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Satarifard V, Heidari M, Mashaghi S, Tans SJ, Ejtehadi MR, Mashaghi A. Topology of polymer chains under nanoscale confinement. NANOSCALE 2017; 9:12170-12177. [PMID: 28805849 DOI: 10.1039/c7nr04220e] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of lp under a spherical confinement of radius Rc. At low values of lp/Rc, the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high lp/Rc, the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of lp/Rc, at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.
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Affiliation(s)
- Vahid Satarifard
- Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden, The Netherlands.
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Abstract
Numerous biological proteins exhibit intrinsic disorder at their termini, which are associated with multifarious functional roles. Here, we show the surprising result that an increased percentage of terminal short transiently disordered regions with enhanced flexibility (TstDREF) is associated with accelerated folding rates of globular proteins. Evolutionary conservation of predicted disorder at TstDREFs and drastic alteration of folding rates upon point-mutations suggest critical regulatory role(s) of TstDREFs in shaping the folding kinetics. TstDREFs are associated with long-range intramolecular interactions and the percentage of native secondary structural elements physically contacted by TstDREFs exhibit another surprising positive correlation with folding kinetics. These results allow us to infer probable molecular mechanisms behind the TstDREF-mediated regulation of folding kinetics that challenge protein biochemists to assess by direct experimental testing.
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Affiliation(s)
- Saurav Mallik
- Department of Biophysics, Molecular Biology and Bioinformatics, University of Calcutta, India.,Center of Excellence in Systems Biology and Biomedical Engineering (TEQIP Phase-II), University of Calcutta, India
| | - Tanaya Ray
- Harish-Chandra Research Institute, HBNI, Allahabad, India
| | - Sudip Kundu
- Department of Biophysics, Molecular Biology and Bioinformatics, University of Calcutta, India.,Center of Excellence in Systems Biology and Biomedical Engineering (TEQIP Phase-II), University of Calcutta, India
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Bastolla U, Dehouck Y, Echave J. What evolution tells us about protein physics, and protein physics tells us about evolution. Curr Opin Struct Biol 2017; 42:59-66. [DOI: 10.1016/j.sbi.2016.10.020] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Revised: 10/19/2016] [Accepted: 10/24/2016] [Indexed: 12/21/2022]
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Heidari M, Satarifard V, Tans SJ, Ejtehadi MR, Mashaghi S, Mashaghi A. Topology of internally constrained polymer chains. Phys Chem Chem Phys 2017; 19:18389-18393. [DOI: 10.1039/c7cp02145c] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
An interacting partner can provide external control over folding rates and realized topologies.
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Affiliation(s)
- Maziar Heidari
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
| | - Vahid Satarifard
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
| | | | | | - Samaneh Mashaghi
- School of Engineering and Applied Sciences and Department of Physics
- Harvard University
- Cambridge
- USA
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
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Sinner C, Lutz B, Verma A, Schug A. Revealing the global map of protein folding space by large-scale simulations. J Chem Phys 2015; 143:243154. [DOI: 10.1063/1.4938172] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Claude Sinner
- Steinbuch Centre for Computing, Karlsruhe Institute of Technology, Karlsruhe, Germany
- Department of Physics, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Benjamin Lutz
- Steinbuch Centre for Computing, Karlsruhe Institute of Technology, Karlsruhe, Germany
- Department of Physics, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Abhinav Verma
- Steinbuch Centre for Computing, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Alexander Schug
- Steinbuch Centre for Computing, Karlsruhe Institute of Technology, Karlsruhe, Germany
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Detecting selection on protein stability through statistical mechanical models of folding and evolution. Biomolecules 2014; 4:291-314. [PMID: 24970217 PMCID: PMC4030984 DOI: 10.3390/biom4010291] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2013] [Revised: 02/13/2014] [Accepted: 02/14/2014] [Indexed: 12/31/2022] Open
Abstract
The properties of biomolecules depend both on physics and on the evolutionary process that formed them. These two points of view produce a powerful synergism. Physics sets the stage and the constraints that molecular evolution has to obey, and evolutionary theory helps in rationalizing the physical properties of biomolecules, including protein folding thermodynamics. To complete the parallelism, protein thermodynamics is founded on the statistical mechanics in the space of protein structures, and molecular evolution can be viewed as statistical mechanics in the space of protein sequences. In this review, we will integrate both points of view, applying them to detecting selection on the stability of the folded state of proteins. We will start discussing positive design, which strengthens the stability of the folded against the unfolded state of proteins. Positive design justifies why statistical potentials for protein folding can be obtained from the frequencies of structural motifs. Stability against unfolding is easier to achieve for longer proteins. On the contrary, negative design, which consists in destabilizing frequently formed misfolded conformations, is more difficult to achieve for longer proteins. The folding rate can be enhanced by strengthening short-range native interactions, but this requirement contrasts with negative design, and evolution has to trade-off between them. Finally, selection can accelerate functional movements by favoring low frequency normal modes of the dynamics of the native state that strongly correlate with the functional conformation change.
