1
|
Gaughran SK, Rickman JM, Haaga J, Gunton JD. Monte Carlo simulations of patch models with applications to soft matter. SOFT MATTER 2020; 16:8628-8638. [PMID: 32844865 DOI: 10.1039/d0sm01110j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Patch models have been employed to describe anisotropic interactions in disparate soft matter systems. In this work, we present a unified study of a patch model to explore particle self-assembly in both monodisperse and polydisperse systems, with applications to both proteins and colloids. In the first case, we obtained a temperature-density phase diagram for a model of the protein polyglutamine from Monte Carlo simulations. These simulations evinced clusters in the gas phase and, via a comparison with the corresponding coarse-grained PLUM model for this system, we verified that dense clustering in the gas phase falls into the supersaturation region of the saturation curve. In the second case, we have investigated the effect of size polydispersity on the phase behavior of binary colloidal mixtures. It was found that the width of gas-liquid phase coexistence increases with increasing polydispersity and that, in addition to the aforementioned particle clustering, small particles decorate patches on large particles, thereby creating large-particle bridges. Our aim is to compare and contrast self-assembly in these two prototypical systems.
Collapse
Affiliation(s)
- S K Gaughran
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA.
| | - J M Rickman
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA. and Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA
| | - J Haaga
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA.
| | - J D Gunton
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA.
| |
Collapse
|
2
|
Trotter D, Wallin S. Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations. Biophys J 2020; 118:1370-1380. [PMID: 32061276 DOI: 10.1016/j.bpj.2020.01.020] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Revised: 12/17/2019] [Accepted: 01/13/2020] [Indexed: 01/18/2023] Open
Abstract
Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or "width" of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.
Collapse
Affiliation(s)
- Daniel Trotter
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland, Canada
| | - Stefan Wallin
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland, Canada.
| |
Collapse
|
3
|
Kaushik AC, Mehmood A, Khan MT, Kumar A, Dai X, Wei DQ. RETRACTED ARTICLE: Protein blueprint and their interactions while approachability struggle for amino acids. J Biomol Struct Dyn 2020; 39:i-ix. [PMID: 31914855 DOI: 10.1080/07391102.2020.1713894] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
| | - Aamir Mehmood
- School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai, China
| | - Muhammad Tahir Khan
- Department of Bioinformatics and Biosciences, Capital University of Science and Technology, Islamabad, Pakistan
| | - Ajay Kumar
- Institute of Biomedical Sciences, National Sun Yat-Sen University, Kaohsiung City, Taiwan
| | - Xiaofeng Dai
- Wuxi School of Medicine, Jiangnan University, Wuxi, China
| | - Dong-Qing Wei
- School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai, China
| |
Collapse
|
4
|
Recent Advances in Coarse-Grained Models for Biomolecules and Their Applications. Int J Mol Sci 2019; 20:ijms20153774. [PMID: 31375023 PMCID: PMC6696403 DOI: 10.3390/ijms20153774] [Citation(s) in RCA: 60] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Revised: 07/28/2019] [Accepted: 07/30/2019] [Indexed: 12/23/2022] Open
Abstract
Molecular dynamics simulations have emerged as a powerful tool to study biological systems at varied length and timescales. The conventional all-atom molecular dynamics simulations are being used by the wider scientific community in routine to capture the conformational dynamics and local motions. In addition, recent developments in coarse-grained models have opened the way to study the macromolecular complexes for time scales up to milliseconds. In this review, we have discussed the principle, applicability and recent development in coarse-grained models for biological systems. The potential of coarse-grained simulation has been reviewed through state-of-the-art examples of protein folding and structure prediction, self-assembly of complexes, membrane systems and carbohydrates fiber models. The multiscale simulation approaches have also been discussed in the context of their emerging role in unravelling hierarchical level information of biosystems. We conclude this review with the future scope of coarse-grained simulations as a constantly evolving tool to capture the dynamics of biosystems.
Collapse
|
5
|
Cardelli C, Nerattini F, Tubiana L, Bianco V, Dellago C, Sciortino F, Coluzza I. General Methodology to Identify the Minimum Alphabet Size for Heteropolymer Design. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201900031] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Chiara Cardelli
- Faculty of PhysicsUniversity of ViennaBoltzmanngasse 5 1090 Vienna Austria
| | | | - Luca Tubiana
- Faculty of PhysicsUniversity of ViennaBoltzmanngasse 5 1090 Vienna Austria
| | - Valentino Bianco
- Faculty of ChemistryChemical Physics DepartmentUniversidad Complutense de Madrid, Plaza de las Ciencias, Ciudad UniversitariaMadrid 28040 Spain
| | - Christoph Dellago
- Faculty of PhysicsUniversity of ViennaBoltzmanngasse 5 1090 Vienna Austria
| | - Francesco Sciortino
- Dipartimento di FisicaSapienza Università di RomaPiazzale Aldo Moro 2 00185 Rome Italy
| | - Ivan Coluzza
- CIC biomaGUNEPaseo Miramon 182 20014 San Sebastian Spain
- IKERBASQUEBasque Foundation for Science48013 Bilbao Spain
| |
Collapse
|
6
|
Nerattini F, Tubiana L, Cardelli C, Bianco V, Dellago C, Coluzza I. Design of Protein–Protein Binding Sites Suggests a Rationale for Naturally Occurring Contact Areas. J Chem Theory Comput 2018; 15:1383-1392. [DOI: 10.1021/acs.jctc.8b00667] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Francesca Nerattini
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Luca Tubiana
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Chiara Cardelli
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Valentino Bianco
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Ivan Coluzza
- CIC biomaGUNE, Paseo Miramon 182, 20014 San Sebastian, Spain
- IKERBASQUE,
Basque Foundation for Science, 48013 Bilbao, Spain
| |
Collapse
|
7
|
Kamberaj H. Faster protein folding using enhanced conformational sampling of molecular dynamics simulation. J Mol Graph Model 2018; 81:32-49. [PMID: 29501958 DOI: 10.1016/j.jmgm.2018.02.008] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2017] [Revised: 01/19/2018] [Accepted: 02/14/2018] [Indexed: 10/18/2022]
Abstract
In this study, we applied swarm particle-like molecular dynamics (SPMD) approach to enhance conformational sampling of replica exchange simulations. In particular, the approach showed significant improvement in sampling efficiency of conformational phase space when combined with replica exchange method (REM) in computer simulation of peptide/protein folding. First we introduce the augmented dynamical system of equations, and demonstrate the stability of the algorithm. Then, we illustrate the approach by using different fully atomistic and coarse-grained model systems, comparing them with the standard replica exchange method. In addition, we applied SPMD simulation to calculate the time correlation functions of the transitions in a two dimensional surface to demonstrate the enhancement of transition path sampling. Our results showed that folded structure can be obtained in a shorter simulation time using the new method when compared with non-augmented dynamical system. Typically, in less than 0.5 ns using replica exchange runs assuming that native folded structure is known and within simulation time scale of 40 ns in the case of blind structure prediction. Furthermore, the root mean square deviations from the reference structures were less than 2Å. To demonstrate the performance of new method, we also implemented three simulation protocols using CHARMM software. Comparisons are also performed with standard targeted molecular dynamics simulation method.
