The infrared （IR） spectra of the N-methylacetamide molecule in water are calculated by using the MD simulation with high-level QM]MM corrections. The B3LYP and MP2 levels with 6-31 I＋＋G＊＊ basis set are used for ...The infrared （IR） spectra of the N-methylacetamide molecule in water are calculated by using the MD simulation with high-level QM]MM corrections. The B3LYP and MP2 levels with 6-31 I＋＋G＊＊ basis set are used for the QM region, respectively, Our results show all IR spectra at the B3LYP level are well consistent with the corresponding MP2 results. A dynamical charge fluctuation is observed for each atom along the simulation trajectories due to the electrostatic polarization （EP） effects from surrounding solvent environment, We find that the QM/MM corrected IR spectra satisfactorily reprodnce the experimental vibrational features of amide 1-11I modes.展开更多
The dioxygen activation catalyzed by 4-hydorxylphenyl pyruvate dioxygenase(HPPD)were reinvestigated by using hybrid quantum mechanics/molecular mechanics(QM/MM)approaches at the B3LYP/6-311++G(d,p):AMBER level.These s...The dioxygen activation catalyzed by 4-hydorxylphenyl pyruvate dioxygenase(HPPD)were reinvestigated by using hybrid quantum mechanics/molecular mechanics(QM/MM)approaches at the B3LYP/6-311++G(d,p):AMBER level.These studies showed that this reaction consisted of two steps including the dioxygen addition/decarboxylation and hetero O-O bond cleavage,where the first step was found to be rate-determining.The former step initially runs on a septet potential energy surface(PES),then switches to a quintet PES after crossing a septet/quintet minimum energy crossing point(MECP)5-7M2,whereas the rest step runs on the quintet PES.The reliability of our theoretical predictions is supported by the excellent agreement of the calculated free-energy barrier value of 16.9 kcal/mol with available experimental value of 16-17 kcal/mol.The present study challenges the widely accepted view which holds that the O2activation catalyzed byα-keto glutamate(α-KG)dioxygenase mainly runs on the quintet PES and provides new insight into the catalytic mechanism ofα-KG dioxygenase and/or other related Fe(Ⅱ)-dependent oxygenase.展开更多
Both a molecule dynamic study and a combined quantum mechanics and mole-cule mechanics（QM/MM） study on the acetylating deactivation mechanism of isoniazid were presented.This type of reaction was catalyzed by arylam...Both a molecule dynamic study and a combined quantum mechanics and mole-cule mechanics（QM/MM） study on the acetylating deactivation mechanism of isoniazid were presented.This type of reaction was catalyzed by arylamine N-acetyltransferases（NATs） and the results strongly support a direct acetyl group transfer process rather than a stepwise one.The isoniazid was strictly restrained in proper relative position to accept the acetyl group by a Hydrogen-bond network formed by the residues at the active center.The residues,His110 and Cys70,would be functioned as ＇general base＇ rather than ＇general acid＇.If all the residues（including H2O molecules） were removed from the system,the activation energy will be increased from 145.1 to 243.3 kJ/mol.The calculations met the experimental data with good agreement.展开更多
P450 cin(CYP176 A1) isolated from Citrobacter braakii is a biodegradation enzyme that catalyzes the enantiospecific conversion of 1,8-cineole to(1 R)-6β-hydroxycineole. In many P450 family members the mechanism of pr...P450 cin(CYP176 A1) isolated from Citrobacter braakii is a biodegradation enzyme that catalyzes the enantiospecific conversion of 1,8-cineole to(1 R)-6β-hydroxycineole. In many P450 family members the mechanism of proton delivery for O2activation is proposed to require a conserved acid-alcohol dyad in the active area, while P450 cin has no such residue with alcohol but asparagine instead. In the present work, the mechanism of the first proton transfer of O2activation in P450 cin has been investigated by molecular dynamics(MD) and hybrid quantum mechanics/molecular mechanics(QM/MM) techniques. The MD simulation suggests there are two hydrogen bonding networks around the active site, one involving Asp241 and the other involving Glu356. According to our MD and QM/MM calculations, this Asp241 channel is proposed to be the energy accessible. MD results show that the hydrogen bonds around the substrate may contribute to regio-and stereo-oxidation of the substrate.展开更多
