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Lopes TJS, Nogueira T, Rios R. A Machine Learning Framework Predicts the Clinical Severity of Hemophilia B Caused by Point-Mutations. FRONTIERS IN BIOINFORMATICS 2022; 2:912112. [DOI: 10.3389/fbinf.2022.912112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 06/01/2022] [Indexed: 11/13/2022] Open
Abstract
Blood coagulation is a vital physiological mechanism to stop blood loss following an injury to a blood vessel. This process starts immediately upon damage to the endothelium lining a blood vessel, and results in the formation of a platelet plug that closes the site of injury. In this repair operation, an essential component is the coagulation factor IX (FIX), a serine protease encoded by the F9 gene and whose deficiency causes hemophilia B. If not treated by prophylaxis or gene therapy, patients with this condition are at risk of life-threatening bleeding episodes. In this sense, a deep understanding of the FIX protein and its activated form (FIXa) is essential to develop efficient therapeutics. In this study, we used well-studied structural analysis techniques to create a residue interaction network of the FIXa protein. Here, the nodes are the amino acids of FIXa, and two nodes are connected by an edge if the two residues are in close proximity in the FIXa 3D structure. This representation accurately captured fundamental properties of each amino acid of the FIXa structure, as we found by validating our findings against hundreds of clinical reports about the severity of HB. Finally, we established a machine learning framework named HemB-Class to predict the effect of mutations of all FIXa residues to all other amino acids and used it to disambiguate several conflicting medical reports. Together, these methods provide a comprehensive map of the FIXa protein architecture and establish a robust platform for the rational design of FIX therapeutics.
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Valikhani A, Mirakhorly M, Namvar A, Rastegarlari G, Toogeh G, Shirayeh FV, Ahmadinejad M. Genetic analysis of non-severe hemophilia A phenotype with A discrepancy between one-stage and chromogenic factor VIII activity assays. Transfus Apher Sci 2021; 60:103194. [PMID: 34275734 DOI: 10.1016/j.transci.2021.103194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Revised: 05/26/2021] [Accepted: 06/11/2021] [Indexed: 10/20/2022]
Abstract
INTRODUCTION The diagnosis of hemophilia A (HA) is based on the measurement of factor VIII activity (VIII:C). About one-third of non-severe HA patients show a discrepancy of VIII:C measured by one-stage (VIII:C 1st) and chromogenic (VIII:C chr) assays. Different mutations in the F8 gene may cause the discrepancy in results of the FVIII activity assay. The aim of this study was to investigate F8 gene mutations in patients with assay discrepancies and to evaluate their impact on the results of VIII:C assays. METHODS Mutation analysis was performed on 41 individuals with a discrepancy in VIII:C 1st and FVIII: C chr assays by direct sequencing. In addition, the effect of the variants on FVIII macromolecule structure was investigated by in silico and bioinformatics tools. RESULTS Genetic analysis disclosed 22 different variants, of which 19 were identified for the first time to be involved in the phenotype of VIII:C discrepancy. Most of the variants related to the higher VIII:C 1st were found in A1, A2, A3 domains. The variant related to VIII:C chr > VIII:C 1st was located in the thrombin cleavage site. In silico analysis showed the effect of variants on FVIII macromolecule stability, which may be the possible mechanism causing the discrepancy. CONCLUSION Our data shed light on the impact of genetic defects on VIII:C assay and provided evidence that the consideration of these mutations may open a new window to the proper diagnosis and treatment monitoring of non-severe HA patients.
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Affiliation(s)
- Amir Valikhani
- Blood Transfusion Research Center, High Institute for Research and Education in Transfusion Medicine, Tehran, Iran
| | | | - Ali Namvar
- Iranian Comprehensive Haemophilia Care Center, Tehran, Iran
| | | | - Gholamreza Toogeh
- Imam Khomeini Hospital, Tehran University of Medical Sciences, Tehran, Iran
| | - Fatemeh Vossough Shirayeh
- Blood Transfusion Research Center, High Institute for Research and Education in Transfusion Medicine, Tehran, Iran
| | - Minoo Ahmadinejad
- Blood Transfusion Research Center, High Institute for Research and Education in Transfusion Medicine, Tehran, Iran.
