量子化学方法对生物体系的研究以及蛋白质折叠
|
摘要
由于蛋白质体系非常大,一般含有几千个原子以上,关于生物大分子的研究方法一般采用建立在原子-原子成对相互作用势基础上的经典力场方法。目前常用的分子力学方法有:AMBER, CHARMM, OPLS, GROMOS等等,分子力学方法将复杂的作用势用键伸缩势能,键角弯曲势能,二面角扭转势能,库仑静电势能和范德华作用势的模型来描述,其中的各项参数是根据量子力学或者实验数据拟合而来的。由于分子力场简易性,它可以直接和快速的计算分子之间的相互作用,已成功的应用于各类分子体系的研究。但是,这些力场方法存在重大的缺陷,由于生物分子一般处于溶液环境,在水溶液中极化的效应是非常显著的。在分子力学计算中将电子运动忽略,将系统的能量视为原子核位置的函数,自然不能处理有很强电子效应的体系,比如不能描述键的断裂和形成,重要的是它一般不包括极化的影响。
只有量子化学理论能够克服传统分子力场的缺陷。然而由于计算条件的限制,处理像蛋白质这样的生物大分子,直接运用量子化学方法是不可能的。为了把量子化学方法运用到蛋白质或其他的生物大分子中,在过去的几十年里发展了多种线性标度的量子化学方法,主要有分而治之方法(D&C),调整密度矩阵近似方法(ADMA),分块的分子轨道方法(FMO),以及本文使用的分子碎片共轭帽方法(MFCC)。
MFCC方法是一套基于电子结构局域性的分子切割方法。这个方法是把蛋白质体系分为以氨基酸为基础的片段,然后在断开的地方接上适当的小分子基团,即共轭帽。引入帽子满足如下条件:第一是保持原来切开前共价键的性质,第二是能够模仿被切掉的原来片段的电子结构的性质。这样对大分子的计算拆分成若干对分子片段的计算,通过简单的加减法还原大分子的性质。MFCC方法是完全线性标度的,可以用量子化学从头算来计算各个片段的物理量,整个蛋白质的物理量由各个片段的物理量组合而得到。MFCC方法计算量与系统的大小严格的成正比,其数值计算可以很容易地并行化,大大提高计算效率。现已成功地应用于蛋白质电荷密度、蛋白质能量、配体在蛋白质靶点的位置优化、蛋白质和药物的相互作用以及导体模型的蛋白质溶剂化和药物设计等的计算。
本论文工作分为六大部分:第一部分用MFCC方法研究了HIV-1蛋白酶与桥梁水分子(W301)之间的相互作用能;第二部分用MFCC和导体极化连续模型(MFCC-CPCM)方法研究了W301水分子对HIV-1蛋白酶与配体复合体自由能的贡献;第三部分将MFCC和泊松-波尔兹曼溶剂化模型(PB Model)结合起来,拟合蛋白质的原子电荷(Polarized protein-specific charge--PPC),使每一个原子都处于真实的环境中。通过对六个蛋白系统的研究证明了用该方法进行分子动力学模拟比用传统的AMBER分子力场模拟蛋白质的结构更加稳定;第四部分:极化的蛋白质专一性电荷(PPC)稳定模拟中蛋白质天然态结构;第五部分:用副本交换分子动力学(REMD)方法研究色氨酸笼(Trp-cage)蛋白折叠。第六部分:实时拟合PPC加速蛋白质折叠。本论文的主要研究内容和结果如下:
一. MFCC方法研究HIV-1蛋白酶与水分子的相互作用能
我们用MFCC方法将HIV-1蛋白酶在肽键位置切开,在每一个切断点插入一对共轭帽(CH3CO-CH3NH-)得到了198个加了帽子的氨基酸片段和196个共轭帽分子。分别用HF, B3LYP和MP2方法在6-31+G*基组下进行计算,我们的结果显示:(1)W301和B链中50号异亮氨酸形成的氢键强于和A链中50号异亮氨酸形成的氢键。(2)W301也和A链中的25号去质子化的天冬氨酸有相互作用,此相互作用是长程的偶极离子间的相互作用,然而W301和B链中的25号质子化的天冬氨酸没有如此的相互作用。(3)W301与药物(ABT-538)形成的氢键强于和50号异亮氨酸形成的氢键。(4)W301与HIV-1蛋白酶中A链和B链形成的相互作用能是非常接近的。
二. MFCC-CPCM方法研究了W301水分子对HIV-1蛋白酶与配体复合体自由能的贡献
我们用分子碎片共轭帽(MFCC)和导体极化连续介质模型(CPCM)结合起来研究蛋白质溶剂化能。在本文中,MFCC-CPCM方法研究了W301水分子对HIV-1蛋白酶和ABT-538复合体自由能的贡献。MFCC方法用来计算气象中水分子和HIV-1蛋白酶的相互作用能,MFCC-CPCM方法用来计算静电相的溶剂化能,非静电相溶剂化能通过用表面积方法(SA)来计算,并且熵变通过正则模态分析(Normal mode analysis)获得。与传统的MM-PBSA方法相比,我们方法显式的包含了极化作用并且我们的结果和先前用热力学积分方法计算的自由能符合的很好,证明了301水分子在HIV-1蛋白酶和药物的作用中起了非常重要的作用。
三.极化的蛋白质专一性电荷(PPC)稳定模拟中的蛋白质内部氢键
由于在传统的分子力场中每个氨基酸中的各原子电荷是固定的,很难正确描述极化的影响。我们将MFCC和泊松-波尔兹曼溶剂化模型(PB Model)结合起来,拟合蛋白质的原子电荷(PPC),PPC能够正确代表蛋白质的静电极化状态并且可以对天然态附近的结构提供精确的静电相互作用。当进行动力学模拟时候,PPC只是简单替换掉AMBER电荷,其它参数保存不变。我们用PPC替换AMBER电荷对6个蛋白质体系进行动力学模拟发现,在整个动力学模拟过程中PPC计算出的氢键的占有率和氢键的数目比AMBER计算出的高,并且在AMEBR力场下一些蛋白质内部的氢键被破坏,这些破坏的氢键引起了一些二级结构的变性,但是用PPC氢键和二级结构很好的保留,蛋白质的结构更加稳定。
四. PPC稳定模拟中蛋白质天然态结构
先前的工作发现,用PPC计算decoy(假的天然态)能量比天然态能量要高,也就是天然态能量是最低的,但是用AMBER力场发现天然态能量不是最低的。所以我们对那些蛋白质进行分子动力学模拟,我们发现,从天然态结构出发,AMBER会使结构走向decoy结构,而PPC则不会。主要原因是用AMBER进行动力学模拟过程中,氢键的打断引起了局部蛋白结构大的改变,从而引起了整体蛋白结构的变化。但是PPC进行动力学模拟蛋白质内部氢键保存非常好。
五.副本交换方法研究Trp-cage蛋白折叠和去折叠热力学行为
我们分别用AMEBR96和AMBER03力场和普适的波恩模型(igb1和igb5)来研究Trp-cage的折叠和去折叠过程。蛋白质的热力学行为对溶剂模型和分子力场是非常敏感的。我们发现当用FF96/igb5,从去折叠模拟中计算的熔解温度和实验值(315K)非常接近,但是在折叠模拟中却不能收敛。当用FF03/igb5时,无论从折叠还是去折叠模拟,给出了过分稳定的动力学结果,计算的熔解温度是345K,并且在两种模拟过程中显示了相似的自由能面。当用FF96/igb1,FF03/igb1在我们50ns的模拟时间内结果很难收敛。
六.实时拟合PPC加速蛋白质折叠
目前的PPC是从固定的结构中计算获得的,更确切的说是从天然态结构,它仅仅反映相空间中很小部分的电荷分布。对于大规模运动,比如蛋白质折叠,它也许并不合适了。所以我们发展了一套实时拟合电荷的方法用来研究2I9M小蛋白的折叠。我们分别用AMBER电荷和实时拟合PPC对2I9M(PDB entry)蛋白进行了30ns的动力学模拟,从线状结构开始,用实时拟合PPC方法,蛋白质在6.3ns成功的折叠到天然态结构,然而AMBER在30ns的动力学模拟中没有任何折叠态出现。
随着MFCC方法不断完善,我们相信我们的MFCC方法和其他线性标度的量子化学方法在研究生物体系中扮演越来越重要的角色,并且我们将线性标度的量子化学方法推广到对动态性质的研究,对α螺旋的折叠给出了理想的结果。
Due to a large number of atoms in protein, force field method which is built with relatively simple atomic pairwise functions is the main method for studying the macromoleculars like proteins. Current standard force fields include AMBER, CHARMM, OPLS, GROMOS and et at. According to force field methods, the complicated interaction is simplified to be the combinations of bond stretch, angle bending, dihedral terms, the Coulomb electrostatic and VDW interactions. Parameters for these potential energy terms are fitted to quantum mechanical calculations or some experimental date. The simple format of the force fields enable the straightforward and rapid evaluation of interaction forces of the complex systems, and they have been used to all kinds of molecular systems successfully in the past several decades. While, they still have significant limitations. Since the biomolecular is usually in a solution environment and the polarization effect is very obvious in water. In force field, the electronic movement is ignored and the energy of system is a function of nuclear location, so it cannot deal with the system with strong electronic effect. For example, the standard force field does not describe chemical bond breaking and bond formation process, and more notably, does not include polarization effect.
Only quantum mechanical theory and computation can truly overcome these deficiencies of the empirical force field. However, straightforward application of the existing quantum chemistry methods to complex systems is beyond the computational limit. In order to apply quantum methods to study properties of proteins or other biomolecules, some linear scaling methods have been proposed in the past several decades, including divide-and-conquer method, adjustable density matrix assembler method, fragment molecular orbital method, and the molecular fragmentation with conjugate caps method (MFCC).
MFCC method is one of the molecular tailoring methods, based on the locality of electronic structure. In this approach, molecular is cut into fragments along the backbone and each position of cut, a pair of conjugate caps is added to saturate the covalent bonds and represent the neighboring environment. Therefore, calculation of a large molecule can be divided into several calculations of small molecules, and return the properties of the large molecule by simple plus and minus. The electronic properties of protein systems can be computed through an efficient linear scaling scheme using a variety of methods. The MFCC method scales linearly with the size of the molecular and, in particular, its numerical computation can be easily parallelized for even greater computational efficiency. This approach has been successfully applied to study the electron density of protein, protein total energy, ligand optimization in binding pocket of protein, protein/ligand interaction, protein salvation and drug design.
This thesis contains mainly six parts: Part I: MFCC study of HIV-1 protease-bridge water interaction. Part II: MFCC-CPCM calculation of the contribution of W301 water for the protein-ligand binding free energy for HIV-1 protease/ligand complex. Part III: The quantum calculation of protein is made possible by developing MFCC in combination with the implicit continuum model to fit the atomic charge (PPC). Our PPC makes each atom into specific protein environment. MD simulations are preformed for a number of benchmark proteins and the computational result shows that the protein structure are more stable using PPC than AMBER. Part IV: Protein’s native structure is dynamically stabilized by PPC. Part V: Thermodynamics of folding and unfolding of TC5B by replica exchange molecular dynamics simulations. Part VI: Ultrafast protein folding accelerated by PPC fitted on-the-fly. The main results obtained in this thesis are as follows.
I. MFCC study of HIV-1 protease-bridge water interaction
According to the MFCC approach, we decompose the protease into 198 amino acid fragments and 196 concaps by cutting all backbone peptide bonds, then every position that is cut is sealed with proper conjugate caps (CH3CO- and CH3NH-). Ab initio methods at HF, B3LYP and MP2 levels with a fixed basis set 6-31+G* have been employed in the present calculation. Our result shows the following features: (1) W301 hydrogen bonds more strongly to ILE50 (B) than ILE50 (A). (2) In additions to strong hydrogen bonding by W301 to ILE50’s, W301 also interacts strongly with the deprotonated ASP25 (A) through relatively long range ion-dipole interaction. But no such long range ion-dipole interaction exits between W301 and the protonated ASP25 (B). (3) W301 hydrogen bonds more strongly to the ligand ABT-538 than to the ILE50’s of protease. (4) However, the total interaction energy between the bridge water W301 and either chain of protease is very close.
II. MFCC-CPCM calculation of the contribution of W301 water for the protein-ligand binding free energy for HIV-1 protease/ligand complex
We developed a novel method that combines the linear scaling quantum mechanical method, termed the molecular fragmentation with conjugate caps (MFCC), with conductor-like polarizable continuum model (CPCM) to study protein salvation. In this work, we apply this MFCC-CPCM approach to study the contribution to the binding free energy from a conserved water molecular in HIV-1 protease/ABT538 complex. The MFCC method is applied to calculate the interaction energy in gas phase at MP2/6-31+G* level and the MFCC-CPCM method is applied to calculate the electrostatic solvation energies at HF/6-31G* level. The non-electrostatic salvation free energy is calculated using surface area (SA) approach and the entropy loss from normal mode analysis. As an advantage over the frequently used MM/PBSA method, this approach includes polarization effect explicitly. The results, which are in good agreement with FEP/TI method, show that the conserved W301 contributes significantly to the binding free energy of HIV-1PR/ABT538 complex.
III. Intra-protein hydrogen bonding is dynamically stabilized by polarized protein-specific charge (PPC)
In current standard force fields, the partical charge of each atom is fixed and therefore they fail to give accurate representation of the electrostatic of the specific protein environment which is highly inhomogeneous and protein-specific. We employ linearized Poisson-Boltzmann method to solve the self-consistent reaction-field equation coupled with quantum chemistry calculation of the solute using the MFCC scheme to fit the polarized protein-specific charge (PPC). The PPC correctly represent the electronically polarized state of the protein and therefore provide accurate electrostatic interaction near the native structure. When MD simulation is preformed, the AMEBR charges are simply by the PPC while the rest of the force field parameters are intact. The computational result of six proteins shows that occupancy percentage of hydrogen bonds averaged over simulation time, as well as the number of hydrogen bonds as a function of simulation time, are consistently higher under PPC than AMBER charge. In particular, some intra-protein hydrogen bonds are found broken during MD simulation using AMBER charge but they are stable using PPC. The breaking of some intra-protein hydrogen bonds in AMBER simulation is responsible for deformation or denaturing of some local structures of proteins during MD simulation. In PPC simulation, the hydrogen bonds and secondary structure are kept intact, and the protein structure is stable.
IV. Protein’s native structure is dynamically stabilized by PPC
Previous study finds that those native energy are the lowest energy using PPC, while using AMBER none of native structures have the lowest energy among decoys. So MD simulation is performed for those proteins using AMBER and PPC. Our results shows that MD simulation can drive the protein away from its native state when standard AMBER force field is used, while PPC can still reflect protein’s real structure after long time simulation. The primary cause of the difference is some intra-protein hydrogen bonds are broken using AMBER charge, and the breaking of intra-protein hydrogen bonds cause the deformation or denaturing of structure, thereby away from their correct structures. In contrast, those intra-protein hydrogen bonds which are significant to stabilize protein structure remain intact using PPC.
V. Thermodynamics of folding and unfolding of TC5B by replica exchange molecular dynamics simulations
Molecular dynamics simulations based on AMBER force fields (ff96 and ff03) and generalized Born models (igb1 and igb5) have been carried out to study folding/unfolding of mini-protein Trp-cage. The thermodynamic properties of Trp-cage are found to be sensitive to the specific version of the solvation model and force field employed. When ff96/igb5 combination is used, the predicted melting temperature from unfolding simulation is in good agreement with the experimental value of 315K, but the folding simulation does not converge. The most stable thermodynamic profile in both folding and unfolding simulations is obtained when ff03/igb5 combination is employed, and the predicted melting temperature is about 345K, showing over-stabilization of the protein. And the free energy landscapes of TC5B have also been explored and the contour maps from unfolding and folding simulations using ff03/igb5 show similar characteristics. Simulations using the igb1 version in combination with ff96 or ff03 are difficult to converge within our simulation time limit (50 ns).
VI. Ultrafast protein folding accelerated by PPC fitted on-the-fly Since PPC is fitted from a static structure, more precisely the native structure, it can only well reflect the charge distribution in a very small portion of phace space, and may not be suitable for the study of large conformation change such as protein folding. In this work, we incorporate PPC into molecular dynamics and propose a on-the-fly charge fitting scheme for folding simulation of a short peptide (PDB entry 2I9M). We carry out two direct folding simulations with AMBER force field and polarized protein-specific charge for 30ns. Starting from a fully extended structure, protein successfully folds to the native conformation in an ultrafast time (6.3ns) in PPC simulation. In AMBER simulation not a single folded structure has been seen during the 30ns MD simulation.
With successive development of MFCC theory, we believe our MFCC method, together with other linear scaling quantum mechanical methods, can play a more and more important role in studying biological systems. We extend the linear scaling quantum mechanical methods to the study about dynamic structure, and it has been successfully used toα-helix folding.
