蛋白质模拟的分子力学力场优化
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摘要
蛋白质是生物功能的执行者。蛋白质的功能跟它的三维结构及动力学密切相关。大多数蛋白质都能够形成独特空间结构。探测和解析蛋白质三维结构的实验工具主要有X射线晶体衍射方法和核磁共振波谱学方法。但实验不能提供蛋白质结构的时空分布,不能在微观尺度刻划蛋白质功能运动的细节。分子动力学模拟方法是一种在原子水平上研究蛋白质结构与功能之间关系的重要工具,在原子水平刻划构象的空间分布和动力学,为实验提供重要补充。经过进一步发展,还可能成为三维结构从头预测的工具。分子动力学模拟通过求解牛顿运动方程追踪体系随时间变化的构象变化过程,获得任意微观量的时空分布。其出发点是依赖于原子坐标的经验能量函数,即分子力学“力场”。蛋白质模拟结果的准确性以及可靠性主要依赖于经验力场的正确性。分子模拟应用和发展存在两大困难,一是用于模拟分子内或分子间相互作用的能量函数的正确性是有限的,另一个就是在高维构象空间的采样是不充分的,现在已经开展了很多研究用于解决这两个问题。
传统的力场优化主要基于拟合小分子体系的结构与能量性质。GROMOS力场主要通过拟合小分子体系在凝聚态下的一系列热力学特性,如密度、蒸发热、超额自由能、溶剂化自由能等来确定力场中的范德华相互作用、静电相互作用等非键相互作用参数。对决定多肽构象平衡的二面角项等未充分优化。并且,由于力场参数空间维数很高,力场拟合过程使用的参考数据不可能唯一确定最优参数组合。
力场对多肽构象平衡的刻划精度对分子模拟非常重要。如何优化分子力场,使其不但能够再现各类凝聚态热力学数据,而且更好刻划构象平衡,是本论文工作的重点。
本论文的主要内容包括两个方面,一是优化GROMOS 53A6力场中关于主链构象的描述用于改善蛋白质模拟的结果,另一个是利用自由能微扰方法预测力场参数的改变对小肽构象平衡模拟实验的影响。
第2章中,我们认为优化GROMOS 53A6力场中关于主链构象的描述能改善蛋白质模拟的结果。许多研究表明,这些广泛使用的分子力学力场在描述蛋白质的局部构象时存在系统偏差,包括分子力场里对主链二面角的描述。分子模拟所得到的二肽主链二面角的自由能面同量子力学计算所得到的势能面和数据库统计得到的主链二面角的自由能面之间的比较表明:重新优化分子力场里关于主链二面角项的描述是必要的。分子模拟结果和量子力学计算结果的高精确性使得我们可以作两种类型的修正,一种是数字格点修正,这种修正能准确的得到量子力学的势能面,另一种是采用数量很少的解析项修正,这种修正使得分子模拟所得到的自由能面能近似的描述量子力学势能面所包含的一些主要特征。另外,为了改善主链-主链之间氢键的方向性,我们对主链羰基上的氧原子采用偏离中心的电荷模型,并对这个模型里的参数进行优化并测试。我们对五个蛋白质和两个小肽在水溶液中进行大量分子动力学模拟,结果表明:对主链二面角项的优化能明显的改善蛋白质模拟的结果。对比较简单的解析修正和严格的数字格点修正进行比较,对蛋白质而言,前者能得到一样好甚至更好的模拟结果。尽管采用偏离中心的电荷模型能稍微改进蛋白质模拟结果,但对氢键方向性的改进并不显著。
第3章中,我们提出一种方法,它结合了自由能微扰理论和增强采样方法,能将小肽体系在不同构象态之间的平衡数据用于力场发展阶段的参数校正过程中。为了验证这个方法,我们把前面在GROMOS 43A1力场中参数化的广义玻恩/溶剂可接触表面积模型作为参考模型,并把这个模型应用到四个具有不同二级结构的小肽中,包含两个α-螺旋和两个β-折叠片。利用温度副本交换分子动力学模拟方法采样小肽的构象空间。我们可以预测需要扰动力场中的那些参数才能对不同体系的天然构象态与其它构象态之间的计算平衡产生影响。我们考虑两种不同的方法描述这四个小肽的构象态,一种是基于反应坐标和两维自由能面;另一种是基于对采样的构象进行聚类分析。我们考虑扰动不同力场参数对天然态和其它构象态之间平衡的影响。对不同的小肽,某一类型的扰动能产生一致的预测结果,我们利用在扰动参数的力场下的真实的模拟来验证这个方法做出的预测是否正确有效。
Proteins carry out biological functions. The function of protein is dependent on its three-dimensional structure and dynamics. Most proteins exist in unique conformations exquisitely suited to their function. Experimentally, the three-dimensional protein structure can be analyzed by x-ray diffraction of protein crystals or nuclear magnetic resonance spectroscopy. Currently, the miscorscopic distributions of protein conformations in time and space are not accessible by experiments. Experiments also can not provide detailed dynamics of proteins when they carry out their functions. Molecular dynamic (MD) simulation can provide such complementary information. Under further developments, simulation may also become an important tool for ab initio structure prediction. In MD simulations, the evolution of molecular structures in space and time are traced by solving Newton's equations of motion. MD is based on representing the energy of the protein as a function of its atomic coordinates by an empirical function, which is also known as molecular mechanics "force field". The quality of molecular dynamic simulations for protein depends greatly on the accuracy of empirical force fields. There are two well-known difficulties in molecular simulations, one is the limited accuracy of the energy functions modeling intra- and inter-molecular interactions and another is limited sampling in the higher dimensional conformational space, many efforts have been made to solve these questions.