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Lopes TJS, Rios R, Nogueira T, Mello RF. Protein residue network analysis reveals fundamental properties of the human coagulation factor VIII. Sci Rep 2021; 11:12625. [PMID: 34135429 PMCID: PMC8209229 DOI: 10.1038/s41598-021-92201-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 06/08/2021] [Indexed: 11/09/2022] Open
Abstract
Hemophilia A is an X-linked inherited blood coagulation disorder caused by the production and circulation of defective coagulation factor VIII protein. People living with this condition receive either prophylaxis or on-demand treatment, and approximately 30% of patients develop inhibitor antibodies, a serious complication that limits treatment options. Although previous studies performed targeted mutations to identify important residues of FVIII, a detailed understanding of the role of each amino acid and their neighboring residues is still lacking. Here, we addressed this issue by creating a residue interaction network (RIN) where the nodes are the FVIII residues, and two nodes are connected if their corresponding residues are in close proximity in the FVIII protein structure. We studied the characteristics of all residues in this network and found important properties related to disease severity, interaction to other proteins and structural stability. Importantly, we found that the RIN-derived properties were in close agreement with in vitro and clinical reports, corroborating the observation that the patterns derived from this detailed map of the FVIII protein architecture accurately capture the biological properties of FVIII.
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Affiliation(s)
- Tiago J S Lopes
- Department of Reproductive Biology, Center for Regenerative Medicine, National Center for Child Health and Development Research Institute, 2-10-1 Okura, Setagaya-ku, Tokyo, 157-8535, Japan.
| | - Ricardo Rios
- Department of Computer Science, Federal University of Bahia, Salvador, Brazil.,Institute of Mathematics and Computer Science, University of São Paulo, São Paulo, Brazil
| | - Tatiane Nogueira
- Department of Computer Science, Federal University of Bahia, Salvador, Brazil.,Institute of Mathematics and Computer Science, University of São Paulo, São Paulo, Brazil
| | - Rodrigo F Mello
- Institute of Mathematics and Computer Science, University of São Paulo, São Paulo, Brazil.,Itaú Unibanco, Av. Eng. Armando de Arruda Pereira, 707, Jabaquara, São Paulo, 04309-010, Brazil
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In silico and in vitro evaluation of the impact of mutations in non-severe haemophilia A patients on assay discrepancies. Ann Hematol 2019; 98:1855-1865. [DOI: 10.1007/s00277-019-03691-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Accepted: 04/07/2019] [Indexed: 11/25/2022]
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Valentino LA, Turecek PL, Gritsch H, Butenas S, Mann KG. Issues complicating precision dosing for factor VIII prophylaxis. Transfus Apher Sci 2018; 57:472-479. [DOI: 10.1016/j.transci.2018.07.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Shearin S, Venkateswarlu D. Computational analysis of Asp519 and Glu665 mutations of coagulation factor FVIIIa: Implications for enhanced binding affinity of A2-domain. J Mol Graph Model 2017; 76:441-447. [DOI: 10.1016/j.jmgm.2017.07.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2017] [Revised: 07/20/2017] [Accepted: 07/21/2017] [Indexed: 11/25/2022]
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Venkateswarlu D. Structural insights into the interaction of blood coagulation co-factor VIIIa with factor IXa: a computational protein-protein docking and molecular dynamics refinement study. Biochem Biophys Res Commun 2014; 452:408-14. [PMID: 25157807 DOI: 10.1016/j.bbrc.2014.08.078] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2014] [Accepted: 08/18/2014] [Indexed: 11/16/2022]
Abstract
Coagulation factor X (FX) zymogen activation by factor IXa (FIXa) enzyme plays a critical role in the middle-phase of coagulation cascade. The activation process is catalytically inert and requires FIXa binding and complex formation with co-factor VIIIa (FVIIIa). In order to understand the structural details of the FVIIIa:FIXa complex, we employed knowledge-driven protein-protein docking and aqueous-phase MD refinement methods to develop a stable structural complex between FVIIIa and FIXa. The model shows that all four domains of FIXa wrap across FVIIIa that spans the co-factor binding surface of A2, A3 and C1 domains. The region surrounding the 558-helix of the A2-domain of FVIIIa is predicted to be the key interaction site with the helical segments of Lys293-Lys301 and Asp332-Arg338 residues of the serine-protease domain of FIXa. The hydrophobic helical stack between the GLA and EGF1 domains of FIXa is predicted to be primary interacting region with the A3-C2 domain interface of FVIIIa.
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Affiliation(s)
- Divi Venkateswarlu
- Department of Chemistry, North Carolina Agricultural and Technical State University, Greensboro, NC 27411, USA.
