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Yu K, Cui Z, Sui X, Qiu X, Zhang J. Biological Network Inference With GRASP: A Bayesian Network Structure Learning Method Using Adaptive Sequential Monte Carlo. Front Genet 2021; 12:764020. [PMID: 34912373 PMCID: PMC8668238 DOI: 10.3389/fgene.2021.764020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 10/25/2021] [Indexed: 11/13/2022] Open
Abstract
Bayesian networks (BNs) provide a probabilistic, graphical framework for modeling high-dimensional joint distributions with complex correlation structures. BNs have wide applications in many disciplines, including biology, social science, finance and biomedical science. Despite extensive studies in the past, network structure learning from data is still a challenging open question in BN research. In this study, we present a sequential Monte Carlo (SMC)-based three-stage approach, GRowth-based Approach with Staged Pruning (GRASP). A double filtering strategy was first used for discovering the overall skeleton of the target BN. To search for the optimal network structures we designed an adaptive SMC (adSMC) algorithm to increase the quality and diversity of sampled networks which were further improved by a third stage to reclaim edges missed in the skeleton discovery step. GRASP gave very satisfactory results when tested on benchmark networks. Finally, BN structure learning using multiple types of genomics data illustrates GRASP’s potential in discovering novel biological relationships in integrative genomic studies.
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Affiliation(s)
- Kaixian Yu
- Department of Statistics, Florida State University, Tallahassee, FL, United States
| | - Zihan Cui
- Department of Statistics, Florida State University, Tallahassee, FL, United States
| | - Xin Sui
- Department of Statistics, Florida State University, Tallahassee, FL, United States
| | - Xing Qiu
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, United States
| | - Jinfeng Zhang
- Department of Statistics, Florida State University, Tallahassee, FL, United States
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Farris ACK, Seaton DT, Landau DP. Effects of lattice constraints in coarse-grained protein models. J Chem Phys 2021; 154:084903. [PMID: 33639740 DOI: 10.1063/5.0038184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We compare and contrast folding behavior in several coarse-grained protein models, both on- and off-lattice, in an attempt to uncover the effect of lattice constraints in these kinds of models. Using modern, extended ensemble Monte Carlo methods-Wang-Landau sampling, multicanonical sampling, replica-exchange Wang-Landau sampling, and replica-exchange multicanonical sampling, we investigate the thermodynamic and structural behavior of the protein Crambin within the context of the hydrophobic-polar, hydrophobic-"neutral"-polar (H0P), and semi-flexible H0P model frameworks. We uncover the folding process in all cases; all models undergo, at least, the two major structural transitions observed in nature-the coil-globule collapse and the folding transition. As the complexity of the model increases, these two major transitions begin to split into multi-step processes, wherein the lattice coarse-graining has a significant impact on the details of these processes. The results show that the level of structural coarse-graining is coupled to the level of interaction coarse-graining.
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Affiliation(s)
- Alfred C K Farris
- Department of Physics and Astronomy, Oxford College of Emory University, Oxford, Georgia 30054, USA
| | - Daniel T Seaton
- Open Learning, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - David P Landau
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
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3
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Shi G, Wüst T, Landau DP. Elucidating thermal behavior, native contacts, and folding funnels of simple lattice proteins using replica exchange Wang-Landau sampling. J Chem Phys 2018; 149:164913. [PMID: 30384708 DOI: 10.1063/1.5026256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.
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Affiliation(s)
- Guangjie Shi
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602-0002, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zurich, 8092 Zurich, Switzerland
| | - David P Landau
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602-0002, USA
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Farris ACK, Shi G, Wüst T, Landau DP. The role of chain-stiffness in lattice protein models: A replica-exchange Wang-Landau study. J Chem Phys 2018; 149:125101. [PMID: 30278675 DOI: 10.1063/1.5045482] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using Monte Carlo simulations, we investigate simple, physically motivated extensions to the hydrophobic-polar lattice protein model for the small (46 amino acid) protein Crambin. We use two-dimensional replica-exchange Wang-Landau sampling to study the effects of a bond angle stiffness parameter on the folding and uncover a new step in the collapse process for particular values of this stiffness parameter. A physical interpretation of the folding is developed by analysis of changes in structural quantities, and the free energy landscape is explored. For these special values of stiffness, we find non-degenerate ground states, a property that is consistent with behavior of real proteins, and we use these unique ground states to elucidate the formation of native contacts during the folding process. Through this analysis, we conclude that chain-stiffness is particularly influential in the low energy, low temperature regime of the folding process once the lattice protein has partially collapsed.
