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Boubeta FM, Contestín García RM, Lorenzo EN, Boechi L, Estrin D, Sued M, Arrar M. Lessons learned about steered molecular dynamics simulations and free energy calculations. Chem Biol Drug Des 2019; 93:1129-1138. [PMID: 30793836 DOI: 10.1111/cbdd.13485] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2018] [Revised: 12/18/2018] [Accepted: 12/22/2018] [Indexed: 01/30/2023]
Abstract
The calculation of free energy profiles is central in understanding differential enzymatic activity, for instance, involving chemical reactions that require QM-MM tools, ligand migration, and conformational rearrangements that can be modeled using classical potentials. The use of steered molecular dynamics (sMD) together with the Jarzynski equality is a popular approach in calculating free energy profiles. Here, we first briefly review the application of the Jarzynski equality to sMD simulations, then revisit the so-called stiff-spring approximation and the consequent expectation of Gaussian work distributions and, finally, reiterate the practical utility of the second-order cumulant expansion, as it coincides with the parametric maximum-likelihood estimator in this scenario. We illustrate this procedure using simulations of CO, both in aqueous solution and in a carbon nanotube as a model system for biologically relevant nanoheterogeneous environments. We conclude the use of the second-order cumulant expansion permits the use of faster pulling velocities in sMD simulations, without introducing bias due to large dispersion in the non-equilibrium work distribution.
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Affiliation(s)
- Fernando Martín Boubeta
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, Universidad de Buenos Aires, Buenos Aires, Argentina.,Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Rocío María Contestín García
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Ezequiel Norberto Lorenzo
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Leonardo Boechi
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Cálculo, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Dario Estrin
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, Universidad de Buenos Aires, Buenos Aires, Argentina.,Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Mariela Sued
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Cálculo, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Mehrnoosh Arrar
- CONICET-Facultad de Ciencias Exactas y Naturales, Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, Universidad de Buenos Aires, Buenos Aires, Argentina.,Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
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Arrar M, Boubeta FM, Szretter ME, Sued M, Boechi L, Rodriguez D. On the accurate estimation of free energies using the jarzynski equality. J Comput Chem 2018; 40:688-696. [DOI: 10.1002/jcc.25754] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Revised: 06/18/2018] [Accepted: 09/03/2018] [Indexed: 11/09/2022]
Affiliation(s)
- Mehrnoosh Arrar
- Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina, Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Fernando Martín Boubeta
- Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina, Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Maria Eugenia Szretter
- Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina, Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Mariela Sued
- Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Leonardo Boechi
- Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Daniela Rodriguez
- Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
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Giovannelli E, Gellini C, Pietraperzia G, Cardini G, Procacci P, Pagliai M, Volkov V, Chelli R. Correspondence between light-absorption spectrum and nonequilibrium work distribution as a mean to access free energy differences between electronic states. J Chem Phys 2018; 149:084101. [PMID: 30193485 DOI: 10.1063/1.5028116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The problem of recovering the free energy difference between two electronic states has been investigated by Frezzato [Chem. Phys. Lett. 533, 106 (2012)], exploring the equivalence between light-absorption spectra and work distribution, hence opening to the application of a spectroscopic version of the Jarzynski equality (JE) [Phys. Rev. Lett. 78, 2690 (1997)]. Here, assuming the validity of the time-dependent perturbation theory, we demonstrate that such equivalence does not lead to the known form of the JE. This is ascribed to the fact that light-absorption processes cannot be described as stochastic processes. To emphasize such an aspect, we devise a stochastic model for the UV-vis (ultraviolet and visible) absorption, suitable for determining the free energy difference between two generic quantum manifolds in a JE-like fashion. However, the model would require explicit knowledge of the transition dipole moments, which are in general not available. Nonetheless, we derive a spectroscopic version of the JE that allows us to recover the free energy difference between the ground and an excited electronic state when the latter state is the only one observed in the spectrum.
