51
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Yang JS, Chen WW, Skolnick J, Shakhnovich EI. All-atom ab initio folding of a diverse set of proteins. Structure 2007; 15:53-63. [PMID: 17223532 DOI: 10.1016/j.str.2006.11.010] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2006] [Revised: 11/15/2006] [Accepted: 11/18/2006] [Indexed: 11/30/2022]
Abstract
Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins by using a minimalist transferable-energy model that consists of two-body atom-atom interactions, hydrogen bonding, and a local sequence-energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native-in the range of 2-6 A root-mean-square deviation (rmsd). Our results demonstrate that the successful folding of a protein chain to its native state is governed by only a few crucial energetic terms.
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Affiliation(s)
- Jae Shick Yang
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
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52
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Frenkel ZM, Trifonov EN. Walking through the protein sequence space: Towards new generation of the homology modeling. Proteins 2007; 67:271-84. [PMID: 17286283 DOI: 10.1002/prot.21325] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
A new method is proposed to reveal apparent evolutionary relationships between protein fragments with similar 3D structures by finding "intermediate" sequences in the proteomic database. Instead of looking for homologies and intermediates for a whole protein domain, we build a chain of intermediate short sequences, which allows one to link similar structural modules of proteins belonging to the same or different families. Several such chains of intermediates can be combined into an evolutionary tree of structural protein modules. All calculations were made for protein fragments of 20 aa residues. Three evolutionary trees for different module structures are described. The aim of the paper is to introduce the new method and to demonstrate its potential for protein structural predictions. The approach also opens new perspectives for protein evolution studies.
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Affiliation(s)
- Zakharia M Frenkel
- Genome Diversity Center, Institute of Evolution, University of Haifa, Haifa 31905, Israel.
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53
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Jiao X, Wang B, Su J, Chen W, Wang C. Protein design based on the relative entropy. Phys Rev E 2006; 73:061903. [PMID: 16906860 DOI: 10.1103/physreve.73.061903] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2006] [Indexed: 11/07/2022]
Abstract
An approach to protein design is proposed based on the relative entropy and a reduced amino acid alphabet. In this approach, the relative entropy is used as a minimization object function. The method has been tested on a real protein's off-lattice model successfully, and the results are similar to those obtained from other design studies. It can be applied as a uniform frame for both folding and inverse folding of protein. An iterative calculation method of the ensemble average of the contact strength is proposed at the same time.
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Affiliation(s)
- Xiong Jiao
- College of Life Science and Bioengineering, Beijing University of Technology, Beijing 100022, China
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54
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Galzitskaya OV, Garbuzinskii SA. Optimal ratio between the average conformational entropy and the average energy of interaction between residues for fast protein folding. Biophysics (Nagoya-shi) 2006. [DOI: 10.1134/s0006350906040075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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55
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Cecconi F, Guardiani C, Livi R. Testing simplified proteins models of the hPin1 WW domain. Biophys J 2006; 91:694-704. [PMID: 16648162 PMCID: PMC1483113 DOI: 10.1529/biophysj.105.069138] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Accepted: 04/06/2006] [Indexed: 11/18/2022] Open
Abstract
The WW domain of the human Pin1 protein for its simple topology and large amount of experimental data is an ideal candidate to assess theoretical approaches to protein folding. The purpose of this work is to compare the reliability of the chemically based Sorenson/Head-Gordon (SHG) model and a standard native centric model in reproducing, through molecular dynamics simulations, some of the well known features of the folding transition of this small domain. Our results show that the Gō model correctly reproduces the cooperative, two-state, folding mechanism of the WW-domain, while the SHG model predicts a transition occurring in two stages: a collapse, followed by a structural rearrangement. The lack of a cooperative folding in the SHG simulations appears to be related to the nonfunnel shape of the energy landscape featuring a partitioning of the native valley in subbasins corresponding to different chain chiralities. However, the SHG approach remains more reliable in estimating the phi-values with respect to Gō-like description. This may suggest that the WW-domain folding process is stirred by energetic and topological factors as well, and it highlights the better suitability of chemically based models in simulating mutations.
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Affiliation(s)
- Fabio Cecconi
- INFM-CNR Istituto dei Sistemi Complessi, Rome, Italy.
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56
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Bloom JD, Drummond DA, Arnold FH, Wilke CO. Structural determinants of the rate of protein evolution in yeast. Mol Biol Evol 2006; 23:1751-61. [PMID: 16782762 DOI: 10.1093/molbev/msl040] [Citation(s) in RCA: 148] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate how a protein's structure influences the rate at which its sequence evolves. Our basic hypothesis is that proteins with highly designable structures (structures that are encoded by many sequences) will evolve more rapidly. Recent theoretical advances argue that structures with a higher density of interresidue contacts are more designable, and we show that high contact density is correlated with an increased rate of sequence evolution in yeast. In addition, we investigate the correlations between the rate of sequence evolution and several other structural descriptors, carefully controlling for the strong effect of expression level on evolutionary rate. Overall, we find that the structural descriptors that we consider appear to explain roughly 10% of the variation in rates of protein evolution in yeast. We also show that despite the well-known trend for buried residues to be more conserved, proteins with a higher fraction of buried residues, nonetheless, tend to evolve their sequences more rapidly. We suggest that this effect is due to the increased designability of structures with more buried residues. Our results provide evidence that protein structure plays an important role in shaping the rate of sequence evolution and provide evidence to support recent theoretical advances linking structural designability to contact density.