Traditional force field refinements are based on the structural and energy properties of small molecule systems. In GROMOS force field, parameters for non-bonded interaction are obtained by fitting thermodynamic quantities such as density, heats of vaporization, excess free energy and free energy of solvation to experimental data for small molecule systems. The torsional angle terms which affect the peptide conformational equilibriums arc usually not fully refined in force field. In addition, because of the high dimensionality of the force field parameters, we cannot confirm the best parameters just relying on the reference data used in force field developments.
The precision of the description of the conformational equilibriums of force field is very important for molecular simulation. The emphases of this paper are how to refine the force field and ensure that it not only reproduces the condensed phase thermodynamics data, but also describes the conformational equilibriums accurately.
There are mainly two works described in this paper, one is refining the description of peptide backbone conformations improves protein simulations using the GROMOS 53A6 force field, the other is using free energy perturbation to predict effects of changing force field parameters on computed conformational equilibriums of peptides.
In chapter 2, we show that refining the descriptions of peptide backbone conformations can improve protein simulations using the GROMOS 53A6 force field. Many research indicated that there existed systematic biases in the description of protein local conformations involving the backbone Ramachandran dihedral angles by widely-used molecular mechanics force fields. Comparisons of molecular mechanics free energy surfaces of dipeptide system with quantum mechanical ones and conformation distributions in protein crystal structures indicated that refined treatments of backbone torsional angle terms are necessary. The high accuracy of the computed free energy surfaces allowed us to consider two types of corrections, one numerically and exactly reproducing the quantum mechanical results, and the other using small analytical terms to correct major deficiencies for the dipeptide systems. In addition, aiming at improving the directionality of backbone-backbone hydrogen bonds, we optimized and tested an off-center charge model for the peptide backbone carbonyl oxygen. Extensive molecular dynamics simulations of five proteins and two peptides in solution indicated that refined treatments of backbone dihedral angles lead to substantial improvements of the simulations. Being much simpler, the analytical terms perform as good as or even slightly better than the exact numerical corrections. While using off-center charges brought some improvements, the directionality of hydrogen bonds have not been significantly improved.