Collapse
Affiliation(s)
- Hiqmet Kamberaj
- Department of Computer Engineering, Faculty of Engineering, International Balkan University, Tashko Karadza 11A, Skopje, Republic of Macedonia.
| |
Collapse
|
8
|
Bore SL, Milano G, Cascella M. Hybrid Particle-Field Model for Conformational Dynamics of Peptide Chains. J Chem Theory Comput 2018; 14:1120-1130. [DOI: 10.1021/acs.jctc.7b01160] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Sigbjørn Løland Bore
- Department
of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, P.O.
Box 1033 Blindern, 0315 Oslo, Norway
| | - Giuseppe Milano
- Department
of Organic Materials Science, University of Yamagata, 4-3-16 Jonan
Yonezawa, Yamagata-ken 992-8510, Japan
| | - Michele Cascella
- Department
of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, P.O.
Box 1033 Blindern, 0315 Oslo, Norway
| |
Collapse
|
9
|
Ramezanghorbani F, Dalgicdir C, Sayar M. A multi-state coarse grained modeling approach for an intrinsically disordered peptide. J Chem Phys 2017; 147:094103. [DOI: 10.1063/1.5001087] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
|
10
|
Williams MJ, Bachmann M. The effect of surface adsorption on tertiary structure formation in helical polymers. J Chem Phys 2017; 147:024902. [DOI: 10.1063/1.4991564] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew J. Williams
- Institute of Engineering, Murray State University, Murray, Kentucky 42071, USA
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| |
Collapse
|
11
|
The role of directional interactions in the designability of generalized heteropolymers. Sci Rep 2017; 7:4986. [PMID: 28694466 PMCID: PMC5504045 DOI: 10.1038/s41598-017-04720-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Accepted: 05/18/2017] [Indexed: 12/31/2022] Open
Abstract
Heteropolymers are important examples of self-assembling systems. However, in the design of artificial heteropolymers the control over the single chain self-assembling properties does not reach that of the natural bio-polymers, and in particular proteins. Here, we introduce a sufficiency criterion to identify polymers that can be designed to adopt a predetermined structure and show that it is fulfilled by polymers made of monomers interacting through directional (anisotropic) interactions. The criterion is based on the appearance of a particular peak in the radial distribution function, that we show being a universal feature of all designable heteropolymers, as it is present also in natural proteins. Our criterion can be used to engineer new self-assembling modular polymers that will open new avenues for applications in materials science.
Collapse
|
12
|
Takeuchi H. Two Perturbations for Geometry Optimization of Off-lattice Bead Protein Models. Mol Inform 2017; 36. [PMID: 28452128 DOI: 10.1002/minf.201600096] [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: 07/11/2016] [Accepted: 04/05/2017] [Indexed: 12/22/2022]
Abstract
Referring to the optimization algorithm previously developed for atomic clusters, the present author develops an efficient method for geometry optimization of a coarse-grained protein model expressed with two kinds of beads (hydrophilic and hydrophobic ones). In the method, two types of geometrical perturbations, center-directed bead move and one bead rotation, are used to explore new configurations and local optimizations are performed after the perturbations. The center-directed bead move is used for hydrophobic beads and the one bead rotation is performed for both hydrophobic and hydrophilic beads. The optimization method was applied to protein models consisting of 13, 20, 21, and 34 beads. The present method produced the global minima of the 13-, 21-, and 34-bead models reported in the literature and updated the lowest energies of the protein models with 20 beads. These results indicate that the present method is efficient for searching for optimal structures of proteins.
Collapse
Affiliation(s)
- Hiroshi Takeuchi
- Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan
| |
Collapse
|
13
|
Coluzza I. Computational protein design: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:143001. [PMID: 28140371 DOI: 10.1088/1361-648x/aa5c76] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Proteins are one of the most versatile modular assembling systems in nature. Experimentally, more than 110 000 protein structures have been identified and more are deposited every day in the Protein Data Bank. Such an enormous structural variety is to a first approximation controlled by the sequence of amino acids along the peptide chain of each protein. Understanding how the structural and functional properties of the target can be encoded in this sequence is the main objective of protein design. Unfortunately, rational protein design remains one of the major challenges across the disciplines of biology, physics and chemistry. The implications of solving this problem are enormous and branch into materials science, drug design, evolution and even cryptography. For instance, in the field of drug design an effective computational method to design protein-based ligands for biological targets such as viruses, bacteria or tumour cells, could give a significant boost to the development of new therapies with reduced side effects. In materials science, self-assembly is a highly desired property and soon artificial proteins could represent a new class of designable self-assembling materials. The scope of this review is to describe the state of the art in computational protein design methods and give the reader an outline of what developments could be expected in the near future.
Collapse
Affiliation(s)
- Ivan Coluzza
- Computational Physics, Faculty of Physics, University of Vienna, Vienna, Austria
| |
Collapse
|
14
|
Krobath H, Chen T, Chan HS. Volumetric Physics of Polypeptide Coil–Helix Transitions. Biochemistry 2016; 55:6269-6281. [DOI: 10.1021/acs.biochem.6b00802] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Heinrich Krobath
- Departments of Biochemistry
and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Tao Chen
- Departments of Biochemistry
and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Departments of Biochemistry
and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| |
Collapse
|
15
|
Williams MJ, Bachmann M. System-Size Dependence of Helix-Bundle Formation for Generic Semiflexible Polymers. Polymers (Basel) 2016; 8:polym8070245. [PMID: 30974521 PMCID: PMC6431926 DOI: 10.3390/polym8070245] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2016] [Revised: 06/20/2016] [Accepted: 06/20/2016] [Indexed: 11/16/2022] Open
Abstract
Helical polymer bundles are an important fixture in biomolecular systems. The particular structural geometry of helix bundles is dependent on many factors including the length of the polymer chain. In this study, we performed Monte Carlo simulations of a coarse-grained model for helical polymers to determine the influence of polymer length on tertiary structure formation. Helical structures of semiflexible polymers are analyzed for several chain lengths under thermal conditions. Structural hyperphase diagrams, parametrized by torsion strength and temperature, are constructed and compared.