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Affiliation(s)
- Alfred C K Farris
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
| | - Guangjie Shi
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zürich, 8092 Zürich, Switzerland
| | - David P Landau
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
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Shi G, Wüst T, Landau DP. Characterizing folding funnels with replica exchange Wang-Landau simulation of lattice proteins. Phys Rev E 2016; 94:050402. [PMID: 27967143 DOI: 10.1103/physreve.94.050402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Indexed: 02/01/2023]
Abstract
We have studied the folding of ribonuclease A by mapping it onto coarse-grained lattice protein models. With replica exchange Wang-Landau sampling, we calculated the free energy vs end-to-end distance as a function of temperature. A mapping to the famous hydrophobic-polar (HP) model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, extending the HP model with an additional "neutral" monomer type (i.e., a mapping to the three-letter H0P model) has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.
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Affiliation(s)
- Guangjie Shi
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zürich, 8092 Zürich, Switzerland
| | - David P Landau
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
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6
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Zhu L, Wang X, Li J, Wang Y. Radius of Gyration, Mean Span, and Geometric Shrinking Factors of Bridged Polycyclic Ring Polymers. MACROMOL THEOR SIMUL 2016. [DOI: 10.1002/mats.201600033] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Lijuan Zhu
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials; Department of Polymer Science and Engineering; College of Chemistry; Chemical Engineering and Materials Science; Soochow University; 199 Ren-ai Road Suzhou 215123 P. R. China
| | - Xiaoyan Wang
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials; Department of Polymer Science and Engineering; College of Chemistry; Chemical Engineering and Materials Science; Soochow University; 199 Ren-ai Road Suzhou 215123 P. R. China
| | - Jianfeng Li
- The State Key Laboratory of Molecular Engineering of Polymers; Department of Macromolecular Science; Fudan University; Shanghai 200433 P. R. China
| | - Yanwei Wang
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials; Department of Polymer Science and Engineering; College of Chemistry; Chemical Engineering and Materials Science; Soochow University; 199 Ren-ai Road Suzhou 215123 P. R. China
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Shi G, Vogel T, Wüst T, Li YW, Landau DP. Effect of single-site mutations on hydrophobic-polar lattice proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033307. [PMID: 25314564 DOI: 10.1103/physreve.90.033307] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Indexed: 06/04/2023]
Abstract
We developed a heuristic method for determining the ground-state degeneracy of hydrophobic-polar (HP) lattice proteins, based on Wang-Landau and multicanonical sampling. It is applied during comprehensive studies of single-site mutations in specific HP proteins with different sequences. The effects in which we are interested include structural changes in ground states, changes of ground-state energy, degeneracy, and thermodynamic properties of the system. With respect to mutations, both extremely sensitive and insensitive positions in the HP sequence have been found. That is, ground-state energies and degeneracies, as well as other thermodynamic and structural quantities, may be either largely unaffected or may change significantly due to mutation.
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Affiliation(s)
- Guangjie Shi
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Thomas Vogel
- Theoretical Division (T-1), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zürich IT Services, 8092 Zürich, Switzerland
| | - Ying Wai Li
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - David P Landau
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
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8
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References. Comput Stat 2013. [DOI: 10.1002/9781118555552.refs] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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10
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Tang W, Zhou Q. Finding multiple minimum-energy conformations of the hydrophobic-polar protein model via multidomain sampling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031909. [PMID: 23030946 DOI: 10.1103/physreve.86.031909] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate the efficiency of the multidomain sampler (MDS) in finding multiple distinct global minima and low-energy local minima in the hydrophobic-polar (HP) lattice protein model. Extending the idea of partitioning energy space in the Wang-Landau algorithm, our approach introduces an additional partitioning scheme to divide the protein conformation space into local basins of attraction. This double-partitioning design is very powerful in guiding the sampler to visit the basins of unexplored local minima. An H-residue subchain distance is used to merge the basins of similar local minima into one domain, which increases the diversity among identified minimum-energy conformations. Moreover, a visit-enhancement factor is introduced for long protein chains to facilitate jumps between basins. Results on three benchmark protein sequences reveal that our approach is capable of finding multiple global minima and hundreds of low-energy local minima of great diversity.
