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Garate JA, Bernardin A, Escalona Y, Yanez C, English NJ, Perez-Acle T. Orientational and Folding Thermodynamics via Electric Dipole Moment Restraining. J Phys Chem B 2019; 123:2599-2608. [PMID: 30831028 DOI: 10.1021/acs.jpcb.8b09374] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
The projection of molecular processes onto a small set of relevant descriptors, the so-called reaction coordinates or collective variables (CVs), is a technique nowadays routinely employed by the biomolecular simulation community. In this work, we implemented two CVs to manipulate the orientation (i.e., angle) (μ⃗a) and magnitude (|μ⃗|) of the electric dipole moment. In doing so, we studied the thermodynamics of water orientation under the application of external voltages and the folding of two polypeptides at zero-field conditions. The projection of the free-energy [potential of mean force (PMF)] along water orientation defined an upper limit of around 0.3 V for irrelevant thermodynamic effects. On the other hand, sufficiently strong μ⃗a restraints applied on 12-alanine (Ala12) triggered structural effects because of the alignment of local dipoles; for lower restraints, a full-body rotation is achieved. The manipulation of |μ⃗| produced strong perturbations on the secondary structure of Ala12, promoting an enhanced sampling to its configurational space. Rigorous free-energy calculations in the form of 2-D PMFs for deca-alanine showed the utility of |μ⃗| as a reaction coordinate to study folding in small α helices. As a whole, we propose that the manipulation of both components of the dipole moment, μ⃗a and |μ⃗|, provides thermodynamics insights into the structural conformation and stability of biomolecules. These new CVs are implemented in the Colvars module, available for NAMD and LAMMPS.
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Affiliation(s)
- Jose Antonio Garate
- Centro Interdisciplinario de Neurociencia de Valparaiso , Universidad de Valparaiso , Pasaje Harrington 287 , Playa Ancha, Valparaiso 2381850 , Chile
| | - Alejandro Bernardin
- Centro Interdisciplinario de Neurociencia de Valparaiso , Universidad de Valparaiso , Pasaje Harrington 287 , Playa Ancha, Valparaiso 2381850 , Chile.,Computational Biology Lab , Fundacion Ciencia & Vida , Avenida Zanartu 1482, Nunoa , Santiago 7780272 , Chile
| | - Yerko Escalona
- Institute for Molecular Modeling and Simulation , Muthgasse 18 , Vienna 1190 , Austria
| | - Carlos Yanez
- Computational Biology Lab , Fundacion Ciencia & Vida , Avenida Zanartu 1482, Nunoa , Santiago 7780272 , Chile
| | - Niall J English
- School of Chemical and Bioprocess Engineering , University College Dublin , Belfield, Dublin 4 , Ireland
| | - Tomas Perez-Acle
- Centro Interdisciplinario de Neurociencia de Valparaiso , Universidad de Valparaiso , Pasaje Harrington 287 , Playa Ancha, Valparaiso 2381850 , Chile.,Computational Biology Lab , Fundacion Ciencia & Vida , Avenida Zanartu 1482, Nunoa , Santiago 7780272 , Chile
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2
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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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3
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SAMPL6 host–guest blind predictions using a non equilibrium alchemical approach. J Comput Aided Mol Des 2018; 32:965-982. [DOI: 10.1007/s10822-018-0151-9] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Accepted: 08/10/2018] [Indexed: 02/07/2023]
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4
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Procacci P. Myeloid Cell Leukemia 1 Inhibition: An in Silico Study Using Non-equilibrium Fast Double Annihilation Technology. J Chem Theory Comput 2018; 14:3890-3902. [DOI: 10.1021/acs.jctc.8b00305] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Piero Procacci
- Department of Chemistry, University of Florence, Via Lastruccia No. 3, Sesto Fiorentino I-50019, Italy
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Giovannelli E, Procacci P, Cardini G, Pagliai M, Volkov V, Chelli R. Binding Free Energies of Host–Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Theoretical Framework. J Chem Theory Comput 2017; 13:5874-5886. [DOI: 10.1021/acs.jctc.7b00594] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Edoardo Giovannelli
- 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
| | - Gianni Cardini
- 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, U.K
| | - Riccardo Chelli
- Dipartimento
di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
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Giovannelli E, Cioni M, Procacci P, Cardini G, Pagliai M, Volkov V, Chelli R. Binding Free Energies of Host–Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Illustrative Calculations and Numerical Validation. J Chem Theory Comput 2017; 13:5887-5899. [DOI: 10.1021/acs.jctc.7b00595] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Edoardo Giovannelli
- Dipartimento
di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Matteo Cioni
- 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
| | - Gianni Cardini
- 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
- Dipartimento
di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Riccardo Chelli
- Interdisciplinary
Biomedical Research Center, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
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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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8