只有量子化学理论能够克服传统分子力场的缺陷。然而由于计算条件的限制,处理像蛋白质这样的生物大分子,直接运用量子化学方法是不可能的。为了把量子化学方法运用到蛋白质或其他的生物大分子中,在过去的几十年里发展了多种线性标度的量子化学方法,主要有分而治之方法(D&C),调整密度矩阵近似方法(ADMA),分块的分子轨道方法(FMO),以及本文使用的分子碎片共轭帽方法(MFCC)。
MFCC方法是一套基于电子结构局域性的分子切割方法。这个方法是把蛋白质体系分为以氨基酸为基础的片段,然后在断开的地方接上适当的小分子基团,即共轭帽。引入帽子满足如下条件:第一是保持原来切开前共价键的性质,第二是能够模仿被切掉的原来片段的电子结构的性质。这样对大分子的计算拆分成若干对分子片段的计算,通过简单的加减法还原大分子的性质。MFCC方法是完全线性标度的,可以用量子化学从头算来计算各个片段的物理量,整个蛋白质的物理量由各个片段的物理量组合而得到。MFCC方法计算量与系统的大小严格的成正比,其数值计算可以很容易地并行化,大大提高计算效率。现已成功地应用于蛋白质电荷密度、蛋白质能量、配体在蛋白质靶点的位置优化、蛋白质和药物的相互作用以及导体模型的蛋白质溶剂化和药物设计等的计算。
本论文工作分为六大部分:第一部分用MFCC方法研究了HIV-1蛋白酶与桥梁水分子(W301)之间的相互作用能;第二部分用MFCC和导体极化连续模型(MFCC-CPCM)方法研究了W301水分子对HIV-1蛋白酶与配体复合体自由能的贡献;第三部分将MFCC和泊松-波尔兹曼溶剂化模型(PB Model)结合起来,拟合蛋白质的原子电荷(Polarized protein-specific charge--PPC),使每一个原子都处于真实的环境中。通过对六个蛋白系统的研究证明了用该方法进行分子动力学模拟比用传统的AMBER分子力场模拟蛋白质的结构更加稳定;第四部分:极化的蛋白质专一性电荷(PPC)稳定模拟中蛋白质天然态结构;第五部分:用副本交换分子动力学(REMD)方法研究色氨酸笼(Trp-cage)蛋白折叠。第六部分:实时拟合PPC加速蛋白质折叠。本论文的主要研究内容和结果如下:
一. MFCC方法研究HIV-1蛋白酶与水分子的相互作用能
我们用MFCC方法将HIV-1蛋白酶在肽键位置切开,在每一个切断点插入一对共轭帽(CH3CO-CH3NH-)得到了198个加了帽子的氨基酸片段和196个共轭帽分子。分别用HF, B3LYP和MP2方法在6-31+G*基组下进行计算,我们的结果显示:(1)W301和B链中50号异亮氨酸形成的氢键强于和A链中50号异亮氨酸形成的氢键。(2)W301也和A链中的25号去质子化的天冬氨酸有相互作用,此相互作用是长程的偶极离子间的相互作用,然而W301和B链中的25号质子化的天冬氨酸没有如此的相互作用。(3)W301与药物(ABT-538)形成的氢键强于和50号异亮氨酸形成的氢键。(4)W301与HIV-1蛋白酶中A链和B链形成的相互作用能是非常接近的。
二. MFCC-CPCM方法研究了W301水分子对HIV-1蛋白酶与配体复合体自由能的贡献
我们用分子碎片共轭帽(MFCC)和导体极化连续介质模型(CPCM)结合起来研究蛋白质溶剂化能。在本文中,MFCC-CPCM方法研究了W301水分子对HIV-1蛋白酶和ABT-538复合体自由能的贡献。MFCC方法用来计算气象中水分子和HIV-1蛋白酶的相互作用能,MFCC-CPCM方法用来计算静电相的溶剂化能,非静电相溶剂化能通过用表面积方法(SA)来计算,并且熵变通过正则模态分析(Normal mode analysis)获得。与传统的MM-PBSA方法相比,我们方法显式的包含了极化作用并且我们的结果和先前用热力学积分方法计算的自由能符合的很好,证明了301水分子在HIV-1蛋白酶和药物的作用中起了非常重要的作用。
三.极化的蛋白质专一性电荷(PPC)稳定模拟中的蛋白质内部氢键
由于在传统的分子力场中每个氨基酸中的各原子电荷是固定的,很难正确描述极化的影响。我们将MFCC和泊松-波尔兹曼溶剂化模型(PB Model)结合起来,拟合蛋白质的原子电荷(PPC),PPC能够正确代表蛋白质的静电极化状态并且可以对天然态附近的结构提供精确的静电相互作用。当进行动力学模拟时候,PPC只是简单替换掉AMBER电荷,其它参数保存不变。我们用PPC替换AMBER电荷对6个蛋白质体系进行动力学模拟发现,在整个动力学模拟过程中PPC计算出的氢键的占有率和氢键的数目比AMBER计算出的高,并且在AMEBR力场下一些蛋白质内部的氢键被破坏,这些破坏的氢键引起了一些二级结构的变性,但是用PPC氢键和二级结构很好的保留,蛋白质的结构更加稳定。
四. PPC稳定模拟中蛋白质天然态结构
先前的工作发现,用PPC计算decoy(假的天然态)能量比天然态能量要高,也就是天然态能量是最低的,但是用AMBER力场发现天然态能量不是最低的。所以我们对那些蛋白质进行分子动力学模拟,我们发现,从天然态结构出发,AMBER会使结构走向decoy结构,而PPC则不会。主要原因是用AMBER进行动力学模拟过程中,氢键的打断引起了局部蛋白结构大的改变,从而引起了整体蛋白结构的变化。但是PPC进行动力学模拟蛋白质内部氢键保存非常好。
五.副本交换方法研究Trp-cage蛋白折叠和去折叠热力学行为
我们分别用AMEBR96和AMBER03力场和普适的波恩模型(igb1和igb5)来研究Trp-cage的折叠和去折叠过程。蛋白质的热力学行为对溶剂模型和分子力场是非常敏感的。我们发现当用FF96/igb5,从去折叠模拟中计算的熔解温度和实验值(315K)非常接近,但是在折叠模拟中却不能收敛。当用FF03/igb5时,无论从折叠还是去折叠模拟,给出了过分稳定的动力学结果,计算的熔解温度是345K,并且在两种模拟过程中显示了相似的自由能面。当用FF96/igb1,FF03/igb1在我们50ns的模拟时间内结果很难收敛。
六.实时拟合PPC加速蛋白质折叠
目前的PPC是从固定的结构中计算获得的,更确切的说是从天然态结构,它仅仅反映相空间中很小部分的电荷分布。对于大规模运动,比如蛋白质折叠,它也许并不合适了。所以我们发展了一套实时拟合电荷的方法用来研究2I9M小蛋白的折叠。我们分别用AMBER电荷和实时拟合PPC对2I9M(PDB entry)蛋白进行了30ns的动力学模拟,从线状结构开始,用实时拟合PPC方法,蛋白质在6.3ns成功的折叠到天然态结构,然而AMBER在30ns的动力学模拟中没有任何折叠态出现。
随着MFCC方法不断完善,我们相信我们的MFCC方法和其他线性标度的量子化学方法在研究生物体系中扮演越来越重要的角色,并且我们将线性标度的量子化学方法推广到对动态性质的研究,对α螺旋的折叠给出了理想的结果。
Due to a large number of atoms in protein, force field method which is built with relatively simple atomic pairwise functions is the main method for studying the macromoleculars like proteins. Current standard force fields include AMBER, CHARMM, OPLS, GROMOS and et at. According to force field methods, the complicated interaction is simplified to be the combinations of bond stretch, angle bending, dihedral terms, the Coulomb electrostatic and VDW interactions. Parameters for these potential energy terms are fitted to quantum mechanical calculations or some experimental date. The simple format of the force fields enable the straightforward and rapid evaluation of interaction forces of the complex systems, and they have been used to all kinds of molecular systems successfully in the past several decades. While, they still have significant limitations. Since the biomolecular is usually in a solution environment and the polarization effect is very obvious in water. In force field, the electronic movement is ignored and the energy of system is a function of nuclear location, so it cannot deal with the system with strong electronic effect. For example, the standard force field does not describe chemical bond breaking and bond formation process, and more notably, does not include polarization effect.
Only quantum mechanical theory and computation can truly overcome these deficiencies of the empirical force field. However, straightforward application of the existing quantum chemistry methods to complex systems is beyond the computational limit. In order to apply quantum methods to study properties of proteins or other biomolecules, some linear scaling methods have been proposed in the past several decades, including divide-and-conquer method, adjustable density matrix assembler method, fragment molecular orbital method, and the molecular fragmentation with conjugate caps method (MFCC).
MFCC method is one of the molecular tailoring methods, based on the locality of electronic structure. In this approach, molecular is cut into fragments along the backbone and each position of cut, a pair of conjugate caps is added to saturate the covalent bonds and represent the neighboring environment. Therefore, calculation of a large molecule can be divided into several calculations of small molecules, and return the properties of the large molecule by simple plus and minus. The electronic properties of protein systems can be computed through an efficient linear scaling scheme using a variety of methods. The MFCC method scales linearly with the size of the molecular and, in particular, its numerical computation can be easily parallelized for even greater computational efficiency. This approach has been successfully applied to study the electron density of protein, protein total energy, ligand optimization in binding pocket of protein, protein/ligand interaction, protein salvation and drug design.
This thesis contains mainly six parts: Part I: MFCC study of HIV-1 protease-bridge water interaction. Part II: MFCC-CPCM calculation of the contribution of W301 water for the protein-ligand binding free energy for HIV-1 protease/ligand complex. Part III: The quantum calculation of protein is made possible by developing MFCC in combination with the implicit continuum model to fit the atomic charge (PPC). Our PPC makes each atom into specific protein environment. MD simulations are preformed for a number of benchmark proteins and the computational result shows that the protein structure are more stable using PPC than AMBER. Part IV: Protein’s native structure is dynamically stabilized by PPC. Part V: Thermodynamics of folding and unfolding of TC5B by replica exchange molecular dynamics simulations. Part VI: Ultrafast protein folding accelerated by PPC fitted on-the-fly. The main results obtained in this thesis are as follows.
I. MFCC study of HIV-1 protease-bridge water interaction
According to the MFCC approach, we decompose the protease into 198 amino acid fragments and 196 concaps by cutting all backbone peptide bonds, then every position that is cut is sealed with proper conjugate caps (CH3CO- and CH3NH-). Ab initio methods at HF, B3LYP and MP2 levels with a fixed basis set 6-31+G* have been employed in the present calculation. Our result shows the following features: (1) W301 hydrogen bonds more strongly to ILE50 (B) than ILE50 (A). (2) In additions to strong hydrogen bonding by W301 to ILE50’s, W301 also interacts strongly with the deprotonated ASP25 (A) through relatively long range ion-dipole interaction. But no such long range ion-dipole interaction exits between W301 and the protonated ASP25 (B). (3) W301 hydrogen bonds more strongly to the ligand ABT-538 than to the ILE50’s of protease. (4) However, the total interaction energy between the bridge water W301 and either chain of protease is very close.
II. MFCC-CPCM calculation of the contribution of W301 water for the protein-ligand binding free energy for HIV-1 protease/ligand complex
We developed a novel method that combines the linear scaling quantum mechanical method, termed the molecular fragmentation with conjugate caps (MFCC), with conductor-like polarizable continuum model (CPCM) to study protein salvation. In this work, we apply this MFCC-CPCM approach to study the contribution to the binding free energy from a conserved water molecular in HIV-1 protease/ABT538 complex. The MFCC method is applied to calculate the interaction energy in gas phase at MP2/6-31+G* level and the MFCC-CPCM method is applied to calculate the electrostatic solvation energies at HF/6-31G* level. The non-electrostatic salvation free energy is calculated using surface area (SA) approach and the entropy loss from normal mode analysis. As an advantage over the frequently used MM/PBSA method, this approach includes polarization effect explicitly. The results, which are in good agreement with FEP/TI method, show that the conserved W301 contributes significantly to the binding free energy of HIV-1PR/ABT538 complex.
III. Intra-protein hydrogen bonding is dynamically stabilized by polarized protein-specific charge (PPC)
In current standard force fields, the partical charge of each atom is fixed and therefore they fail to give accurate representation of the electrostatic of the specific protein environment which is highly inhomogeneous and protein-specific. We employ linearized Poisson-Boltzmann method to solve the self-consistent reaction-field equation coupled with quantum chemistry calculation of the solute using the MFCC scheme to fit the polarized protein-specific charge (PPC). The PPC correctly represent the electronically polarized state of the protein and therefore provide accurate electrostatic interaction near the native structure. When MD simulation is preformed, the AMEBR charges are simply by the PPC while the rest of the force field parameters are intact. The computational result of six proteins shows that occupancy percentage of hydrogen bonds averaged over simulation time, as well as the number of hydrogen bonds as a function of simulation time, are consistently higher under PPC than AMBER charge. In particular, some intra-protein hydrogen bonds are found broken during MD simulation using AMBER charge but they are stable using PPC. The breaking of some intra-protein hydrogen bonds in AMBER simulation is responsible for deformation or denaturing of some local structures of proteins during MD simulation. In PPC simulation, the hydrogen bonds and secondary structure are kept intact, and the protein structure is stable.
IV. Protein’s native structure is dynamically stabilized by PPC
Previous study finds that those native energy are the lowest energy using PPC, while using AMBER none of native structures have the lowest energy among decoys. So MD simulation is performed for those proteins using AMBER and PPC. Our results shows that MD simulation can drive the protein away from its native state when standard AMBER force field is used, while PPC can still reflect protein’s real structure after long time simulation. The primary cause of the difference is some intra-protein hydrogen bonds are broken using AMBER charge, and the breaking of intra-protein hydrogen bonds cause the deformation or denaturing of structure, thereby away from their correct structures. In contrast, those intra-protein hydrogen bonds which are significant to stabilize protein structure remain intact using PPC.
V. Thermodynamics of folding and unfolding of TC5B by replica exchange molecular dynamics simulations
Molecular dynamics simulations based on AMBER force fields (ff96 and ff03) and generalized Born models (igb1 and igb5) have been carried out to study folding/unfolding of mini-protein Trp-cage. The thermodynamic properties of Trp-cage are found to be sensitive to the specific version of the solvation model and force field employed. When ff96/igb5 combination is used, the predicted melting temperature from unfolding simulation is in good agreement with the experimental value of 315K, but the folding simulation does not converge. The most stable thermodynamic profile in both folding and unfolding simulations is obtained when ff03/igb5 combination is employed, and the predicted melting temperature is about 345K, showing over-stabilization of the protein. And the free energy landscapes of TC5B have also been explored and the contour maps from unfolding and folding simulations using ff03/igb5 show similar characteristics. Simulations using the igb1 version in combination with ff96 or ff03 are difficult to converge within our simulation time limit (50 ns).
VI. Ultrafast protein folding accelerated by PPC fitted on-the-fly Since PPC is fitted from a static structure, more precisely the native structure, it can only well reflect the charge distribution in a very small portion of phace space, and may not be suitable for the study of large conformation change such as protein folding. In this work, we incorporate PPC into molecular dynamics and propose a on-the-fly charge fitting scheme for folding simulation of a short peptide (PDB entry 2I9M). We carry out two direct folding simulations with AMBER force field and polarized protein-specific charge for 30ns. Starting from a fully extended structure, protein successfully folds to the native conformation in an ultrafast time (6.3ns) in PPC simulation. In AMBER simulation not a single folded structure has been seen during the 30ns MD simulation.
With successive development of MFCC theory, we believe our MFCC method, together with other linear scaling quantum mechanical methods, can play a more and more important role in studying biological systems. We extend the linear scaling quantum mechanical methods to the study about dynamic structure, and it has been successfully used toα-helix folding.
引文
1. Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., M, D., Spellmeyer, D.C., Fox, T., Caldwell, J.W., and Kollman, P. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules [J]. J. Am. Chem. SOC., 1995, 117(19): 5179-5197.
2. MacKerell, A.D., Jr., Bashford, D., Bellott, R.L., Dunbrack, R.L., Jr., Evanseck, J.D., Field, M.J., Fischer, S., Gao, J., Guo, H., Ha, S., Joseph‐ McCarthy, D., Kuchnir, L., Kuczera, K., Lau, F.T.K., Mattos, C., Michnick, S., Ngo, T., Nguyen, D.T., Prodhom, B., Reiher, W.E., III, R., B., Schlenkrich, M., Smith, J.C., Stote, R., Straub, J., Watanabe, M., Wiorkiewicz‐K uczera, J., Yin, D., and Karplus, M. All-atom empirical potential for molecular modeling and dynamics studies of proteins [J]. J. Phys. Chem. B., 1998, 102(18): 3586-3616.