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Affiliation(s)
- Jesse D Bloom
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California, USA
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57
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Shakhnovich E. Protein folding thermodynamics and dynamics: where physics, chemistry, and biology meet. Chem Rev 2006; 106:1559-88. [PMID: 16683745 PMCID: PMC2735084 DOI: 10.1021/cr040425u] [Citation(s) in RCA: 253] [Impact Index Per Article: 14.1] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eugene Shakhnovich
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA.
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58
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Chikenji G, Fujitsuka Y, Takada S. Shaping up the protein folding funnel by local interaction: lesson from a structure prediction study. Proc Natl Acad Sci U S A 2006; 103:3141-6. [PMID: 16488978 PMCID: PMC1413881 DOI: 10.1073/pnas.0508195103] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2005] [Indexed: 11/18/2022] Open
Abstract
Predicting protein tertiary structure by folding-like simulations is one of the most stringent tests of how much we understand the principle of protein folding. Currently, the most successful method for folding-based structure prediction is the fragment assembly (FA) method. Here, we address why the FA method is so successful and its lesson for the folding problem. To do so, using the FA method, we designed a structure prediction test of "chimera proteins." In the chimera proteins, local structural preference is specific to the target sequences, whereas nonlocal interactions are only sequence-independent compaction forces. We find that these chimera proteins can find the native folds of the intact sequences with high probability indicating dominant roles of the local interactions. We further explore roles of local structural preference by exact calculation of the HP lattice model of proteins. From these results, we suggest principles of protein folding: For small proteins, compact structures that are fully compatible with local structural preference are few, one of which is the native fold. These local biases shape up the funnel-like energy landscape.
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Affiliation(s)
- George Chikenji
- *Department of Chemistry, Faculty of Science, and
- Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan; and
| | - Yoshimi Fujitsuka
- Graduate School of Science and Technology, Kobe University, Nada, Kobe 657-8501, Japan
| | - Shoji Takada
- *Department of Chemistry, Faculty of Science, and
- Graduate School of Science and Technology, Kobe University, Nada, Kobe 657-8501, Japan
- Core Research for Evolutionary Science and Technology, Japan Science and Technology Agency, Nada, Kobe 657-8501, Japan
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59
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Zeldovich KB, Berezovsky IN, Shakhnovich EI. Physical origins of protein superfamilies. J Mol Biol 2006; 357:1335-43. [PMID: 16483605 DOI: 10.1016/j.jmb.2006.01.081] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2005] [Accepted: 01/23/2006] [Indexed: 10/25/2022]
Abstract
In this work, we discovered a fundamental connection between selection for protein stability and emergence of preferred structures of proteins. Using a standard exact three-dimensional lattice model we evolve sequences starting from random ones and determine the exact native structure after each mutation. Acceptance of mutations is biased to select for stable proteins. We found that certain structures, "wonderfolds", are independently discovered numerous times as native states of stable proteins in many unrelated runs of selection. The strong dependence of lattice fold usage on the structural determinant of designability quantitatively reproduces uneven fold usage in natural proteins. Diversity of sequences that fold into wonderfold structures gives rise to superfamilies, i.e. sets of dissimilar sequences that fold into the same or very similar structures. The present work establishes a model of pre-biotic structure selection, which identifies dominant structural patterns emerging upon optimization of proteins for survival in a hot environment. Convergently discovered pre-biotic initial superfamilies with wonderfold structures could have served as a seed for subsequent biological evolution involving gene duplications and divergence.
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Affiliation(s)
- Konstantin B Zeldovich
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
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60
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Huang L, Ma X, Liang H. What is the origin of those common structures of protein-model chains? POLYMER 2006. [DOI: 10.1016/j.polymer.2005.11.036] [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]
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61
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Floudas C, Fung H, McAllister S, Mönnigmann M, Rajgaria R. Advances in protein structure prediction and de novo protein design: A review. Chem Eng Sci 2006. [DOI: 10.1016/j.ces.2005.04.009] [Citation(s) in RCA: 175] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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62
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Abstract
Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates.
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Affiliation(s)
- Oxana V Galzitskaya
- Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region, Russia.
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63
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Shell MS, Debenedetti PG, Panagiotopoulos AZ. Computational characterization of the sequence landscape in simple protein alphabets. Proteins 2005; 62:232-43. [PMID: 16284961 DOI: 10.1002/prot.20714] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
We characterize the "sequence landscapes" in several simple, heteropolymer models of proteins by examining their mutation properties. Using an efficient flat-histogram Monte Carlo search method, our approach involves determining the distribution in energy of all sequences of a given length when threaded through a common backbone. These calculations are performed for a number of Protein Data Bank structures using two variants of the 20-letter contact potential developed by Miyazawa and Jernigan [Miyazawa S, Jernigan WL. Macromolecules 1985;18:534], and the 2-monomer HP model of Lau and Dill [Lau KF, Dill KA. Macromolecules 1989;22:3986]. Our results indicate significant differences among the energy functions in terms of the "smoothness" of their landscapes. In particular, one of the Miyazawa-Jernigan contact potentials reveals unusual cooperative behavior among its species' interactions, resulting in what is essentially a set of phase transitions in sequence space. Our calculations suggest that model-specific features can have a profound effect on protein design algorithms, and our methods offer a number of ways by which sequence landscapes can be quantified.
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Affiliation(s)
- M Scott Shell
- Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA.