Collapse
Affiliation(s)
- Matthew J Williams
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, GA 30602, USA.
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, GA 30602, USA.
- Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá (MT), Brazil.
- Departamento de Física, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte (MG), Brazil.
| |
Collapse
|
16
|
Williams MJ, Bachmann M. Significance of bending restraints for the stability of helical polymer conformations. Phys Rev E 2016; 93:062501. [PMID: 27415311 DOI: 10.1103/physreve.93.062501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Indexed: 01/30/2023]
Abstract
We performed parallel-tempering Monte Carlo simulations to investigate the formation and stability of helical tertiary structures for flexible and semiflexible polymers, employing a generic coarse-grained model. Structural conformations exhibit helical order with tertiary ordering into single helices, multiple helical segments organized into bundles, and disorganized helical arrangements. For both bending-restrained semiflexible and bending-unrestrained flexible helical polymers, the stability of the structural phases is discussed systematically by means of hyperphase diagrams parametrized by suitable order parameters, temperature, and torsion strength. This exploration lends insight into the restricted flexibility of biological polymers such as double-stranded DNA and proteins.
Collapse
Affiliation(s)
- Matthew J Williams
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.,Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá (MT), Brazil.,Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte (MG), Brazil
| |
Collapse
|
17
|
From residue coevolution to protein conformational ensembles and functional dynamics. Proc Natl Acad Sci U S A 2015; 112:13567-72. [PMID: 26487681 DOI: 10.1073/pnas.1508584112] [Citation(s) in RCA: 101] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
The analysis of evolutionary amino acid correlations has recently attracted a surge of renewed interest, also due to their successful use in de novo protein native structure prediction. However, many aspects of protein function, such as substrate binding and product release in enzymatic activity, can be fully understood only in terms of an equilibrium ensemble of alternative structures, rather than a single static structure. In this paper we combine coevolutionary data and molecular dynamics simulations to study protein conformational heterogeneity. To that end, we adapt the Boltzmann-learning algorithm to the analysis of homologous protein sequences and develop a coarse-grained protein model specifically tailored to convert the resulting contact predictions to a protein structural ensemble. By means of exhaustive sampling simulations, we analyze the set of conformations that are consistent with the observed residue correlations for a set of representative protein domains, showing that (i) the most representative structure is consistent with the experimental fold and (ii) the various regions of the sequence display different stability, related to multiple biologically relevant conformations and to the cooperativity of the coevolving pairs. Moreover, we show that the proposed protocol is able to reproduce the essential features of a protein folding mechanism as well as to account for regions involved in conformational transitions through the correct sampling of the involved conformers.
Collapse
|
18
|
Affiliation(s)
- Ivan Coluzza
- Department of Computational Physics, Faculty of Physics, University of Vienna , Vienna, Austria
| |
Collapse
|
19
|
Shao Q. Important roles of hydrophobic interactions in folding and charge interactions in misfolding of α-helix bundle protein. RSC Adv 2015. [DOI: 10.1039/c4ra14265a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
An enhanced-sampling molecular dynamics simulation is presented to quantitatively demonstrate the important roles of hydrophobic and charge interactions in the folding and misfolding of α-helix bundle protein, respectively.
Collapse
Affiliation(s)
- Qiang Shao
- Drug Discovery and Design Center
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
- China
| |
Collapse
|
20
|
Kar P, Feig M. Recent advances in transferable coarse-grained modeling of proteins. ADVANCES IN PROTEIN CHEMISTRY AND STRUCTURAL BIOLOGY 2014; 96:143-80. [PMID: 25443957 PMCID: PMC5366245 DOI: 10.1016/bs.apcsb.2014.06.005] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Computer simulations are indispensable tools for studying the structure and dynamics of biological macromolecules. Biochemical processes occur on different scales of length and time. Atomistic simulations cannot cover the relevant spatiotemporal scales at which the cellular processes occur. To address this challenge, coarse-grained (CG) modeling of the biological systems is employed. Over the last few years, many CG models for proteins continue to be developed. However, many of them are not transferable with respect to different systems and different environments. In this review, we discuss those CG protein models that are transferable and that retain chemical specificity. We restrict ourselves to CG models of soluble proteins only. We also briefly review recent progress made in the multiscale hybrid all-atom/CG simulations of proteins.
Collapse
Affiliation(s)
- Parimal Kar
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan, USA
| | - Michael Feig
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan, USA; Department of Chemistry, Michigan State University, East Lansing, Michigan, USA.
| |
Collapse
|
21
|
Ganesan SJ, Matysiak S. Role of Backbone Dipole Interactions in the Formation of Secondary and Supersecondary Structures of Proteins. J Chem Theory Comput 2014; 10:2569-2576. [PMID: 24932137 PMCID: PMC4053078 DOI: 10.1021/ct401087a] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2013] [Indexed: 11/28/2022]
Abstract
![]()
We present a generic solvated coarse-grained
protein model that
can be used to characterize the driving forces behind protein folding.
Each amino acid is coarse-grained with two beads, a backbone, and
a side chain. Although the backbone beads are modeled as polar entities,
side chains are hydrophobic, polar, or charged, thus allowing the
exploration of how sequence patterning determines a protein fold.
The change in orientation of the atoms of the coarse-grained unit
is captured by the addition of two oppositely charged dummy particles
inside the backbone coarse-grained bead. These two dummy charges represent
a dipole that can fluctuate, thus introducing structural polarization
into the coarse-grained model. Realistic α/β content is
achieved de novo without any biases in the force
field toward a particular secondary structure. The dipoles created
by the dummy particles interact with each other and drive the protein
models to fold into unique structures depending on the amino acid
patterning and presence of capping residues. We have also characterized
the role of dipole–dipole and dipole–charge interactions
in shaping the secondary and supersecondary structure of proteins.