3. Jorgensen, W.L., Maxwell, D.S., and J. Tirado-Rives. Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids [J]. J. Am. Chem. Soc. , 1996, 118(45): 11225-11236.
4. Kaminski, G.A., Friesner, R.A., Tirado-Rives, J., and Jorgensen, W.L. Evaluation and reparameterization of the OPLS‐ AA force field for proteins via comparison with accurate quantum chemical calculations on peptides [J]. J. Phys. Chem. B. , 2001, 105(28): 6474-6487.
5. Warshel, A. and Levitt, M. Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme [J]. J. Mol. Biol., 1976, 103(2): 227-249.
6. Singh, U.C. and Kollman, P. A Combined Ab Initio Quantum Mechanical and ... Protonation of Polyethers [J]. J. Comput. Chem., 1986, 7(6): 718-730.
7. Field, M.J., Bash, P.A., and Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations [J]. J. Comput. Chem., 1990, 11(6): 700–733.
8. Gao, J. and Xia, X. A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations [J]. Science, 1992, 258(5082): 631-635.
9. Stanton, R.V., Hartsough, D.S., and Merz. Jr, K.M. Calculation of Solvation FreeEnergies Using a Density Functional/Molecular Dynamics Coupled Potential [J]. J. Phys. Chem. B., 1993, 97: 11868-11870.
10. Thery, V., Rinaldi, D., and Rivail, J.-L. Quantum mechanical computations on very large molecular-systems-the local self-consistent-field method [J]. J. Comput. Chem. , 1994, 15(3): 269-282.
11. Maseras, F. and Morokuma, K. A new‘ab initio+molecular mechanics’geometry optimization scheme of equilibrium structures and transition states [J]. J. Comput. Chem., 1995, 16: 1170-1179.
12. Bakowies, D. and Thiel, W. Hybrid Models for Combined Quantum Mechanical and Molecular Approaches [J]. J. Phys. Chem. B., 1996, 100(25): 10580-10594.
13. Eurenius, K.P., Charfield, D.C., Brooks, B.R., and Hodoscek, M. Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations [J]. Int. J. Quantum Chem., 1996, 60(6): 1189-1200.
14. Bersuker, I.B., Leong, M.K., and Pearlman, J.E.B.R.S. A Method of Combined QuantumMechanical (QM)/Molecular Mechanics (MM) Treatment of Large Polyatomic Systems with Charge Transfer Between the QM and MM Fragments [J]. Int. J. Quantum Chem., 1997, 63(6): 1051–1063
15. Gao, J., Amara, P., Alhambra, C., and Field, M.J. A generalized hybrid orbital (gho) method for the treatment of boundary atoms in combined qm/mm calculations [J]. J. Phys. Chem. A, 1998, 102(24): 4714-4721.
16. Antes, I. and Thiel, W. Adjusted Connection Atoms for Combined Quantum Mechanical and Molecular Mechanical Methods [J]. J. Phys. Chem. A, 1999, 103(46): 9290-9295.
17. Lyne, P.D., Hodoscek, M., and Karplus, M. A hybrid QM/MM potential employing Hartree-Fock or density functional methods in the quantum region [J]. J. Phys. Chem. A 1999, 103: 3462-3471.
18. Monard, G. and Merz Jr., K.M. Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems [J]. Acc. Chem. Res., 1999, 32: 904-911.
19. Philipp, D.M. and Friesner, R.A. Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide [J]. J. Comput. Chem., 1999, 20: 1468-1494.
20. Zhang, Y., Lee, T.-S., and Yang, W. A Pseudobond Approach to Combining Quantum Mechanical and Molecular Mechanical Methods [J]. J. Chem. Phys., 1999, 110: 46-54.
21. Amara, P., Field, M.J., Alhambra, C., and Gao, J. The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives [J]. Theor. Chem. Acc., 2000, 104(5): 336-343.
22. Kairys, V. and Jensen, J.H. QM/MM boundaries across covalent bonds: frozen LMO based approach for the Effective Fragment Potential method [J]. J. Phys. Chem. A 2000, 104: 6656-6665.
23. Reuter, N., Dejaegere, A., Maigret, B., and Karplus, M. Frontier bonds in QM/MM methods: a comparison of different approaches [J]. J. Phys. Chem. A, 2000, 104: 1720-1735.
24. Assfeld, X. and Rivail, J.-L. Quantum chemical computations on parts of large molecules: the ab initio local self consistent field method [J]. Chem. Phys. Lett., 1996, 263(1-2): 100-106.
25. Rosta, E., Klahn, M., and Warshel., A. Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions [J]. J. Phys. Chem. B, 2006, 110(6): 2934-2941.
26. Grater, F., Schwarzl, S.M., Dejaegere, A., Fischer, S., and Smith., J.C. Protein/ligand binding free energies calculated with quantum mechanics/molecular mechanics [J]. J. Phys. Chem. B, 2005, 109(20): 10474-10483.
27. Riccardi, D., Schaefer, P., and Cui.., Q. pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: A quantitative test of QM/MM protocols [J]. J. Phys. Chem. B, 2005, 109(37): 17715-17733.
28. Titmuss, S.J., Cummins, P.L., Bliznyuk, A.A., Rendell, A.P., and E.Gready, J. Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods applied to the study of enzume reactions [J]. Chem. Phys. Lett. , 2000, 320: 169-176.
29. Kohn, W. Density Functional Theory for Systems of Very Many Atoms,Proceedings of the 1994 Satellite Symposium on ``Thirty Years of Density Functional Theory'' [J]. Int. J. Quantum Chem., 1995, 56(4): 229-232.
30. Nunes, R.W. and Vanderbilt, D. Generalisation of the density-matrix method to a non-orthogonal basis [J]. Phys. Rev. B, 1994, 50(23): 17611-17614.
31. Dixon, S.L. and Merz Ji, K.M. Semiempirical Molecular Orbital Calculations with Linear System Size Scaling [J]. J. Chem. Phys., 1996, 104(17): 6643-6649.
32. Daniels, A.D., William, J.M., and Scuseria, G.E. Semiempirical methods with conjugate gradient density matrix search to replace diagonalization for molecular systems containing thousands of atoms [J]. J. Chem. Phys., 1997, 107(2): 425-431
33. Yokojima, S. and Chen, G.H. Linear-scaling localized-density-matrix method for the ground and excited states of one-dimensional molecular systems [J]. Chem. Phys. Lett., 1999, 300: 540-544.
34. Lee, T., York, D.M., and Yang., W. Linear-scaling semiempirical quantum calculations for macromolecules [J]. J. Chem. Phys., 1996, 105(7): 2744-2750.
35. York, D.M., Lee, T., and Yang., W. Parameterization and efficient implementation of a solvent model for linear-scaling semiempirical quantum mechanical calculations of biological macromolecules. [J]. Chem. Phys. Lett., 1996, 263: 297-306.
36. York, D.M., Lee, T., and Yang., W. Quantum mechanical treatment of biological macromolecules in solution using linear-scaling electronic structure methods [J]. Phys. Rev. Lett., 1998, 80(22): 5011-5014.
37. Stewart., J.J.P. Application of localized molecular orbitals to the solution of semiempirical self-consistent field equations [J]. Int. J. Quantum Chem., 1996, 58(2): 133-146.
38. Liang, W., Yokojima, S., and Chen., G. Generalized linear-scaling localized-density-matrix method [J]. J. Chem. Phys., 1999, 110(4): 1844-1855.
39. Gibson, A., Haydock, R., and LaFemina., J.P. Ab initio electronic-structure computations with the recursion method [J]. Phys. Rev. B, 1993, 47(15): 9229-9237.
40. Millam, J.M. and Scuseria., G.E. Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations [J]. J. Chem. Phys., 1997, 106(13): 5569-5577.
41. Challacombe, M. A simplified density matrix minimization for linear scaling self-consistent field theory [J]. J. Chem. Phys., 1999, 110(5): 2332-2342.
42. Galli, G. and Parrinello, M. Large scale electronic structure calculations [J]. Phys. Rev. Lett., 1992, 69(24): 3547-3550.
43. Kohn., W. Density Functional Theory for Systems of Very Many Atoms,Proceedings of the 1994 Satellite Symposium on ``Thirty Years of Density Functional Theory'' [J]. Int. J. Quantum Chem., 1995, 56(4): 229-232.
44. Yang, W. Direct calculation of electron density in density-functional theory: Implementation for benzene and a tetrapeptide [J]. Phys. Rev. A, 1991, 44(11): 7823-7826.
45. Ayala, P.Y. and Scuseria, G.E. Linear scaling second-order M?ller-Plesset theory in the atomic orbital basis for large molecular systems [J]. J. Chem. Phys., 1999, 110(8): 3660.
46. Sch¨utz, M., G. Hetzer, and Werner., H. Low-order scaling local electron correlation methods. I. Linear scaling local MP2 [J]. J. Chem. Phys., 1999, 111(13): 5691-5705.
47. Gadre, S.R., Shirsat, R.N., and Limaye., A.C. Molecular tailoring approach for simulation of electrostatic properties [J]. J. Phys. Chem. A, 1994, 98(37): 9165-9169.
48. Nakano, T., Kaminuma, T., Sato, T., Akiyama, Y., Uebayasi, M., and Kitaura, K. Fragment molecular orbital method: application to polypeptides [J]. Chem. Phys. Lett., 2000, 318(6): 614-618.
49. Fedorov, D.G. and Kitaura., K. The importance of three-body terms in the fragment molecular orbital method [J]. J. Chem. Phys., 2004, 120(15): 6832-6840.
50. Mochizuki, Y., Koikegami, S., Nakano, T., Amari, S., and Kitaura, K. Large scale MP2 calculations with fragment molecular orbital scheme [J]. Chem. Phys. Lett., 2004, 396: 473-479.
51. Deev, V. and Collins, M.A. Approximate ab initio energies by systematic molecular fragmentation [J]. J. Chem. Phys., 2005, 122(15): 154102.
52. Fedorov, D.G. and Kitaura., K. The three-body fragment molecular orbital method for accurate calculations of large systems [J]. Chem. Phys. Lett., 2006, 433(1-3): 182-187.
53. Yasuda, K. and Yamaki, D. The extension of the fragment molecular orbital method with the many-particle green’s function [J]. J. Chem. Phys., 2006, 125(15): 154101.
54. Li, W. and Li., S. Divide-and-conquer local correlation approach to the correlation energy of large molecules [J]. J. Chem. Phys., 2004, 121(14): 6649-6657.
55. Gao, A.M., Zhang, D.W., Zhang, J.Z.H., and Zhang, Y.K. An efficient linear scaling method for ab initio calculation of electron density of proteins [J]. Chem. Phys. Lett., 2004, 394: 293-297.
56. Mei, Y., Zhang, D.W., and Zhang., J.Z.H. New method for direct linear-scaling calculation of electron density of proteins [J]. J. Phys. Chem. A, 2005, 109: 2-5.
57. Chen, X.H. and Zhang, J.Z.H. Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation [J]. J. Chem. Phys., 2006, 125(4): 044903.
58. Chen, X.H., Zhang, Y.K., and Zhang, J.Z.H. MFCC-DM with pairwise interaction correction for quantum chemical study of protein [J]. Abstracts of Papers of the American Chemical Society, 2006, 231: 318.
59. Chen, X.H., Zhang, Y.K., and Zhang, J.Z.H. An efficient approach for ab initio energy calculation of biopolymers [J]. J. Chem. Phys., 2005, 122(18): 184105.
60. He, X. and Zhang, J.Z.H. A new method for direct calculation of total energy of protein [J]. J. Chem. Phys. , 2005, 122(3): 031103.
61. He, X. and Zhang, J.Z.H. The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy [J]. J. Chem. Phys., 2006, 124(18): 184703.
62. Chen, X.H. and Zhang, J.Z.H. MFCC-downhill simplex method for molecular structure optimization [J]. J. Theor. Comput. Chem., 2004, 3(3): 277.
63. Xiang, Y., Zhang, D.W., and Zhang, J.Z.H. Fully quantum mechanical energy optimization for protein-ligand structure [J]. J. Comput. Chem., 2004, 25(12): 1431-1437.
64. Zhang, D.W., Xiang, Y., Gao, A.M., and Zhang, J.Z.H. Quantum mechanical map for protein-ligand binding with application to beta-trypsin/benzamidine complex [J]. J. Chem. Phys. , 2004, 120(3): 1145-1148.
65. Zhang, D.W., Xiang, Y., and Zhang, J.Z.H. New advance in computational chemistry: Full quantum mechanical ab initio computation of streptavidin-biotin interaction energy [J]. J. Phys. Chem. B, 2003, 107(44): 12039-12041.
66. Zhang, D.W. and Zhang, J.Z.H. Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy [J]. J. Chem.Phys., 2003, 119(7): 3599-3605.
67. Zhang, D.W. and Zhang., J.Z.H. Full quantum mechanical study of binding of HIV-1 protease drugs [J]. Int. J. Quantum Chem., 2005, 103(3): 246-257.
68. He, X., Mei, Y., Xiang, Y., Zhang, D.W., and Zhang, J.Z.H. Quantum computational analysis for drug resistance of HIV-1 reverse transcriptase to nevirapine through point mutations [J]. Proteins, 2005, 61(2): 423-432.
69. Mei, Y., He, X., Xiang, Y., Zhang, D.W., and Zhang, J.Z.H. Quantum study of mutational effect in binding of efavirenz to HIV-1 RT [J]. Proteins, 2005, 59(3): 489-495.
70. Chen, X.H. and Zhang, J.Z.H. Theoretical method for full ab initio calculation of DNA/RNA-ligand interaction energy [J]. J. Chem. Phys., 2004, 120(24): 11386-11391.
71. Mei, Y., Ji, C.G., and Zhang, J.Z.H. A new quantum method for electrostatic solvation energy of protein [J]. J. Chem. Phys., 2006, 125(9): 094906.
72. Zhang, D.W., Chen, X.H., and Zhang, J.Z.H. Molecular caps for full quantum mechanical computation of peptide-water interaction energy [J]. J. Comput. Chem., 2003, 24(15): 1846-1852.
73. Chen, X.H., Zhang, D.W., and Zhang, J.Z.H. Fractionation of peptide with disulfide bond for quantum mechanical calculation of interaction energy with molecules [J]. J. Chem. Phys., 2004, 120(2): 839-844.
74. Zhang, D.W. and Zhang, J.Z.H. Quantum mechanical studies of HIV-1 protease inhibitors and drug design based on full ab initio MFCC computation [J]. Abstracts of Papers of the American Chemical Society, 2004, 228: u535.
75. Duan, L.L., Tong, Y., Mei, Y., Zhang, Q.G., and Zhang, J.Z.H. Quantum study of HIV-1 protease-bridge water interaction [J]. J. Chem. Phys., 2007, 127(14): 145101.
76. Ji, C.G., Mei, Y., and Zhang, J.Z.H. Developing Polarized Protein-Specific Charges for Protein Dynamics: MD Free Energy Calculation of pKa Shifts for Asp26/Asp20 in Thioredoxin [J]. Biophys. J., 2008, 95(3): 1080-1088.
77. Ji, C.G. and Zhang, J.Z.H. Protein polarization is critical to stabilizing AF-2 and Helix-2′domains in ligand binding to PPARγ[J]. J. Am. Chem. Soc. , 2008, 130(5): 17129-17133.
78. Mei, Y., Wu, E.L., Han, K.L., and Zhang, J.Z.H. Treating hydrogen bonding in ab initio calculation of biopolymers [J]. Int. J. Quantum Chem., 2006, 106(5): 1267-1276.
79. Fedorov, D.G. and Kitaura, K. On the accuracy of the 3-body fragment molecular orbital method (FMO) applied to density functional theory [J]. Chem. Phys. Lett., 2004, 389(1-3): 129-134.
80. Fedorov, D.G., Ishida, T., and Kitaura, K. Multilayer formulation of the fragment molecular orbital method (FMO). [J]. J. Phys. Chem. A, 2005, 109(11): 2638-2646.
81. Miertuˇs, S., Scrocco, E., and Tomasi, J. Electrostatic interaction of a solute with a continuum a direct utilization of ab initio molecular potentials for the prevision of solvent effects [J]. Chem. Phys., 1981, 55(1): 117-129.
82.朱权,傅克祥,李象远.非平衡溶剂化的连续介质模型和超快过程溶剂效应[J].高等学校化学学报, 2006, 27(2): 274-286.
83. Klamt, A. and Sch¨u¨urmann, G. Cosmo: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient [J]. J. Chem. Soc. Perkin. Trans., 1993, 2: 799-805.