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64
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Shakhnovich BE, Deeds E, Delisi C, Shakhnovich E. Protein structure and evolutionary history determine sequence space topology. Genome Res 2005; 15:385-92. [PMID: 15741509 PMCID: PMC551565 DOI: 10.1101/gr.3133605] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2004] [Accepted: 11/23/2004] [Indexed: 11/24/2022]
Abstract
Understanding the observed variability in the number of homologs of a gene is a very important unsolved problem that has broad implications for research into coevolution of structure and function, gene duplication, pseudogene formation, and possibly for emerging diseases. Here, we attempt to define and elucidate some possible causes behind the observed irregularity in sequence space. We present evidence that sequence variability and functional diversity of a gene or fold family is influenced by quantifiable characteristics of the protein structure. These characteristics reflect the structural potential for sequence plasticity, i.e., the ability to accept mutation without losing thermodynamic stability. We identify a structural feature of a protein domain-contact density-that serves as a determinant of entropy in sequence space, i.e., the ability of a protein to accept mutations without destroying the fold (also known as fold designability). We show that (log) of average gene family size exhibits statistical correlation (R(2) > 0.9.) with contact density of its three-dimensional structure. We present evidence that the size of individual gene families are influenced not only by the designability of the structure, but also by evolutionary history, e.g., the amount of time the gene family was in existence. We further show that our observed statistical correlation between gene family size and contact density of the structure is valid on many levels of evolutionary divergence, i.e., not only for closely related sequence, but also for less-related fold and superfamily levels of homology.
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65
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Miao J, Klein-Seetharaman J, Meirovitch H. The Optimal Fraction of Hydrophobic Residues Required to Ensure Protein Collapse. J Mol Biol 2004; 344:797-811. [PMID: 15533446 DOI: 10.1016/j.jmb.2004.09.061] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2004] [Revised: 09/14/2004] [Accepted: 09/21/2004] [Indexed: 11/30/2022]
Abstract
The hydrophobic interaction is the main driving force for protein folding. Here, we address the question of what is the optimal fraction, f of hydrophobic (H) residues required to ensure protein collapse. For very small f (say f<0.1), the protein chain is expected to behave as a random coil, where the H residues are "wrapped" locally by polar (P) residues. However, for large enough f this local coverage cannot be achieved and the thermodynamic alternative to avoid contact with water is burying the H residues in the interior of a compact chain structure. The interior also contains P residues that are known to be clustered to optimize their electrostatic interactions. This means that the H residues are clustered as well, i.e. they effectively attract each other like the H-monomers in Dill's HP lattice model. Previously, we asked the question: assuming that the H monomers in the HP model are distributed randomly along the chain, what fraction of them is required to ensure a compact ground state? We claimed there that f approximately p(c), where p(c) is the site percolation threshold of the lattice (in a percolation experiment, each site of an initially empty lattice is visited and a particle is placed there with a probability p. The interest is in the critical (minimal) value, p(c), for which percolation occurs, i.e. a cluster connecting the opposite sides of the lattice is created). Due to the above correspondence between the HP model and real proteins (and assuming that the H residues are distributed at random) we suggest that the experimental f should lead to percolating clusters of H residues over the highly dense protein core, i.e. clusters of the core size. To check this theory, we treat a simplified model consisting of H and P residues represented by their alpha-carbon atoms only. The structure is defined by the C(alpha)-C(alpha) virtual bond lengths, angles and dihedral angles, and the X-ray structure is best-fitted onto a face-centered cubic lattice. Percolation experiments are carried out for 103 single-chain proteins using six different hydrophobic sets of residues. Indeed, on average, percolating clusters are generated, which supports our theory; however, some sets lead to a better core coverage than others. We also calculate the largest actual hydrophobic cluster of each protein and show that, on average, these clusters span the core, again in accord with our theory. We discuss the effect of protein size, deviations from the average picture, and implications of this study for defining reliable simplified models of proteins.
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Affiliation(s)
- Jiangbo Miao
- Carnegie Mellon University School of Computer Science, Language Technologies Institute, Pittsburgh, PA 15213, USA
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66
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Bloom JD, Wilke CO, Arnold FH, Adami C. Stability and the evolvability of function in a model protein. Biophys J 2004; 86:2758-64. [PMID: 15111394 PMCID: PMC1304146 DOI: 10.1016/s0006-3495(04)74329-5] [Citation(s) in RCA: 82] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2003] [Accepted: 01/12/2004] [Indexed: 11/18/2022] Open
Abstract
Functional proteins must fold with some minimal stability to a structure that can perform a biochemical task. Here we use a simple model to investigate the relationship between the stability requirement and the capacity of a protein to evolve the function of binding to a ligand. Although our model contains no built-in tradeoff between stability and function, proteins evolved function more efficiently when the stability requirement was relaxed. Proteins with both high stability and high function evolved more efficiently when the stability requirement was gradually increased than when there was constant selection for high stability. These results show that in our model, the evolution of function is enhanced by allowing proteins to explore sequences corresponding to marginally stable structures, and that it is easier to improve stability while maintaining high function than to improve function while maintaining high stability. Our model also demonstrates that even in the absence of a fundamental biophysical tradeoff between stability and function, the speed with which function can evolve is limited by the stability requirement imposed on the protein.
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Affiliation(s)
- Jesse D Bloom
- Department of Chemistry, California Institute of Technology, Pasadena, California 91125, USA.