Formation of helix bundles and β-strands are also discussed.
Collapse
Affiliation(s)
- Sai J Ganesan
- Fischell Department of Bioengineering, University of Maryland , College Park, Maryland 20742, United States
| | - S Matysiak
- Fischell Department of Bioengineering, University of Maryland , College Park, Maryland 20742, United States
| |
Collapse
|
22
|
Abstract
By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.
Collapse
Affiliation(s)
- W G Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| |
Collapse
|
23
|
Hills RD. Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics. Methods Mol Biol 2014; 1084:123-140. [PMID: 24061919 DOI: 10.1007/978-1-62703-658-0_7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.
Collapse
Affiliation(s)
- Ronald D Hills
- Department of Pharmaceutical Sciences, University of New England, Portland, ME, USA
| |
Collapse
|
24
|
Várnai C, Burkoff NS, Wild DL. Efficient Parameter Estimation of Generalizable Coarse-Grained Protein Force Fields Using Contrastive Divergence: A Maximum Likelihood Approach. J Chem Theory Comput 2013; 9:5718-5733. [PMID: 24683370 PMCID: PMC3966533 DOI: 10.1021/ct400628h] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2013] [Indexed: 01/05/2023]
Abstract
Maximum Likelihood (ML) optimization schemes are widely used for parameter inference. They maximize the likelihood of some experimentally observed data, with respect to the model parameters iteratively, following the gradient of the logarithm of the likelihood. Here, we employ a ML inference scheme to infer a generalizable, physics-based coarse-grained protein model (which includes Go̅-like biasing terms to stabilize secondary structure elements in room-temperature simulations), using native conformations of a training set of proteins as the observed data. Contrastive divergence, a novel statistical machine learning technique, is used to efficiently approximate the direction of the gradient ascent, which enables the use of a large training set of proteins. Unlike previous work, the generalizability of the protein model allows the folding of peptides and a protein (protein G) which are not part of the training set. We compare the same force field with different van der Waals (vdW) potential forms: a hard cutoff model, and a Lennard-Jones (LJ) potential with vdW parameters inferred or adopted from the CHARMM or AMBER force fields. Simulations of peptides and protein G show that the LJ model with inferred parameters outperforms the hard cutoff potential, which is consistent with previous observations. Simulations using the LJ potential with inferred vdW parameters also outperforms the protein models with adopted vdW parameter values, demonstrating that model parameters generally cannot be used with force fields with different energy functions. The software is available at https://sites.google.com/site/crankite/.
Collapse
Affiliation(s)
- Csilla Várnai
- Systems Biology Centre, University of Warwick, Coventry, United Kingdom
| | | | - David L. Wild
- Systems Biology Centre, University of Warwick, Coventry, United Kingdom
| |
Collapse
|
25
|
Kapoor A, Travesset A. Folding 19 proteins to their native state and stability of large proteins from a coarse-grained model. Proteins 2013; 82:505-16. [PMID: 24115081 DOI: 10.1002/prot.24416] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2013] [Revised: 08/23/2013] [Accepted: 09/04/2013] [Indexed: 11/10/2022]
Abstract
We develop an intermediate resolution model, where the backbone is modeled with atomic resolution but the side chain with a single bead, by extending our previous model (Proteins (2013) DOI: 10.1002/prot.24269) to properly include proline, preproline residues and backbone rigidity. Starting from random configurations, the model properly folds 19 proteins (including a mutant 2A3D sequence) into native states containing β sheet, α helix, and mixed α/β. As a further test, the stability of H-RAS (a 169 residue protein, critical in many signaling pathways) is investigated: The protein is stable, with excellent agreement with experimental B-factors. Despite that proteins containing only α helices fold to their native state at lower backbone rigidity, and other limitations, which we discuss thoroughly, the model provides a reliable description of the dynamics as compared with all atom simulations, but does not constrain secondary structures as it is typically the case in more coarse-grained models. Further implications are described.
Collapse
Affiliation(s)
- Abhijeet Kapoor
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011
| | | |
Collapse
|
26
|
Kar P, Gopal SM, Cheng YM, Predeus A, Feig M. PRIMO: A Transferable Coarse-grained Force Field for Proteins. J Chem Theory Comput 2013; 9:3769-3788. [PMID: 23997693 PMCID: PMC3755638 DOI: 10.1021/ct400230y] [Citation(s) in RCA: 81] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We describe here the PRIMO (PRotein Intermediate Model) force field, a physics-based fully transferable additive coarse-grained potential energy function that is compatible with an all-atom force field for multi-scale simulations. The energy function consists of standard molecular dynamics energy terms plus a hydrogen-bonding potential term and is mainly parameterized based on the CHARMM22/CMAP force field in a bottom-up fashion. The solvent is treated implicitly via the generalized Born model. The bonded interactions are either harmonic or distance-based spline interpolated potentials. These potentials are defined on the basis of all-atom molecular dynamics (MD) simulations of dipeptides with the CHARMM22/CMAP force field. The non-bonded parameters are tuned by matching conformational free energies of diverse set of conformations with that of CHARMM all-atom results. PRIMO is designed to provide a correct description of conformational distribution of the backbone (ϕ/ψ) and side chains (χ1) for all amino acids with a CMAP correction term. The CMAP potential in PRIMO is optimized based on the new CHARMM C36 CMAP. The resulting optimized force field has been applied in MD simulations of several proteins of 36-155 amino acids and shown that the root-mean-squared-deviation of the average structure from the corresponding crystallographic structure varies between 1.80 and 4.03 Å. PRIMO is shown to fold several small peptides to their native-like structures from extended conformations. These results suggest the applicability of the PRIMO force field in the study of protein structures in aqueous solution, structure predictions as well as ab initio folding of small peptides.
Collapse
Affiliation(s)
- Parimal Kar
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Srinivasa Murthy Gopal
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Yi-Ming Cheng
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Alexander Predeus
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Michael Feig
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
- Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA
| |
Collapse
|
27
|
Chen Y, Ding J. Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation. J Biomol Struct Dyn 2013; 32:792-803. [PMID: 23746129 DOI: 10.1080/07391102.2013.791645] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56 Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.