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Das A, Sin BK, Mohazab AR, Plotkin SS. Unfolded protein ensembles, folding trajectories, and refolding rate prediction. J Chem Phys 2013; 139:121925. [DOI: 10.1063/1.4817215] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
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Mohazab AR, Plotkin SS. Polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways. PLoS One 2013; 8:e53642. [PMID: 23365638 PMCID: PMC3554774 DOI: 10.1371/journal.pone.0053642] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2012] [Accepted: 11/30/2012] [Indexed: 11/19/2022] Open
Abstract
We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Formula: see text], [Formula: see text], [Formula: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation "alignment". The consensus minimal pathway is constructed and shown schematically for representative cases of an [Formula: see text], [Formula: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Formula: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Formula: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.
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Affiliation(s)
- Ali R. Mohazab
- Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C, Canada
| | - Steven S. Plotkin
- Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C, Canada
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Rustad M, Ghosh K. Why and how does native topology dictate the folding speed of a protein? J Chem Phys 2012. [DOI: 10.1063/1.4767567] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bastolla U, Bruscolini P, Velasco JL. Sequence determinants of protein folding rates: Positive correlation between contact energy and contact range indicates selection for fast folding. Proteins 2012; 80:2287-304. [DOI: 10.1002/prot.24118] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2011] [Revised: 05/14/2012] [Accepted: 05/17/2012] [Indexed: 11/12/2022]
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Naganathan AN, Orozco M. The protein folding transition-state ensemble from a Gō-like model. Phys Chem Chem Phys 2011; 13:15166-74. [DOI: 10.1039/c1cp20964g] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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12
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Chang L, Wang J, Wang W. Composition-based effective chain length for prediction of protein folding rates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051930. [PMID: 21230523 DOI: 10.1103/physreve.82.051930] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2010] [Indexed: 05/30/2023]
Abstract
Folding rate prediction is a useful way to find the key factors affecting folding kinetics of proteins. Structural information is more or less required in the present prediction methods, which limits the application of these methods to various proteins. In this work, an "effective length" is defined solely based on the composition of a protein, namely, the number of specific types of amino acids in a protein. A physical theory based on a minimalist model is employed to describe the relation between the folding rates and the effective length of proteins. Based on the resultant relationship between folding rates and effective length, the optimal sets of amino acids are found through the enumeration over all possible combinations of amino acids. This optimal set achieves a high correlation (with the coefficient of 0.84) between the folding rates and the optimal effective length. The features of these amino acids are consistent with our model and landscape theory. Further comparisons between our effective length and other factors are carried out. The effective length is physically consistent with structure-based prediction methods and has the best predictability for folding rates. These results all suggest that both entropy and energetics contribute importantly to folding kinetics. The ability to accurately and efficiently predict folding rates from composition enables the analysis of the kinetics for various kinds of proteins. The underlying physics in our method may be helpful to stimulate further understanding on the effects of various amino acids in folding dynamics.
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Affiliation(s)
- Le Chang
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University, Nanjing 210093, China
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13
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Harihar B, Selvaraj S. Refinement of the long-range order parameter in predicting folding rates of two-state proteins. Biopolymers 2009; 91:928-35. [DOI: 10.1002/bip.21281] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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14
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Abstract
The minimal folding pathway or trajectory for a biopolymer can be defined as the transformation that minimizes the total distance traveled between a folded and an unfolded structure. This involves generalizing the usual Euclidean distance from points to one-dimensional objects such as a polymer. We apply this distance here to find minimal folding pathways for several candidate protein fragments, including the helix, the beta-hairpin, and a nonplanar structure where chain noncrossing is important. Comparing the distances traveled with root mean-squared distance and mean root-squared distance, we show that chain noncrossing can have large effects on the kinetic proximity of apparently similar conformations. Structures that are aligned to the beta-hairpin by minimizing mean root-squared distance, a quantity that closely approximates the true distance for long chains, show globally different orientation than structures aligned by minimizing root mean-squared distance.
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Bruscolini P, Pelizzola A, Zamparo M. Rate determining factors in protein model structures. PHYSICAL REVIEW LETTERS 2007; 99:038103. [PMID: 17678333 DOI: 10.1103/physrevlett.99.038103] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2007] [Indexed: 05/16/2023]
Abstract
Previous research has shown a strong correlation of protein folding rates to the native state geometry, yet a complete explanation for this dependence is still lacking. Here we study the rate-geometry relationship with a simple statistical physics model, and focus on two classes of model geometries, representing ideal parallel and antiparallel structures. We find that the logarithm of the rate shows an almost perfect linear correlation with the "absolute contact order", but the slope depends on the particular class considered. We discuss these findings in the light of experimental results.
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Affiliation(s)
- Pierpaolo Bruscolini
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, c. Corona de Aragón 42, 50009 Zaragoza, Spain.
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