, Andricioaei I. Weighted ensemble milestoning (WEM): A combined approach for rare event simulations. J Chem Phys 2020; 152:234114. [DOI: 10.1063/5.0008028] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, California 92697, USA
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, California 92697, USA
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10
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Rudzinski JF, Radu M, Bereau T. Automated detection of many-particle solvation states for accurate characterizations of diffusion kinetics. J Chem Phys 2019; 150:024102. [PMID: 30646696 DOI: 10.1063/1.5064808] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations that accurately characterize the relevant dynamics. Well-established, low-dimensional order parameters for constructing this representation have led to widespread application of Markov state models to study conformational dynamics in biomolecular systems. On the contrary, applications to characterize single-molecule diffusion processes have been scarce and typically employ system-specific, higher-dimensional order parameters to characterize the local solvation state of the molecule. In this work, we propose an automated method for generating a coarse configuration-space representation, using generic features of the solvation structure-the coordination numbers about each particle. To overcome the inherent noisy behavior of these low-dimensional observables, we treat the features as indicators of an underlying, latent Markov process. The resulting hidden Markov models filter the trajectories of each feature into the most likely latent solvation state at each time step. The filtered trajectories are then used to construct a configuration-space discretization, which accurately describes the diffusion kinetics. The method is validated on a standard model for glassy liquids, where particle jumps between local cages determine the diffusion properties of the system. Not only do the resulting models provide quantitatively accurate characterizations of the diffusion constant, but they also reveal a mechanistic description of diffusive jumps, quantifying the heterogeneity of local diffusion.
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Affiliation(s)
| | - Marc Radu
- Max Planck Institute for Polymer Research, Mainz 55128, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, Mainz 55128, Germany
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11
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Abstract
The kinetics of biochemical and biophysical events determined the course of life processes and attracted considerable interest and research. For example, modeling of biological networks and cellular responses relies on the availability of information on rate coefficients. Atomically detailed simulations hold the promise of supplementing experimental data to obtain a more complete kinetic picture. However, simulations at biological time scales are challenging. Typical computer resources are insufficient to provide the ensemble of trajectories at the correct length that is required for straightforward calculations of time scales. In the last years, new technologies emerged that make atomically detailed simulations of rate coefficients possible. Instead of computing complete trajectories from reactants to products, these approaches launch a large number of short trajectories at different positions. Since the trajectories are short, they are computed trivially in parallel on modern computer architecture. The starting and termination positions of the short trajectories are chosen, following statistical mechanics theory, to enhance efficiency. These trajectories are analyzed. The analysis produces accurate estimates of time scales as long as hours. The theory of Milestoning that exploits the use of short trajectories is discussed, and several applications are described.
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12
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Lee BL, Kuczera K. Simulating the free energy of passive membrane permeation for small molecules. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1407029] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Brent L. Lee
- Department of Chemistry, The University of Kansas , Lawrence, KS, USA
| | - Krzysztof Kuczera
- Department of Chemistry, The University of Kansas , Lawrence, KS, USA
- Department of Molecular Biosciences, The University of Kansas , Lawrence, KS, USA
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13
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Chipot C, Comer J. Subdiffusion in Membrane Permeation of Small Molecules. Sci Rep 2016; 6:35913. [PMID: 27805049 PMCID: PMC5090971 DOI: 10.1038/srep35913] [Citation(s) in RCA: 50] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2016] [Accepted: 10/05/2016] [Indexed: 12/22/2022] Open
Abstract
Within the solubility-diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous free-energy and diffusivity landscape. This equation, however, cannot accommodate subdiffusive regimes, which have long been recognized in lipid bilayer dynamics, notably in the lateral diffusion of individual lipids. Through extensive biased and unbiased molecular dynamics simulations, we show that one-dimensional translocation of methanol across a pure lipid membrane remains subdiffusive on timescales approaching typical permeation times. Analysis of permeant motion within the lipid bilayer reveals that, in the absence of a net force, the mean squared displacement depends on time as t0.7, in stark contrast with the conventional model, which assumes a strictly linear dependence. We further show that an alternate model using a fractional-derivative generalization of the Smoluchowski equation provides a rigorous framework for describing the motion of the permeant molecule on the pico- to nanosecond timescale. The observed subdiffusive behavior appears to emerge from a crossover between small-scale rattling of the permeant around its present position in the membrane and larger-scale displacements precipitated by the formation of transient voids.
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Affiliation(s)
- Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7565, Université de Lorraine, B.P. 70239, 54506, Vandœuvre-lès-Nancy cedex, France
- Theoretical and Computational Biophysics Group, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 North Mathews Avenue, Urbana, Illinois 61801, USA
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Jeffrey Comer
- Institute of Computational Comparative Medicine, Nanotechnology Innovation Center of Kansas State, Department of Anatomy and Physiology, 1800 Denison Ave, Kansas State University, Manhattan, Kansas 66506, USA
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