In chapter 3, we have proposed an approach combines free energy perturbation with improved sampling techniques which may allow data about the conformational equilibriums of peptides to enter the parameter calibration phase in force field developments. To demonstrate the method, we consider a previously parameterized generalized born/solvent accessible surface area model for the GROMOS 43a1 force field. The model is applied to four peptides, including twoα-helices and twoβ-hairpins. Based on conformations sampled using temperature replica exchange molecular dynamics simulations, we predict how perturbations of various force field parameters would shift the computed equilibriums between the native conformational states and other conformational states of different systems. We considered two different approaches to define conformational states of four peptides. One is based on reaction coordinates and two-dimensional free energy surfaces. The other is based on clustering analysis of sampled conformations. Effects of perturbing various model parameters on the equilibriums between native-like states with other conformational states were considered. For one type of perturbation predicted to have consistent effects on different peptides, the predictions have been verified by actual simulations using a perturbed model.
传统的力场优化主要基于拟合小分子体系的结构与能量性质。GROMOS力场主要通过拟合小分子体系在凝聚态下的一系列热力学特性,如密度、蒸发热、超额自由能、溶剂化自由能等来确定力场中的范德华相互作用、静电相互作用等非键相互作用参数。对决定多肽构象平衡的二面角项等未充分优化。并且,由于力场参数空间维数很高,力场拟合过程使用的参考数据不可能唯一确定最优参数组合。
力场对多肽构象平衡的刻划精度对分子模拟非常重要。如何优化分子力场,使其不但能够再现各类凝聚态热力学数据,而且更好刻划构象平衡,是本论文工作的重点。
本论文的主要内容包括两个方面,一是优化GROMOS 53A6力场中关于主链构象的描述用于改善蛋白质模拟的结果,另一个是利用自由能微扰方法预测力场参数的改变对小肽构象平衡模拟实验的影响。
第2章中,我们认为优化GROMOS 53A6力场中关于主链构象的描述能改善蛋白质模拟的结果。许多研究表明,这些广泛使用的分子力学力场在描述蛋白质的局部构象时存在系统偏差,包括分子力场里对主链二面角的描述。分子模拟所得到的二肽主链二面角的自由能面同量子力学计算所得到的势能面和数据库统计得到的主链二面角的自由能面之间的比较表明:重新优化分子力场里关于主链二面角项的描述是必要的。分子模拟结果和量子力学计算结果的高精确性使得我们可以作两种类型的修正,一种是数字格点修正,这种修正能准确的得到量子力学的势能面,另一种是采用数量很少的解析项修正,这种修正使得分子模拟所得到的自由能面能近似的描述量子力学势能面所包含的一些主要特征。另外,为了改善主链-主链之间氢键的方向性,我们对主链羰基上的氧原子采用偏离中心的电荷模型,并对这个模型里的参数进行优化并测试。我们对五个蛋白质和两个小肽在水溶液中进行大量分子动力学模拟,结果表明:对主链二面角项的优化能明显的改善蛋白质模拟的结果。对比较简单的解析修正和严格的数字格点修正进行比较,对蛋白质而言,前者能得到一样好甚至更好的模拟结果。尽管采用偏离中心的电荷模型能稍微改进蛋白质模拟结果,但对氢键方向性的改进并不显著。
第3章中,我们提出一种方法,它结合了自由能微扰理论和增强采样方法,能将小肽体系在不同构象态之间的平衡数据用于力场发展阶段的参数校正过程中。为了验证这个方法,我们把前面在GROMOS 43A1力场中参数化的广义玻恩/溶剂可接触表面积模型作为参考模型,并把这个模型应用到四个具有不同二级结构的小肽中,包含两个α-螺旋和两个β-折叠片。利用温度副本交换分子动力学模拟方法采样小肽的构象空间。我们可以预测需要扰动力场中的那些参数才能对不同体系的天然构象态与其它构象态之间的计算平衡产生影响。我们考虑两种不同的方法描述这四个小肽的构象态,一种是基于反应坐标和两维自由能面;另一种是基于对采样的构象进行聚类分析。我们考虑扰动不同力场参数对天然态和其它构象态之间平衡的影响。对不同的小肽,某一类型的扰动能产生一致的预测结果,我们利用在扰动参数的力场下的真实的模拟来验证这个方法做出的预测是否正确有效。
Proteins carry out biological functions. The function of protein is dependent on its three-dimensional structure and dynamics. Most proteins exist in unique conformations exquisitely suited to their function. Experimentally, the three-dimensional protein structure can be analyzed by x-ray diffraction of protein crystals or nuclear magnetic resonance spectroscopy. Currently, the miscorscopic distributions of protein conformations in time and space are not accessible by experiments. Experiments also can not provide detailed dynamics of proteins when they carry out their functions. Molecular dynamic (MD) simulation can provide such complementary information. Under further developments, simulation may also become an important tool for ab initio structure prediction. In MD simulations, the evolution of molecular structures in space and time are traced by solving Newton's equations of motion. MD is based on representing the energy of the protein as a function of its atomic coordinates by an empirical function, which is also known as molecular mechanics "force field". The quality of molecular dynamic simulations for protein depends greatly on the accuracy of empirical force fields. There are two well-known difficulties in molecular simulations, one is the limited accuracy of the energy functions modeling intra- and inter-molecular interactions and another is limited sampling in the higher dimensional conformational space, many efforts have been made to solve these questions.