84. Barone, V., Rienzo, F.D., Langella, E., Menziani, M.C., Regal, N., and Sola, M. A computational protocol to probe the role of solvation effects on the reduction potential of azurin mutants [J]. Proteins, 2006, 62(1): 262-269.
85. Barone, V. and Cossi, M. Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent mode [J]. J. Phys. Chem. A, 1998, 102(11): 1995-2001.
86. Cammi, R. and Mennucci, B. Linear response theory for the polarizable continuum model [J]. J. Chem. Phys., 1999, 110(20): 9877-9886.
87. Honig, B., Sharp, K.A., and Yang, A.-S. Macroscopic models of aqueous solutions: biological and chemical applications. [J]. J. Phys. Chem. , 1993, 97: 1101-1109.
88. Tannor, D.J., Marten, B., Murphy, R., Friesner, R.A., Sitkoff, D., Nicholls, D.A., Ringnalda, M., Goddard, W.A., and Honig, B. Accurate first principles calculation of molecular charge distributions and solvation energies from ab initio quantum mechanics and continuum dielectric theory [J]. J. Am. Chem. Soc., 1994, 116: 11875-11882.
89.陈正隆,徐为人,汤立达.分子模拟的理论与实践[M].北京:化学工业出版社化学工业出版社, 2007.
90.徐筱杰,侯廷军,乔学斌,章威.计算机辅助药物分子设计[M].北京:化学工业出版社, 2004.
91. Still, W.C., Tempczyk, A., Hawley, R.C., and Hendrickson, T. Semianalytical treatment of solvation for molecular mechanics and dynamics [J]. J. Am. Chem. Soc., 1990, 112(16): 6127-6129.
92. Onufriev, A., Bashford, D., and Case, D.A. Modification of the generalized Born model suitable for macromolecules [J]. J. Phys. Chem. B, 2000, 104(15): 3712-3720.
93. Hawkins, G.D., Cramer, C.J., and Truhlar, D.G. Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. [J]. J. Phys. Chem., 1996, 100: 19824-19839
94. Schaefer, M. and Karplus, M. A comprehensive analytical treatment of continuum electrostatics [J]. J. Phys. Chem., 1996, 100(5): 1578-1599.
95. Bashford, D. and Case, D.A. Generalized Born models of macromolecular solvation effects [J]. Annu. Rev. Phys. Chem., 2000, 51: 129-152.
96. Schaefer, M. and Froemmel, C. A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution [J]. J. Mol. Biol., 1990, 216(4): 1045-1066.
97. Onufriev, A., Bashford, D., and Case, D.A. Exploring protein native states and large-scale conformational changes with a modified generalized Born model [J]. Proteins, 2004, 55(2): 383-394.
98. Kohl, N.E., Emini, E.A., Schleif, W.A., Davis, L.J., Heimbach, J.C., Dixon, R.A.F., Scolnick, E.M., and Sigal, I.S. Active human immunodeficiency virus protease is required for viral infectivity [J]. Proc. Natl. Acad. Sci. U.S.A., 1988, 85: 4686-4690.
99. McQuade, T.J., Tomasselli, A.G., Liu, L., Karacostas, B., Moss, B., Sawyer, T.K., Heinrikson, R.L., and Tarpley, W.G. A Synthetic HIV-1 Protease Inhibitor with Antiviral Activity Arrests HIV-Like Particle Maturation [J]. Science, 1990, 247: 454-456.
100. Wlodawer, A. Rational approach to AIDS drug design through structural biology [J]. Annu. Rev. Med. , 2002, 53: 595-614.
101. Miller, M., Jaskolski, M., Rao, J.K., Leis, J., and Wlodawer, A. Crystal structure of a retroviral protease proves relationship to aspartic protease family [J]. Nature (London), 1989, 337(6207): 576-579.
102. Navia, M.A., Fitzgerald, P.M., McKeever, B.M., Leu, C.T., Heimbach, J.C., Herber, W.K., Sigal, I.S., Darke, P.L., and Springer, J.P. Three-dimensional Structure of Aspartyl Protease from Human Immunodeficiency Virus HIV-1 [J]. Nature (London), 1989, 337(6208): 615-620.
103. Wlodawer, A., Miller, M., Sathyanarayana, M.J.B.K., Baldwin, E., Weber, I.T., Selk, L.M., Clawson, L., Schneider, J., and Kent, S.B. Conserved Folding in Retroviral Proteases - Crystal-Structure of a Synthetic HIV-1 Protease [J]. Science, 1989, 245: 616-621.
104. Lapatto, R., Blundell, T., Hemmings, A., and et al. X-ray analysis of HIV-1 proteinase at 2.7A resolution confirms structural homology among re-troviral enzymes [J]. Nature (London), 1989, 342: 299-302.
105. Kempf, D.J., Marsh, K.C., Denissen, J.F., and et al. ABT-538 is a potent inhibitor of human immunodeficiency virus protease and has high oral bioavailability in humans [J]. Proc. Natl. Acad. Sci. U.S.A., 1995, 92(7): 2484–2488.
106. Kempf, D.J., Marsh, K.C., Denissen, J.F., and et al. ABT-538 is a potent inhibitor of human immunodeficiency virus protease and has high oral bioavailability in humans [J]. Proc. Natl. Acad. Sci. U.S.A. , 1995, 92(7): 2484–2488.
107. Bayly, C.I., Cieplak, P., Cornell, W.D., and Kollman, P.A. Application of RESP Charges to Calculate Conformational Energies, Hydrogen Bond Energies, and Free Energies of Solvation [J]. J. Phys. Chem., 1993, 97(21): 10269-10280.
108. Duan, Y., Wu, C., Chowdhury, S., and et al. A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations [J]. J. Comput. Chem., 2003, 24(16): 1999-2012.
109. Ryckaert , J.P., Ciccotti, G., and Berendsen, H.J.C. Numerical integration of the cartesian equations of motion of a system with constrains: molecular dynamics of n-alkanes [J]. J. Comput. Phys. , 1977, 23: 327-341.
110. Lu, Y.P., Yang, C.Y., and W, S.M. Binding free energy contributions of interfacial waters in HIV-1 protease/inhibitor complexes [J]. J. Am. Chem. Soc., 2006, 128(36): 11830-11839.
111. Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., and Karplus,M. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations [J]. J. Comp. Chem., 1983, 4(2): 187-217.
112. Pearlman, D.A., Case, D.A., Caldwell, J.W., Ross, W.S., Cheatham, T.E., DeBolt, S., Ferguson, D., Seibel, G., and Kollman, P.A. AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules [J]. Comp. Phys. Commun., 1995, 91: 1-41.
113. Hagler, A.T., Huler, E., and Lifson, S. Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals [J]. J. Am. Chem. Soc., 1974, 96(17): 5319-5327.
114. Nemethy, G., Pottle, M.S., and Scheraga, H.A. Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions, and hydrogen bond interactions for the naturally occurring amino acids [J]. J. Phys. Chem., 1983, 87: 1883-1887.
115. Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., Dinola, A., and Haak, J.R. Molecular dynamics with coupling to an external bath [J]. J. Chem. Phys., 1984, 81(8): 3684-3690.
116. Warshel, A., Kato, M., and Pisliakov, A.V. Polarizable force fields: History, test cases, and prospects [J]. J. Chem. Theor. Comp., 2007, 3(6): 2034-2045.
117. Zwanzig, R.W. High-temperature equation of state by a perturbation method [J]. J. Chem. Phys., 1954, 22: 1420-1426.
118. Kirkwood, J.G. Statistical Mechanics of Fluid Mixtures [J]. J. Chem. Phys., 1935, 3: 300-313.
119. ?qvist, J., Medina, C., and Samuelsson, J.E. A new method for predicting binding affinity in computer-aided drug design [J]. Protein Engineering, 1994, 7(3): 385-391.
120. Srinivasan, J., Cheatham, T.E., Cieplak, P., Kollman, P.A., and Case, D.A. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate - DNA helices [J]. J. Am. Chem. Soc., 1998, 120(37): 9401-9409.
121. Simonson, T., Carlsson, J., and Case, D.A. Proton binding to proteins: pK(a) calculations with explicit and implicit solvent models [J]. J. Am. Chem. Soc., 2004, 126(13):4167-4180.
122. Kollman, P.A. Free Energy Calculations: Applications to Chemical and Biochemical Phenomena [J]. Chem. Rev., 1993, 93(7): 2395-2417.
123. Su, Y., Gallicchio, E., Das, K., Arnold, E., and Levy, R.M. Linear interaction energy (LIE) models for ligand binding in implicit solvent: Theory and application to the binding of NNRTIs to HIV-1 reverse transcriptase [J]. J. Chem. Theor. Comp., 2007, 3: 256-277.
124. JonesHertzog, D.K. and Jorgensen, W.L. Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method [J]. J. Med. Chem., 1997, 40(10): 1539-1549.
125. Wang, W., Lim, W.A., Jakalian, A., Wang, J., Wang, J.M., Luo, R., Bayly, C.T., and Kollman, P.A. An analysis of the interactions between the Sem-5 SH3 domain and its ligands using molecular dynamics, free energy calculations, and sequence analysis [J]. J. Am. Chem. Soc., 2001, 123: 3986-3994.
126. Gouda, H., Kuntz, I.D., Case, D.A., and Kollman, P.A. Free energy calculations for theophylline binding to an RNA aptamer: MM-PBSA and comparison of thermodynamic integration methods [J]. Biopolymers, 2003, 68(1): 16-34.
127. Massova, I. and Kollman, P.A. Computational alanine scanning to probe protein-protein interactions: A novel approach to evaluate binding free energies [J]. J. Am. Chem. Soc., 1999, 121(36): 8133-8143.
128. Reyes, C.M. and Kollman, P. A. Structure and thermodynamics of RNA-protein binding: Using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change [J]. J. Mol. Biol., 2000, 297(5): 1145-1158.
129. Chong, L.T., Duan, Y., Wang, L., Massova, I., and Kollman, P.A. Proc. Natl. Acad. Sci. U.S.A. [J]. Molecular dynamics and free-energy calculations applied to affinity maturation in antibody 48G7, 1999, 96(25): 14330-14335.
130. Woo, H.J. and Roux, B. Calculation of absolute protein-ligand binding free energy from computer simulations [J]. Proc. Natl. Acad. Sci. U.S.A. , 2005, 102(19): 6825-6830.
131. Pearlman, D.A. Evaluating the molecular mechanics Poisson-Boltzmann surface area free energy method using a congeneric series of ligands to p38 MAP kinase [J]. J. Med. Chem., 2005, 48(24): 7796-7807.
132. Kuhn, B., Gerber, P., Schulz-Gasch, T., and Stahl, M. Validation and use of the MM-PBSA approach for drug discovery [J]. J. Med. Chem., 2005, 48(12): 4040-4048.
133. Wang, J.M., Wolf, R.M., Caldwell, J.W., Kollman, P.A., and Case, D.A. Development and testing of a general amber force field [J]. J. Comput. Chem., 2004, 25(9): 1157-1174.
134. Tan, C.H., Yang, L.J., and Luo, R. How well does Poisson-Boltzmann implicit solvent agree with explicit solvent? A quantitative analysis [J]. J. Phys. Chem. B., 2006, 110(37): 18680-18687.
135. Halgren, T.A. Polarizable force fields [J]. Curr. Opin. Struct. Biol., 2001, 11(2): 236-242.
136. Kaminski, G.A., Stern, H.A., Berne, B.J., Friesner, R.A., Cao, Y.X.X., Murphy, R.B., Zhou, R.H., and Halgren, T.A. Development of a polarizable force field for proteins via ab initio quantum chemistry: first-generation model and gas phase tests [J]. J. Comput. Chem. , 2002, 23: 1515-1531.
137. Jorgensen, W.L. Special issue on polarization [J]. J. Chem. Theory Comput., 2007, 3(6): 1877-2145
138. Bayly, C.I., Cieplak, P., Cornell, W., and Kollman, P.A. A wellbehaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model [J]. J. Phys. Chem., 1993, 97(40): 10269-10280.
139. Cornell, W.D., Cieplak, P., Bayly, C.I., and Kollman, P.A. [J]. J. Am. Chem. Soc., 1993, 115: 9620.
140. Ji, C. and Zhang, J.Z.H. Protein polarization is critical to stabilizing AF-2 and Helix-2′domains in ligand binding to PPARγ[J]. J. Am. Chem. Soc., 2008, 130(50): 17129-17133.
141. Ji, C., Mei, Y., and Zhang, J.Z.H. Developing polarized protein-specific for protein dynamics: MD free energy calculation of Pka shifts for Asp26/Asp20 in thioredoxin [J]. Biophys. J., 2008, 95: 1080-1088.
142. Rocchia, W., Sridharan, S., Nicholls, A., Alexov, E., Chiabrera, A., and Honig, B. Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects [J]. J. Comput. Chem., 2002, 23: 128-137.
143. Kabsch, W. and Sander, C. Dictionary of protein secondary structure: Pattern recognitionof hydrogen-bonded and geometrical features [J]. Biopolymers, 1983, 22(12): 2577-2637.
144. Zhou, R. Free energy landscape of protein folding in water: explicit vs. implicit solvent [J]. Proteins: Struct.,Funct., Genet. , 2003, 53(2): 148-161.
145. Pokala, N. and Handel, T.M. Review: protein design—where we were, where we are, where we're going [J]. J. Struct. Biol., 2001, 134(2-3): 269-281.
146. Ma, B., Lii, J.-H., and Allinger, N.L. Molecular polarizabilities and Induced Dipole Moments in Molecular Mechanics [J]. J. Comp. Chem. , 2000, 21: 813-825.
147. Wroblewska, L. and Skolnick, J. Can a physics-based, all-atom potential find a protein's native structure among misfolded structures? I. Large scale amber benchmarking [J]. J. Comput. Chem. , 2007, 28(12): 2059-2066.
148. Ji, C.G. and Zhang, J.Z.H. Electronic Polarization Is Important in Stabilizing the Native Structures of Proteins [J]. The journal of physical chemistry. B, 2009, 113(49): 16059-16064
149. Weiser, J.R., Shenkin, P.S., and Still, W.C. Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO) [J]. J. Comput. Chem. , 1999, 20(12): 217-230.
150. Mirsky, A.E. and Pauling, L. On the structure of native, denatured, and coagulated proteins [J]. Proc. Natl. Acad. Sci. U.S.A., 1936, 22: 439-447.
151. Berg, B.A. and Neuhaus, T. Multicanonical algorithms for first order phase transition [J]. Phys. Lett. B., 1991, 267: 249-253.
152. Berg, B.A. and Neuhaus, T. Multicanonical ensemble: A new approach to simulate first-order phase transitions [J]. Phys. Rev. Lett., 1992, 68(1): 9-12.
153. Kumar, S., Bouzida, D., Swendsen, R.H., Kollman, P.A., and Rosenberg, J.M. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method [J]. J. Comput. Chem., 1992, 13(8): 1011-1021.
154. Mitsutake, A., Sugita, Y., and Okamoto, Y. Generalized-Ensemble algorithms for molecular simulations of biopolymers [J]. Biopolymers 2001, 60(2): 96-123.
155. Swendsen, R.H. and Wang, J.S. Replica Monte-Carlo simulation of spin-glasses [J]. Phys. ReV. Lett., 1986, 57(21): 2607-2609.
156. Hukushima, K. and Nemoto, K. Exchange Monto carlo method and application to spinglass simulations [J]. J. Phys. Soc., 1996, 65: 1604-1608.
157. Tesi, M.C., van Rensburg, E.J.J., Orlandini, E., and Whittington, S.G. Monte Carlo study of the interacting self-avoiding walk model in three dimensions [J]. J. Stat. Phys., 1996, 82: 155-181.
158. Hansmann, U.H.E. Parallel tempering algorithm for conformational studies of biological molecules [J]. Chem. Phys. Lett., 1997, 281: 140-150.
159. Neidigh, J.W., Fesinmeyer, R.M., and Andersen, N.H. Designing a 20-residue protein [J]. Nat. Struct. Biol. , 2002, 9(6): 425-430.
160. Qiu, L., Pabit, S.A., Roitberg, A.E., and Hagen, S.J. Smaller and faster:The 20-residue Trp-cage protein folds in 4μs [J]. J. Am. Chem. Soc., 2002, 124(44): 12952-12953.
161. Simmerling, C., Strockbine, B., and Roitberg, A.E. All-Atom structure prediction and folding simulations of a stable protein [J]. J. Am. Chem. Soc., 2002, 124(38): 11258-11259.
162. Snow, C.D., Zagrovic, B., and Pande, V.S. The Trp Cage: Folding kinetics and unfolded state topology via molecular dynamics simulations [J]. J. Am. Chem. Soc., 2002, 124(49): 14548-14549.
163. Chowdhury, S., Lee, M.C., Xiong, G., and Duan, Y. Ab initio folding simulation of the Trp-cage mini-protein approaches NMR resolution [J]. J. Mol. Biol., 2003, 327(3): 711-717.