A new reversibly switchable fluorescent protein（RSFP）, namely Dreiklang, exhibits prominent feature that the wavelengths for switching and fluorescence are decoupled due to its great different structures between bri...A new reversibly switchable fluorescent protein（RSFP）, namely Dreiklang, exhibits prominent feature that the wavelengths for switching and fluorescence are decoupled due to its great different structures between bright and dark states. This feature might also induce some nonlinear optic（NLO） properties changing as switching between two states, which might promote new method of biological science. We employ the QM/MM method to simulate the structures of different states, and study their second harmonic generation（SHG） and two-photon absorption（TPA） properties. And we found different states of Dreiklang have different SHG and TPA responses. The SHG and TPA properties of Dreiklang are correlated to particularly geometrical structures of different states, especially the centrosymmetric or nocentrosymmetric π-stacking structures which are formed by chromophore and beside residue Tyr203, so the SHG and TPA responses could be changed as the light induces switching among different states of Dreiklang. This work would prospectively guide the application of Dreiklang on the NLO technology, and help the development of new RSFP with special NLO function.展开更多
Multi-scale quantum-mechanical/molecular-mechanical(QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded t...Multi-scale quantum-mechanical/molecular-mechanical(QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded through these methods can enhance our understanding of how the enzyme environment modulates reactivity at the enzyme active site. From this perspective, tools from conceptual density functional theory to interrogate electron densities can provide added insight into enzyme function. We recently introduced the highly parallelizable Fukui shift analysis(FSA) method, which identifies how frontier states of an active site are altered by the presence of an additional QM residue to identify when QM treatment of a residue is essential as a result of quantum-mechanically affecting the behavior of the active site. We now demonstrate and analyze distance and residue dependence of Fukui function shifts in pairs of residues representing different non-covalent interactions. We also show how the interpretation of the Fukui function as a measure of relative nucleophilicity provides insight into enzymes that carry out S_N2 methyl transfer. The FSA method represents a promising approach for the systematic, unbiased determination of quantum mechanical effects in enzymes and for other complex systems that necessitate multi-scale modeling.展开更多
Drug metabolism is an important issue in drug discovery. Understanding how a drug is metabolized in the body will provide helpful information for lead optimization. Cytochrome P450 2D6 （CYP2D6） is a key enzyme for d...Drug metabolism is an important issue in drug discovery. Understanding how a drug is metabolized in the body will provide helpful information for lead optimization. Cytochrome P450 2D6 （CYP2D6） is a key enzyme for drug metabolism and responsible for the metabolism of about one third marketed drugs. Aripiprazole is an atypical an- tipsychotic and metabolized by CYP2D6 to its hydroxylated form. In this study, a series of computational methods were performed to understand how CYP2D6 accomplishes the 4-hydroxylation of aripiprazole. Molecular docking and molecular dynamics simulations were first performed to prepare the initial conformations for QM/MM calcula- tions. The results revealed two possible conformations for the drug-CYP2D6 complex. The ONIOM method for QM/MM calculations was then carried out to show detailed reaction pathways for the CYP2D6-catalyzed aripipra- zole hydroxylation reaction, which demonstrated that the dominant reactive channel was electrophilic and involved an initial attack on the n-system of the dichlorophenyl group of aripiprazole to produce cation δ-complex. Further- more, the product complex for each conformation was thermodynamically stable, which is in good agreement with previous reports.展开更多
目的:评估QM/MM方法和Surflex-Dock分子对接程序对DNA-配体复合物模拟的准确性。方法:从蛋白质数据库(Protein Data Bank)下载DNA-配体复合物的三维结构,利用计算机辅助药物设计的分子对接程序Surflex-Dock模拟出147个诱饵化合物(decoys...目的:评估QM/MM方法和Surflex-Dock分子对接程序对DNA-配体复合物模拟的准确性。方法:从蛋白质数据库(Protein Data Bank)下载DNA-配体复合物的三维结构,利用计算机辅助药物设计的分子对接程序Surflex-Dock模拟出147个诱饵化合物(decoys)并计算其结合分数(binding score)。然后将得出的分数与从QM/MM计算的结合能力以Z-score和辨别力(DP)作比较。从而评估Surflex-Dock和QM/MM的准确性。结果:Surflex-Dock的DPi值比QM/MM高,显示Surflex-Dock的辨别力较低。结论:因QM/MM计算速度慢,本研究认为Surflex-Dock可用作快速虚拟筛选,而较准确的QM/MM则适合用于对拥有较高结合分数的化合物进行再评分(rescoring)。展开更多
