BAR-based Optimum Adaptive Steered MD for Configurational Sampling

Wang, Xiaohui; Tu, Xingzhao; Deng, Boming; Zhang, John Z. H.; Sun, Zhaoxi

doi:10.26434/chemrxiv.7322417

“…We note that in our previous studies and the current work, the round-trip error is very small (about 0.1 kcal/mol). 85 This small size of cycle closure error indicates well-converged sampling in the nonequilibrium ensemble. The curve or surface plotted from the free energy differences is the free energy profile or the free energy landscape of base flipping.…”

Section: Methodsmentioning

confidence: 94%

“…This setting in dihedral pulling is employed in our previous works and satisfactory results can be obtained. [85][86] As a result, there are 180 conformational states in total, as is shown in Fig. 1.…”

Section: Methodsmentioning

confidence: 99%

Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

Wang¹,

Sun²

2019

Preprint

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Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for efficient calculation of the free energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of equilibrium umbrella sampling and nonequilibrium stratification is given. The results show that nonequilibrium free energy simulation is able to give similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence behavior determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size.

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“…The application of such a force constant to achieve the stiff spring limit can be seen in references. 27 Normally, in MD simulation, with bond-length-constraint algorithms such as SHAKE, [86][87][88] we can use an ITS as long as 2 fs. The application of the biasing potential or force may lead to a smaller T than the motions involving hydrogen atoms and lowers the maximum value applicable for ITS.…”

Section: / 48mentioning

confidence: 99%

“…We employ the time step 0.5 fs in our pulling simulation, although 1 fs has been tested to be also applicable in our previous work. 27,[84][85]89 Therefore, the pulling time along the alchemical CV is thus 0 fs, 1 fs, 5 fs, and 25 fs in each direction.…”

Section: Computational Detailsmentioning

confidence: 99%

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

Sun¹

2019

Preprint

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0

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The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

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“…As a result, such a large force constant is often used to get initial configurations for nonequilibrium free energy simulations. 27,[84][85] In the normal case, we recommend a force constant of 2000 kcal/(mol*rad 2 ) (width of distribution ~0.7…”

Section: Achieving the Stiff Spring Limitmentioning

confidence: 99%

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

Sun

¹

2019

Preprint

Self Cite

0

View full text Add to dashboard Cite

The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

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BAR-based Optimum Adaptive Steered MD for Configurational Sampling

Cited by 15 publications

References 7 publications

Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

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