164. Chen, J., Im, W., and L.Brooks, C. Balancing solvation and intramolecular interactions: toward a consistent generalized born force field [J]. J. Am. Chem. Soc. , 2006, 128(11): 3728-3736.
165. Pitera, J.W. and Swope, W. Understanding folding and design: Replica-exchange simulations of“Trp-cage”miniproteins [J]. Proc. Natl. Acad. Sci. U. S. A. , 2003, 100(13): 7587-7592.
166. Zhou, R.H. Trp-cage: Folding free energy landscape in explicit water [J]. Proc. Natl. Acad. Sci. U. S. A., 2003, 100(23): 13280-13285.
167. Paschek, D., Nymeyer, H., and Garc?′a, A.E. Replica exchange simulation of reversible folding/unfolding of the Trp-cage miniprotein in explicit solvent: On the structure and possible role of internal water [J]. J. Struct. Biol. , 2007, 157(3): 524-533.
168. Shell, M.S., Ritterson, R., and Dill, K.A. A Test on peptide stability of AMBER force fields with implicit solvation [J]. J. Phys. Chem. B. , 2008, 112(22): 6878-6886.
169. Hawkins, G.D., Cramer, C.J., and Truhlar, D.G. Pairwise solute descreening of solute charges from a dielectric medium [J]. Chem. Phys. Lett., 1995, 246(1-2): 122-129.
170. Tsui, V. and Case, D.A. Theory and applications of the generalized Born solvation model in macromolecular simulations [J]. Biopolymers, 2001, 56(4): 275-291.
171. Sugita, Y. and Okamoto, Y. Replica-exchange molecular dynamics method for protein folding [J]. Chem. Phys. Lett., 1999, 314(1-2): 141-151.
172. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. Equation of state calculations by fast computing machines [J]. J. Chem. Phys., 1953, 21: 1087-1092.
173. Zhou, R.H. and Berne, B.J. Can a continuum solvent model reproduce the free energy landscape of aβ-hairpin folding in water? [J]. Proc. Natl. Acad. Sci. U. S. A., 2002, 99(20): 12777-12782
174. Roe, D.R., Hornak, V., and Simmerling, C. Folding cooperativity in a three-strandedβ-sheet model [J]. J. Mol. Biol. , 2005, 352(2): 370-381.
175. Zhang, W., Wu, C., and Duan, Y. Convergence of replica exchange molecular dynamics [J]. J. Chem. Phys., 2005, 123(15): 154105.
176. Sugita, Y., Kitao, A., and Okamoto, Y. Multidimensional replica exchange method for free-energy calculations [J]. J. Chem. Phys. , 2000, 113(15): 6042-6051.
177. Garc′?a, A.E. and Sanbonmatsu, K.Y. Exploring the energylandscape of a beta-hairpin in explicit solvent [J]. Proteins: Struct., Funct., Genet., 2001, 42(3): 345-354
178. Zhou, R.H., Berne, B.J., and Germain, R. The free energy landscape forβhairpin folding in explicit water [J]. Proc. Natl. Acad. Sci. U. S. A., 2001, 98(26): 14931-14936.
179. Garc′?a, A.E. and Sanbonmatsu, K.Y.α-Helical stabilization by side chain shielding of backbone hydrogen bonds [J]. Proc. Natl. Acad. Sci. U. S. A. , 2002, 99(5): 2782-2787.
180. Karanicolas, J. and Brooks, C.L. The structural basis for biphasic kinetics in the folding of the WW domain from a forminbinding protein: Lessons for protein design? [J]. Proc. Natl. Acad. Sci. U. S. A. , 2003, 100(7): 3954-3959.
181. Feig, M., Karanicolas, J., and Brooks, C.L. MMTSB tool set: Enhanced sampling andmultiscale modeling methods for applications in structural biology [J]. J. Mol. Graphics Modell., 2004, 22(5): 377-395.
182. Kinnear, B.S., Jarrold, M.F., and Hansmann, U.H.E. All-atom generalized-ensemble simulations of small proteins [J]. J. Mol. Graphics Modell. , 2004, 22(5): 397-403.
183. Jang, S., Kim, E., and Pak, Y. Free energy surfaces of miniproteins with aββαmotif: replica exchange molecular dynamics simulation with an implicit solvation model [J]. Proteins: Struct., Funct., Bioinformatics, 2006, 62: 663 -671.
184. Lei, H., Wu, C., Liu, H., and Duan, Y. Folding free-energy landscape of villin headpiece subdomain from molecular dynamics simulations [J]. Proc. Natl. Acad. Sci. U. S. A., 2007, 104(12): 4925-4930.
185. van der. Spoel , D. and Seibert, M.M. Protein folding kinetics and thermodynamics from atomistic simulations [J]. Phys. Rev. Lett., 2006, 96(23): 238102.
186. Chowdhury, S., Lee, M.C., and Duan, Y. Characterizing the ratelimiting step of trp-cage folding by all-atom molecular dynamics simulations [J]. J. Phys. Chem. B., 2004, 108(36): 13855-13865.
187. Linhananta, A., Boer, J., and MacKay, I. The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage [J]. J. Chem. Phys., 2005, 122(11): 114901.
188. Juraszek, J. and Bolhuis, P.G. Sampling the multiple folding mechanisms of Trp-cage in explicit solvent [J]. Proc. Natl. Acad. Sci. U. S. A. , 2006, 103(43): 15859-15864
189. Juraszek, J. and Bolhuis, P.G. Rate constant and reaction coordinate of Trp-cage folding in explicit water [J]. Biophys. J . , 2008, 95 (9): 4246-4257.
190. Dobson, C.M. Protein Misfolding, Evolution and Disease [J]. Rrends Biochem. Sci., 1999, 24(9): 329-332.
191. Muchowski, P.J. Protein Misfolding, Amyloid Minireview Formation, and Neurodegeneration: A Critical Role for Molecular Chaperones? [J]. Neuron, 2002, 35(1): 9-12.
192. Slepoy, A., Singh, R.R.P., Pázmándi, F., Kulkarni, R.V., and Cox, D.L. Statistical Mechanics of Prion Diseases [J]. Phys. Rev. Lett. , 2001, 87: 058101-1-4.
193. Baumketner, A. and Shea, J.E. The Structure of The Alzheimer, Amyloid Beta 10-35 Peptide Probed Through Replica Exchange Molecular Dynamics Simulations In ExplicitSolvent [J]. J. Mol. Biol., 2007, 366: 275-285.
194. Berg, B.A. and Neuhaus, T. Multicanonical Algorithms for First Order Phase Transition [J]. Phys. Lett. B., 1991, 267: 249.
195. Berg, B.A. and Neuhaus, T. Multicanonical ensemble: A new approach to simulate first-order phase transitions [J]. Phys. Rev. Lett., 1992, 68: 9.
196. Brooks, C.I. Protein and Peptide Folding Explored with Molecular Simulations [J]. Acc. Chem. Res., 2002, 35: 447-454.
197. Chowdhury, S., Lei, H.X., and Duan, Y. Denatured State Ensemble and Early Stage of Folding of the G29A Mutant of B-domain of Protein A: An All Atom Molecular Dynamics Study [J]. J. Phys. Chem. B, 2005, 109: 9073-9081.
198. Daggett, V. Molecular Dynamics Simulations of The Protein Unfolding/Folding Reaction [J]. Acc. Chem. Res., 2002, 35: 422-449.
199. Duan, Y. and Kollman, P.A. Pathways to a Protein Folding Intermediate Observed in a 1-microsecond Simulation in Aqueous Solution [J]. Science, 1998, 282: 740-744.
200. Duan, Y., Wang, L., and Kollman, P.A. The Early Stage of Folding of Villin Headpiece Subdomain Observed In a 200-nanosecond Fully Solvated Molecular Dynamics Simulation [J]. Proc. Natl. Acad. Sci. U.S.A., 1998, 95(17): 9897-9902.
201. Eleftheriou, M., Germain, R.S., Royyuru, A.K., and Zhou, R. Thermal Denaturing of Mutant Lysozyme With Both The OPLSAA and The CHARMM Force Fields [J]. J. Am. Chem. Soc., 2006, 128: 13388-13395.
202. Juraszek, J. and Bolhuis, P.G. Sampling the Multiple Folding Mechanisms of Trp-cage In Explicit Solvent [J]. Proc. Natl. Acad. Sci., 2006, 103: 15859-15864.
203. Lei, H., Wang, Z.-X., Wu, C., and Duan, Y. Dual Folding Pathways of anα/βProtein From All-Atom ab initio Folding Simulations [J]. J. Chem. Phys., 2009, 131(16): 165105-1-165105-7.
204. Lei, H., Wu, C., Liu, H., and Duan, Y. Folding Free-Energy Landscape of Villin Headpiece Subdomain From Molecular Dynamics Simulations [J]. PNAS, 2007, 104(12): 4925-4930.
205. Mitsutake, A., Sugita, Y., and Okamoto, Y. Generalized-Ensemble Algorithms for Molecular Simulations of Biopolymers [J]. Biopolymers, 2001, 60: 96-123.
206. Nelson, E.D. and Grishin, N.V. Folding Domain B of Protein A On a Dynamically Partitioned Free Energy Landscape [J]. Proc. Natl. Acad. Sci. U. S. A., 2008, 105: 1489.
207. Pande, V.S., Baker, I., Chapman, J., Elmer, S.P., Khaliq, S., Larson, S.M., Rhee, Y.M., Shirts, M.R., Snow, C.D., Sorin, E.J., and Zagrovic, B. Atomistic Protein Folding Simulations On The Submillisecond Time Scale Using Worldwide Distributed Computing [J]. Biopolymers, 2003, 68: 91-109.
208. Paschek, D., Nymeyer, H., and Garcia, A.E. Replica Exchange Simulation of Reversible Folding/Unfolding of The Trp-cage Miniprotein In Explicit Solvent: On The Structure And Possible Role of Internal Water [J]. J. Struct. Biol., 2007, 157: 524-533.
209. Periole, X. and Mark, A.E. Convergence and Sampling Efficiency In Replica Exchange Simulations of Peptide Folding In Explicit Solvent [J]. J. Chem. Phys., 2007, 126: 014903.
210. Scheraga, H.A., Khalili, M., and Liwo, A. Protein-Folding Dynamics: Overview of Molecular Simulation Techniques [J]. Ann. ReV. Phys. Chem., 2007, 58: 57-83.
211. Simmerling, C., Strockbine, B., and Roitberg, A. All-atom Structure Prediction and Folding Simulations of A Stable Protein [J]. J. Am. Chem. Soc., 2002, 124: 11258-11259.
212. Wickstrom, L., Okur, A., Song, K., Hornak, V., Raleigh, D.P., and Simmerling, C.L. The Unfolded State of The Villin Headpiece Helical Subdomain: Computational Studies of The Role of Locally Stabilized Structure [J]. J. Mol. Biol., 2006, 360: 1094-1107.
213. Xu, W.X., Lai, T.F., Yang, Y., and Mu, Y.G. Reversible Folding Simulation By Hybrid Hamiltonian Replica Exchange [J]. J. Chem. Phys., 2008, 128: 175105.
214. Yoda, T., Sugita, Y., and Okamoto, Y. Cooperative Folding Mechanism of A Beta-hairpin Peptide Studied By a Multicanonical Replica-Exchange Molecular Dynamics Simulation [J]. Proteins: Struct.,Funct., Bioinformatics 2007, 66: 846-859.
215. Zhou, R.H. Trp-cage: Folding Free Energy Landscape in Explicit Water [J]. Proc. Natl. Acad. Sci. U. S. A., 2003, 100(23): 13280-13285.
216. Zhou, R.H., Berne, B.J., and Germain, R. The Free Energy Landscape forβHairpin Folding in Explicit Water [J]. Proc. Natl. Acad. Sci. U.S.A., 2001, 98(26): 14931–14936
217. Williams, S., Causgrove, T.P., Gilmanshin, R., Fang, K.S., Callender, R.H., and Dyer, W.H.W.R.B. Fast Events in Protein Folding: Helix Melting and Formation in a SmallPeptide [J]. Biochemistry, 1996, 35: 691-697.
218. Mu?oz, V., Thompson, P.A., Hofrichter, J., and Eaton, W.A. Folding Dynamics and Mechanism ofβ-Hairpin Formation [J]. Nature, 1997, 390: 196-199.
219. Duan, L.L., Zhang, Y.M.Q.G., and Zhang, J.Z.H. Intra-Protein hydrogen bonding is dynamically stabilized by electronic polarization [J]. J. Chem. Phys., 2009, 130(11): 115102.
220. Ji, C., Mei, Y., and Zhang, J.Z.H. Developing Polarized Protein-Specific Charges for Protein Dynamics: MD Free Energy Calculation of pKa Shifts for Asp26/Asp20 in Thioredoxin [J]. Biophys. J . 2008, 95: 1080-1088.
221. Ji, C.G. and Zhang, J.Z.H. Protein Polarization Is Critical to Stabilizing AF-2 and Helix-2′Domains in Ligand Binding to PPAR-γ[J]. J. Am. Chem. Soc., 2008, 130: 17129.
222. Tong, Y., Ji, C.G., Mei, Y., and Zhang, J.Z.H. Simulation of NMR Data Reveals That Proteins’Local Structures Are Stabilized by Electronic Polarization [J]. J. Am. Chem. Soc., 2009, 131(24): 8636-8641.
223. Ji, C.G. and Zhang, J.Z.H. Electronic Polarization Is Important in Stabilizing the Native Structures of Proteins [J]. The journal of physical chemistry. B, 2009, 113(49): 16059-16064
224. Ji, C.G. and Zhang, J.Z.H. NMR Scalar Coupling Constant Reveals That Intraprotein Hydrogen Bonds Are Dynamically Stabilized by Electronic Polarization [J]. J. Phys. Chem. B, 2009, 113(42): 13898-13900.
225. Pantoja, U.D., Pastor, M.T., Salgado, J., Pineda, L.A., and Pérez, P.E. Design of A Bivalent Peptide With Two Independent Elements of Secondary Structure Able to Fold Autonomously [J]. J. Pept. Sci., 2008, (14): 845-854.
226. Lin, E. and Shell, M.S. Convergence and Heterogeneity in Peptide Folding with Replica Exchange Molecular Dynamics [J]. J. Chem.Theory Comput., 2009, 5: 2062-2073.
227. Onufriev, A., Bashford, D., and Case, D.A. A Modification of the Generalized Born Model Suitable for Macromolecules [J]. J. Phys. Chem. B, 2000, 104: 3712.
228. Kim, E., Jang, S., and Pak, Y. Consistent Free Energy Landscapes and Thermodynamic Properties of Small Proteins Based on A Single All-Atom Force Field Employing anImplicit Solvation [J]. J. Chem. Phys., 2007, 127: 145104.
229. Kim, E., Jang, S., and Pak, Y. Direct Folding of VariousαandβStrands Using Replica Exchange Molecular Dynamics Simulation [J]. J. Chem. Phys., 2008, 128: 175104.
230. Onufriev, A., Bashford, D., and Case, D.A. Exploring Protein Native States and Large-Scale Conformational Changes with A Modified Generalized Born Model [J]. Proteins: Struct., Funct., Bioinformatics, 2004, 55: 383-394.
231. Ryckaert, J.P., Ciccotti, G., and Berendsen, H.J.C. Numerical integration of the Cartesian equations of motion of a system with constrains: Molecular dynamics of n-alkanes [J]. J. Comput. Phys., 1977, 23: 327.
232. Pastor, R.W., Brooks, B.R., and Szabo, A. An Analysis of The Accuracy of Langevin and Molecular Dynamics Algorithm [J]. Mol. Phys., 1988, 65: 1409.
233. McDonald, I.K. and Thornton, J.M. Satisfying hydrogen bonding potential inproteins [J]. J. Mol. Bio., 1994, 238(5): 777-793.
234. Shao, J., Tanner, S.W., Nephi Thompson, and Cheatham III, T.E. Clustering Molecular Dynamics Trajectories: 1. Characterizing the Performance of Different Clustering Algorithms [J]. J. Chem. Theroy Comput., 2007, 3(6): 2312-2334.
235. Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., and Kollman, P.A. Multidimensional Free-Energy Calculations Using the Weighted Histogram Analysis Method [J]. J. Comput. Chem., 1995, 16(11): 1339-1350.
236. Roux, B. The Calculation of The Potential of Mean Force Using Computer Simulations [J]. Comput. Phys. Comm, 1995, 91(1-3): 275-282.