Thermally activated delayed fluorescence(TADF)and room temperature phosphorescence(RTP)molecules hold promising application prospects in the field of organic light emitting diodes(OLEDs),primarily attributed to their ...Thermally activated delayed fluorescence(TADF)and room temperature phosphorescence(RTP)molecules hold promising application prospects in the field of organic light emitting diodes(OLEDs),primarily attributed to their significant advantages in enhancing device stability and lumines-cence efficiency.Notably,TADF and RTP molecules can achieve nearly 100%exciton utilization without necessitating costly and limited precious metal elements.However,the primary challenges confronting TADF and RTP molecules at present encompass limitations in emission color,low luminescence efficien-cy,severe efficiency roll-off and so on.Given these points,this paper presents a comprehensive overview of the latest research progress in TADF and RTP molecules.We delve into the mechanisms by which TADF molecules achieve efficient fluorescence emission through unique molecular structural designs,fre-quently involving sophisticated intramolecular charge transfer processes and precise energy level modula-tion.Simultaneously,we provide an in-depth analysis of the unique luminescence properties and photo-physical mechanisms of RTP molecules.Furthermore,the article focuses on the design strategies for TADF and RTP molecules,encompassing the manipulation of molecular structures,electronic structures and the enhancement of charge transfer effects.By examining these strategies,we aim to provide a com-prehensive perspective on the research of TADF and RTP molecules.We hope that through this review,it could offer some guidance for future research and inspire the exploration of more innovative TADF and RTP molecules.展开更多
Formate oxidase(FOx),which contains 8-formyl flavin adenine dinucleotide(FAD),exhibits a distinct advantage in utilizing ambient oxygen molecules for the oxidation of formic acid compared to other glucose-methanol-cho...Formate oxidase(FOx),which contains 8-formyl flavin adenine dinucleotide(FAD),exhibits a distinct advantage in utilizing ambient oxygen molecules for the oxidation of formic acid compared to other glucose-methanol-choline(GMC)oxidoreductase enzymes that contain only the standard FAD cofactor.The FOx-mediated conversion of FAD to 8-formyl FAD results in an approximate 10-fold increase in formate oxidase activity.However,the mechanistic details underlying the autocatalytic formation of 8-formyl FAD are still not well understood,which impedes further utilization of FOx.In this study,we employ molecular dynamics simulation,QM/MM umbrella sampling simulation,enzyme activity assay,site-directed mutagenesis,and spectroscopic analysis to elucidate the oxidation mechanism of FAD to 8-formyl FAD.Our results reveal that a catalytic water molecule,rather than any catalytic amino acids,serves as a general base to deprotonate the C8 methyl group on FAD,thus facilitating the formation of a quinone-methide tautomer intermediate.An oxygen molecule subsequently oxidizes this intermediate,resulting in a C8 methyl hydroperoxide anion that is protonated and dissociated to form OHC-RP and OH−.During the oxidation of FAD to 8-formyl FAD,the energy barrier for the rate-limiting step is calculated to be 22.8 kcal/mol,which corresponds to the required 14-hour transformation time observed experimentally.Further,the elucidated oxidation mechanism reveals that the autocatalytic formation of 8-formyl FAD depends on the proximal arginine and serine residues,R87 and S94,respectively.Enzymatic activity assay validates that the mutation of R87 to lysine reduces the kcat value to 75%of the wild-type,while the mutation to histidine results in a complete loss of activity.Similarly,the mutant S94I also leads to the deactivation of enzyme.This dependency arises because the nucleophilic OH−group and the quinone-methide tautomer intermediate are stabilized through the noncovalent interaction provided by R87 and S94.These findings not only explain the mechanistic details of each reaction step but also clarify the functional role of R87 and S94 during the oxidative maturation of 8-formyl FAD,thereby providing crucial theoretical support for the development of novel flavoenzymes with enhanced redox properties.展开更多
基金supported by the Natural Science Foundation of China(Nos.21306070 and 20966003)the Science&Technology Programs of Education Department of Jiangxi Province(No.GJJ12191)
文摘The infrared （IR） spectra of the N-methylacetamide molecule in water are calculated by using the MD simulation with high-level QM]MM corrections. The B3LYP and MP2 levels with 6-31 I＋＋G＊＊ basis set are used for the QM region, respectively, Our results show all IR spectra at the B3LYP level are well consistent with the corresponding MP2 results. A dynamical charge fluctuation is observed for each atom along the simulation trajectories due to the electrostatic polarization （EP） effects from surrounding solvent environment, We find that the QM/MM corrected IR spectra satisfactorily reprodnce the experimental vibrational features of amide 1-11I modes.