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Affiliation(s)
- Edoardo Giovannelli
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Cristina Gellini
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Giangaetano Pietraperzia
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Gianni Cardini
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Piero Procacci
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Marco Pagliai
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Victor Volkov
- Interdisciplinary Biomedical Research Center, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, United Kingdom
| | - Riccardo Chelli
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
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Giovannelli E, Cardini G, Chelli R. Elastic Barrier Dynamical Freezing in Free Energy Calculations: A Way To Speed Up Nonequilibrium Molecular Dynamics Simulations by Orders of Magnitude. J Chem Theory Comput 2016; 12:1029-39. [PMID: 26771534 DOI: 10.1021/acs.jctc.5b01117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
An important issue concerning computer simulations addressed to free energy estimates via nonequilibrium work theorems, such as the Jarzynski equality [Phys. Rev. Lett. 1997, 78, 2690], is the computational effort required to achieve results with acceptable accuracy. In this respect, the dynamical freezing approach [Phys. Rev. E 2009, 80, 041124] has been shown to improve the efficiency of this kind of simulations, by blocking the dynamics of particles located outside an established mobility region. In this report, we show that dynamical freezing produces a systematic spurious decrease of the particle density inside the mobility region. As a consequence, the requirements to apply nonequilibrium work theorems are only approximately met. Starting from these considerations, we have developed a simulation scheme, called "elastic barrier dynamical freezing", according to which a stiff potential-energy barrier is enforced at the boundaries of the mobility region, preventing the particles from leaving this region of space during the nonequilibrium trajectories. The method, tested on the calculation of the distance-dependent free energy of a dimer immersed into a Lennard-Jones fluid, provides an accuracy comparable to the conventional steered molecular dynamics, with a computational speedup exceeding a few orders of magnitude.
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Affiliation(s)
- Edoardo Giovannelli
- Dipartimento di Chimica, Università di Firenze , Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Gianni Cardini
- Dipartimento di Chimica, Università di Firenze , Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Riccardo Chelli
- Dipartimento di Chimica, Università di Firenze , Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
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Siders PD. Conformational free energy of alkylsilanes by nonequilibrium-pulling Monte Carlo simulation. MOLECULAR SIMULATION 2015. [DOI: 10.1080/08927022.2015.1083101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Giovannelli E, Cardini G, Gellini C, Pietraperzia G, Chelli R. Annealed importance sampling with constant cooling rate. J Chem Phys 2015; 142:074102. [PMID: 25701997 DOI: 10.1063/1.4907883] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Annealed importance sampling is a simulation method devised by Neal [Stat. Comput. 11, 125 (2001)] to assign weights to configurations generated by simulated annealing trajectories. In particular, the equilibrium average of a generic physical quantity can be computed by a weighted average exploiting weights and estimates of this quantity associated to the final configurations of the annealed trajectories. Here, we review annealed importance sampling from the perspective of nonequilibrium path-ensemble averages [G. E. Crooks, Phys. Rev. E 61, 2361 (2000)]. The equivalence of Neal's and Crooks' treatments highlights the generality of the method, which goes beyond the mere thermal-based protocols. Furthermore, we show that a temperature schedule based on a constant cooling rate outperforms stepwise cooling schedules and that, for a given elapsed computer time, performances of annealed importance sampling are, in general, improved by increasing the number of intermediate temperatures.
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Affiliation(s)
- Edoardo Giovannelli
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Gianni Cardini
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Cristina Gellini
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Giangaetano Pietraperzia
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Riccardo Chelli
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
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Zerbetto M, Frezzato D. Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study. Phys Chem Chem Phys 2015; 17:1966-79. [DOI: 10.1039/c4cp03815k] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
The equation of state of bulk materials is achieved via thermodynamic derivatives of the free energy yielded by nonequilibrium transformations and Jarzynski equality.
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Affiliation(s)
- Mirco Zerbetto
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
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Piserchia A, Zerbetto M, Frezzato D. Probing the conformational energetics of alkyl thiols on gold surfaces by means of a morphing/steering non-equilibrium tool. Phys Chem Chem Phys 2015; 17:8038-52. [DOI: 10.1039/c4cp05505e] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Jarzynski's equality is applied to compute the torsion free energy, bond-by-bond, for a probe alkyl thiol tethered to a gold surface.
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Affiliation(s)
- Andrea Piserchia
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
| | - Mirco Zerbetto
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
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