1
|
Wang M, Mei Y, Ryde U. Convergence criteria for single-step free-energy calculations: the relation between the Π bias measure and the sample variance. Chem Sci 2024; 15:8786-8799. [PMID: 38873060 PMCID: PMC11168088 DOI: 10.1039/d4sc00140k] [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: 01/08/2024] [Accepted: 05/08/2024] [Indexed: 06/15/2024] Open
Abstract
Free energy calculations play a crucial role in simulating chemical processes, enzymatic reactions, and drug design. However, assessing the reliability and convergence of these calculations remains a challenge. This study focuses on single-step free-energy calculations using thermodynamic perturbation. It explores how the sample distributions influence the estimated results and evaluates the reliability of various convergence criteria, including Kofke's bias measure Π and the standard deviation of the energy difference ΔU, σ ΔU . The findings reveal that for Gaussian distributions, there is a straightforward relationship between Π and σ ΔU , free energies can be accurately approximated using a second-order cumulant expansion, and reliable results are attainable for σ ΔU up to 25 kcal mol-1. However, interpreting non-Gaussian distributions is more complex. If the distribution is skewed towards more positive values than a Gaussian, converging the free energy becomes easier, rendering standard convergence criteria overly stringent. Conversely, distributions that are skewed towards more negative values than a Gaussian present greater challenges in achieving convergence, making standard criteria unreliable. We propose a practical approach to assess the convergence of estimated free energies.
Collapse
Affiliation(s)
- Meiting Wang
- School of Medical Engineering & Henan International Joint Laboratory of Neural Information Analysis and Drug Intelligent Design, Xinxiang Medical University Xinxiang 453003 China
- Department of Computational Chemistry, Lund University, Chemical Centre P.O. Box 124 SE-221 00 Lund Sweden
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University Shanghai 200241 China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai Shanghai 200062 China
- Collaborative Innovation Center of Extreme Optics, Shanxi University Taiyuan Shanxi 030006 China
| | - Ulf Ryde
- Department of Computational Chemistry, Lund University, Chemical Centre P.O. Box 124 SE-221 00 Lund Sweden
| |
Collapse
|
2
|
York DM. Modern Alchemical Free Energy Methods for Drug Discovery Explained. ACS PHYSICAL CHEMISTRY AU 2023; 3:478-491. [PMID: 38034038 PMCID: PMC10683484 DOI: 10.1021/acsphyschemau.3c00033] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Revised: 09/12/2023] [Accepted: 09/13/2023] [Indexed: 12/02/2023]
Abstract
This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.
Collapse
Affiliation(s)
- Darrin M. York
- Laboratory for Biomolecular
Simulation Research, Institute for Quantitative Biomedicine, and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854, United States
| |
Collapse
|
3
|
Zeng J, Tao Y, Giese TJ, York DM. QDπ: A Quantum Deep Potential Interaction Model for Drug Discovery. J Chem Theory Comput 2023; 19:1261-1275. [PMID: 36696673 PMCID: PMC9992268 DOI: 10.1021/acs.jctc.2c01172] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
We report QDπ-v1.0 for modeling the internal energy of drug molecules containing H, C, N, and O atoms. The QDπ model is in the form of a quantum mechanical/machine learning potential correction (QM/Δ-MLP) that uses a fast third-order self-consistent density-functional tight-binding (DFTB3/3OB) model that is corrected to a quantitatively high-level of accuracy through a deep-learning potential (DeepPot-SE). The model has the advantage that it is able to properly treat electrostatic interactions and handle changes in charge/protonation states. The model is trained against reference data computed at the ωB97X/6-31G* level (as in the ANI-1x data set) and compared to several other approximate semiempirical and machine learning potentials (ANI-1x, ANI-2x, DFTB3, MNDO/d, AM1, PM6, GFN1-xTB, and GFN2-xTB). The QDπ model is demonstrated to be accurate for a wide range of intra- and intermolecular interactions (despite its intended use as an internal energy model) and has shown to perform exceptionally well for relative protonation/deprotonation energies and tautomers. An example application to model reactions involved in RNA strand cleavage catalyzed by protein and nucleic acid enzymes illustrates QDπ has average errors less than 0.5 kcal/mol, whereas the other models compared have errors over an order of magnitude greater. Taken together, this makes QDπ highly attractive as a potential force field model for drug discovery.
Collapse
Affiliation(s)
- Jinzhe Zeng
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Yujun Tao
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| |
Collapse
|
4
|
Schaller KS, Kari J, Molina GA, Tidemand KD, Borch K, Peters GHJ, Westh P. Computing Cellulase Kinetics with a Two-Domain Linear Interaction Energy Approach. ACS OMEGA 2021; 6:1547-1555. [PMID: 33490814 PMCID: PMC7818601 DOI: 10.1021/acsomega.0c05361] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Accepted: 12/24/2020] [Indexed: 05/21/2023]
Abstract
While heterogeneous enzyme reactions play an essential role in both nature and green industries, computational predictions of their catalytic properties remain scarce. Recent experimental work demonstrated the applicability of the Sabatier principle for heterogeneous biocatalysis. This provides a simple relationship between binding strength and the catalytic rate and potentially opens a new way for inexpensive computational determination of kinetic parameters. However, broader implementation of this approach will require fast and reliable prediction of binding free energies of complex two-phase systems, and computational procedures for this are still elusive. Here, we propose a new framework for the assessment of the binding strengths of multidomain proteins, in general, and interfacial enzymes, in particular, based on an extended linear interaction energy (LIE) method. This two-domain LIE (2D-LIE) approach was successfully applied to predict binding and activation free energies of a diverse set of cellulases and resulted in robust models with high accuracy. Overall, our method provides a fast computational screening tool for cellulases that have not been experimentally characterized, and we posit that it may also be applicable to other heterogeneously acting biocatalysts.