Collapse
Affiliation(s)
- Yantao Chen
- a State Key Laboratory of Molecular Engineering of Polymers, Shenzhen Key Laboratory of Functional Polymer , College of Chemistry and Chemical Engineering, Shenzhen University , Shenzhen , 518060 , China
| | | |
Collapse
|
28
|
Kapoor A, Travesset A. Folding and stability of helical bundle proteins from coarse-grained models. Proteins 2013; 81:1200-11. [DOI: 10.1002/prot.24269] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2012] [Revised: 01/13/2013] [Accepted: 01/29/2013] [Indexed: 11/10/2022]
Affiliation(s)
- Abhijeet Kapoor
- Department of Physics and Astronomy; Iowa State University; Ames; Iowa 50011
| | - Alex Travesset
- Department of Physics and Astronomy; Iowa State University; Ames; Iowa 50011
| |
Collapse
|
29
|
Irbäck A, Sjunnesson F, Wallin S. Hydrogen bonds, hydrophobicity forces and the character of the collapse transition. J Biol Phys 2013; 27:169-79. [PMID: 23345742 DOI: 10.1023/a:1013155018382] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We study the thermodynamic behavior of a model protein with 54 amino acidsthat is designed to form a three-helix bundle in its native state. The model contains three types of amino acids and five to six atoms per amino acid, and has the Ramachandran torsion angles as its only degrees of freedom.The force field is based on hydrogen bonds and effective hydrophobicity forces. We study how the character of the collapse transition depends on the strengths of these forces. For a suitable choice of these two parameters, it is found that the collapse transition is first-order-like and coincides with the folding transition. Also shown is that the corresponding one- and two-helix segments make less stable secondary structure than the three-helix sequence.
Collapse
Affiliation(s)
- A Irbäck
- Complex Systems Division, Department of Theoretical Physics, Lund University, Sölvegatan 14A, S-223 62 Lund, Sweden
| | | | | |
Collapse
|
30
|
Grünberger A, Lai PK, Blanco MA, Roberts CJ. Coarse-grained modeling of protein second osmotic virial coefficients: sterics and short-ranged attractions. J Phys Chem B 2013; 117:763-70. [PMID: 23245189 DOI: 10.1021/jp308234j] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
A series of coarse-grained models, with different levels of structural resolution, were tested to calculate the steric contributions to protein osmotic second virial coefficients (B(22,S)) for proteins ranging from small single-domain molecules to large multidomain molecules, using the recently developed Mayer sampling method. B(22,S) was compared for different levels of coarse-graining: four-beads-per-amino-acid (4bAA), one-bead-per-amino-acid (1bAA), one-sphere-per-domain (1sD), and one-sphere-per-protein (1sP). Values for the 1bAA and 4bAA models were quantitatively indistinguishable for both spherical and nonspherical proteins, and the agreement with values from all-atom models improved with increasing protein size, making the CG approach attractive for large proteins of biotechnological interest. Interestingly, in the absence of detailed structural information, the hydrodynamic radius (R(h)) along with a simple 1sP approximation provided reasonably accurate values for B(22,S) for both globular and highly asymmetric protein structures, while other 1sP approximations gave poorer agreement; this helps to justify the currently empirical practice of estimating B(22,S) from R(h) for large proteins such as antibodies. The results also indicate that either 1bAA or 4bAA CG models may be good starting points for incorporating short-range attractions. Comparison of gD-crystallin B(22) values including both sterics and short-range attractions shows that 1bAA and 4bAA models give equivalent results when properly scaled to account for differences in the number of surface beads in the two CG descriptions. This provides a basis for future work that will also incorporate long-ranged electrostatic attractions and repulsions.
Collapse
Affiliation(s)
- Alexander Grünberger
- Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA
| | | | | | | |
Collapse
|
31
|
Abstract
Coarse-grained models for protein folding and aggregation are used to explore large dimension scales and timescales that are inaccessible to all-atom models in explicit aqueous solution. Combined with enhanced configuration search methods, these simplified models with various levels of granularity offer the possibility to determine equilibrium structures, compare folding kinetics and thermodynamics with experiments for single proteins and understand the dynamic assembly of amyloid proteins leading to neurodegenerative diseases. I shall describe recent progress in developing such models, and discuss their potentials and limitations in probing the folding and misfolding of proteins with computer simulations.
Collapse
|
32
|
Scully MA, Pandya S, Moxley RT. Review of Phase II and Phase III clinical trials for Duchenne muscular dystrophy. Expert Opin Orphan Drugs 2012. [DOI: 10.1517/21678707.2013.746939] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
|
33
|
Wagenmann A, Geyer T. Coarse-Grained Simulations of Protein Backbone Dynamics. 1. Local Sterics Define the Dihedral Angles. J Chem Theory Comput 2012; 8:4732-45. [PMID: 26605627 DOI: 10.1021/ct3005529] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Here, we present a coarse-grained model targeted for implicit solvent simulations of unfolded or intrinsically disordered proteins. The hierarchical model with its nonspherical building blocks allows one to reproduce the local dynamics of the backbone with simple harmonic bonds and steric collisions between a small number of atoms at the correct off-center positions on the building blocks. Here in part 1, we also describe the implementation of the global shape of the protein chain and the extended local interactions that add a first secondary structure bias, which will subsequently be augmented by additional hydrophobic interactions, hydrogen bonds, and dipole dipole couplings along the backbone. Due to its hierarchical setup, the model has a near-atomistic resolution on the local scale and the overall numerical efficiency of a coarse-grained model such that even long protein chains can be simulated efficiently.
Collapse
Affiliation(s)
- Andreas Wagenmann
- Zentrum für Bioinformatik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
| | - Tihamér Geyer
- Zentrum für Bioinformatik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
| |
Collapse
|
34
|
Coluzza I, Dellago C. The configurational space of colloidal patchy polymers with heterogeneous sequences. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:284111. [PMID: 22738904 DOI: 10.1088/0953-8984/24/28/284111] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In this work we characterize the configurational space of a short chain of colloidal particles as a function of the range of directional and heterogeneous isotropic interactions. The individual particles forming the chain are colloids decorated with patches that act as interaction sites between them. We show, using computer simulations, that it is possible to sample the relative probability of occurrence of a structure with a sequence in the space of all possible realizations of the chain. The results presented here represent a first attempt to map the space of possible configurations that a chain of colloidal particles may adopt. Knowledge of such a space is crucial for a possible application of colloidal chains as models for designable self-assembling systems.