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Affiliation(s)
- Wei Tang
- Department of Materials Science and Engineering, University of California, Los Angeles, California 90095, USA
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11
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Wüst T, Landau DP. Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins. J Chem Phys 2012; 137:064903. [DOI: 10.1063/1.4742969] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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12
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Liu J, Li G, Yu J. Protein-folding simulations of the hydrophobic-hydrophilic model by combining pull moves with energy landscape paving. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:031934. [PMID: 22060430 DOI: 10.1103/physreve.84.031934] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2011] [Revised: 07/29/2011] [Indexed: 05/31/2023]
Abstract
The energy landscape paving (ELP) method is a class of heuristic global optimization algorithms based on Monte Carlo sampling. By incorporating the generation of an initial conformation based on a greedy strategy, the conformation update mechanism based on pull moves, and some heuristic off-trap strategies into an improved ELP method, we propose an alternative version of the ELP method, called the ELP-pull move method. We test the ELP-pull move method on both two-dimensional (2D) and 3D hydrophobic-hydrophilic protein-folding models. For ten 2D benchmark sequences of length ranging from 20 to 100, the proposed algorithm finds the lowest energies so far. Within the achieved results, the algorithm converges more rapidly and efficiently than previous methods. For all ten 3D sequences with a length of 64, the ELP-pull move method finds lower energies within comparable computational times. The numerical results demonstrate that our algorithm is a powerful method to study the lattice protein-folding model.
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Affiliation(s)
- Jingfa Liu
- School of Computer & Software, Nanjing University of Information Science & Technology, Nanjing 210044, China.
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13
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Mamonov AB, Zhang X, Zuckerman DM. Rapid sampling of all-atom peptides using a library-based polymer-growth approach. J Comput Chem 2011; 32:396-405. [PMID: 20734315 PMCID: PMC3005036 DOI: 10.1002/jcc.21626] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2010] [Revised: 05/17/2010] [Accepted: 06/12/2010] [Indexed: 12/30/2022]
Abstract
We adapted existing polymer growth strategies for equilibrium sampling of peptides described by modern atomistic forcefields with a simple uniform dielectric solvent. The main novel feature of our approach is the use of precalculated statistical libraries of molecular fragments. A molecule is sampled by combining fragment configurations-of single residues in this study-which are stored in the libraries. Ensembles generated from the independent libraries are reweighted to conform with the Boltzmann-factor distribution of the forcefield describing the full molecule. In this way, high-quality equilibrium sampling of small peptides (4-8 residues) typically requires less than one hour of single-processor wallclock time and can be significantly faster than Langevin simulations. Furthermore, approximate, clash-free ensembles can be generated for larger peptides (up to 32 residues in this study) in less than a minute of single-processor computing. We discuss possible applications of our growth procedure to free energy calculation, fragment assembly protein-structure prediction protocols, and to "multi-resolution" sampling.
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Affiliation(s)
- Artem B Mamonov
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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14
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Abstract
Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to parallelization to novel uses of hardware. Special focus is placed on classifying algorithms--most of which are underpinned by a few key ideas--in order to understand their fundamental strengths and limitations. Although algorithms have proliferated, progress resulting from novel hardware use appears to be more clear-cut than from algorithms alone, due partly to the lack of widely used sampling measures.
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Affiliation(s)
- Daniel M Zuckerman
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA 15213, USA.
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15
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Zhang X, Mamonov AB, Zuckerman DM. Absolute free energies estimated by combining precalculated molecular fragment libraries. J Comput Chem 2009; 30:1680-91. [PMID: 19504588 DOI: 10.1002/jcc.21337] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The absolute free energy--or partition function, equivalently--of a molecule can be estimated computationally using a suitable reference system. Here, we demonstrate a practical method for staging such calculations by growing a molecule based on a series of fragments. Significant computer time is saved by precalculating fragment configurations and interactions for reuse in a variety of molecules. We use such fragment libraries and interaction tables for amino acids and capping groups to estimate free energies for small peptides. Equilibrium ensembles for the molecules are generated at no additional computational cost and are used to check our results by comparison to standard dynamics simulation. We explain how our work can be extended to estimate relative binding affinities.