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Venkateswarlu D. Role of hydrophobic mutations on the binding affinity and stability of blood coagulation factor VIIIa: a computational molecular dynamics and free-energy analysis. Biochem Biophys Res Commun 2014; 450:735-40. [PMID: 24952158 DOI: 10.1016/j.bbrc.2014.06.043] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2014] [Accepted: 06/10/2014] [Indexed: 10/25/2022]
Abstract
Factor VIIIa is a non-covalently bound hetero-trimer among A1, A2 and A3-C1-C2 domains and an essential co-factor for factor IXa enzyme during proteolytic activation of factor X zymogen. The relatively weak interactions between A2 and the interface A1/A3 domains dampen the functional stability of FVIIIa in plasma and results in rapid degradation. We studied the mutational effect of three charged residues (Asp519, Glu665 and Asp666) to several hydrophobic residues by molecular dynamics simulations. Analysis of the binding free energy by MM-PBSA and MM-GBSA methods shows that the mutation of Asp519 and Glu665 residues to either Val or Ala enhance the A2 domain binding affinity in agreement with the experimental site-specific mutagenesis data. Mutation of Asp666 to Val, Tyr, Met and Phe showed largest improvement in the A2-domain binding among the eight hydrophobic mutants studied. Our studies suggest that the enrichment of hydrophobic interactions in the buried surface regions of A2 domain plays crucial role in improving the overall stability of FVIIIa.
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Affiliation(s)
- Divi Venkateswarlu
- Department of Chemistry, North Carolina Agricultural and Technical State University, Greensboro, NC 27411, USA.
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Lapalud P, Ali T, Cayzac C, Mathieu-Dupas E, Levesque H, Pfeiffer C, Balicchi J, Gruel Y, Borg JY, Schved JF, Granier C, Lavigne-Lissalde G. The IgG autoimmune response in postpartum acquired hemophilia A targets mainly the A1a1 domain of FVIII. J Thromb Haemost 2012; 10:1814-22. [PMID: 22784315 DOI: 10.1111/j.1538-7836.2012.04850.x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
BACKGROUND Acquired hemophilia A (AHA) is a severe life-threatening autoimmune disease due to the development of autoantibodies that neutralize the procoagulant activity of factor VIII (FVIII). In rare cases, AHA occurs in the postpartum period as a serious complication of an otherwise normal pregnancy and delivery. Due to its rarity, little is known about the features of the antibody response to FVIII in AHA. OBJECTIVES Our study wanted to (i) determine the epitope specificity and the immunoglobulin (Ig) subclasses of anti-FVIII autoantibodies in plasma samples from a large cohort of AHA patients, and (ii) compare the epitope specificity of anti-FVIII autoantibodies in plasma samples from postpartum AHA and other AHA patients. PATIENTS/METHODS Seventy-three plasma samples from patients with postpartum AHA (n = 10) or associated with malignancies (n = 16) or autoimmune diseases (n = 11) or without underlying disease (n = 36) were analyzed with three multiplexed assays. RESULTS AND CONCLUSIONS Our results showed a stronger response against the A1a1-A2a2-B fragments of FVIII and more specifically against the A1a1 domain in patients with postpartum AHA than in the other AHA groups (P < 0.01). Moreover, although IgG4 was the predominant IgG subclass in all groups, anti-A1a1-A2a2-B and anti-A1a1 domain autoantibodies of the IgG(1) and IgG3 subclasses were more frequently detected in postpartum AHA than in the other AHA groups. These findings support the involvement of the Th1-driven response in the generation of autoantibodies in women with postpartum AHA compared with the other groups of AHA patients in whom production of Th2-driven IgG4 was predominant.
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Affiliation(s)
- P Lapalud
- SysDiag, UMR3145 CNRS/BioRad, Montpellier, France.
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Click TH, Ponomarev SY, Kaminski GA. Importance of electrostatic polarizability in calculating cysteine acidity constants and copper(I) binding energy of Bacillus subtilis CopZ. J Comput Chem 2012; 33:1142-51. [PMID: 22370900 DOI: 10.1002/jcc.22944] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2011] [Revised: 12/13/2011] [Accepted: 01/08/2012] [Indexed: 11/09/2022]
Abstract
CopZ is a copper chaperone from Bacillus subtilis. It is an important part of Cu(I) trafficking. We have calculated pK(a) values for the CXXC motif of this protein, which is responsible for the Cu(I) binding, and the Cu(I) binding constants. Polarizable and fixed-charges formalisms were used, and solvation parameters for the both models have been refitted. We had to partially redevelop parameters for the protonated and deprotonated cysteine residues. We have discovered that the polarizable force field (PFF) is qualitatively superior and allows a uniformly better level of energetic results. The PFF pK(a) values for cysteine are within about 0.8-2.8 pH units of the experimental data, while the fixed-charges OPLS formalism yields errors of up to tens of units. The PFF magnitude of the copper binding energy is about 10 kcal/mol or 50% higher than the experimental value, while the using the refitted OPLS parameters leads to an overall positive binding energy, thus predicting no thermodynamically stable complex. At the same time, the agreement of the polarizable S···Cu(I) distances with the experimental results is within 0.08 Å range, and the nonpolarizable calculations lead to an error of about 0.4 Å. Moreover, the accuracy of the PFF has been achieved without any explicit fitting to either pK(a) or CopZ···Cu(I) binding energies. We believe that this makes our polarizable technique a choice method in reproducing protein-copper binding and further supports the notion that explicit treatment of electrostatic polarization is crucial in many biologically relevant studies, especially ion binding and transport.