基金supported by the National Key R&D Program(No.2021YFD1700100)National Natural Science Foundation of China(Nos.21837001,21273089)+2 种基金the Open Project Fund of the Key Laboratory of the Pesticides and Chemical Biology of Central China Normal University(No.2018-A01)the Fundamental Research Funds for the Central Universitiesthe Fundamental Research Funds for the South-Central University for Nationalities(No.CZW20020)。
文摘The dioxygen activation catalyzed by 4-hydorxylphenyl pyruvate dioxygenase(HPPD)were reinvestigated by using hybrid quantum mechanics/molecular mechanics(QM/MM)approaches at the B3LYP/6-311++G(d,p):AMBER level.These studies showed that this reaction consisted of two steps including the dioxygen addition/decarboxylation and hetero O-O bond cleavage,where the first step was found to be rate-determining.The former step initially runs on a septet potential energy surface(PES),then switches to a quintet PES after crossing a septet/quintet minimum energy crossing point(MECP)5-7M2,whereas the rest step runs on the quintet PES.The reliability of our theoretical predictions is supported by the excellent agreement of the calculated free-energy barrier value of 16.9 kcal/mol with available experimental value of 16-17 kcal/mol.The present study challenges the widely accepted view which holds that the O2activation catalyzed byα-keto glutamate(α-KG)dioxygenase mainly runs on the quintet PES and provides new insight into the catalytic mechanism ofα-KG dioxygenase and/or other related Fe(Ⅱ)-dependent oxygenase.
基金Supported by the National Natural Science Foundation of China (No. 20603030 and No. 21103080)the Natural Science Foundation of Shandong Province (No. ZR2010BL023)
文摘Both a molecule dynamic study and a combined quantum mechanics and mole-cule mechanics（QM/MM） study on the acetylating deactivation mechanism of isoniazid were presented.This type of reaction was catalyzed by arylamine N-acetyltransferases（NATs） and the results strongly support a direct acetyl group transfer process rather than a stepwise one.The isoniazid was strictly restrained in proper relative position to accept the acetyl group by a Hydrogen-bond network formed by the residues at the active center.The residues,His110 and Cys70,would be functioned as ＇general base＇ rather than ＇general acid＇.If all the residues（including H2O molecules） were removed from the system,the activation energy will be increased from 145.1 to 243.3 kJ/mol.The calculations met the experimental data with good agreement.
基金supported by the National Natural Science Foundation of China(No.21573237,21603227,21403242,21703246)the Natural Science Foundation of Fujian Province(2017J05032)
文摘P450 cin(CYP176 A1) isolated from Citrobacter braakii is a biodegradation enzyme that catalyzes the enantiospecific conversion of 1,8-cineole to(1 R)-6β-hydroxycineole. In many P450 family members the mechanism of proton delivery for O2activation is proposed to require a conserved acid-alcohol dyad in the active area, while P450 cin has no such residue with alcohol but asparagine instead. In the present work, the mechanism of the first proton transfer of O2activation in P450 cin has been investigated by molecular dynamics(MD) and hybrid quantum mechanics/molecular mechanics(QM/MM) techniques. The MD simulation suggests there are two hydrogen bonding networks around the active site, one involving Asp241 and the other involving Glu356. According to our MD and QM/MM calculations, this Asp241 channel is proposed to be the energy accessible. MD results show that the hydrogen bonds around the substrate may contribute to regio-and stereo-oxidation of the substrate.