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67
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Tiana G, Shakhnovich BE, Dokholyan NV, Shakhnovich EI. Imprint of evolution on protein structures. Proc Natl Acad Sci U S A 2004; 101:2846-51. [PMID: 14970345 PMCID: PMC365708 DOI: 10.1073/pnas.0306638101] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2003] [Accepted: 12/22/2003] [Indexed: 11/18/2022] Open
Abstract
We attempt to understand the evolutionary origin of protein folds by simulating their divergent evolution with a three-dimensional lattice model. Starting from an initial seed lattice structure, evolution of model proteins progresses by sequence duplication and subsequent point mutations. A new gene's ability to fold into a stable and unique structure is tested each time through direct kinetic folding simulations. Where possible, the algorithm accepts the new sequence and structure and thus a "new protein structure" is born. During the course of each run, this model evolutionary algorithm provides several thousand new proteins with diverse structures. Analysis of evolved structures shows that later evolved structures are more designable than seed structures as judged by recently developed structural determinant of protein designability, as well as direct estimate of designability for selected structures by thermodynamic sampling of their sequence space. We test the significance of this trend predicted on lattice models on real proteins and show that protein domains that are found in eukaryotic organisms only feature statistically significant higher designability than their prokaryotic counterparts. These results present a fundamental view on protein evolution highlighting the relative roles of structural selection and evolutionary dynamics on genesis of modern proteins.
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Affiliation(s)
- Guido Tiana
- Department of Physics and Istituto Nazionale di Fisica Nucleare, University of Milano, Via Celoria 16, 20133 Milan, Italy
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68
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Khatun J, Khare SD, Dokholyan NV. Can Contact Potentials Reliably Predict Stability of Proteins? J Mol Biol 2004; 336:1223-38. [PMID: 15037081 DOI: 10.1016/j.jmb.2004.01.002] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2003] [Revised: 01/08/2004] [Accepted: 01/08/2004] [Indexed: 11/17/2022]
Abstract
The simplest approximation of interaction potential between amino acid residues in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein's thermodynamic stabilities (DeltaDeltaG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental (DeltaDeltaG) values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters may yield reliable predictions of DeltaDeltaG for datasets of mutations confined to the same amino acid positions in the sequence of a single protein.
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Affiliation(s)
- Jainab Khatun
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
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69
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Ding F, Borreguero JM, Buldyrey SV, Stanley HE, Dokholyan NV. Mechanism for the alpha-helix to beta-hairpin transition. Proteins 2004; 53:220-8. [PMID: 14517973 DOI: 10.1002/prot.10468] [Citation(s) in RCA: 208] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The aggregation of alpha-helix-rich proteins into beta-sheet-rich amyloid fibrils is associated with fatal diseases, such as Alzheimer's disease and prion disease. During an aggregation process, protein secondary structure elements-alpha-helices-undergo conformational changes to beta-sheets. The fact that proteins with different sequences and structures undergo a similar transition on aggregation suggests that the sequence nonspecific hydrogen bond interaction among protein backbones is an important factor. We perform molecular dynamics simulations of a polyalanine model, which is an alpha-helix in its native state and observe a metastable beta-hairpin intermediate. Although a beta-hairpin has larger potential energy than an alpha-helix, the entropy of a beta-hairpin is larger because of fewer constraints imposed by the hydrogen bonds. In the vicinity of the transition temperature, we observe the interconversion of the alpha-helix and beta-sheet states via a random coil state. We also study the effect of the environment by varying the relative strength of side-chain interactions for a designed peptide-an alpha-helix in its native state. For a certain range of side-chain interaction strengths, we find that the intermediate beta-hairpin state is destabilized and even disappears, suggesting an important role of the environment in the aggregation propensity of a peptide.
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Affiliation(s)
- Feng Ding
- Center for Polymer Studies, Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
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70
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Abstract
Selecting a protein sequence that corresponds to a specific three-dimensional protein structure is known as the protein design problem. One principal bottleneck in solving this problem is our lack of knowledge of precise atomic interactions. Using a simple model of amino acid interactions, we determine three crucial factors that are important for solving the protein design problem. Among these factors is the protein alphabet-a set of sequence elements that encodes protein structure. Our model predicts that alphabet size is independent of protein length, suggesting the possibility of designing a protein of arbitrary length with the natural protein alphabet. We also find that protein alphabet size is governed by protein structural properties and the energetic properties of the protein alphabet units. We discover that the usage of average types of amino acid in proteins is less than expected if amino acids were chosen randomly with naturally occurring frequencies. We propose three possible scenarios that account for amino acid underusage in proteins. These scenarios suggest the possibility that amino acids themselves might not constitute the alphabet of natural proteins.
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Affiliation(s)
- Nikolay V Dokholyan
- Department of Biochemistry and Biophysics, School of Medicine, University of North Carolina at Chapel Hill, 27599, USA.
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71
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72
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Chertovich AV, Govorun EN, Ivanov VA, Khalatur PG, Khokhlov AR. Conformation-dependent sequence design: evolutionary approach. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2004; 13:15-25. [PMID: 15024612 DOI: 10.1140/epje/e2004-00036-1] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
A new modification of evolutionary approach to sequence design of copolymers has been proposed. A model of step-by-step evolution of a two-letter ( HP) copolymer sequence has been studied by means of a coarse-grained Monte Carlo algorithm. The conditions for accepting a change in the primary sequence depend on the spatial conformation of HP-copolymer chain. This leads to a coupling between sequence and conformation and to formation of protein-like conformations and primary sequences (for some values of parameters of the model) independently of initial sequence and/or conformation. Simple theory describing these computer simulation observations is developed.
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Affiliation(s)
- A V Chertovich
- Physics Department, Moscow State University, 119992, Moscow, Russia.
