Accurate Estimation of Protein-ligand Binding Free Energies Based on Geometric Restraints

doi:10.6023/A20100489

Acta Chimica Sinica ›› 2021, Vol. 79 ›› Issue (4): 472-480.DOI: 10.6023/A20100489 Previous Articles Next Articles

Special Issue: 纪念南开大学化学学科创建100周年

Review

基于几何约束的蛋白质-配体准确结合自由能计算

付浩浩^a, 陈淏川^a, 张宏^a, 邵学广^a^,^b^,^*(), 蔡文生^a^,^*()

a 南开大学化学学院分析科学研究中心天津市生物传感与分子识别重点实验室天津 300071
b 南开大学药物化学生物学国家重点实验室天津 300071

投稿日期:2020-10-24 发布日期:2020-12-02
通讯作者: 邵学广, 蔡文生

作者简介:

付浩浩, 本科和博士均毕业于南开大学化学系. 现为南开大学博士后、助理研究员. 研究方向为增强采样算法开发、蛋白质-配体准确结合自由能计算策略研究和复杂体系中高度耦合的运动研究.

邵学广, 南开大学教授, 博士生导师, 1992年获中国科学技术大学中日联合培养博士学位. 2002 年获教育部第三届高校青年教师奖, 2003 年获国家自然科学基金委杰出青年基金. 主要从事化学计量学及近红外光谱分析方面的研究工作. 建立了小波变换和免疫算法用于复杂信号解析和在线处理的新方法以及一系列用于近红外光谱信号处理和建模的化学计量学方法.

蔡文生, 南开大学教授, 博士生导师. 1994年获中国科学技术大学博士学位. 主要从事分子模拟与理论化学计算领域的研究工作, 包括优化算法、自由能计算方法、分子模拟及理论化学计算在蛋白质-配体、药物载体、分子机器中的应用研究.

基金资助:
国家自然科学基金(22073050); 国家自然科学基金(21773125); 南开大学中央高校基本科研业务费专项资金(63191743); 南开大学中央高校基本科研业务费专项资金(63201015); 中国博士后科学基金(bs6619012)

Accurate Estimation of Protein-ligand Binding Free Energies Based on Geometric Restraints

Haohao Fu^a, Haochuan Chen^a, Hong Zhang^a, Xueguang Shao^a^,^b^,^*(), Wensheng Cai^a^,^*()

a Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin 300071, China
b State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China

Received:2020-10-24 Published:2020-12-02
Contact: Xueguang Shao, Wensheng Cai
About author:
* E-mail: xshao@nankai.edu.cn
E-mail: wscai@nankai.edu.cn, Tel.: 022-23503430
Supported by:
National Natural Science Foundation of China(22073050); National Natural Science Foundation of China(21773125); Fundamental Research Funds for the Central Universities, Nankai University(63191743); Fundamental Research Funds for the Central Universities, Nankai University(63201015); and the China Post-doctoral Science Foundation(bs6619012)

Binding free energy is the most crucial physical quantity for describing recognition-association of protein-ligand hybrids. Accurate estimation of protein-ligand binding free energies is of paramount importance in the field of drug design and biological engineering. However, the association process of protein-ligand hybrids is usually coupled with complex conformational changes of molecular objects, which is not amenable to the timescale of classical molecular simulations. This limitation makes it difficult to accurately estimate the protein-ligand binding free energies using classical free-energy calculation strategies. An effective solution is to apply geometric restraints to reduce the configurational space needed to be sampled, so as to boost up the convergence rate of simulations, and then calculate and deduct the contribution of these restraints to the binding free energy by post-processing. In this review, we firstly introduce the recent developments of three geometric restraints, namely, funnel, spherical, and seven-degree-of-freedom restraints, used in accurate binding free-energy calculations, with emphasis on the latest progress of the third one. Specifically, the theoretically rigorous seven-degree-of-freedom restraint describes translational, orientational, rotational, and conformational degrees of freedom by means of a center-of-mass distance, spherical angles, Euler angles and the root-mean-square deviation. Moreover, we demonstrate the theoretical backgrounds and methods of how to achieve accurate protein-ligand binding free-energy estimation by combination of geometric restraints and importance-sampling or alchemical algorithms. In the geometric routes, the degrees of freedom of the relative movement of the protein-ligand complex are addressed in a stepwise fashion by one-dimensional importance-sampling simulations. In the alchemical routes, a special thermodynamics cycle is designed, in which additional simulations are performed to address the contribution of the restraints. A general suggestion for how to choose a suitable strategy for a given molecular assembly based on our experience is provided. Last but not least, we discuss the applications and challenges of using accurate protein-ligand binding free-energy calculation methods in fields such as drug design, and present the possibility of extending these methods for investigating complex protein-protein interaction.

Key words: protein-ligand, binding free energy, molecular dynamics, free-energy perturbation, importance sampling

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Haohao Fu, Haochuan Chen, Hong Zhang, Xueguang Shao, Wensheng Cai. Accurate Estimation of Protein-ligand Binding Free Energies Based on Geometric Restraints[J]. Acta Chimica Sinica, 2021, 79(4): 472-480.

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Fig. & Tab. 9

Figure 1. The classical strategy of protein-ligand binding free-energy calculations using alchemical algorithms. “:” represents the binding state

Figure 2. (A) Funnel and (B) spherical restraints used in binding free-energy calculations. Region for free move of the ligand is shown in red. The ligand will be pushed back by the restraint if it moves outside the red region.