Collapse
Affiliation(s)
- Kay S. Schaller
- Department
of Biotechnology and Biomedicine, Technical
University of Denmark, Søltofts Plads, DK-2800 Kgs. Lyngby, Denmark
- Department
of Chemistry, Technical University of Denmark, Kemitorvet, DK-2800 Kgs. Lyngby, Denmark
| | - Jeppe Kari
- Department
of Biotechnology and Biomedicine, Technical
University of Denmark, Søltofts Plads, DK-2800 Kgs. Lyngby, Denmark
| | - Gustavo A. Molina
- Department
of Biotechnology and Biomedicine, Technical
University of Denmark, Søltofts Plads, DK-2800 Kgs. Lyngby, Denmark
| | | | - Kim Borch
- Novozymes
A/S, Biologiens Vej 2, DK-2800 Kgs. Lyngby, Denmark
| | - Günther H. J. Peters
- Department
of Chemistry, Technical University of Denmark, Kemitorvet, DK-2800 Kgs. Lyngby, Denmark
| | - Peter Westh
- Department
of Biotechnology and Biomedicine, Technical
University of Denmark, Søltofts Plads, DK-2800 Kgs. Lyngby, Denmark
- . Phone: +45 45 25 26 41
| |
Collapse
|
5
|
Kearns FL, Warrensford L, Boresch S, Woodcock HL. The Good, the Bad, and the Ugly: "HiPen", a New Dataset for Validating (S)QM/MM Free Energy Simulations. Molecules 2019; 24:E681. [PMID: 30769826 PMCID: PMC6413162 DOI: 10.3390/molecules24040681] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2018] [Revised: 01/28/2019] [Accepted: 01/29/2019] [Indexed: 11/25/2022] Open
Abstract
Indirect (S)QM/MM free energy simulations (FES) are vital to efficiently incorporating sufficient sampling and accurate (QM) energetic evaluations when estimating free energies of practical/experimental interest. Connecting between levels of theory, i.e., calculating Δ A l o w → h i g h , remains to be the most challenging step within an indirect FES protocol. To improve calculations of Δ A l o w → h i g h , we must: (1) compare the performance of all FES methods currently available; and (2) compile and maintain datasets of Δ A l o w → h i g h calculated for a wide-variety of molecules so that future practitioners may replicate or improve upon the current state-of-the-art. Towards these two aims, we introduce a new dataset, "HiPen", which tabulates Δ A g a s M M → 3 o b (the free energy associated with switching from an M M to an S C C - D F T B molecular description using the 3ob parameter set in gas phase), calculated for 22 drug-like small molecules. We compare the calculation of this value using free energy perturbation, Bennett's acceptance ratio, Jarzynski's equation, and Crooks' equation. We also predict the reliability of each calculated Δ A g a s M M → 3 o b by evaluating several convergence criteria including sample size hysteresis, overlap statistics, and bias metric ( Π ). Within the total dataset, three distinct categories of molecules emerge: the "good" molecules, for which we can obtain converged Δ A g a s M M → 3 o b using Jarzynski's equation; "bad" molecules which require Crooks' equation to obtain a converged Δ A g a s M M → 3 o b ; and "ugly" molecules for which we cannot obtain reliably converged Δ A g a s M M → 3 o b with either Jarzynski's or Crooks' equations. We discuss, in depth, results from several example molecules in each of these categories and describe how dihedral discrepancies between levels of theory cause convergence failures even for these gas phase free energy simulations.
Collapse
Affiliation(s)
- Fiona L Kearns
- Department of Chemistry, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
| | - Luke Warrensford
- Department of Chemistry, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
| | - Stefan Boresch
- Department of Computational Biological Chemistry, Faculty of Chemistry, University of Vienna, Waehringerstrasse 17, A-1090 Vienna, Austria.
| | - H Lee Woodcock
- Department of Chemistry, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
| |
Collapse
|
6
|
Wang M, Mei Y, Ryde U. Predicting Relative Binding Affinity Using Nonequilibrium QM/MM Simulations. J Chem Theory Comput 2018; 14:6613-6622. [DOI: 10.1021/acs.jctc.8b00685] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Meiting Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
- NYU−ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Ulf Ryde
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden
| |
Collapse
|
7
|
Kearns FL, Hudson PS, Woodcock HL, Boresch S. Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities. J Comput Chem 2017; 38:1376-1388. [PMID: 28272811 DOI: 10.1002/jcc.24706] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2016] [Accepted: 10/29/2016] [Indexed: 01/09/2023]
Abstract
We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Fiona L Kearns
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave, CHE205, Tampa, Florida, 33620-5250
| | - Phillip S Hudson
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave, CHE205, Tampa, Florida, 33620-5250
| | - Henry L Woodcock
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave, CHE205, Tampa, Florida, 33620-5250
| | - Stefan Boresch
- Faculty of Chemistry, Department of Computational Biological Chemistry, University of Vienna, Währingerstraße 17, Vienna, A-1090, Austria
| |
Collapse
|