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73
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Deeds EJ, Dokholyan NV, Shakhnovich EI. Protein evolution within a structural space. Biophys J 2003; 85:2962-72. [PMID: 14581198 PMCID: PMC1303574 DOI: 10.1016/s0006-3495(03)74716-x] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2003] [Accepted: 07/28/2003] [Indexed: 10/21/2022] Open
Abstract
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analogous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.
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Affiliation(s)
- Eric J Deeds
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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74
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Pei J, Dokholyan NV, Shakhnovich EI, Grishin NV. Using protein design for homology detection and active site searches. Proc Natl Acad Sci U S A 2003; 100:11361-6. [PMID: 12975528 PMCID: PMC208762 DOI: 10.1073/pnas.2034878100] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2003] [Indexed: 11/18/2022] Open
Abstract
We describe a method of designing artificial sequences that resemble naturally occurring sequences in terms of their compatibility with a template structure and its functional constraints. The design procedure is a Monte Carlo simulation of amino acid substitution process. The selective fixation of substitutions is dictated by a simple scoring function derived from the template structure and a multiple alignment of its homologs. Designed sequences represent an enlargement of sequence space around native sequences. We show that the use of designed sequences improves the performance of profile-based homology detection. The difference in position-specific conservation between designed sequences and native sequences is helpful for prediction of functionally important residues. Our sequence selection criteria in evolutionary simulations introduce amino acid substitution rate variation among sites in a natural way, providing a better model to test phylogenetic methods.
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Affiliation(s)
- Jimin Pei
- Department of Biochemistry and Howard Hughes Medical Institute, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
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75
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Blackburne BP, Hirst JD. Three-dimensional functional model proteins: Structure function and evolution. J Chem Phys 2003. [DOI: 10.1063/1.1590310] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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76
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England JL, Shakhnovich BE, Shakhnovich EI. Natural selection of more designable folds: a mechanism for thermophilic adaptation. Proc Natl Acad Sci U S A 2003; 100:8727-31. [PMID: 12843403 PMCID: PMC166380 DOI: 10.1073/pnas.1530713100] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2003] [Indexed: 11/18/2022] Open
Abstract
An open question of great interest in biophysics is whether variations in structure cause protein folds to differ in the number of amino acid sequences that can fold to them stably, i.e., in their designability. Recently, we have shown that a novel quantitative measure of a fold's tertiary topology, called its contact trace, strongly correlates with the fold's designability. Here, we investigate the relationship between a fold's contact trace and its relative frequency of usage in mesophilic vs. thermophilic eubacteria. We observe that thermophilic organisms exhibit a bias toward using folds of higher contact trace when compared with mesophiles. We establish this difference both for the distributions of folds at the whole-proteome level and also through more focused structural comparisons of orthologous proteins. Our findings suggest that thermophilic adaptation in bacterial genomes occurs in part through natural selection of more designable folds, pointing to designability as a key component of protein fitness.
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Affiliation(s)
- Jeremy L England
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
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77
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Qin M, Wang J, Tang Y, Wang W. Folding behaviors of lattice model proteins with three kinds of contact potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:061905. [PMID: 16241259 DOI: 10.1103/physreve.67.061905] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2003] [Indexed: 05/04/2023]
Abstract
The interaction potentials between the amino acids are very important in the study of protein folding and design. In this work, the folding behaviors of lattice model protein chains are studied using three kinds of contact potentials between the beads. For these three cases, a number of sequences are designed using the Z-score method, and then their folding behaviors are obtained via Monte Carlo simulations for different sizes of the chains. It is found that the proper weakening of hydrophobicity may speed up the folding and the elimination of the mixing interaction terms may deteriorate the foldability. The different features of the foldability are discussed by comparing the characteristics of the energy landscapes of these model chains. The formations of various contacts are also analyzed, which provide us with some microscopic information on the model systems and interaction potentials.
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Affiliation(s)
- Meng Qin
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University, China
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78
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England JL, Shakhnovich EI. Structural determinant of protein designability. PHYSICAL REVIEW LETTERS 2003; 90:218101. [PMID: 12786593 DOI: 10.1103/physrevlett.90.218101] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2002] [Indexed: 05/24/2023]
Abstract
Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with the most low-energy sequences are the same as those predicted by the theory. We argue that, given sufficiently strict requirements for foldability, these structures are the most designable, and we propose a simple means to test whether the results in this paper hold true for real proteins.
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Affiliation(s)
- Jeremy L England
- Harvard University, Department of Chemistry and Chemical Biology, 12 Oxford Street, Cambridge, Massachusetts 02138, USA
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79
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Khalatur PG, Novikov VV, Khokhlov AR. Conformation-dependent evolution of copolymer sequences. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:051901. [PMID: 12786172 DOI: 10.1103/physreve.67.051901] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2002] [Revised: 01/08/2003] [Indexed: 05/24/2023]
Abstract
A "toy model" of molecular evolution of sequences in copolymers is proposed and implemented using a molecular-dynamics-based algorithm. The model involves coupling of conformation-dependent and sequence-dependent properties. It is shown that this model allows the realization of two main possibilities: ascending and descending branches of evolution (in terms of information content of a sequence), depending on the interaction parameters shaping the conformation of a polymer globule. The problem of adequate description of information complexity of copolymer sequences is studied. It is shown that Shannon's entropy or compressibility of a sequence gives preference to random sequences and therefore cannot be applied for this purpose. On the other hand, the Jensen-Shannon divergence measure turns out to give the description of information complexity which corresponds to our intuitive expectations. In particular, this characteristic can adequately describe two branches of evolution mentioned above, exhibiting a singularity on the boundary of these regimes.