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Affiliation(s)
- Xin Zhang
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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Wei W, Yanlin T. A new algorithm for 2D hydrophobic-polar model: an algorithm based on hydrophobic core in square lattice. Pak J Biol Sci 2008; 11:1815-1819. [PMID: 18817222 DOI: 10.3923/pjbs.2008.1815.1819] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
This study was engaged in a new algorithm which was used to solve the problem of protein folding. The conformation of hydrophobic core of protein was key factor of structure of protein. So, in our algorithm, we set a hydrophobic core which was restricted by new aggregate. Then, the hydrophilic residues between two hydrophobic residues were ranged, the optimal conformation was gained if all residues were not overlap and continuous. The algorithm in this study can be prevented effectively falls into partially smallest energy.
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Affiliation(s)
- Wang Wei
- College of Science, Guizhou University, Guiyang, Guizhou Province, China
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17
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Zhang J, Lin M, Chen R, Wang W, Liang J. Discrete state model and accurate estimation of loop entropy of RNA secondary structures. J Chem Phys 2008; 128:125107. [PMID: 18376982 DOI: 10.1063/1.2895050] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson-Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson-Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at http://gila.bioengr.uic.edu/resources/RNA.html.
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Affiliation(s)
- Jian Zhang
- Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA
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Lin M, Chen R, Liang J. Statistical geometry of lattice chain polymers with voids of defined shapes: sampling with strong constraints. J Chem Phys 2008; 128:084903. [PMID: 18315083 DOI: 10.1063/1.2831905] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Proteins contain many voids, which are unfilled spaces enclosed in the interior. A few of them have shapes compatible to ligands and substrates and are important for protein functions. An important general question is how the need for maintaining functional voids is influenced by, and affects other aspects of proteins structures and properties (e.g., protein folding stability, kinetic accessibility, and evolution selection pressure). In this paper, we examine in detail the effects of maintaining voids of different shapes and sizes using two-dimensional lattice models. We study the propensity for conformations to form a void of specific shape, which is related to the entropic cost of void maintenance. We also study the location that voids of a specific shape and size tend to form, and the influence of compactness on the formation of such voids. As enumeration is infeasible for long chain polymer, a key development in this work is the design of a novel sequential Monte Carlo strategy for generating large number of sample conformations under very constraining restrictions. Our method is validated by comparing results obtained from sampling and from enumeration for short polymer chains. We succeeded in accurate estimation of entropic cost of void maintenance, with and without an increasing number of restrictive conditions, such as loops forming the wall of void with fixed length, with additionally fixed starting position in the sequence. Additionally, we have identified the key structural properties of voids that are important in determining the entropic cost of void formation. We have further developed a parametric model to predict quantitatively void entropy. Our model is highly effective, and these results indicate that voids representing functional sites can be used as an improved model for studying the evolution of protein functions and how protein function relates to protein stability.
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Affiliation(s)
- Ming Lin
- Department of Information & Decision Science, University of Illinois at Chicago, 845 S. Morgan St., Chicago, Illinois 60607, USA
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19
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Advances on protein folding simulations based on the lattice HP models with natural computing. Appl Soft Comput 2008. [DOI: 10.1016/j.asoc.2007.03.012] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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20
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Zhang J, Kou SC, Liu JS. Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo. J Chem Phys 2007; 126:225101. [PMID: 17581081 DOI: 10.1063/1.2736681] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.
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Affiliation(s)
- Jinfeng Zhang
- Department of Statistics, Harvard University, Science Center, Cambridge, Massachusetts 02138, USA
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21
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Zhang J, Lin M, Chen R, Liang J, Liu JS. Monte Carlo sampling of near-native structures of proteins with applications. Proteins 2006; 66:61-8. [PMID: 17039507 DOI: 10.1002/prot.21203] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Since a protein's dynamic fluctuation inside cells affects the protein's biological properties, we present a novel method to study the ensemble of near-native structures (NNS) of proteins, namely, the conformations that are very similar to the experimentally determined native structure. We show that this method enables us to (i) quantify the difficulty of predicting a protein's structure, (ii) choose appropriate simplified representations of protein structures, and (iii) assess the effectiveness of knowledge-based potential functions. We found that well-designed simple representations of protein structures are likely as accurate as those more complex ones for certain potential functions. We also found that the widely used contact potential functions stabilize NNS poorly, whereas potential functions incorporating local structure information significantly increase the stability of NNS.