基金based on work supported by the National Natural Science Foundation of China(No.21703246 and 21403242)Natural Science Foundation of Fujian Province(2014J05021)
文摘A new reversibly switchable fluorescent protein（RSFP）, namely Dreiklang, exhibits prominent feature that the wavelengths for switching and fluorescence are decoupled due to its great different structures between bright and dark states. This feature might also induce some nonlinear optic（NLO） properties changing as switching between two states, which might promote new method of biological science. We employ the QM/MM method to simulate the structures of different states, and study their second harmonic generation（SHG） and two-photon absorption（TPA） properties. And we found different states of Dreiklang have different SHG and TPA responses. The SHG and TPA properties of Dreiklang are correlated to particularly geometrical structures of different states, especially the centrosymmetric or nocentrosymmetric π-stacking structures which are formed by chromophore and beside residue Tyr203, so the SHG and TPA responses could be changed as the light induces switching among different states of Dreiklang. This work would prospectively guide the application of Dreiklang on the NLO technology, and help the development of new RSFP with special NLO function.
文摘Multi-scale quantum-mechanical/molecular-mechanical(QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded through these methods can enhance our understanding of how the enzyme environment modulates reactivity at the enzyme active site. From this perspective, tools from conceptual density functional theory to interrogate electron densities can provide added insight into enzyme function. We recently introduced the highly parallelizable Fukui shift analysis(FSA) method, which identifies how frontier states of an active site are altered by the presence of an additional QM residue to identify when QM treatment of a residue is essential as a result of quantum-mechanically affecting the behavior of the active site. We now demonstrate and analyze distance and residue dependence of Fukui function shifts in pairs of residues representing different non-covalent interactions. We also show how the interpretation of the Fukui function as a measure of relative nucleophilicity provides insight into enzymes that carry out S_N2 methyl transfer. The FSA method represents a promising approach for the systematic, unbiased determination of quantum mechanical effects in enzymes and for other complex systems that necessitate multi-scale modeling.
基金supported by the National Science Foundation(Grant number:0817940to HG)the DOE Office of Biological and Environmental Research-Genome to Life Program through the BioEnergy Science Center(BESC)(to FC)+2 种基金the Sun Grant Initiative(to FC)the computer resources(Newton)from University of Tennessee Knoxvillethe NSF TeraGrid resources provided by the University of Texas at Austin
基金the China Postdoctoral Science Foundation，Shanghai Committee of Science and Technology，National Natural Science Foundation of China，Innovation Program of Shanghai Municipal Education Commission
文摘Drug metabolism is an important issue in drug discovery. Understanding how a drug is metabolized in the body will provide helpful information for lead optimization. Cytochrome P450 2D6 （CYP2D6） is a key enzyme for drug metabolism and responsible for the metabolism of about one third marketed drugs. Aripiprazole is an atypical an- tipsychotic and metabolized by CYP2D6 to its hydroxylated form. In this study, a series of computational methods were performed to understand how CYP2D6 accomplishes the 4-hydroxylation of aripiprazole. Molecular docking and molecular dynamics simulations were first performed to prepare the initial conformations for QM/MM calcula- tions. The results revealed two possible conformations for the drug-CYP2D6 complex. The ONIOM method for QM/MM calculations was then carried out to show detailed reaction pathways for the CYP2D6-catalyzed aripipra- zole hydroxylation reaction, which demonstrated that the dominant reactive channel was electrophilic and involved an initial attack on the n-system of the dichlorophenyl group of aripiprazole to produce cation δ-complex. Further- more, the product complex for each conformation was thermodynamically stable, which is in good agreement with previous reports.
文摘目的:评估QM/MM方法和Surflex-Dock分子对接程序对DNA-配体复合物模拟的准确性。方法:从蛋白质数据库(Protein Data Bank)下载DNA-配体复合物的三维结构,利用计算机辅助药物设计的分子对接程序Surflex-Dock模拟出147个诱饵化合物(decoys)并计算其结合分数(binding score)。然后将得出的分数与从QM/MM计算的结合能力以Z-score和辨别力(DP)作比较。从而评估Surflex-Dock和QM/MM的准确性。结果:Surflex-Dock的DPi值比QM/MM高,显示Surflex-Dock的辨别力较低。结论:因QM/MM计算速度慢,本研究认为Surflex-Dock可用作快速虚拟筛选,而较准确的QM/MM则适合用于对拥有较高结合分数的化合物进行再评分(rescoring)。
基金supported by the National Natural Science Foundation of China(12274266,12374269,12104248 and 12474258)supporting of the Open Fund of the State Key Laboratory of Luminescent Materials and Devices(South China University of Technology)and Taishan Scholar Project of Shandong Province.