Figure 3. Atom-group-based definition of the six degrees of freedom r , θ , φ , Θ , Φ , Ψ . The black dot line, red arrows and purple arrows represent the distance, angles and dihedral angles, respectively.

步骤	对应项	集合变量	约束	体系
1	$∆ G c site$	RMSD	-	蛋白质-配体
2	$∆ G Θ site$	$Θ$	RMSD	蛋白质-配体
3	$∆ G Φ site$	$Φ$	RMSD, $Θ$	蛋白质-配体
4	$∆ G Ψ site$	$Ψ$	RMSD, $Θ$ , $Φ$	蛋白质-配体
5	$∆ G θ site$	$θ$	RMSD, $Θ$ , $Φ$ , $Ψ$	蛋白质-配体
6	$∆ G φ site$	$φ$	RMSD, $Θ$ , $Φ$ , $Ψ$ , $θ$	蛋白质-配体
7	$- 1 β ln S * I * C °$	$r$	RMSD, $Θ$ , $Φ$ , $Ψ$ , $θ$ , $φ$	蛋白质-配体
8	$∆ G c bulk$	RMSD	-	配体
9	$∆ G o bulk$	-	-	解析计算

步骤	对应项	集合变量	约束	体系
1	$∆ G c site$	RMSD	-	蛋白质-配体
2	$∆ G Θ site$	$Θ$	RMSD	蛋白质-配体
3	$∆ G Φ site$	$Φ$	RMSD, $Θ$	蛋白质-配体
4	$∆ G Ψ site$	$Ψ$	RMSD, $Θ$ , $Φ$	蛋白质-配体
5	$∆ G θ site$	$θ$	RMSD, $Θ$ , $Φ$ , $Ψ$	蛋白质-配体
6	$∆ G φ site$	$φ$	RMSD, $Θ$ , $Φ$ , $Ψ$ , $θ$	蛋白质-配体
7	$- 1 β ln S * I * C °$	$r$	RMSD, $Θ$ , $Φ$ , $Ψ$ , $θ$ , $φ$	蛋白质-配体
8	$∆ G c bulk$	RMSD	-	配体
9	$∆ G o bulk$	-	-	解析计算

Table 1. Detailed process of the accurate protein-ligand binding free-energy calculation strategy using the combination of the seven- degree-of-freedom restraints and an importance-sampling algorithm

Figure 4. Thermodynamic cycle of the protein-ligand binding free-energy calculation using the combination of the six-/seven-degree-of-free restraints and an alchemical algorithm

步骤	对应项	消失/生长部分	体系
1	$∆ G bound$	配体	蛋白质-配体
2	$∆ G unbound$	配体	配体
3	$∆ G restraint, bound$	七自由度约束	蛋白质-配体
4	$∆ G restraint, 0$ (RMSD贡献)	RMSD约束	配体
5	$∆ G restraint, 0 ($ RMSD贡献以外部分)	无	解析计算(式8)

步骤	对应项	消失/生长部分	体系
1	$∆ G bound$	配体	蛋白质-配体
2	$∆ G unbound$	配体	配体
3	$∆ G restraint, bound$	七自由度约束	蛋白质-配体
4	$∆ G restraint, 0$ (RMSD贡献)	RMSD约束	配体
5	$∆ G restraint, 0 ($ RMSD贡献以外部分)	无	解析计算(式8)

Table 2. Detailed process of the accurate protein-ligand binding free-energy calculation strategy using the combination of the seven- degree-of-freedom restraints and an alchemical algorithm

Figure 5. DNA-netropsin binding free-energy calculation by the combination of the optimal-rotation-based seven-degree-of-freedom restraints and the WTM-eABF algorithm

作者	使用策略	小分子配体个数	计算误差/ (kJ•mol^–1)	文献
Aldeghi等	alchemistry	11	MAE=2.5	[54]
Boyce等	alchemistry	13	RMSE=7.5	[29]
Li等	alchemistry	100	RMSE=2.59~6.44	[30]
Laury等	alchemistry	14	MAE=5.02	[62]
Xie等	alchemistry	141	RMSE=6.65	[63]
Deng等	alchemistry/重要性采样	3	AE=6.7~18 (alchemistry), 6.3~14 (重要性采样)	[27]
Fu等	重要性采样	3(十肽)	AE<1.7	[23]

Table 3. Comparison between calculated and experimental binding free energies

场景	建议	说明
基于数据库的药物筛选	分子对接	效率最高
结构相似配体结合能力的定性对比	MM-G(P)BSA	效率高, 使用简单
刚性小分子、结合位点在蛋白质表面	漏斗状约束或球状约束结合重要性采样方法	效率较高, 使用简单, 无需考虑小分子结构变化
刚性小分子、结合位点在蛋白质内部	基于六自由度约束的Alchemistry方法	无法使用重要性采样方法, 使用六自由度约束可以简单地解析计算约束贡献
柔性配体、结合位点在蛋白质表面	基于七自由度的重要性采样方法	同等条件下重要性采样算法收敛较快, 需要采用七自由度策略捕获柔性配体结构变化
柔性配体、结合位点在蛋白质内部	基于七自由度约束的Alchemistry方法	其他策略均不适合时最为“安全”的策略

Table 4. Suggestion of strategies for protein-ligand binding free-energy estimation

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基于几何约束的蛋白质-配体准确结合自由能计算

Accurate Estimation of Protein-ligand Binding Free Energies Based on Geometric Restraints

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