Collapse
Affiliation(s)
- Ivan Coluzza
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | | |
Collapse
|
35
|
Chebaro Y, Pasquali S, Derreumaux P. The Coarse-Grained OPEP Force Field for Non-Amyloid and Amyloid Proteins. J Phys Chem B 2012; 116:8741-52. [DOI: 10.1021/jp301665f] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Yassmine Chebaro
- Laboratoire de Biochimie Théorique,
CNRS UPR 9080, Université Paris Diderot, Sorbonne Paris Cité, Institut de Biologie Physico-Chimique,
13 rue Pierre et Marie Curie, 75005 Paris
| | - Samuela Pasquali
- Laboratoire de Biochimie Théorique,
CNRS UPR 9080, Université Paris Diderot, Sorbonne Paris Cité, Institut de Biologie Physico-Chimique,
13 rue Pierre et Marie Curie, 75005 Paris
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique,
CNRS UPR 9080, Université Paris Diderot, Sorbonne Paris Cité, Institut de Biologie Physico-Chimique,
13 rue Pierre et Marie Curie, 75005 Paris
- Institut Universitaire de France, 103 Bvd Saint-Michel, Paris 75005, France
| |
Collapse
|
36
|
Noel JK, Schug A, Verma A, Wenzel W, Garcia AE, Onuchic JN. Mirror images as naturally competing conformations in protein folding. J Phys Chem B 2012; 116:6880-8. [PMID: 22497217 DOI: 10.1021/jp212623d] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Evolution has selected a protein's sequence to be consistent with the native state geometry, as this configuration must be both thermodynamically stable and kinetically accessible to prevent misfolding and loss of function. In simple protein geometries, such as coiled-coil helical bundles, symmetry produces a competing, globally different, near mirror image with identical secondary structure and similar native contact interactions. Experimental techniques such as circular dichroism, which rely on probing secondary structure content, cannot readily distinguish these folds. Here, we want to clarify whether the native fold and mirror image are energetically competitive by investigating the free energy landscape of three-helix bundles. To prevent a bias from a specific computational approach, the present study employs the structure prediction forcefield PFF01/02, explicit solvent replica exchange molecular dynamics (REMD) with the Amber94 forcefield, and structure-based simulations based on energy landscape theory. We observe that the native fold and its mirror image have a similar enthalpic stability and are thermodynamically competitive. There is evidence that the mirror fold has faster folding kinetics and could function as a kinetic trap. All together, our simulations suggest that mirror images might not just be a computational annoyance but are competing folds that might switch depending on environmental conditions or functional considerations.
Collapse
Affiliation(s)
- Jeffrey K Noel
- Center for Theoretical Biological Physics and Department of Physics, Rice University, Houston, Texas 77005, USA
| | | | | | | | | | | |
Collapse
|
37
|
Bhattacherjee A, Wallin S. Coupled folding-binding in a hydrophobic/polar protein model: impact of synergistic folding and disordered flanks. Biophys J 2012; 102:569-78. [PMID: 22325280 DOI: 10.1016/j.bpj.2011.12.008] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2011] [Revised: 11/18/2011] [Accepted: 12/01/2011] [Indexed: 11/28/2022] Open
Abstract
Coupled folding-binding is central to the function of many intrinsically disordered proteins, yet not fully understood. With a continuous three-letter protein model, we explore the free-energy landscape of pairs of interacting sequences and how it is impacted by 1), variations in the binding mechanism; and 2), the addition of disordered flanks to the binding region. In particular, we focus on two sequences, one with 16 and one with 35 amino acids, which make a stable dimeric three-helix bundle at low temperatures. Three distinct binding mechanisms are realized by altering the stabilities of the individual monomers: docking, coupled folding-binding of a single α-helix, and synergistic folding and binding. Compared to docking, the free-energy barrier for binding is reduced when the single α-helix is allowed to fold upon binding, but only marginally. A greater reduction is found for synergistic folding, which in addition results in a binding transition state characterized by very few interchain contacts. Disordered flanking chain segments attached to the α-helix sequence can, despite a negligible impact on the dimer stability, lead to a downhill free-energy surface in which the barrier for binding is eliminated.
Collapse
Affiliation(s)
- Arnab Bhattacherjee
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Lund, Sweden
| | | |
Collapse
|
38
|
Coluzza I. A coarse-grained approach to protein design: learning from design to understand folding. PLoS One 2011; 6:e20853. [PMID: 21747930 PMCID: PMC3128589 DOI: 10.1371/journal.pone.0020853] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2011] [Accepted: 05/10/2011] [Indexed: 11/20/2022] Open
Abstract
Computational studies have given a great contribution in building our current understanding of the complex behavior of protein molecules; nevertheless, a complete characterization of their free energy landscape still represents a major challenge. Here, we introduce a new coarse-grained approach that allows for an extensive sampling of the conformational space of a large number of sequences. We explicitly discuss its application in protein design, and by studying four representative proteins, we show that the method generates sequences with a relatively smooth free energy surface directed towards the target structures.
Collapse
Affiliation(s)
- Ivan Coluzza
- Department of Physics, University of Vienna, Vienna, Austria.