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Affiliation(s)
- Timothy H Click
- Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Worcester, MA 01609, USA
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Bloem E, Meems H, van den Biggelaar M, van der Zwaan C, Mertens K, Meijer AB. Mass spectrometry-assisted study reveals that lysine residues 1967 and 1968 have opposite contribution to stability of activated factor VIII. J Biol Chem 2012; 287:5775-83. [PMID: 22215677 PMCID: PMC3285348 DOI: 10.1074/jbc.m111.308627] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2011] [Revised: 12/13/2011] [Indexed: 11/06/2022] Open
Abstract
The A2 domain rapidly dissociates from activated factor VIII (FVIIIa) resulting in a dampening of the activity of the activated factor X-generating complex. The amino acid residues that affect A2 domain dissociation are therefore critical for FVIII cofactor function. We have now employed chemical footprinting in conjunction with mass spectrometry to identify lysine residues that contribute to the stability of activated FVIII. We hypothesized that lysine residues, which are buried in FVIII and surface-exposed in dissociated activated FVIII (dis-FVIIIa), may contribute to interdomain interactions. Mass spectrometry analysis revealed that residues Lys(1967) and Lys(1968) of region Thr(1964)-Tyr(1971) are buried in FVIII and exposed to the surface in dis-FVIIIa. This result, combined with the observation that the FVIII variant K1967I is associated with hemophilia A, suggests that these residues contribute to the stability of activated FVIII. Kinetic analysis revealed that the FVIII variants K1967A and K1967I exhibit an almost normal cofactor activity. However, these variants also showed an increased loss in cofactor activity over time compared with that of FVIII WT. Remarkably, the cofactor activity of a K1968A variant was enhanced and sustained for a prolonged time relative to that of FVIII WT. Surface plasmon resonance analysis demonstrated that A2 domain dissociation from activated FVIII was reduced for K1968A and enhanced for K1967A. In conclusion, mass spectrometry analysis combined with site-directed mutagenesis studies revealed that the lysine couple Lys(1967)-Lys(1968) within region Thr(1964)-Tyr(1971) has an opposite contribution to the stability of FVIIIa.
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Affiliation(s)
- Esther Bloem
- From the Department of Plasma Proteins, Sanquin Research, 1066 CX Amsterdam, The Netherlands and
| | - Henriet Meems
- From the Department of Plasma Proteins, Sanquin Research, 1066 CX Amsterdam, The Netherlands and
| | | | - Carmen van der Zwaan
- From the Department of Plasma Proteins, Sanquin Research, 1066 CX Amsterdam, The Netherlands and
| | - Koen Mertens
- From the Department of Plasma Proteins, Sanquin Research, 1066 CX Amsterdam, The Netherlands and
- Pharmaceutical Sciences, Utrecht Institute for Pharmaceutical Sciences, Utrecht University, 3584 CG Utrecht, The Netherlands
| | - Alexander B. Meijer
- From the Department of Plasma Proteins, Sanquin Research, 1066 CX Amsterdam, The Netherlands and
- Pharmaceutical Sciences, Utrecht Institute for Pharmaceutical Sciences, Utrecht University, 3584 CG Utrecht, The Netherlands
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Ponomarev SY, Click TH, Kaminski GA. Electrostatic polarization is crucial in reproducing Cu(I) interaction energies and hydration. J Phys Chem B 2011; 115:10079-85. [PMID: 21761909 DOI: 10.1021/jp2051933] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We have explored the suitability of fixed-charges and polarizable force fields for modeling interactions of the monovalent Cu(I) ion. Parameters for this ion have been tested and refitted within the fixed-charges OPLS-AA and polarizable force field (PFF) frameworks. While this ion plays an important role in many protein interactions, the attention to it in developing empirical force fields is limited. Our PFF parameters for the copper ion worked very well for the Cu(I) interactions with water, while both the original OPLS2005 and our refitted OPLS versions moderately underestimated the copper-water interaction energy. However, the greatest problem in using the nonpolarizable fixed-charges OPLS force field was observed while calculating interaction energies and distances for Cu(I)-benzene complexes. The OPLS2005 model underestimates the interaction energy by a factor of 4. Refitting the OPLS parameters reduced this underestimation to a factor of 2.2-2.4, but only at a cost of distorting the complex geometry. At the same time, the polarizable calculations had an error of about 4%. Moreover, we then used the PFF and nonpolarizable refitted OPLS models for finding free energy of hydration for copper ion via molecular dynamics simulations. While the OPLS calculations lead to a 22% error in the solvation energy, the PFF result was off by only 1.8%. This was achieved with no refitting of the parameters but simply by employing the model developed for the Cu(I) interaction with a single water molecule. We believe that the presented results not only lead to a conclusion about a qualitatively greater suitability of polarizable force fields for simulating molecular interactions with ions but also attest to the excellent level of transferability of PFF parameters.
