Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and Bennett's acceptance ratio method

Brückner, Stefan; Boresch, Stefan

doi:10.1002/jcc.21713

Cited by 106 publications

(145 citation statements)

References 68 publications

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“…E.g., the arguably "simplest" and only nonadaptive subroutine (D)QNG in the QUADPACK library for numerical integration 19 use a 10-21 Gauss-Kronrod rule, 20 requiring the evaluation of the integrand at 21 points. Ideally, we would like to use far fewer than 21 λ-states in free energy simulations since, as shown in the companion paper, 2 21 λ-states usually suffice even when using the trapezoidal rule. A main motivation of this work was to find TI protocols that give reliable results with significantly fewer λ-values.…”

Section: Introductory Remarksmentioning

confidence: 98%

“…For this reason, it was the only quadrature method considered in the companion paper. 2 Some workers in the field have argued for a long time that it should be replaced by more advanced methods, in particular Gauss-Legendre integration, 9 but widespread adoption did not occur. Even Simpson's rule, which should already be significantly more accurate than the trapezoidal rule, 10 is used only rarely.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we, therefore, focus first on the suitability of various integration algorithms and strategies for TI. As in the companion paper, 2 we begin by searching for the minimal number of λ-states that are necessary to calculate absolute and relative free energy differences accurately and precisely. In addition, we present guidelines for devising efficient simulation protocols for TI from scratch; i.e., instead of looking for the most efficient protocol by using fewer and fewer trajectories from an extensive super-set of initial simulation data, we put ourselves in the position of a computational chemist who is about to start free energy simulations with TI for a yet unstudied system, and who has neither time nor computational means for exhaustive preliminary simulations.…”

Section: Introductionmentioning

confidence: 99%

“…Lately, the efficiency of TI, as defined as the minimal number of λ-states required to compute a free energy difference accurately and precisely, was found to be severely wanting compared with BAR; see, e.g., a study by Shirts and Pande. 1 In the companion paper, 2 we analyzed the efficiency of the "exponential formula" (EF), thermodynamic integration (TI), and Bennett's acceptance ratio method (BAR) to compute absolute and relative solvation free energy differences. The clear winners were BAR and DW-EF, the "double-wide" variant of EF, the clear losers, not unexpectedly, were strict forward (FW-EF) and backward EF (BW-EF).…”

Section: Introductionmentioning

confidence: 99%

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Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

2010

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We attempt to optimize the efficiency of thermodynamic integration, as defined by the minimal number of unphysical intermediate states required for the computation of accurate and precise free energy differences. The suitability of various numerical quadrature methods is tested. In particular, we compare the trapezoidal rule, Simpson's rule, Gauss-Legendre, Gauss-Kronrod-Patterson, and Clenshaw-Curtis integration, as well as integration based on a cubic spline approximation of the integrand. We find that Simpson's rule and spline integration are already significantly more efficient that the trapezoidal rule, i.e., correct free energy differences can be obtained using fewer λ-states. We demonstrate that Simpson's rule can be used advantageously with nonequidistant values of the abscissa, which increases the flexibility of the method. Efficiency is enhanced even further if higher order methods, such as Gauss-Legendre, Gauss-Kronrod-Patterson, or Clenshaw-Curtis integration, are used; no more than seven λ-states, which in the case of Clenshaw-Curtis integration include the physical end states, were required for accurate results in all test problems studied. Thus, the performance of thermodynamic integration can equal that of Bennett's acceptance ratio method. We also show, however, that the high efficiency found here relies on the particular functional form of the soft-core potential used; overall, thermodynamic integration is more susceptible to the details of the hybrid Hamiltonian used than Bennett's acceptance ratio method. Therefore, we recommend Bennett's acceptance ratio method as the most robust method to compute alchemical free energy differences; nevertheless, scenarios when thermodynamic integration may be preferable are discussed.