2. MacKerell, A.D., Jr., Bashford, D., Bellott, R.L., Dunbrack, R.L., Jr., Evanseck, J.D., Field, M.J., Fischer, S., Gao, J., Guo, H., Ha, S., Joseph‐ McCarthy, D., Kuchnir, L., Kuczera, K., Lau, F.T.K., Mattos, C., Michnick, S., Ngo, T., Nguyen, D.T., Prodhom, B., Reiher, W.E., III, R., B., Schlenkrich, M., Smith, J.C., Stote, R., Straub, J., Watanabe, M., Wiorkiewicz‐K uczera, J., Yin, D., and Karplus, M. All-atom empirical potential for molecular modeling and dynamics studies of proteins [J]. J. Phys. Chem. B., 1998, 102(18): 3586-3616.
3. Jorgensen, W.L., Maxwell, D.S., and J. Tirado-Rives. Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids [J]. J. Am. Chem. Soc. , 1996, 118(45): 11225-11236.
4. Kaminski, G.A., Friesner, R.A., Tirado-Rives, J., and Jorgensen, W.L. Evaluation and reparameterization of the OPLS‐ AA force field for proteins via comparison with accurate quantum chemical calculations on peptides [J]. J. Phys. Chem. B. , 2001, 105(28): 6474-6487.
5. Warshel, A. and Levitt, M. Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme [J]. J. Mol. Biol., 1976, 103(2): 227-249.
6. Singh, U.C. and Kollman, P. A Combined Ab Initio Quantum Mechanical and ... Protonation of Polyethers [J]. J. Comput. Chem., 1986, 7(6): 718-730.
7. Field, M.J., Bash, P.A., and Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations [J]. J. Comput. Chem., 1990, 11(6): 700–733.
8. Gao, J. and Xia, X. A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations [J]. Science, 1992, 258(5082): 631-635.
9. Stanton, R.V., Hartsough, D.S., and Merz. Jr, K.M. Calculation of Solvation FreeEnergies Using a Density Functional/Molecular Dynamics Coupled Potential [J]. J. Phys. Chem. B., 1993, 97: 11868-11870.
10. Thery, V., Rinaldi, D., and Rivail, J.-L. Quantum mechanical computations on very large molecular-systems-the local self-consistent-field method [J]. J. Comput. Chem. , 1994, 15(3): 269-282.
11. Maseras, F. and Morokuma, K. A new‘ab initio+molecular mechanics’geometry optimization scheme of equilibrium structures and transition states [J]. J. Comput. Chem., 1995, 16: 1170-1179.
12. Bakowies, D. and Thiel, W. Hybrid Models for Combined Quantum Mechanical and Molecular Approaches [J]. J. Phys. Chem. B., 1996, 100(25): 10580-10594.
13. Eurenius, K.P., Charfield, D.C., Brooks, B.R., and Hodoscek, M. Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations [J]. Int. J. Quantum Chem., 1996, 60(6): 1189-1200.
14. Bersuker, I.B., Leong, M.K., and Pearlman, J.E.B.R.S. A Method of Combined QuantumMechanical (QM)/Molecular Mechanics (MM) Treatment of Large Polyatomic Systems with Charge Transfer Between the QM and MM Fragments [J]. Int. J. Quantum Chem., 1997, 63(6): 1051–1063
15. Gao, J., Amara, P., Alhambra, C., and Field, M.J. A generalized hybrid orbital (gho) method for the treatment of boundary atoms in combined qm/mm calculations [J]. J. Phys. Chem. A, 1998, 102(24): 4714-4721.
16. Antes, I. and Thiel, W. Adjusted Connection Atoms for Combined Quantum Mechanical and Molecular Mechanical Methods [J]. J. Phys. Chem. A, 1999, 103(46): 9290-9295.
17. Lyne, P.D., Hodoscek, M., and Karplus, M. A hybrid QM/MM potential employing Hartree-Fock or density functional methods in the quantum region [J]. J. Phys. Chem. A 1999, 103: 3462-3471.
18. Monard, G. and Merz Jr., K.M. Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems [J]. Acc. Chem. Res., 1999, 32: 904-911.
19. Philipp, D.M. and Friesner, R.A. Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide [J]. J. Comput. Chem., 1999, 20: 1468-1494.
20. Zhang, Y., Lee, T.-S., and Yang, W. A Pseudobond Approach to Combining Quantum Mechanical and Molecular Mechanical Methods [J]. J. Chem. Phys., 1999, 110: 46-54.
21. Amara, P., Field, M.J., Alhambra, C., and Gao, J. The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives [J]. Theor. Chem. Acc., 2000, 104(5): 336-343.
22. Kairys, V. and Jensen, J.H. QM/MM boundaries across covalent bonds: frozen LMO based approach for the Effective Fragment Potential method [J]. J. Phys. Chem. A 2000, 104: 6656-6665.
23. Reuter, N., Dejaegere, A., Maigret, B., and Karplus, M. Frontier bonds in QM/MM methods: a comparison of different approaches [J]. J. Phys. Chem. A, 2000, 104: 1720-1735.
24. Assfeld, X. and Rivail, J.-L. Quantum chemical computations on parts of large molecules: the ab initio local self consistent field method [J]. Chem. Phys. Lett., 1996, 263(1-2): 100-106.
25. Rosta, E., Klahn, M., and Warshel., A. Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions [J]. J. Phys. Chem. B, 2006, 110(6): 2934-2941.
26. Grater, F., Schwarzl, S.M., Dejaegere, A., Fischer, S., and Smith., J.C. Protein/ligand binding free energies calculated with quantum mechanics/molecular mechanics [J]. J. Phys. Chem. B, 2005, 109(20): 10474-10483.
27. Riccardi, D., Schaefer, P., and Cui.., Q. pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: A quantitative test of QM/MM protocols [J]. J. Phys. Chem. B, 2005, 109(37): 17715-17733.
28. Titmuss, S.J., Cummins, P.L., Bliznyuk, A.A., Rendell, A.P., and E.Gready, J. Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods applied to the study of enzume reactions [J]. Chem. Phys. Lett. , 2000, 320: 169-176.
29. Kohn, W. Density Functional Theory for Systems of Very Many Atoms,Proceedings of the 1994 Satellite Symposium on ``Thirty Years of Density Functional Theory'' [J]. Int. J. Quantum Chem., 1995, 56(4): 229-232.
30. Nunes, R.W. and Vanderbilt, D. Generalisation of the density-matrix method to a non-orthogonal basis [J]. Phys. Rev. B, 1994, 50(23): 17611-17614.
31. Dixon, S.L. and Merz Ji, K.M. Semiempirical Molecular Orbital Calculations with Linear System Size Scaling [J]. J. Chem. Phys., 1996, 104(17): 6643-6649.
32. Daniels, A.D., William, J.M., and Scuseria, G.E. Semiempirical methods with conjugate gradient density matrix search to replace diagonalization for molecular systems containing thousands of atoms [J]. J. Chem. Phys., 1997, 107(2): 425-431
33. Yokojima, S. and Chen, G.H. Linear-scaling localized-density-matrix method for the ground and excited states of one-dimensional molecular systems [J]. Chem. Phys. Lett., 1999, 300: 540-544.
34. Lee, T., York, D.M., and Yang., W. Linear-scaling semiempirical quantum calculations for macromolecules [J]. J. Chem. Phys., 1996, 105(7): 2744-2750.
35. York, D.M., Lee, T., and Yang., W. Parameterization and efficient implementation of a solvent model for linear-scaling semiempirical quantum mechanical calculations of biological macromolecules. [J]. Chem. Phys. Lett., 1996, 263: 297-306.
36. York, D.M., Lee, T., and Yang., W. Quantum mechanical treatment of biological macromolecules in solution using linear-scaling electronic structure methods [J]. Phys. Rev. Lett., 1998, 80(22): 5011-5014.
37. Stewart., J.J.P. Application of localized molecular orbitals to the solution of semiempirical self-consistent field equations [J]. Int. J. Quantum Chem., 1996, 58(2): 133-146.
38. Liang, W., Yokojima, S., and Chen., G. Generalized linear-scaling localized-density-matrix method [J]. J. Chem. Phys., 1999, 110(4): 1844-1855.
39. Gibson, A., Haydock, R., and LaFemina., J.P. Ab initio electronic-structure computations with the recursion method [J]. Phys. Rev. B, 1993, 47(15): 9229-9237.
40. Millam, J.M. and Scuseria., G.E. Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations [J]. J. Chem. Phys., 1997, 106(13): 5569-5577.
41. Challacombe, M. A simplified density matrix minimization for linear scaling self-consistent field theory [J]. J. Chem. Phys., 1999, 110(5): 2332-2342.
42. Galli, G. and Parrinello, M. Large scale electronic structure calculations [J]. Phys. Rev. Lett., 1992, 69(24): 3547-3550.
43. Kohn., W. Density Functional Theory for Systems of Very Many Atoms,Proceedings of the 1994 Satellite Symposium on ``Thirty Years of Density Functional Theory'' [J]. Int. J. Quantum Chem., 1995, 56(4): 229-232.
44. Yang, W. Direct calculation of electron density in density-functional theory: Implementation for benzene and a tetrapeptide [J]. Phys. Rev. A, 1991, 44(11): 7823-7826.
45. Ayala, P.Y. and Scuseria, G.E. Linear scaling second-order M?ller-Plesset theory in the atomic orbital basis for large molecular systems [J]. J. Chem. Phys., 1999, 110(8): 3660.
46. Sch¨utz, M., G. Hetzer, and Werner., H. Low-order scaling local electron correlation methods. I. Linear scaling local MP2 [J]. J. Chem. Phys., 1999, 111(13): 5691-5705.
47. Gadre, S.R., Shirsat, R.N., and Limaye., A.C. Molecular tailoring approach for simulation of electrostatic properties [J]. J. Phys. Chem. A, 1994, 98(37): 9165-9169.
48. Nakano, T., Kaminuma, T., Sato, T., Akiyama, Y., Uebayasi, M., and Kitaura, K. Fragment molecular orbital method: application to polypeptides [J]. Chem. Phys. Lett., 2000, 318(6): 614-618.
49. Fedorov, D.G. and Kitaura., K. The importance of three-body terms in the fragment molecular orbital method [J]. J. Chem. Phys., 2004, 120(15): 6832-6840.
50. Mochizuki, Y., Koikegami, S., Nakano, T., Amari, S., and Kitaura, K. Large scale MP2 calculations with fragment molecular orbital scheme [J]. Chem. Phys. Lett., 2004, 396: 473-479.
51. Deev, V. and Collins, M.A. Approximate ab initio energies by systematic molecular fragmentation [J]. J. Chem. Phys., 2005, 122(15): 154102.
52. Fedorov, D.G. and Kitaura., K. The three-body fragment molecular orbital method for accurate calculations of large systems [J]. Chem. Phys. Lett., 2006, 433(1-3): 182-187.
53. Yasuda, K. and Yamaki, D. The extension of the fragment molecular orbital method with the many-particle green’s function [J]. J. Chem. Phys., 2006, 125(15): 154101.
54. Li, W. and Li., S. Divide-and-conquer local correlation approach to the correlation energy of large molecules [J]. J. Chem. Phys., 2004, 121(14): 6649-6657.
55. Gao, A.M., Zhang, D.W., Zhang, J.Z.H., and Zhang, Y.K. An efficient linear scaling method for ab initio calculation of electron density of proteins [J]. Chem. Phys. Lett., 2004, 394: 293-297.
56. Mei, Y., Zhang, D.W., and Zhang., J.Z.H. New method for direct linear-scaling calculation of electron density of proteins [J]. J. Phys. Chem. A, 2005, 109: 2-5.
57. Chen, X.H. and Zhang, J.Z.H. Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation [J]. J. Chem. Phys., 2006, 125(4): 044903.
58. Chen, X.H., Zhang, Y.K., and Zhang, J.Z.H. MFCC-DM with pairwise interaction correction for quantum chemical study of protein [J]. Abstracts of Papers of the American Chemical Society, 2006, 231: 318.
59. Chen, X.H., Zhang, Y.K., and Zhang, J.Z.H. An efficient approach for ab initio energy calculation of biopolymers [J]. J. Chem. Phys., 2005, 122(18): 184105.
60. He, X. and Zhang, J.Z.H. A new method for direct calculation of total energy of protein [J]. J. Chem. Phys. , 2005, 122(3): 031103.
61. He, X. and Zhang, J.Z.H. The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy [J]. J. Chem. Phys., 2006, 124(18): 184703.
62. Chen, X.H. and Zhang, J.Z.H. MFCC-downhill simplex method for molecular structure optimization [J]. J. Theor. Comput. Chem., 2004, 3(3): 277.
63. Xiang, Y., Zhang, D.W., and Zhang, J.Z.H. Fully quantum mechanical energy optimization for protein-ligand structure [J]. J. Comput. Chem., 2004, 25(12): 1431-1437.
64. Zhang, D.W., Xiang, Y., Gao, A.M., and Zhang, J.Z.H. Quantum mechanical map for protein-ligand binding with application to beta-trypsin/benzamidine complex [J]. J. Chem. Phys. , 2004, 120(3): 1145-1148.
65. Zhang, D.W., Xiang, Y., and Zhang, J.Z.H. New advance in computational chemistry: Full quantum mechanical ab initio computation of streptavidin-biotin interaction energy [J]. J. Phys. Chem. B, 2003, 107(44): 12039-12041.
66. Zhang, D.W. and Zhang, J.Z.H. Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy [J]. J. Chem.Phys., 2003, 119(7): 3599-3605.
67. Zhang, D.W. and Zhang., J.Z.H. Full quantum mechanical study of binding of HIV-1 protease drugs [J]. Int. J. Quantum Chem., 2005, 103(3): 246-257.
68. He, X., Mei, Y., Xiang, Y., Zhang, D.W., and Zhang, J.Z.H. Quantum computational analysis for drug resistance of HIV-1 reverse transcriptase to nevirapine through point mutations [J]. Proteins, 2005, 61(2): 423-432.
69. Mei, Y., He, X., Xiang, Y., Zhang, D.W., and Zhang, J.Z.H. Quantum study of mutational effect in binding of efavirenz to HIV-1 RT [J]. Proteins, 2005, 59(3): 489-495.
70. Chen, X.H. and Zhang, J.Z.H. Theoretical method for full ab initio calculation of DNA/RNA-ligand interaction energy [J]. J. Chem. Phys., 2004, 120(24): 11386-11391.
71. Mei, Y., Ji, C.G., and Zhang, J.Z.H. A new quantum method for electrostatic solvation energy of protein [J]. J. Chem. Phys., 2006, 125(9): 094906.
72. Zhang, D.W., Chen, X.H., and Zhang, J.Z.H. Molecular caps for full quantum mechanical computation of peptide-water interaction energy [J]. J. Comput. Chem., 2003, 24(15): 1846-1852.
73. Chen, X.H., Zhang, D.W., and Zhang, J.Z.H. Fractionation of peptide with disulfide bond for quantum mechanical calculation of interaction energy with molecules [J]. J. Chem. Phys., 2004, 120(2): 839-844.
74. Zhang, D.W. and Zhang, J.Z.H. Quantum mechanical studies of HIV-1 protease inhibitors and drug design based on full ab initio MFCC computation [J]. Abstracts of Papers of the American Chemical Society, 2004, 228: u535.
75. Duan, L.L., Tong, Y., Mei, Y., Zhang, Q.G., and Zhang, J.Z.H. Quantum study of HIV-1 protease-bridge water interaction [J]. J. Chem. Phys., 2007, 127(14): 145101.
76. Ji, C.G., Mei, Y., and Zhang, J.Z.H. Developing Polarized Protein-Specific Charges for Protein Dynamics: MD Free Energy Calculation of pKa Shifts for Asp26/Asp20 in Thioredoxin [J]. Biophys. J., 2008, 95(3): 1080-1088.
77. Ji, C.G. and Zhang, J.Z.H. Protein polarization is critical to stabilizing AF-2 and Helix-2′domains in ligand binding to PPARγ[J]. J. Am. Chem. Soc. , 2008, 130(5): 17129-17133.
78. Mei, Y., Wu, E.L., Han, K.L., and Zhang, J.Z.H. Treating hydrogen bonding in ab initio calculation of biopolymers [J]. Int. J. Quantum Chem., 2006, 106(5): 1267-1276.
79. Fedorov, D.G. and Kitaura, K. On the accuracy of the 3-body fragment molecular orbital method (FMO) applied to density functional theory [J]. Chem. Phys. Lett., 2004, 389(1-3): 129-134.
80. Fedorov, D.G., Ishida, T., and Kitaura, K. Multilayer formulation of the fragment molecular orbital method (FMO). [J]. J. Phys. Chem. A, 2005, 109(11): 2638-2646.
81. Miertuˇs, S., Scrocco, E., and Tomasi, J. Electrostatic interaction of a solute with a continuum a direct utilization of ab initio molecular potentials for the prevision of solvent effects [J]. Chem. Phys., 1981, 55(1): 117-129.
82.朱权,傅克祥,李象远.非平衡溶剂化的连续介质模型和超快过程溶剂效应[J].高等学校化学学报, 2006, 27(2): 274-286.