| |
Collapse
|
39
|
Engin O, Villa A, Peter C, Sayar M. A Challenge for Peptide Coarse Graining: Transferability of Fragment-Based Models. MACROMOL THEOR SIMUL 2011. [DOI: 10.1002/mats.201100005] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
40
|
Kim J, Straub JE. Generalized simulated tempering for exploring strong phase transitions. J Chem Phys 2011; 133:154101. [PMID: 20969364 DOI: 10.1063/1.3503503] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An extension of the simulation tempering algorithm is proposed. It is shown to be particularly suited to the exploration of first-order phase transition systems characterized by the backbending or S-loop in the statistical temperature or a microcanonical caloric curve. A guided Markov process in an auxiliary parameter space systematically combines a set of parametrized Tsallis-weight ensemble simulations, which are targeted to transform unstable or metastable energy states of canonical ensembles into stable ones and smoothly join ordered and disordered phases across phase transition regions via a succession of unimodal energy distributions. The inverse mapping between the sampling weight and the effective temperature enables an optimal selection of relevant Tsallis-weight parameters. A semianalytic expression for the biasing weight in parameter space is adaptively updated "on the fly" during the simulation to achieve rapid convergence. Accelerated tunneling transitions with a comprehensive sampling for phase-coexistent states are explicitly demonstrated in systems subject to strong hysteresis including Potts and Ising spin models and a 147 atom Lennard-Jones cluster.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | |
Collapse
|
41
|
Chang L, Wang J, Wang W. Composition-based effective chain length for prediction of protein folding rates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051930. [PMID: 21230523 DOI: 10.1103/physreve.82.051930] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2010] [Indexed: 05/30/2023]
Abstract
Folding rate prediction is a useful way to find the key factors affecting folding kinetics of proteins. Structural information is more or less required in the present prediction methods, which limits the application of these methods to various proteins. In this work, an "effective length" is defined solely based on the composition of a protein, namely, the number of specific types of amino acids in a protein. A physical theory based on a minimalist model is employed to describe the relation between the folding rates and the effective length of proteins. Based on the resultant relationship between folding rates and effective length, the optimal sets of amino acids are found through the enumeration over all possible combinations of amino acids. This optimal set achieves a high correlation (with the coefficient of 0.84) between the folding rates and the optimal effective length. The features of these amino acids are consistent with our model and landscape theory. Further comparisons between our effective length and other factors are carried out. The effective length is physically consistent with structure-based prediction methods and has the best predictability for folding rates. These results all suggest that both entropy and energetics contribute importantly to folding kinetics. The ability to accurately and efficiently predict folding rates from composition enables the analysis of the kinetics for various kinds of proteins. The underlying physics in our method may be helpful to stimulate further understanding on the effects of various amino acids in folding dynamics.
Collapse
Affiliation(s)
- Le Chang
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University, Nanjing 210093, China
| | | | | |
Collapse
|
42
|
Wang ZJ, Deserno M. A systematically coarse-grained solvent-free model for quantitative phospholipid bilayer simulations. J Phys Chem B 2010; 114:11207-20. [PMID: 20695631 PMCID: PMC2928645 DOI: 10.1021/jp102543j] [Citation(s) in RCA: 96] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2010] [Revised: 06/10/2010] [Indexed: 11/30/2022]
Abstract
We present an implicit solvent coarse-grained (CG) model for quantitative simulations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. The absence of explicit solvent enables membrane simulations on large length and time scales at moderate computational expense. Despite improved computational efficiency, the model preserves chemical specificity and quantitative accuracy. The bonded and nonbonded interactions together with the effective cohesion mimicking the hydrophobic effect were systematically tuned by matching structural and mechanical properties from experiments and all-atom bilayer simulations, such as saturated area per lipid, radial distribution functions, density and pressure profiles across the bilayer, P(2) order, etc. The CG lipid model is shown to self-assemble into a bilayer starting from a random dispersion. Its line tension and elastic properties, such as bending and stretching modulus, are semiquantitatively consistent with experiments. The effects of (i) reduced molecular friction and (ii) more efficient integration combine to an overall speed-up of 3-4 orders of magnitude compared to all-atom bilayer simulations. Our CG lipid model is especially useful for studies of large-scale phenomena in membranes that nevertheless require a fair description of chemical specificity, e.g., membrane patches interacting with movable and transformable membrane proteins and peptides.
Collapse
Affiliation(s)
- Zun-Jing Wang
- Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA
| | | |
Collapse
|
43
|
Multiscale coarse-graining of the protein energy landscape. PLoS Comput Biol 2010; 6:e1000827. [PMID: 20585614 PMCID: PMC2891700 DOI: 10.1371/journal.pcbi.1000827] [Citation(s) in RCA: 103] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2010] [Accepted: 05/21/2010] [Indexed: 12/05/2022] Open
Abstract
A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states. Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.
Collapse
|
44
|
Bereau T, Deserno M. Generic coarse-grained model for protein folding and aggregation. J Chem Phys 2009; 130:235106. [PMID: 19548767 DOI: 10.1063/1.3152842] [Citation(s) in RCA: 154] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A generic coarse-grained (CG) protein model is presented. The intermediate level of resolution (four beads per amino acid, implicit solvent) allows for accurate sampling of local conformations. It relies on simple interactions that emphasize structure, such as hydrogen bonds and hydrophobicity. Realistic alpha/beta content is achieved by including an effective nearest-neighbor dipolar interaction. Parameters are tuned to reproduce both local conformations and tertiary structures. The thermodynamics and kinetics of a three-helix bundle are studied. We check that the CG model is able to fold proteins with tertiary structures and amino acid sequences different from the one used for parameter tuning. By studying both helical and extended conformations we make sure the force field is not biased toward any particular secondary structure. The accuracy involved in folding not only the test protein but also other ones show strong evidence for amino acid cooperativity embedded in the model. Without any further adjustments or bias a realistic oligopeptide aggregation scenario is observed.
Collapse
Affiliation(s)
- Tristan Bereau
- Department of Physics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, USA.
| | | |
Collapse
|
45
|
Li D, Liu MS, Ji B, Hwang K, Huang Y. Coarse-grained molecular dynamics of ligands binding into protein: The case of HIV-1 protease inhibitors. J Chem Phys 2009; 130:215102. [DOI: 10.1063/1.3148022] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
46
|
Oliveira LC, Schug A, Onuchic JN. Geometrical features of the protein folding mechanism are a robust property of the energy landscape: a detailed investigation of several reduced models. J Phys Chem B 2008; 112:6131-6. [PMID: 18251535 DOI: 10.1021/jp0769835] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The concept of a funneled energy landscape and the principle of minimal frustration are the theoretical foundation justifying the applicability of structure-based models. In simulations, a protein is commonly reduced to a C(alpha)-bead representation. These simulations are sufficient to predict the geometrical features of the folding mechanism observed experimentally utilizing a concise formulation of the Hamiltonian with low computational costs. Toward a better understanding of the interplay between energetic and geometrical features in folding, the side chain is now explicitly included in the simulations. The simplest choice is the addition of C(beta)-beads at the center-of-mass position of the side chains. While one varies the energetic parameters of the model, the geometric aspects of the folding mechanism remain robust for a broad range of parameters. Energetic properties like folding barriers and protein stability are sensitive to the details of simulations. This robustness to geometry and sensitivity to energetic properties provide flexibility in choosing different parameters to represent changes in sequences, environments, stability or folding rate effects. Therefore, minimal frustration and the funnel concept guarantee that the geometrical features are robust properties of the folding landscape, while mutations and/or changes in the environment easily influence energy-dependent properties like folding rates or stability.