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Affiliation(s)
- Pavel G Khalatur
- Department of Polymer Science, University of Ulm, Ulm D-89069, Germany
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80
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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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81
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Jin W, Kambara O, Sasakawa H, Tamura A, Takada S. De novo design of foldable proteins with smooth folding funnel: automated negative design and experimental verification. Structure 2003; 11:581-90. [PMID: 12737823 DOI: 10.1016/s0969-2126(03)00075-3] [Citation(s) in RCA: 66] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
De novo sequence design of foldable proteins provides a way of investigating principles of protein architecture. We performed fully automated sequence design for a target structure having a three-helix bundle topology and synthesized the designed sequences. Our design principle is different from the conventional approach, in that instead of optimizing interactions within the target structure, we design the global shape of the protein folding funnel. This includes automated implementation of negative design by explicitly requiring higher free energy of the denatured state. The designed sequences do not have significant similarity to those of any natural proteins. The NMR and CD spectroscopic data indicated that one designed sequence has a well-defined three-dimensional structure as well as alpha-helical content consistent with the target.
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Affiliation(s)
- Wenzhen Jin
- Graduate School of Science and Technology, Japan Science and Technology Corporation, Kobe University, Rokkodai, Nada, 657-8501, Kobe, Japan
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82
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Zou J, Saven JG. Using self-consistent fields to bias Monte Carlo methods with applications to designing and sampling protein sequences. J Chem Phys 2003. [DOI: 10.1063/1.1539845] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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83
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Dokholyan NV, Borreguero JM, Buldyrev SV, Ding F, Stanley HE, Shakhnovich EI. Identifying importance of amino acids for protein folding from crystal structures. Methods Enzymol 2003; 374:616-38. [PMID: 14696390 DOI: 10.1016/s0076-6879(03)74025-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Nikolay V Dokholyan
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
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84
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Miyazawa S, Jernigan RL. Long- and short-range interactions in native protein structures are consistent/minimally frustrated in sequence space. Proteins 2003; 50:35-43. [PMID: 12471597 DOI: 10.1002/prot.10242] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
We show that long- and short-range interactions in almost all protein native structures are actually consistent with each other for coarse-grained energy scales; specifically we mean the long-range inter-residue contact energies and the short-range secondary structure energies based on peptide dihedral angles, which are potentials of mean force evaluated from residue distributions observed in protein native structures. This consistency is observed at equilibrium in sequence space rather than in conformational space. Statistical ensembles of sequences are generated by exchanging residues for each of 797 protein native structures with the Metropolis method. It is shown that adding the other category of interaction to either the short- or long-range interactions decreases the means and variances of those energies for essentially all protein native structures, indicating that both interactions consistently work by more-or-less restricting sequence spaces available to one of the interactions. In addition to this consistency, independence by these interaction classes is also indicated by the fact that there are almost no correlations between them when equilibrated using both interactions and significant but small, positive correlations at equilibrium using only one of the interactions. Evidence is provided that protein native sequences can be regarded approximately as samples from the statistical ensembles of sequences with these energy scales and that all proteins have the same effective conformational temperature. Designing protein structures and sequences to be consistent and minimally frustrated among the various interactions is a most effective way to increase protein stability and foldability.
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Affiliation(s)
- Sanzo Miyazawa
- Faculty of Technology, Gunma University, Kiryu, Gunma, Japan.
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85
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Larson SM, England JL, Desjarlais JR, Pande VS. Thoroughly sampling sequence space: large-scale protein design of structural ensembles. Protein Sci 2002; 11:2804-13. [PMID: 12441379 PMCID: PMC2373757 DOI: 10.1110/ps.0203902] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2002] [Revised: 08/16/2002] [Accepted: 09/04/2002] [Indexed: 10/27/2022]
Abstract
Modeling the inherent flexibility of the protein backbone as part of computational protein design is necessary to capture the behavior of real proteins and is a prerequisite for the accurate exploration of protein sequence space. We present the results of a broad exploration of sequence space, with backbone flexibility, through a novel approach: large-scale protein design to structural ensembles. A distributed computing architecture has allowed us to generate hundreds of thousands of diverse sequences for a set of 253 naturally occurring proteins, allowing exciting insights into the nature of protein sequence space. Designing to a structural ensemble produces a much greater diversity of sequences than previous studies have reported, and homology searches using profiles derived from the designed sequences against the Protein Data Bank show that the relevance and quality of the sequences is not diminished. The designed sequences have greater overall diversity than corresponding natural sequence alignments, and no direct correlations are seen between the diversity of natural sequence alignments and the diversity of the corresponding designed sequences. For structures in the same fold, the sequence entropies of the designed sequences cluster together tightly. This tight clustering of sequence entropies within a fold and the separation of sequence entropy distributions for different folds suggest that the diversity of designed sequences is primarily determined by a structure's overall fold, and that the designability principle postulated from studies of simple models holds in real proteins. This has important implications for experimental protein design and engineering, as well as providing insight into protein evolution.
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Affiliation(s)
- Stefan M Larson
- Chemistry Department and Biophysics Program, Stanford University, California 94305, USA
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86
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Li H, Tang C, Wingreen NS. Designability of protein structures: a lattice-model study using the Miyazawa-Jernigan matrix. Proteins 2002; 49:403-12. [PMID: 12360530 DOI: 10.1002/prot.10239] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
We study the designability of all compact 3 x 3 x 3 and 6 x 6 lattice-protein structures using the Miyazawa-Jernigan (MJ) matrix. The designability of a structure is the number of sequences that design the structure, i.e., sequences that have that structure as their unique lowest-energy state. Previous studies of hydrophobic-polar (HP) models showed a wide distribution of structure designabilities. Recently, questions were raised concerning the use of a two-letter (HP) code in such studies. Here, we calculate designabilities using all 20 amino acids, with empirically determined interaction potentials (MJ matrix) and compare with HP model results. We find good qualitative agreement between the two models. In particular, highly designable structures in the HP model are also highly designable in the MJ model-and vice versa-with the associated sequences having enhanced thermodynamic stability.