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Affiliation(s)
- Jinfeng Zhang
- Department of Statistics, Harvard University, Cambridge, Massachusetts, USA
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22
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Liang F. Annealing contour Monte Carlo algorithm for structure optimization in an off-lattice protein model. J Chem Phys 2006; 120:6756-63. [PMID: 15267570 DOI: 10.1063/1.1665529] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a space annealing version for a contour Monte Carlo algorithm and show that it can be applied successfully to finding the ground states for an off-lattice protein model. The comparison shows that the algorithm has made a significant improvement over the pruned-enriched-Rosenbluth method and the Metropolis Monte Carlo method in finding the ground states for AB models. For all sequences, the algorithm has renewed the putative ground energy values in the two-dimensional AB model and set the putative ground energy values in the three-dimensional AB model.
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Affiliation(s)
- Faming Liang
- Department of Statistics, Texas A&M University, College Station, Texas 77843-3143, USA.
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23
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Zhang J, Chen R, Liang J. Empirical potential function for simplified protein models: combining contact and local sequence-structure descriptors. Proteins 2006; 63:949-60. [PMID: 16477624 DOI: 10.1002/prot.20809] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
An effective potential function is critical for protein structure prediction and folding simulation. Simplified protein models such as those requiring only Calpha or backbone atoms are attractive because they enable efficient search of the conformational space. We show residue-specific reduced discrete-state models can represent the backbone conformations of proteins with small RMSD values. However, no potential functions exist that are designed for such simplified protein models. In this study, we develop optimal potential functions by combining contact interaction descriptors and local sequence-structure descriptors. The form of the potential function is a weighted linear sum of all descriptors, and the optimal weight coefficients are obtained through optimization using both native and decoy structures. The performance of the potential function in a test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. Our potential function requiring only backbone atoms or Calpha atoms have comparable or better performance than several residue-based potential functions that require additional coordinates of side-chain centers or coordinates of all side-chain atoms. By reducing the residue alphabets down to size 10 for contact descriptors, the performance of the potential function can be further improved. Our results also suggest that local sequence-structure correlation may play important role in reducing the entropic cost of protein folding.
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Affiliation(s)
- Jinfeng Zhang
- Department of Bioengineering, University of Illinois, Chicago, Illinois, USA
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Kou SC, Oh J, Wong WH. A study of density of states and ground states in hydrophobic-hydrophilic protein folding models by equi-energy sampling. J Chem Phys 2006; 124:244903. [PMID: 16821999 DOI: 10.1063/1.2208607] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose an equi-energy (EE) sampling approach to study protein folding in the two-dimensional hydrophobic-hydrophilic (HP) lattice model. This approach enables efficient exploration of the global energy landscape and provides accurate estimates of the density of states, which then allows us to conduct a detailed study of the thermodynamics of HP protein folding, in particular, on the temperature dependence of the transition from folding to unfolding and on how sequence composition affects this phenomenon. With no extra cost, this approach also provides estimates on global energy minima and ground states. Without using any prior structural information of the protein the EE sampler is able to find the ground states that match the best known results in most benchmark cases. The numerical results demonstrate it as a powerful method to study lattice protein folding models.
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Affiliation(s)
- S C Kou
- Department of Statistics, Science Center, Harvard University, Cambridge, Massachusetts 02138, USA.
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25
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Abstract
We studied a three-dimensional off-lattice AB model with two species of monomers, hydrophobic (A) and hydrophilic (B), and present two optimization algorithms: face-centered-cubic (FCC)-lattice pruned-enriched-Rosenbluth method (PERM) and subsequent conjugate gradient (PERM++) minimization and heuristic conjugate gradient (HCG) simulation based on "off-trap" strategy. In PERM++, we apply the PERM to the FCC-lattice to produce the initial conformation, and conjugate gradient minimization is then used to reach the minimum energy state. Both algorithms have been tested in the three-dimensional AB model for all sequences with lengths 13 < or = n < or = 55. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we renew the putative ground states energy values.