Collapse
Affiliation(s)
- Leandro C Oliveira
- University of California San Diego, Center for Theoretical Biological Physics, La Jolla, California 92093-0374, USA
| | | | | |
Collapse
|
47
|
Mu Y, Gao YQ. Effects of hydrophobic and dipole-dipole interactions on the conformational transitions of a model polypeptide. J Chem Phys 2007; 127:105102. [PMID: 17867781 DOI: 10.1063/1.2768062] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We studied the effects of hydrophobicity and dipole-dipole interactions between the nearest-neighbor amide planes on the secondary structures of a model polypeptide by calculating the free energy differences between different peptide structures. The free energy calculations were performed with low computational costs using the accelerated Monte Carlo simulation (umbrella sampling) method, with a bias-potential method used earlier in our accelerated molecular dynamics simulations. It was found that the hydrophobic interaction enhances the stability of alpha helices at both low and high temperatures but stabilizes beta structures only at high temperatures at which alpha helices are not stable. The nearest-neighbor dipole-dipole interaction stabilizes beta structures under all conditions, especially in the low temperature region where alpha helices are the stable structures. Our results indicate clearly that the dipole-dipole interaction between the nearest neighboring amide planes plays an important role in determining the peptide structures. Current research provides a more unified and quantitative picture for understanding the effects of different forms of interactions on polypeptide structures. In addition, the present model can be extended to describe DNA/RNA, polymer, copolymer, and other chain systems.
Collapse
Affiliation(s)
- Yan Mu
- Department of Chemistry, Texas A&M University, College Station, Texas 77843, USA
| | | |
Collapse
|
48
|
Lucas A, Huang L, Joshi A, Dill KA. Statistical mechanics of helix bundles using a dynamic programming approach. J Am Chem Soc 2007; 129:4272-81. [PMID: 17362002 DOI: 10.1021/ja067153s] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Despite much study, biomolecule folding cooperativity is not well understood. There are quantitative models for helix-coil transitions and for coil-to-globule transitions, but no accurate models yet treat both chain collapse and secondary structure formation together. We develop here a dynamic programming approach to statistical mechanical partition functions of foldamer chain molecules. We call it the ascending levels model. We apply it to helix-coil and helix-bundle folding and cooperativity. For 14- to 50-mer Baldwin peptides, the model gives good predictions for the heat capacity and helicity versus temperature and urea. The model also gives good fits for the denaturation of Oas's three-helix bundle B domain of protein A (F13W*) and synthetic protein alpha3C by temperature and guanidine. The model predicts the conformational distributions. It shows that these proteins fold with transitions that are two-state, although the transitions in the Baldwin helices are nearly higher order. The model shows that the recently developed three-helix bundle polypeptoids of Lee et al. fold anti-cooperatively, with a predicted value of DeltaHvH/DeltaHcal = 0.72. The model also predicts that two-helix bundles are unstable in proteins but stable in peptoids. Our dynamic programming approach provides a general way to explore cooperativity in complex foldable polymers.
Collapse
Affiliation(s)
- Adam Lucas
- Department of Mathematics, Saint Mary's College of California, Moraga, California 94575-3517, USA
| | | | | | | |
Collapse
|
49
|
Abstract
Backbone hydrogen bonds contribute very importantly to the stability of proteins and therefore they must be appropriately represented in protein folding simulations. Simple models are frequently used in theoretical approaches to this process, but their simplifications are often confronted with the need to be true to the physics of the interactions. Here we study the effects of different levels of coarse graining in the modeling of backbone hydrogen bonds. We study three different models taken from the bibliography in a twofold fashion. First, we calculate the hydrogen bonds in 2gb1, an (alpha + beta)-protein, and see how different backbone representations and potentials can mimic the effects of real hydrogen bonds both in helices and sheets. Second, we use an evolutionary method for protein fragment assembly to locate the global energy minimum for a set of small beta-proteins with these models. This way, we assess the effects of coarse graining in hydrogen bonding models and show what can be expected from them when used in simulation experiments.
Collapse
Affiliation(s)
- David De Sancho
- Departamento de Química Física I, Universidad Complutense, Madrid, Spain
| | | |
Collapse
|
50
|
Knott M, Chan HS. Criteria for downhill protein folding: Calorimetry, chevron plot, kinetic relaxation, and single-molecule radius of gyration in chain models with subdued degrees of cooperativity. Proteins 2006; 65:373-91. [PMID: 16909416 DOI: 10.1002/prot.21066] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
Recent investigations of possible downhill folding of small proteins such as BBL have focused on the thermodynamics of non-two-state, "barrierless" folding/denaturation transitions. Downhill folding is noncooperative and thermodynamically "one-state," a phenomenon underpinned by a unimodal conformational distribution over chain properties such as enthalpy, hydrophobic exposure, and conformational dimension. In contrast, corresponding distributions for cooperative two-state folding are bimodal with well-separated population peaks. Using simplified atomic modeling of a three-helix bundle-in a scheme that accounts for hydrophobic interactions and hydrogen bonding-and coarse-grained C(alpha) models of four real proteins with various degrees of cooperativity, we evaluate the effectiveness of several observables at defining the underlying distribution. Bimodal distributions generally lead to sharper transitions, with a higher heat capacity peak at the transition midpoint, compared with unimodal distributions. However, the observation of a sigmoidal transition is not a reliable criterion for two-state behavior, and the heat capacity baselines, used to determine the van't Hoff and calorimetric enthalpies of the transition, can introduce ambiguity. Interestingly we find that, if the distribution of the single-molecule radius of gyration were available, it would permit discrimination between unimodal and bimodal underlying distributions. We investigate kinetic implications of thermodynamic noncooperativity using Langevin dynamics. Despite substantial chevron rollovers, the relaxation of the models considered is essentially single-exponential over an extended range of native stabilities. Consistent with experiments, significant deviations from single-exponential behavior occur only under strongly folding conditions.
Collapse
Affiliation(s)
- Michael Knott
- Department of Biochemistry, and of Medical Genetics and Microbiology, Protein Engineering Network of Centres of Excellence, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | | |
Collapse
|