83. Klamt, A. and Sch¨u¨urmann, G. Cosmo: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient [J]. J. Chem. Soc. Perkin. Trans., 1993, 2: 799-805.
84. Barone, V., Rienzo, F.D., Langella, E., Menziani, M.C., Regal, N., and Sola, M. A computational protocol to probe the role of solvation effects on the reduction potential of azurin mutants [J]. Proteins, 2006, 62(1): 262-269.
85. Barone, V. and Cossi, M. Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent mode [J]. J. Phys. Chem. A, 1998, 102(11): 1995-2001.
86. Cammi, R. and Mennucci, B. Linear response theory for the polarizable continuum model [J]. J. Chem. Phys., 1999, 110(20): 9877-9886.
87. Honig, B., Sharp, K.A., and Yang, A.-S. Macroscopic models of aqueous solutions: biological and chemical applications. [J]. J. Phys. Chem. , 1993, 97: 1101-1109.
88. Tannor, D.J., Marten, B., Murphy, R., Friesner, R.A., Sitkoff, D., Nicholls, D.A., Ringnalda, M., Goddard, W.A., and Honig, B. Accurate first principles calculation of molecular charge distributions and solvation energies from ab initio quantum mechanics and continuum dielectric theory [J]. J. Am. Chem. Soc., 1994, 116: 11875-11882.
89.陈正隆,徐为人,汤立达.分子模拟的理论与实践[M].北京:化学工业出版社化学工业出版社, 2007.
90.徐筱杰,侯廷军,乔学斌,章威.计算机辅助药物分子设计[M].北京:化学工业出版社, 2004.
91. Still, W.C., Tempczyk, A., Hawley, R.C., and Hendrickson, T. Semianalytical treatment of solvation for molecular mechanics and dynamics [J]. J. Am. Chem. Soc., 1990, 112(16): 6127-6129.
92. Onufriev, A., Bashford, D., and Case, D.A. Modification of the generalized Born model suitable for macromolecules [J]. J. Phys. Chem. B, 2000, 104(15): 3712-3720.
93. Hawkins, G.D., Cramer, C.J., and Truhlar, D.G. Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. [J]. J. Phys. Chem., 1996, 100: 19824-19839
94. Schaefer, M. and Karplus, M. A comprehensive analytical treatment of continuum electrostatics [J]. J. Phys. Chem., 1996, 100(5): 1578-1599.
95. Bashford, D. and Case, D.A. Generalized Born models of macromolecular solvation effects [J]. Annu. Rev. Phys. Chem., 2000, 51: 129-152.
96. Schaefer, M. and Froemmel, C. A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution [J]. J. Mol. Biol., 1990, 216(4): 1045-1066.
97. Onufriev, A., Bashford, D., and Case, D.A. Exploring protein native states and large-scale conformational changes with a modified generalized Born model [J]. Proteins, 2004, 55(2): 383-394.
98. Kohl, N.E., Emini, E.A., Schleif, W.A., Davis, L.J., Heimbach, J.C., Dixon, R.A.F., Scolnick, E.M., and Sigal, I.S. Active human immunodeficiency virus protease is required for viral infectivity [J]. Proc. Natl. Acad. Sci. U.S.A., 1988, 85: 4686-4690.
99. McQuade, T.J., Tomasselli, A.G., Liu, L., Karacostas, B., Moss, B., Sawyer, T.K., Heinrikson, R.L., and Tarpley, W.G. A Synthetic HIV-1 Protease Inhibitor with Antiviral Activity Arrests HIV-Like Particle Maturation [J]. Science, 1990, 247: 454-456.
100. Wlodawer, A. Rational approach to AIDS drug design through structural biology [J]. Annu. Rev. Med. , 2002, 53: 595-614.
101. Miller, M., Jaskolski, M., Rao, J.K., Leis, J., and Wlodawer, A. Crystal structure of a retroviral protease proves relationship to aspartic protease family [J]. Nature (London), 1989, 337(6207): 576-579.
102. Navia, M.A., Fitzgerald, P.M., McKeever, B.M., Leu, C.T., Heimbach, J.C., Herber, W.K., Sigal, I.S., Darke, P.L., and Springer, J.P. Three-dimensional Structure of Aspartyl Protease from Human Immunodeficiency Virus HIV-1 [J]. Nature (London), 1989, 337(6208): 615-620.
103. Wlodawer, A., Miller, M., Sathyanarayana, M.J.B.K., Baldwin, E., Weber, I.T., Selk, L.M., Clawson, L., Schneider, J., and Kent, S.B. Conserved Folding in Retroviral Proteases - Crystal-Structure of a Synthetic HIV-1 Protease [J]. Science, 1989, 245: 616-621.
104. Lapatto, R., Blundell, T., Hemmings, A., and et al. X-ray analysis of HIV-1 proteinase at 2.7A resolution confirms structural homology among re-troviral enzymes [J]. Nature (London), 1989, 342: 299-302.
105. Kempf, D.J., Marsh, K.C., Denissen, J.F., and et al. ABT-538 is a potent inhibitor of human immunodeficiency virus protease and has high oral bioavailability in humans [J]. Proc. Natl. Acad. Sci. U.S.A., 1995, 92(7): 2484–2488.
106. Kempf, D.J., Marsh, K.C., Denissen, J.F., and et al. ABT-538 is a potent inhibitor of human immunodeficiency virus protease and has high oral bioavailability in humans [J]. Proc. Natl. Acad. Sci. U.S.A. , 1995, 92(7): 2484–2488.
107. Bayly, C.I., Cieplak, P., Cornell, W.D., and Kollman, P.A. Application of RESP Charges to Calculate Conformational Energies, Hydrogen Bond Energies, and Free Energies of Solvation [J]. J. Phys. Chem., 1993, 97(21): 10269-10280.
108. Duan, Y., Wu, C., Chowdhury, S., and et al. A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations [J]. J. Comput. Chem., 2003, 24(16): 1999-2012.
109. Ryckaert , J.P., Ciccotti, G., and Berendsen, H.J.C. Numerical integration of the cartesian equations of motion of a system with constrains: molecular dynamics of n-alkanes [J]. J. Comput. Phys. , 1977, 23: 327-341.
110. Lu, Y.P., Yang, C.Y., and W, S.M. Binding free energy contributions of interfacial waters in HIV-1 protease/inhibitor complexes [J]. J. Am. Chem. Soc., 2006, 128(36): 11830-11839.
111. Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., and Karplus,M. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations [J]. J. Comp. Chem., 1983, 4(2): 187-217.
112. Pearlman, D.A., Case, D.A., Caldwell, J.W., Ross, W.S., Cheatham, T.E., DeBolt, S., Ferguson, D., Seibel, G., and Kollman, P.A. AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules [J]. Comp. Phys. Commun., 1995, 91: 1-41.
113. Hagler, A.T., Huler, E., and Lifson, S. Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals [J]. J. Am. Chem. Soc., 1974, 96(17): 5319-5327.
114. Nemethy, G., Pottle, M.S., and Scheraga, H.A. Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions, and hydrogen bond interactions for the naturally occurring amino acids [J]. J. Phys. Chem., 1983, 87: 1883-1887.
115. Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., Dinola, A., and Haak, J.R. Molecular dynamics with coupling to an external bath [J]. J. Chem. Phys., 1984, 81(8): 3684-3690.
116. Warshel, A., Kato, M., and Pisliakov, A.V. Polarizable force fields: History, test cases, and prospects [J]. J. Chem. Theor. Comp., 2007, 3(6): 2034-2045.
117. Zwanzig, R.W. High-temperature equation of state by a perturbation method [J]. J. Chem. Phys., 1954, 22: 1420-1426.
118. Kirkwood, J.G. Statistical Mechanics of Fluid Mixtures [J]. J. Chem. Phys., 1935, 3: 300-313.
119. ?qvist, J., Medina, C., and Samuelsson, J.E. A new method for predicting binding affinity in computer-aided drug design [J]. Protein Engineering, 1994, 7(3): 385-391.
120. Srinivasan, J., Cheatham, T.E., Cieplak, P., Kollman, P.A., and Case, D.A. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate - DNA helices [J]. J. Am. Chem. Soc., 1998, 120(37): 9401-9409.
121. Simonson, T., Carlsson, J., and Case, D.A. Proton binding to proteins: pK(a) calculations with explicit and implicit solvent models [J]. J. Am. Chem. Soc., 2004, 126(13):4167-4180.
122. Kollman, P.A. Free Energy Calculations: Applications to Chemical and Biochemical Phenomena [J]. Chem. Rev., 1993, 93(7): 2395-2417.
123. Su, Y., Gallicchio, E., Das, K., Arnold, E., and Levy, R.M. Linear interaction energy (LIE) models for ligand binding in implicit solvent: Theory and application to the binding of NNRTIs to HIV-1 reverse transcriptase [J]. J. Chem. Theor. Comp., 2007, 3: 256-277.
124. JonesHertzog, D.K. and Jorgensen, W.L. Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method [J]. J. Med. Chem., 1997, 40(10): 1539-1549.
125. Wang, W., Lim, W.A., Jakalian, A., Wang, J., Wang, J.M., Luo, R., Bayly, C.T., and Kollman, P.A. An analysis of the interactions between the Sem-5 SH3 domain and its ligands using molecular dynamics, free energy calculations, and sequence analysis [J]. J. Am. Chem. Soc., 2001, 123: 3986-3994.
126. Gouda, H., Kuntz, I.D., Case, D.A., and Kollman, P.A. Free energy calculations for theophylline binding to an RNA aptamer: MM-PBSA and comparison of thermodynamic integration methods [J]. Biopolymers, 2003, 68(1): 16-34.
127. Massova, I. and Kollman, P.A. Computational alanine scanning to probe protein-protein interactions: A novel approach to evaluate binding free energies [J]. J. Am. Chem. Soc., 1999, 121(36): 8133-8143.
128. Reyes, C.M. and Kollman, P. A. Structure and thermodynamics of RNA-protein binding: Using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change [J]. J. Mol. Biol., 2000, 297(5): 1145-1158.
129. Chong, L.T., Duan, Y., Wang, L., Massova, I., and Kollman, P.A. Proc. Natl. Acad. Sci. U.S.A. [J]. Molecular dynamics and free-energy calculations applied to affinity maturation in antibody 48G7, 1999, 96(25): 14330-14335.
130. Woo, H.J. and Roux, B. Calculation of absolute protein-ligand binding free energy from computer simulations [J]. Proc. Natl. Acad. Sci. U.S.A. , 2005, 102(19): 6825-6830.
131. Pearlman, D.A. Evaluating the molecular mechanics Poisson-Boltzmann surface area free energy method using a congeneric series of ligands to p38 MAP kinase [J]. J. Med. Chem., 2005, 48(24): 7796-7807.
132. Kuhn, B., Gerber, P., Schulz-Gasch, T., and Stahl, M. Validation and use of the MM-PBSA approach for drug discovery [J]. J. Med. Chem., 2005, 48(12): 4040-4048.
133. Wang, J.M., Wolf, R.M., Caldwell, J.W., Kollman, P.A., and Case, D.A. Development and testing of a general amber force field [J]. J. Comput. Chem., 2004, 25(9): 1157-1174.
134. Tan, C.H., Yang, L.J., and Luo, R. How well does Poisson-Boltzmann implicit solvent agree with explicit solvent? A quantitative analysis [J]. J. Phys. Chem. B., 2006, 110(37): 18680-18687.
135. Halgren, T.A. Polarizable force fields [J]. Curr. Opin. Struct. Biol., 2001, 11(2): 236-242.
136. Kaminski, G.A., Stern, H.A., Berne, B.J., Friesner, R.A., Cao, Y.X.X., Murphy, R.B., Zhou, R.H., and Halgren, T.A. Development of a polarizable force field for proteins via ab initio quantum chemistry: first-generation model and gas phase tests [J]. J. Comput. Chem. , 2002, 23: 1515-1531.
137. Jorgensen, W.L. Special issue on polarization [J]. J. Chem. Theory Comput., 2007, 3(6): 1877-2145
138. Bayly, C.I., Cieplak, P., Cornell, W., and Kollman, P.A. A wellbehaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model [J]. J. Phys. Chem., 1993, 97(40): 10269-10280.
139. Cornell, W.D., Cieplak, P., Bayly, C.I., and Kollman, P.A. [J]. J. Am. Chem. Soc., 1993, 115: 9620.
140. Ji, C. and Zhang, J.Z.H. Protein polarization is critical to stabilizing AF-2 and Helix-2′domains in ligand binding to PPARγ[J]. J. Am. Chem. Soc., 2008, 130(50): 17129-17133.
141. Ji, C., Mei, Y., and Zhang, J.Z.H. Developing polarized protein-specific for protein dynamics: MD free energy calculation of Pka shifts for Asp26/Asp20 in thioredoxin [J]. Biophys. J., 2008, 95: 1080-1088.
142. Rocchia, W., Sridharan, S., Nicholls, A., Alexov, E., Chiabrera, A., and Honig, B. Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects [J]. J. Comput. Chem., 2002, 23: 128-137.
143. Kabsch, W. and Sander, C. Dictionary of protein secondary structure: Pattern recognitionof hydrogen-bonded and geometrical features [J]. Biopolymers, 1983, 22(12): 2577-2637.
144. Zhou, R. Free energy landscape of protein folding in water: explicit vs. implicit solvent [J]. Proteins: Struct.,Funct., Genet. , 2003, 53(2): 148-161.
145. Pokala, N. and Handel, T.M. Review: protein design—where we were, where we are, where we're going [J]. J. Struct. Biol., 2001, 134(2-3): 269-281.
146. Ma, B., Lii, J.-H., and Allinger, N.L. Molecular polarizabilities and Induced Dipole Moments in Molecular Mechanics [J]. J. Comp. Chem. , 2000, 21: 813-825.
147. Wroblewska, L. and Skolnick, J. Can a physics-based, all-atom potential find a protein's native structure among misfolded structures? I. Large scale amber benchmarking [J]. J. Comput. Chem. , 2007, 28(12): 2059-2066.
148. Ji, C.G. and Zhang, J.Z.H. Electronic Polarization Is Important in Stabilizing the Native Structures of Proteins [J]. The journal of physical chemistry. B, 2009, 113(49): 16059-16064
149. Weiser, J.R., Shenkin, P.S., and Still, W.C. Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO) [J]. J. Comput. Chem. , 1999, 20(12): 217-230.
150. Mirsky, A.E. and Pauling, L. On the structure of native, denatured, and coagulated proteins [J]. Proc. Natl. Acad. Sci. U.S.A., 1936, 22: 439-447.
151. Berg, B.A. and Neuhaus, T. Multicanonical algorithms for first order phase transition [J]. Phys. Lett. B., 1991, 267: 249-253.
152. Berg, B.A. and Neuhaus, T. Multicanonical ensemble: A new approach to simulate first-order phase transitions [J]. Phys. Rev. Lett., 1992, 68(1): 9-12.
153. Kumar, S., Bouzida, D., Swendsen, R.H., Kollman, P.A., and Rosenberg, J.M. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method [J]. J. Comput. Chem., 1992, 13(8): 1011-1021.
154. Mitsutake, A., Sugita, Y., and Okamoto, Y. Generalized-Ensemble algorithms for molecular simulations of biopolymers [J]. Biopolymers 2001, 60(2): 96-123.
155. Swendsen, R.H. and Wang, J.S. Replica Monte-Carlo simulation of spin-glasses [J]. Phys. ReV. Lett., 1986, 57(21): 2607-2609.
156. Hukushima, K. and Nemoto, K. Exchange Monto carlo method and application to spinglass simulations [J]. J. Phys. Soc., 1996, 65: 1604-1608.
157. Tesi, M.C., van Rensburg, E.J.J., Orlandini, E., and Whittington, S.G. Monte Carlo study of the interacting self-avoiding walk model in three dimensions [J]. J. Stat. Phys., 1996, 82: 155-181.
158. Hansmann, U.H.E. Parallel tempering algorithm for conformational studies of biological molecules [J]. Chem. Phys. Lett., 1997, 281: 140-150.
159. Neidigh, J.W., Fesinmeyer, R.M., and Andersen, N.H. Designing a 20-residue protein [J]. Nat. Struct. Biol. , 2002, 9(6): 425-430.
160. Qiu, L., Pabit, S.A., Roitberg, A.E., and Hagen, S.J. Smaller and faster:The 20-residue Trp-cage protein folds in 4μs [J]. J. Am. Chem. Soc., 2002, 124(44): 12952-12953.
161. Simmerling, C., Strockbine, B., and Roitberg, A.E. All-Atom structure prediction and folding simulations of a stable protein [J]. J. Am. Chem. Soc., 2002, 124(38): 11258-11259.