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Affiliation(s)
- Sergei Y Ponomarev
- Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, USA
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Anandakrishnan R, Daga M, Onufriev AV. An n log n Generalized Born Approximation. J Chem Theory Comput 2011; 7:544-59. [PMID: 26596289 DOI: 10.1021/ct100390b] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Molecular dynamics (MD) simulations based on the generalized Born (GB) model of implicit solvation offer a number of important advantages over the traditional explicit solvent based simulations. Yet, in MD simulations, the GB model has not been able to reach its full potential partly due to its computational cost, which scales as ∼n(2), where n is the number of solute atoms. We present here an ∼n log n approximation for the generalized Born (GB) implicit solvent model. The approximation is based on the hierarchical charge partitioning (HCP) method (Anandakrishnan and Onufriev J. Comput. Chem. 2010 , 31 , 691 - 706 ) previously developed and tested for electrostatic computations in gas-phase and distant dependent dielectric models. The HCP uses the natural organization of biomolecular structures to partition the structures into multiple hierarchical levels of components. The charge distribution for each of these components is approximated by a much smaller number of charges. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. To apply the HCP concept to the GB model, we define the equivalent of the effective Born radius for components. The component effective Born radius is then used in GB computations for points that are distant from the component. This HCP approximation for GB (HCP-GB) is implemented in the open source MD software, NAB in AmberTools, and tested on a set of representative biomolecular structures ranging in size from 632 atoms to ∼3 million atoms. For this set of test structures, the HCP-GB method is 1.1-390 times faster than the GB computation without additional approximations (the reference GB computation), depending on the size of the structure. Similar to the spherical cutoff method with GB (cutoff-GB), which also scales as ∼n log n, the HCP-GB is relatively simple. However, for the structures considered here, we show that the HCP-GB method is more accurate than the cutoff-GB method as measured by relative RMS error in electrostatic force compared to the reference (no cutoff) GB computation. MD simulations of four biomolecular structures on 50 ns time scales show that the backbone RMS deviation for the HCP-GB method is in reasonable agreement with the reference GB simulation. A critical difference between the cutoff-GB and HCP-GB methods is that the cutoff-GB method completely ignores interactions due to atoms beyond the cutoff distance, whereas the HCP-GB method uses an approximation for interactions due to distant atoms. Our testing suggests that completely ignoring distant interactions, as the cutoff-GB does, can lead to qualitatively incorrect results. In general, we found that the HCP-GB method reproduces key characteristics of dynamics, such as residue fluctuation, χ1/χ2 flips, and DNA flexibility, more accurately than the cutoff-GB method. As a practical demonstration, the HCP-GB simulation of a 348 000 atom chromatin fiber was used to refine the starting structure. Our findings suggest that the HCP-GB method is preferable to the cutoff-GB method for molecular dynamics based on pairwise implicit solvent GB models.
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Affiliation(s)
- Ramu Anandakrishnan
- Department of Computer Science and ‡Department of Computer Science and Physics, Virginia Tech , Blacksburg, Virginia 24061, United States
| | - Mayank Daga
- Department of Computer Science and ‡Department of Computer Science and Physics, Virginia Tech , Blacksburg, Virginia 24061, United States
| | - Alexey V Onufriev
- Department of Computer Science and ‡Department of Computer Science and Physics, Virginia Tech , Blacksburg, Virginia 24061, United States
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