文摘Thermally activated delayed fluorescence(TADF)and room temperature phosphorescence(RTP)molecules hold promising application prospects in the field of organic light emitting diodes(OLEDs),primarily attributed to their significant advantages in enhancing device stability and lumines-cence efficiency.Notably,TADF and RTP molecules can achieve nearly 100%exciton utilization without necessitating costly and limited precious metal elements.However,the primary challenges confronting TADF and RTP molecules at present encompass limitations in emission color,low luminescence efficien-cy,severe efficiency roll-off and so on.Given these points,this paper presents a comprehensive overview of the latest research progress in TADF and RTP molecules.We delve into the mechanisms by which TADF molecules achieve efficient fluorescence emission through unique molecular structural designs,fre-quently involving sophisticated intramolecular charge transfer processes and precise energy level modula-tion.Simultaneously,we provide an in-depth analysis of the unique luminescence properties and photo-physical mechanisms of RTP molecules.Furthermore,the article focuses on the design strategies for TADF and RTP molecules,encompassing the manipulation of molecular structures,electronic structures and the enhancement of charge transfer effects.By examining these strategies,we aim to provide a com-prehensive perspective on the research of TADF and RTP molecules.We hope that through this review,it could offer some guidance for future research and inspire the exploration of more innovative TADF and RTP molecules.
基金supported by the National Natural Science Foundation of China(32201030,32271319 and 32071267)the Science and Technology Department of Jilin Province(20230402041GH and YDZJ202301ZYTS537)+2 种基金the Education Department of Jilin Province(JJKH20220970KJ)the Development and Reform Commission of Jilin Province(2023C015)the Fundamental Research Funds of the Central Universities in China(2024-JCXK-11).
文摘Formate oxidase(FOx),which contains 8-formyl flavin adenine dinucleotide(FAD),exhibits a distinct advantage in utilizing ambient oxygen molecules for the oxidation of formic acid compared to other glucose-methanol-choline(GMC)oxidoreductase enzymes that contain only the standard FAD cofactor.The FOx-mediated conversion of FAD to 8-formyl FAD results in an approximate 10-fold increase in formate oxidase activity.However,the mechanistic details underlying the autocatalytic formation of 8-formyl FAD are still not well understood,which impedes further utilization of FOx.In this study,we employ molecular dynamics simulation,QM/MM umbrella sampling simulation,enzyme activity assay,site-directed mutagenesis,and spectroscopic analysis to elucidate the oxidation mechanism of FAD to 8-formyl FAD.Our results reveal that a catalytic water molecule,rather than any catalytic amino acids,serves as a general base to deprotonate the C8 methyl group on FAD,thus facilitating the formation of a quinone-methide tautomer intermediate.An oxygen molecule subsequently oxidizes this intermediate,resulting in a C8 methyl hydroperoxide anion that is protonated and dissociated to form OHC-RP and OH−.During the oxidation of FAD to 8-formyl FAD,the energy barrier for the rate-limiting step is calculated to be 22.8 kcal/mol,which corresponds to the required 14-hour transformation time observed experimentally.Further,the elucidated oxidation mechanism reveals that the autocatalytic formation of 8-formyl FAD depends on the proximal arginine and serine residues,R87 and S94,respectively.Enzymatic activity assay validates that the mutation of R87 to lysine reduces the kcat value to 75%of the wild-type,while the mutation to histidine results in a complete loss of activity.Similarly,the mutant S94I also leads to the deactivation of enzyme.This dependency arises because the nucleophilic OH−group and the quinone-methide tautomer intermediate are stabilized through the noncovalent interaction provided by R87 and S94.These findings not only explain the mechanistic details of each reaction step but also clarify the functional role of R87 and S94 during the oxidative maturation of 8-formyl FAD,thereby providing crucial theoretical support for the development of novel flavoenzymes with enhanced redox properties.