162. Snow, C.D., Zagrovic, B., and Pande, V.S. The Trp Cage: Folding kinetics and unfolded state topology via molecular dynamics simulations [J]. J. Am. Chem. Soc., 2002, 124(49): 14548-14549.
163. Chowdhury, S., Lee, M.C., Xiong, G., and Duan, Y. Ab initio folding simulation of the Trp-cage mini-protein approaches NMR resolution [J]. J. Mol. Biol., 2003, 327(3): 711-717.
164. Chen, J., Im, W., and L.Brooks, C. Balancing solvation and intramolecular interactions: toward a consistent generalized born force field [J]. J. Am. Chem. Soc. , 2006, 128(11): 3728-3736.
165. Pitera, J.W. and Swope, W. Understanding folding and design: Replica-exchange simulations of“Trp-cage”miniproteins [J]. Proc. Natl. Acad. Sci. U. S. A. , 2003, 100(13): 7587-7592.
166. Zhou, R.H. Trp-cage: Folding free energy landscape in explicit water [J]. Proc. Natl. Acad. Sci. U. S. A., 2003, 100(23): 13280-13285.
167. Paschek, D., Nymeyer, H., and Garc?′a, A.E. Replica exchange simulation of reversible folding/unfolding of the Trp-cage miniprotein in explicit solvent: On the structure and possible role of internal water [J]. J. Struct. Biol. , 2007, 157(3): 524-533.
168. Shell, M.S., Ritterson, R., and Dill, K.A. A Test on peptide stability of AMBER force fields with implicit solvation [J]. J. Phys. Chem. B. , 2008, 112(22): 6878-6886.
169. Hawkins, G.D., Cramer, C.J., and Truhlar, D.G. Pairwise solute descreening of solute charges from a dielectric medium [J]. Chem. Phys. Lett., 1995, 246(1-2): 122-129.
170. Tsui, V. and Case, D.A. Theory and applications of the generalized Born solvation model in macromolecular simulations [J]. Biopolymers, 2001, 56(4): 275-291.
171. Sugita, Y. and Okamoto, Y. Replica-exchange molecular dynamics method for protein folding [J]. Chem. Phys. Lett., 1999, 314(1-2): 141-151.
172. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. Equation of state calculations by fast computing machines [J]. J. Chem. Phys., 1953, 21: 1087-1092.
173. Zhou, R.H. and Berne, B.J. Can a continuum solvent model reproduce the free energy landscape of aβ-hairpin folding in water? [J]. Proc. Natl. Acad. Sci. U. S. A., 2002, 99(20): 12777-12782
174. Roe, D.R., Hornak, V., and Simmerling, C. Folding cooperativity in a three-strandedβ-sheet model [J]. J. Mol. Biol. , 2005, 352(2): 370-381.
175. Zhang, W., Wu, C., and Duan, Y. Convergence of replica exchange molecular dynamics [J]. J. Chem. Phys., 2005, 123(15): 154105.
176. Sugita, Y., Kitao, A., and Okamoto, Y. Multidimensional replica exchange method for free-energy calculations [J]. J. Chem. Phys. , 2000, 113(15): 6042-6051.
177. Garc′?a, A.E. and Sanbonmatsu, K.Y. Exploring the energylandscape of a beta-hairpin in explicit solvent [J]. Proteins: Struct., Funct., Genet., 2001, 42(3): 345-354
178. Zhou, R.H., Berne, B.J., and Germain, R. The free energy landscape forβhairpin folding in explicit water [J]. Proc. Natl. Acad. Sci. U. S. A., 2001, 98(26): 14931-14936.
179. Garc′?a, A.E. and Sanbonmatsu, K.Y.α-Helical stabilization by side chain shielding of backbone hydrogen bonds [J]. Proc. Natl. Acad. Sci. U. S. A. , 2002, 99(5): 2782-2787.
180. Karanicolas, J. and Brooks, C.L. The structural basis for biphasic kinetics in the folding of the WW domain from a forminbinding protein: Lessons for protein design? [J]. Proc. Natl. Acad. Sci. U. S. A. , 2003, 100(7): 3954-3959.
181. Feig, M., Karanicolas, J., and Brooks, C.L. MMTSB tool set: Enhanced sampling andmultiscale modeling methods for applications in structural biology [J]. J. Mol. Graphics Modell., 2004, 22(5): 377-395.
182. Kinnear, B.S., Jarrold, M.F., and Hansmann, U.H.E. All-atom generalized-ensemble simulations of small proteins [J]. J. Mol. Graphics Modell. , 2004, 22(5): 397-403.
183. Jang, S., Kim, E., and Pak, Y. Free energy surfaces of miniproteins with aββαmotif: replica exchange molecular dynamics simulation with an implicit solvation model [J]. Proteins: Struct., Funct., Bioinformatics, 2006, 62: 663 -671.
184. Lei, H., Wu, C., Liu, H., and Duan, Y. Folding free-energy landscape of villin headpiece subdomain from molecular dynamics simulations [J]. Proc. Natl. Acad. Sci. U. S. A., 2007, 104(12): 4925-4930.
185. van der. Spoel , D. and Seibert, M.M. Protein folding kinetics and thermodynamics from atomistic simulations [J]. Phys. Rev. Lett., 2006, 96(23): 238102.
186. Chowdhury, S., Lee, M.C., and Duan, Y. Characterizing the ratelimiting step of trp-cage folding by all-atom molecular dynamics simulations [J]. J. Phys. Chem. B., 2004, 108(36): 13855-13865.
187. Linhananta, A., Boer, J., and MacKay, I. The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage [J]. J. Chem. Phys., 2005, 122(11): 114901.
188. Juraszek, J. and Bolhuis, P.G. Sampling the multiple folding mechanisms of Trp-cage in explicit solvent [J]. Proc. Natl. Acad. Sci. U. S. A. , 2006, 103(43): 15859-15864
189. Juraszek, J. and Bolhuis, P.G. Rate constant and reaction coordinate of Trp-cage folding in explicit water [J]. Biophys. J . , 2008, 95 (9): 4246-4257.
190. Dobson, C.M. Protein Misfolding, Evolution and Disease [J]. Rrends Biochem. Sci., 1999, 24(9): 329-332.
191. Muchowski, P.J. Protein Misfolding, Amyloid Minireview Formation, and Neurodegeneration: A Critical Role for Molecular Chaperones? [J]. Neuron, 2002, 35(1): 9-12.
192. Slepoy, A., Singh, R.R.P., Pázmándi, F., Kulkarni, R.V., and Cox, D.L. Statistical Mechanics of Prion Diseases [J]. Phys. Rev. Lett. , 2001, 87: 058101-1-4.
193. Baumketner, A. and Shea, J.E. The Structure of The Alzheimer, Amyloid Beta 10-35 Peptide Probed Through Replica Exchange Molecular Dynamics Simulations In ExplicitSolvent [J]. J. Mol. Biol., 2007, 366: 275-285.
194. Berg, B.A. and Neuhaus, T. Multicanonical Algorithms for First Order Phase Transition [J]. Phys. Lett. B., 1991, 267: 249.
195. Berg, B.A. and Neuhaus, T. Multicanonical ensemble: A new approach to simulate first-order phase transitions [J]. Phys. Rev. Lett., 1992, 68: 9.
196. Brooks, C.I. Protein and Peptide Folding Explored with Molecular Simulations [J]. Acc. Chem. Res., 2002, 35: 447-454.
197. Chowdhury, S., Lei, H.X., and Duan, Y. Denatured State Ensemble and Early Stage of Folding of the G29A Mutant of B-domain of Protein A: An All Atom Molecular Dynamics Study [J]. J. Phys. Chem. B, 2005, 109: 9073-9081.
198. Daggett, V. Molecular Dynamics Simulations of The Protein Unfolding/Folding Reaction [J]. Acc. Chem. Res., 2002, 35: 422-449.
199. Duan, Y. and Kollman, P.A. Pathways to a Protein Folding Intermediate Observed in a 1-microsecond Simulation in Aqueous Solution [J]. Science, 1998, 282: 740-744.
200. Duan, Y., Wang, L., and Kollman, P.A. The Early Stage of Folding of Villin Headpiece Subdomain Observed In a 200-nanosecond Fully Solvated Molecular Dynamics Simulation [J]. Proc. Natl. Acad. Sci. U.S.A., 1998, 95(17): 9897-9902.
201. Eleftheriou, M., Germain, R.S., Royyuru, A.K., and Zhou, R. Thermal Denaturing of Mutant Lysozyme With Both The OPLSAA and The CHARMM Force Fields [J]. J. Am. Chem. Soc., 2006, 128: 13388-13395.
202. Juraszek, J. and Bolhuis, P.G. Sampling the Multiple Folding Mechanisms of Trp-cage In Explicit Solvent [J]. Proc. Natl. Acad. Sci., 2006, 103: 15859-15864.
203. Lei, H., Wang, Z.-X., Wu, C., and Duan, Y. Dual Folding Pathways of anα/βProtein From All-Atom ab initio Folding Simulations [J]. J. Chem. Phys., 2009, 131(16): 165105-1-165105-7.
204. Lei, H., Wu, C., Liu, H., and Duan, Y. Folding Free-Energy Landscape of Villin Headpiece Subdomain From Molecular Dynamics Simulations [J]. PNAS, 2007, 104(12): 4925-4930.
205. Mitsutake, A., Sugita, Y., and Okamoto, Y. Generalized-Ensemble Algorithms for Molecular Simulations of Biopolymers [J]. Biopolymers, 2001, 60: 96-123.
206. Nelson, E.D. and Grishin, N.V. Folding Domain B of Protein A On a Dynamically Partitioned Free Energy Landscape [J]. Proc. Natl. Acad. Sci. U. S. A., 2008, 105: 1489.
207. Pande, V.S., Baker, I., Chapman, J., Elmer, S.P., Khaliq, S., Larson, S.M., Rhee, Y.M., Shirts, M.R., Snow, C.D., Sorin, E.J., and Zagrovic, B. Atomistic Protein Folding Simulations On The Submillisecond Time Scale Using Worldwide Distributed Computing [J]. Biopolymers, 2003, 68: 91-109.
208. Paschek, D., Nymeyer, H., and Garcia, A.E. Replica Exchange Simulation of Reversible Folding/Unfolding of The Trp-cage Miniprotein In Explicit Solvent: On The Structure And Possible Role of Internal Water [J]. J. Struct. Biol., 2007, 157: 524-533.
209. Periole, X. and Mark, A.E. Convergence and Sampling Efficiency In Replica Exchange Simulations of Peptide Folding In Explicit Solvent [J]. J. Chem. Phys., 2007, 126: 014903.
210. Scheraga, H.A., Khalili, M., and Liwo, A. Protein-Folding Dynamics: Overview of Molecular Simulation Techniques [J]. Ann. ReV. Phys. Chem., 2007, 58: 57-83.
211. Simmerling, C., Strockbine, B., and Roitberg, A. All-atom Structure Prediction and Folding Simulations of A Stable Protein [J]. J. Am. Chem. Soc., 2002, 124: 11258-11259.
212. Wickstrom, L., Okur, A., Song, K., Hornak, V., Raleigh, D.P., and Simmerling, C.L. The Unfolded State of The Villin Headpiece Helical Subdomain: Computational Studies of The Role of Locally Stabilized Structure [J]. J. Mol. Biol., 2006, 360: 1094-1107.
213. Xu, W.X., Lai, T.F., Yang, Y., and Mu, Y.G. Reversible Folding Simulation By Hybrid Hamiltonian Replica Exchange [J]. J. Chem. Phys., 2008, 128: 175105.
214. Yoda, T., Sugita, Y., and Okamoto, Y. Cooperative Folding Mechanism of A Beta-hairpin Peptide Studied By a Multicanonical Replica-Exchange Molecular Dynamics Simulation [J]. Proteins: Struct.,Funct., Bioinformatics 2007, 66: 846-859.
215. Zhou, R.H. Trp-cage: Folding Free Energy Landscape in Explicit Water [J]. Proc. Natl. Acad. Sci. U. S. A., 2003, 100(23): 13280-13285.
216. Zhou, R.H., Berne, B.J., and Germain, R. The Free Energy Landscape forβHairpin Folding in Explicit Water [J]. Proc. Natl. Acad. Sci. U.S.A., 2001, 98(26): 14931–14936
217. Williams, S., Causgrove, T.P., Gilmanshin, R., Fang, K.S., Callender, R.H., and Dyer, W.H.W.R.B. Fast Events in Protein Folding: Helix Melting and Formation in a SmallPeptide [J]. Biochemistry, 1996, 35: 691-697.
218. Mu?oz, V., Thompson, P.A., Hofrichter, J., and Eaton, W.A. Folding Dynamics and Mechanism ofβ-Hairpin Formation [J]. Nature, 1997, 390: 196-199.
219. Duan, L.L., Zhang, Y.M.Q.G., and Zhang, J.Z.H. Intra-Protein hydrogen bonding is dynamically stabilized by electronic polarization [J]. J. Chem. Phys., 2009, 130(11): 115102.
220. Ji, C., Mei, Y., and Zhang, J.Z.H. Developing Polarized Protein-Specific Charges for Protein Dynamics: MD Free Energy Calculation of pKa Shifts for Asp26/Asp20 in Thioredoxin [J]. Biophys. J . 2008, 95: 1080-1088.
221. Ji, C.G. and Zhang, J.Z.H. Protein Polarization Is Critical to Stabilizing AF-2 and Helix-2′Domains in Ligand Binding to PPAR-γ[J]. J. Am. Chem. Soc., 2008, 130: 17129.
222. Tong, Y., Ji, C.G., Mei, Y., and Zhang, J.Z.H. Simulation of NMR Data Reveals That Proteins’Local Structures Are Stabilized by Electronic Polarization [J]. J. Am. Chem. Soc., 2009, 131(24): 8636-8641.
223. Ji, C.G. and Zhang, J.Z.H. Electronic Polarization Is Important in Stabilizing the Native Structures of Proteins [J]. The journal of physical chemistry. B, 2009, 113(49): 16059-16064
224. Ji, C.G. and Zhang, J.Z.H. NMR Scalar Coupling Constant Reveals That Intraprotein Hydrogen Bonds Are Dynamically Stabilized by Electronic Polarization [J]. J. Phys. Chem. B, 2009, 113(42): 13898-13900.
225. Pantoja, U.D., Pastor, M.T., Salgado, J., Pineda, L.A., and Pérez, P.E. Design of A Bivalent Peptide With Two Independent Elements of Secondary Structure Able to Fold Autonomously [J]. J. Pept. Sci., 2008, (14): 845-854.
226. Lin, E. and Shell, M.S. Convergence and Heterogeneity in Peptide Folding with Replica Exchange Molecular Dynamics [J]. J. Chem.Theory Comput., 2009, 5: 2062-2073.
227. Onufriev, A., Bashford, D., and Case, D.A. A Modification of the Generalized Born Model Suitable for Macromolecules [J]. J. Phys. Chem. B, 2000, 104: 3712.
228. Kim, E., Jang, S., and Pak, Y. Consistent Free Energy Landscapes and Thermodynamic Properties of Small Proteins Based on A Single All-Atom Force Field Employing anImplicit Solvation [J]. J. Chem. Phys., 2007, 127: 145104.
229. Kim, E., Jang, S., and Pak, Y. Direct Folding of VariousαandβStrands Using Replica Exchange Molecular Dynamics Simulation [J]. J. Chem. Phys., 2008, 128: 175104.
230. Onufriev, A., Bashford, D., and Case, D.A. Exploring Protein Native States and Large-Scale Conformational Changes with A Modified Generalized Born Model [J]. Proteins: Struct., Funct., Bioinformatics, 2004, 55: 383-394.
231. Ryckaert, J.P., Ciccotti, G., and Berendsen, H.J.C. Numerical integration of the Cartesian equations of motion of a system with constrains: Molecular dynamics of n-alkanes [J]. J. Comput. Phys., 1977, 23: 327.
232. Pastor, R.W., Brooks, B.R., and Szabo, A. An Analysis of The Accuracy of Langevin and Molecular Dynamics Algorithm [J]. Mol. Phys., 1988, 65: 1409.
233. McDonald, I.K. and Thornton, J.M. Satisfying hydrogen bonding potential inproteins [J]. J. Mol. Bio., 1994, 238(5): 777-793.
234. Shao, J., Tanner, S.W., Nephi Thompson, and Cheatham III, T.E. Clustering Molecular Dynamics Trajectories: 1. Characterizing the Performance of Different Clustering Algorithms [J]. J. Chem. Theroy Comput., 2007, 3(6): 2312-2334.
235. Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., and Kollman, P.A. Multidimensional Free-Energy Calculations Using the Weighted Histogram Analysis Method [J]. J. Comput. Chem., 1995, 16(11): 1339-1350.
236. Roux, B. The Calculation of The Potential of Mean Force Using Computer Simulations [J]. Comput. Phys. Comm, 1995, 91(1-3): 275-282.