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Section: Introductory Remarksmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

2010

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“…While there have been many different approaches to addressing the issue of sufficient sampling in TI calculations [5][6][7] the most straightforward manner of improving on the sampling is to write faster code. This paper details a substantially faster implementation of alchemical transformations using cost effective, NVIDIA GeForce graphics processors (GPUs).…”

Section: Introductionmentioning

confidence: 99%

Fast and Flexible GPU Accelerated Binding Free Energy Calculations within the AMBER Molecular Dynamics Package

Mermelstein

Lin

Nelson

et al. 2018

Preprint

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Abstract:Alchemical free energy calculations (AFE) based on molecular dynamics (MD) simulations are key tools in both improving our understanding of a wide variety of biological processes and accelerating the design and optimization of therapeutics for numerous diseases. Computing power and theory have, however, long been insufficient to enable AFE calculations to be routinely applied in early stage drug discovery. One of the major difficulties in performing AFE calculations is the length of time required for calculations to converge to an ensemble average. CPU implementations of MD based free energy algorithms can effectively only reach tens of nanoseconds per day for systems on the order of 50,000 atoms, even running on massively parallel supercomputers. Therefore, converged free energy calculations on large numbers of potential lead compounds are often untenable, preventing researchers from gaining crucial insight into molecular recognition, potential druggability, and other crucial areas of interest. Graphics Processing Units (GPUs) can help address this. We present here a seamless GPU implementation, within the PMEMD module of the AMBER molecular dynamics package, of thermodynamic integration (TI) capable of reaching speeds of >140 ns/day for a 44,907-atom system, with accuracy equivalent to the existing CPU implementation in AMBER. The implementation described here is currently part of the AMBER 18 beta code and will be an integral part of the upcoming version 18 release of AMBER.

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Sirolimus‐ versus paclitaxel‐eluting stents for unselected patients with coronary artery disease

Park

2010

Cathet Cardio Intervent

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Millauer et al. reported that sirolimus-eluting stent (SES) decreased the incidence of major adverse cardiac events over 2 years compared with paclitaxel-eluting stent (PES) in 904 unselected patients with coronary artery stenosis [1]. In spite of a nonrandomized study design, a selection bias may be minimized, because this study has been conducted before the publication of randomized studies comparing SES and PES. The major finding of this study was in line with the previous randomized or registry studies showing the superior benefit of SES over PES in the reduction of restenosis and subsequent repeat revascularization [2]. In the meta-analysis, SES significantly reduced the risk of reintervention by 26% (P 5 0.001) and stent thrombosis by 34% (P 5 0.02) [2]. Because of this finding and anticipation of better safety and deliverability, the first generation drug-eluting stent (DES) has increasingly been exchanged with the second-generation DES in the current practices.The risk of mortality or myocardial infarction has not been affected by the type of DES. However, when it comes to the incidence of repeat revascularization, there may be a difference among the diverse DES. The previous studies having mandatory angiographic follow-up showed that the limus-analog DES decreased the late loss and reintervention rate by the stronger inhibition of neointima compared with PES [2,3]. In contrast, a randomized study without mandatory angiographic surveillance showed no difference in the clinical outcomes between SES and PES [4]. This study of Millauer et al, however, suggests that greater reduction of late loss can improve clinical outcomes by the reduction of repeat revascularization in unselected patients even when angiographic follow-up was not routinely performed.A superior benefit of SES in reduction of restenosis or repeat revascularization did not exist for a subgroup of diabetic patients. Although the mechanism is not clear, the clinical impact of SES may be less pronounced because multiple comorbidities and extensive coronary disease in diabetic patients independently influence the clinical outcomes [5]. In addition, the risk of reintervention may be underestimated, because medical treatment is occasionally adopted for complex patterns of restenosis [3]. Alternatively, antimitotic activity of limus-analog DES may be attenuated in the presence of hyperglycemia. Nonetheless, it is noteworthy that this finding of the subgroup analysis can only be regarded as exploratory. This study and all other studies showing the similarity in repeat reavascularization rate between SES and PES were performed as the post hoc subgroup analysis without adequate statistical power. In fact, results from the previous randomized studies have consistently proposed that SES may offer an angiographic and clinical advantage over PES even in patients with diabetes [6,7]. Further large randomized studies to compare diverse type of DES are required in diabetic population.

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Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and Bennett's acceptance ratio method

Cited by 106 publications

References 68 publications

Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

Fast and Flexible GPU Accelerated Binding Free Energy Calculations within the AMBER Molecular Dynamics Package

Sirolimus‐ versus paclitaxel‐eluting stents for unselected patients with coronary artery disease

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