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Affiliation(s)
- Wenqi Huang
- School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, China
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26
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Liu JF, Huang WQ. A quasi-physical algorithm for the structure optimization in an off-lattice protein model. GENOMICS, PROTEOMICS & BIOINFORMATICS 2006; 4:61-6. [PMID: 16689704 PMCID: PMC5054034 DOI: 10.1016/s1672-0229(06)60018-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
In this paper, we study an off-lattice protein AB model with two species of monomers, hydrophobic and hydrophilic, and present a heuristic quasi-physical algorithm. First, by elaborately simulating the movement of the smooth solids in the physical world, we find low-energy conformations for a given monomer chain. A subsequent off-trap strategy is then proposed to trigger a jump for a stuck situation in order to get out of the local minima. The algorithm has been tested in the three-dimensional AB model for all sequences with lengths of 13-55 monomers. In several cases, we renew the putative ground state energy values. The numerical results show that the proposed methods are very promising for finding the ground states of proteins.
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Affiliation(s)
- Jing-Fa Liu
- School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China.
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27
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Bezáková I, Sinclair A, Štefankovič D, Vigoda E. Negative Examples for Sequential Importance Sampling of Binary Contingency Tables. LECTURE NOTES IN COMPUTER SCIENCE 2006. [DOI: 10.1007/11841036_15] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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28
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Huang W, Lü Z, Shi H. Growth algorithm for finding low energy configurations of simple lattice proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:016704. [PMID: 16090131 DOI: 10.1103/physreve.72.016704] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2004] [Indexed: 05/03/2023]
Abstract
PERM and its new variant nPERMis have been developed to optimize the energy function of protein folding based on HP simple lattice model and were found to outperform all other previous fully blind general purpose algorithms. Using the concept of core-guiding and life-forecasting, we propose a new version of nPERMis, called nPERMh. A major difference with respect to nPERMis is that criteria for further growth of new residue are based on the species of current growing monomer and its position in the HP sequence. Seventeen sequences of length ranging from 46 to 124 residues were tested by nPERMh on the cubic lattice and our algorithm proved very efficient. It should be pointed out that our new version of nPERMis is exclusively designed for conformational search. We hope that similar methods will ultimately be useful for finding native states of more realistic protein models.
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Affiliation(s)
- Wenqi Huang
- School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei Province, 430074, China
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29
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Lee HK, Okabe Y. Reweighting for nonequilibrium Markov processes using sequential importance sampling methods. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:015102. [PMID: 15697640 DOI: 10.1103/physreve.71.015102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2004] [Indexed: 05/24/2023]
Abstract
We present a generic reweighting method for nonequilibrium Markov processes. With nonequilibrium Monte Carlo simulations at a single temperature, one calculates the time evolution of physical quantities at different temperatures, which greatly saves computational time. Using the dynamical finite-size scaling analysis for the nonequilibrium relaxation, one can study the dynamical properties of phase transitions together with the equilibrium ones. We demonstrate the procedure for the Ising model with the Metropolis algorithm, but the present formalism is general and can be applied to a variety of systems as well as with different Monte Carlo update schemes.
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Affiliation(s)
- Hwee Kuan Lee
- Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
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30
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Hsu HP, Mehra V, Nadler W, Grassberger P. Growth-based optimization algorithm for lattice heteropolymers. ACTA ACUST UNITED AC 2003; 68:021113. [PMID: 14524959 DOI: 10.1103/physreve.68.021113] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2002] [Indexed: 11/07/2022]
Abstract
An improved version of the pruned-enriched-Rosenbluth method (PERM) is proposed and tested on finding lowest energy states in simple models of lattice heteropolymers. It is found to outperform not only the previous version of PERM, but also all other fully blind general purpose stochastic algorithms which have been employed on this problem. In many cases, it found new lowest energy states missed in previous papers. Limitations are discussed.
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Affiliation(s)
- Hsiao-Ping Hsu
- John-von-Neumann Institute for Computing, Forschungszentrum Jülich, D-52425 Jülich, Germany
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31
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Jiang T, Cui Q, Shi G, Ma S. Protein folding simulations of the hydrophobic–hydrophilic model by combining tabu search with genetic algorithms. J Chem Phys 2003. [DOI: 10.1063/1.1592796] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Berezkin AV, Khalatur PG, Khokhlov AR. Computer modeling of synthesis of proteinlike copolymer via copolymerization with simultaneous globule formation. J Chem Phys 2003. [DOI: 10.1063/1.1563603] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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