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Affiliation(s)
- Hao Li
- NEC Research Institute, Princeton, New Jersey 08540, USA
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87
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Dokholyan NV, Shakhnovich B, Shakhnovich EI. Expanding protein universe and its origin from the biological Big Bang. Proc Natl Acad Sci U S A 2002; 99:14132-6. [PMID: 12384571 PMCID: PMC137849 DOI: 10.1073/pnas.202497999] [Citation(s) in RCA: 153] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The bottom-up approach to understanding the evolution of organisms is by studying molecular evolution. With the large number of protein structures identified in the past decades, we have discovered peculiar patterns that nature imprints on protein structural space in the course of evolution. In particular, we have discovered that the universe of protein structures is organized hierarchically into a scale-free network. By understanding the cause of these patterns, we attempt to glance at the very origin of life.
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Affiliation(s)
- Nikolay V Dokholyan
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA.
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88
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Miller J, Zeng C, Wingreen NS, Tang C. Emergence of highly designable protein-backbone conformations in an off-lattice model. Proteins 2002; 47:506-12. [PMID: 12001229 DOI: 10.1002/prot.10107] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Despite the variety of protein sizes, shapes, and backbone configurations found in nature, the design of novel protein folds remains an open problem. Within simple lattice models it has been shown that all structures are not equally suitable for design. Rather, certain structures are distinguished by unusually high designability: the number of amino acid sequences for which they represent the unique lowest energy state; sequences associated with such structures possess both robustness to mutation and thermodynamic stability. Here we report that highly designable backbone conformations also emerge in a realistic off-lattice model. The highly designable conformations of a chain of 23 amino acids are identified and found to be remarkably insensitive to model parameters. Although some of these conformations correspond closely to known natural protein folds, such as the zinc finger and the helix-turn-helix motifs, others do not resemble known folds and may be candidates for novel fold design.
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89
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Abstract
Synthetic polymers and gels capable of molecular recognition are very useful in designing novel intelligent biomaterials. In this article we review the recent progress in both theoretical and experimental studies toward making heteropolymers and gels with biomimetic properties, specifically in relation to protein recognition. Knowledge obtained from protein-folding studies sheds much light on our understanding of the heteropolymer behavior. Consequently, it is possible to design synthetic heteropolymers with specific structure that can fold into unique conformations, form receptor-like cavities and recognize specific target molecules. Recent studies towards simplifying the requirement for the heteropolymer structures and the polymerization procedures are reviewed. Intelligent polymer gels can be designed with new and interesting characteristics of molecular imprinting. The results are encouraging for further investigation and design of synthetic gels with programmable collapsed structure might be achieved.
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Affiliation(s)
- Nicholas A Peppas
- Department of Biochemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283, USA.
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90
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Abstract
We study the transition of polymers in the dilute regime from a swollen shape at high temperatures to their low-temperature structures. The polymers are modeled by a single self-avoiding walk (SAW) on a lattice for which l of the monomers (the H monomers) are self-attracting, i.e., if two nonbonded H monomers become nearest neighbors on the lattice they gain energy of interaction (epsilon = -/epsilon/); the second type of monomers, denoted P, are neutral. This HP model was suggested by Lau and Dill (Macromolecules 1989, 22, 3986-3997) to study protein folding, where H and P are the hydrophobic and polar amino acid residues, respectively. The model is simulated on the square and simple cubic (SC) lattices using the scanning method. We show that the ground state and the sharpness of the transition depend on the lattice, the fraction g of the H monomers, as well as on their arrangement along the chain. In particular, if the H monomers are distributed at random and g is larger than the site percolation threshold of the lattice, a collapsed transition is very likely to occur. This conclusion, drawn for the lattice models, is also applicable to proteins where an effective lattice with coordination number between that of the SC lattice and the body centered cubic lattice is defined. Thus, the average fraction of hydrophobic amino acid residues in globular proteins is found to be close to the percolation threshold of the effective lattice.
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Affiliation(s)
- Hagai Meirovitch
- University of Pittsburgh, School of Medicine, Center for Computational Biology and Bioinformatics (CCBB), Pennsylvania 15213, USA.
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91
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Peppas NA, Huang Y, Torres-Lugo M, Ward JH, Zhang J. Physicochemical foundations and structural design of hydrogels in medicine and biology. Annu Rev Biomed Eng 2002; 2:9-29. [PMID: 11701505 DOI: 10.1146/annurev.bioeng.2.1.9] [Citation(s) in RCA: 622] [Impact Index Per Article: 28.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Hydrogels are cross-linked hydrophilic polymers that can imbibe water or biological fluids. Their biomedical and pharmaceutical applications include a very wide range of systems and processes that utilize several molecular design characteristics. This review discusses the molecular structure, dynamic behavior, and structural modifications of hydrogels as well as the various applications of these biohydrogels. Recent advances in the preparation of three-dimensional structures with exact chain conformations, as well as tethering of functional groups, allow for the preparation of promising new hydrogels. Meanwhile, intelligent biohydrogels with pH- or temperature-sensitivity continue to be important materials in medical applications.