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Giovannelli E, Gellini C, Pietraperzia G, Cardini G, Chelli R. Nonequilibrium Candidate Monte Carlo Simulations with Configurational Freezing Schemes. J Chem Theory Comput 2015; 10:4273-83. [PMID: 26588124 DOI: 10.1021/ct500340b] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Nonequilibrium Candidate Monte Carlo simulation [Nilmeier et al., Proc. Natl. Acad. Sci. U.S.A. 2011, 108, E1009-E1018] is a tool devised to design Monte Carlo moves with high acceptance probabilities that connect uncorrelated configurations. Such moves are generated through nonequilibrium driven dynamics, producing candidate configurations accepted with a Monte Carlo-like criterion that preserves the equilibrium distribution. The probability of accepting a candidate configuration as the next sample in the Markov chain basically depends on the work performed on the system during the nonequilibrium trajectory and increases with decreasing such a work. It is thus strategically relevant to find ways of producing nonequilibrium moves with low work, namely moves where dissipation is as low as possible. This is the goal of our methodology, in which we combine Nonequilibrium Candidate Monte Carlo with Configurational Freezing schemes developed by Nicolini et al. (J. Chem. Theory Comput. 2011, 7, 582-593). The idea is to limit the configurational sampling to particles of a well-established region of the simulation sample, namely the region where dissipation occurs, while leaving fixed the other particles. This allows to make the system relaxation faster around the region perturbed by the finite-time switching move and hence to reduce the dissipated work, eventually enhancing the probability of accepting the generated move. Our combined approach enhances significantly configurational sampling, as shown by the case of a bistable dimer immersed in a dense fluid.
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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.,European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy
| | - Giangaetano Pietraperzia
- Dipartimento di Chimica, Università di Firenze , Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy.,European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy
| | - Gianni Cardini
- Dipartimento di Chimica, Università di Firenze , Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy.,European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy
| | - Riccardo Chelli
- Dipartimento di Chimica, Università di Firenze , Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy.,European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy
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9
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Gu J, Li H, Wang X. A Self-Adaptive Steered Molecular Dynamics Method Based on Minimization of Stretching Force Reveals the Binding Affinity of Protein-Ligand Complexes. Molecules 2015; 20:19236-51. [PMID: 26506335 PMCID: PMC6332444 DOI: 10.3390/molecules201019236] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2015] [Revised: 10/14/2015] [Accepted: 10/14/2015] [Indexed: 01/22/2023] Open
Abstract
Binding affinity prediction of protein–ligand complexes has attracted widespread interest. In this study, a self-adaptive steered molecular dynamics (SMD) method is proposed to reveal the binding affinity of protein–ligand complexes. The SMD method is executed through adjusting pulling direction to find an optimum trajectory of ligand dissociation, which is realized by minimizing the stretching force automatically. The SMD method is then used to simulate the dissociations of 19 common protein–ligand complexes which are derived from two homology families, and the binding free energy values are gained through experimental techniques. Results show that the proposed SMD method follows a different dissociation pathway with lower a rupture force and energy barrier when compared with the conventional SMD method, and further analysis indicates the rupture forces of the complexes in the same protein family correlate well with their binding free energy, which reveals the possibility of using the proposed SMD method to identify the active ligand.
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Affiliation(s)
- Junfeng Gu
- State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China.
| | - Hongxia Li
- School of Mechanical Engineering, Dalian University of Technology, Dalian 116023, China.
| | - Xicheng Wang
- State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China.
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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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11
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Zerbetto M, Piserchia A, Frezzato D. Looking for some free energy? Call JEFREE (…). J Comput Chem 2014; 35:1865-81. [DOI: 10.1002/jcc.23701] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2013] [Revised: 04/09/2014] [Accepted: 07/13/2014] [Indexed: 11/09/2022]
Affiliation(s)
- Mirco Zerbetto
- Dipartimento di Scienze Chimiche; Università degli Studi di Padova; via Marzolo 1 I-35131 Padova Italy
| | - Andrea Piserchia
- Dipartimento di Scienze Chimiche; Università degli Studi di Padova; via Marzolo 1 I-35131 Padova Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche; Università degli Studi di Padova; via Marzolo 1 I-35131 Padova Italy
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