Traditional force field refinements are based on the structural and energy properties of small molecule systems. In GROMOS force field, parameters for non-bonded interaction are obtained by fitting thermodynamic quantities such as density, heats of vaporization, excess free energy and free energy of solvation to experimental data for small molecule systems. The torsional angle terms which affect the peptide conformational equilibriums arc usually not fully refined in force field. In addition, because of the high dimensionality of the force field parameters, we cannot confirm the best parameters just relying on the reference data used in force field developments.
The precision of the description of the conformational equilibriums of force field is very important for molecular simulation. The emphases of this paper are how to refine the force field and ensure that it not only reproduces the condensed phase thermodynamics data, but also describes the conformational equilibriums accurately.
There are mainly two works described in this paper, one is refining the description of peptide backbone conformations improves protein simulations using the GROMOS 53A6 force field, the other is using free energy perturbation to predict effects of changing force field parameters on computed conformational equilibriums of peptides.
In chapter 2, we show that refining the descriptions of peptide backbone conformations can improve protein simulations using the GROMOS 53A6 force field. Many research indicated that there existed systematic biases in the description of protein local conformations involving the backbone Ramachandran dihedral angles by widely-used molecular mechanics force fields. Comparisons of molecular mechanics free energy surfaces of dipeptide system with quantum mechanical ones and conformation distributions in protein crystal structures indicated that refined treatments of backbone torsional angle terms are necessary. The high accuracy of the computed free energy surfaces allowed us to consider two types of corrections, one numerically and exactly reproducing the quantum mechanical results, and the other using small analytical terms to correct major deficiencies for the dipeptide systems. In addition, aiming at improving the directionality of backbone-backbone hydrogen bonds, we optimized and tested an off-center charge model for the peptide backbone carbonyl oxygen. Extensive molecular dynamics simulations of five proteins and two peptides in solution indicated that refined treatments of backbone dihedral angles lead to substantial improvements of the simulations. Being much simpler, the analytical terms perform as good as or even slightly better than the exact numerical corrections. While using off-center charges brought some improvements, the directionality of hydrogen bonds have not been significantly improved.
In chapter 3, we have proposed an approach combines free energy perturbation with improved sampling techniques which may allow data about the conformational equilibriums of peptides to enter the parameter calibration phase in force field developments. To demonstrate the method, we consider a previously parameterized generalized born/solvent accessible surface area model for the GROMOS 43a1 force field. The model is applied to four peptides, including twoα-helices and twoβ-hairpins. Based on conformations sampled using temperature replica exchange molecular dynamics simulations, we predict how perturbations of various force field parameters would shift the computed equilibriums between the native conformational states and other conformational states of different systems. We considered two different approaches to define conformational states of four peptides. One is based on reaction coordinates and two-dimensional free energy surfaces. The other is based on clustering analysis of sampled conformations. Effects of perturbing various model parameters on the equilibriums between native-like states with other conformational states were considered. For one type of perturbation predicted to have consistent effects on different peptides, the predictions have been verified by actual simulations using a perturbed model.
引文
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