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Affiliation(s)
- N A Peppas
- Program on Therapeutic and Diagnostic Devices, Biomaterials and Drug Delivery Laboratories, School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283, USA.
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92
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Abstract
Most globular proteins are marginally stable regardless of size or activity. The most common interpretation is that proteins must be marginally stable in order to function, and so marginal stability represents the results of positive selection. We consider the issue of marginal stability directly using model proteins and the dynamical aspects of protein evolution in populations. We find that the marginal stability of proteins is an inherent property of proteins due to the high dimensionality of the sequence space, without regard to protein function. In this way, marginal stability can result from neutral, non-adaptive evolution. By allowing evolving protein sub-populations with different stability requirements for functionality to complete, we find that marginally stable populations of proteins tend to dominate. Our results show that functionalities consistent with marginal stability have a strong evolutionary advantage, and might arise because of the natural tendency of proteins towards marginal stability.
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Affiliation(s)
- Darin M Taverna
- Biophysics Research Division, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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93
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Affiliation(s)
- Marcos R. Betancourt
- Laboratory of Computational Genomics, The Donald Danforth Plant Science Center, 893 North Warson Road, Creve Coeur, Missouri 63141
| | - D. Thirumalai
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
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94
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Plotkin SS. Speeding protein folding beyond the G(o) model: how a little frustration sometimes helps. Proteins 2001; 45:337-45. [PMID: 11746681 DOI: 10.1002/prot.1154] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
By perturbing a G(o) model toward a realistic protein Hamiltonian by adding non-native interactions, we find that the folding rate is in general enhanced as ruggedness is initially increased, as long as the protein is sufficiently large and flexible. Eventually, the rate drops rapidly toward zero when ruggedness significantly slows conformational transitions. Energy landscape arguments for thermodynamics and kinetics are coupled with a treatment of non-native collapse to elucidate this effect.
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Affiliation(s)
- S S Plotkin
- Department of Physics, University of California, San Diego, California, USA.
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95
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Affiliation(s)
- J G Saven
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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96
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Abstract
We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time-scales. By studying the relaxation of the correlation function between consecutive mutations at a given position in proteins, we observe separation of the evolutionary time-scales: at short time intervals families of proteins with similar sequences and structures are formed, while at long time intervals the families of structurally similar proteins that have low sequence similarity are formed. We discuss the evolutionary implications of our model. We provide a "profile" solution to our model and find agreement between predicted patterns of conserved amino acids and those actually observed in nature.
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Affiliation(s)
- N V Dokholyan
- Department of Chemistry, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA.
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97
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Dimitrievski K, Kasemo B, Zhdanov VP. Rate-determining moves in protein folding. J Chem Phys 2001. [DOI: 10.1063/1.1386419] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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98
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Abstract
We propose a coarse-grained lattice model for Monte Carlo simulations of folding of proteins consisting of several alpha-helices. A chain representing a protein is considered to contain A and B monomers forming relatively stiff A subchains, mimicking helices, and flexible B links between these subchains, respectively. Using this model, we simulate (1) folding of four-helix proteins in solution; (2) folding of membrane proteins containing one, two, or four helices; and (3) refolding of four-helix proteins adsorbed at the liquid-solid interface. For these cases, we show typical scenarios of protein folding and refolding and study the dependence of the folding time on the chain length. Combining the latter results with those already available in the literature, we discuss the relative rates of folding of proteins belonging to different classes.
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Affiliation(s)
- V P Zhdanov
- Department of Applied Physics, Chalmers University of Technology, Göteborg, Sweden.
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99
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Kono H, Saven JG. Statistical theory for protein combinatorial libraries. Packing interactions, backbone flexibility, and the sequence variability of a main-chain structure. J Mol Biol 2001; 306:607-28. [PMID: 11178917 DOI: 10.1006/jmbi.2000.4422] [Citation(s) in RCA: 107] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Combinatorial experiments provide new ways to probe the determinants of protein folding and to identify novel folding amino acid sequences. These types of experiments, however, are complicated both by enormous conformational complexity and by large numbers of possible sequences. Therefore, a quantitative computational theory would be helpful in designing and interpreting these types of experiment. Here, we present and apply a statistically based, computational approach for identifying the properties of sequences compatible with a given main-chain structure. Protein side-chain conformations are included in an atom-based fashion. Calculations are performed for a variety of similar backbone structures to identify sequence properties that are robust with respect to minor changes in main-chain structure. Rather than specific sequences, the method yields the likelihood of each of the amino acids at preselected positions in a given protein structure. The theory may be used to quantify the characteristics of sequence space for a chosen structure without explicitly tabulating sequences. To account for hydrophobic effects, we introduce an environmental energy that it is consistent with other simple hydrophobicity scales and show that it is effective for side-chain modeling. We apply the method to calculate the identity probabilities of selected positions of the immunoglobulin light chain-binding domain of protein L, for which many variant folding sequences are available. The calculations compare favorably with the experimentally observed identity probabilities.
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Affiliation(s)
- H Kono
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, USA
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100
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Abstract
We study the evolution of protein functionality using a two-dimensional lattice model. The characteristics particular to evolution, such as population dynamics and early evolutionary trajectories, have a large effect on the distribution of observed structures. Only subtle differences are observed between the distribution of structures evolved for function and those evolved for their ability to form compact structures.
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Affiliation(s)
- P D Williams
- Department of Chemistry, University of Michigan, Ann Arbor, MI 48109-1055, USA
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