1
|
Keith A, Brichtová EP, Barber JG, Wales DJ, Jackson SE, Röder K. Energy Landscapes and Structural Ensembles of Glucagon-like Peptide-1 Monomers. J Phys Chem B 2024; 128:5601-5611. [PMID: 38831581 PMCID: PMC11182347 DOI: 10.1021/acs.jpcb.4c01794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Revised: 05/16/2024] [Accepted: 05/20/2024] [Indexed: 06/05/2024]
Abstract
While GLP-1 and its analogues are important pharmaceutical agents in the treatment of type 2 diabetes and obesity, their susceptibility to aggregate into amyloid fibrils poses a significant safety issue. Many factors may contribute to the aggregation propensity, including pH. While it is known that the monomeric structure of GLP-1 has a strong impact on primary nucleation, probing its diverse structural ensemble is challenging. Here, we investigated the monomer structural ensembles at pH 3, 4, and 7.5 using state-of-the-art computational methods in combination with experimental data. We found significant stabilization of β-strand structures and destabilization of helical structures at lower pH, correlating with observed aggregation lag times, which are lower under these conditions. We further identified helical defects at pH 4, which led to the fastest observed aggregation, in agreement with our far-UV circular dichroism data. The detailed atomistic structures that result from the computational studies help to rationalize the experimental results on the aggregation propensity of GLP-1. This work provides a new insight into the pH-dependence of monomeric structural ensembles of GLP-1 and connects them to experimental observations.
Collapse
Affiliation(s)
- Alasdair
D. Keith
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
- Now:
Department of Biochemistry, School of Medicine, Emory University, 1510 Clifton Rd NE, Atlanta, Georgia 30322, United States
| | - Eva Přáda Brichtová
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
- Now:
Institute of Chemical, Environmental and Bioscience Engineering, Technische Universität Wien, Gumpendorferstr. 1A, Vienna 1060, Austria
| | - Jack G. Barber
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
| | - David J. Wales
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
| | - Sophie E. Jackson
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
| | - Konstantin Röder
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
- Now:
Randall Centre for Cell & Molecular Biophysics, King’s College London, Great Maze Pond, London SE1 1UL, U.K.
| |
Collapse
|
2
|
Nagahata Y, Kobayashi M, Toda M, Maeda S, Taketsugu T, Komatsuzaki T. An encompassed representation of timescale hierarchies in first-order reaction network. Proc Natl Acad Sci U S A 2024; 121:e2317781121. [PMID: 38758700 PMCID: PMC11126998 DOI: 10.1073/pnas.2317781121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 04/16/2024] [Indexed: 05/19/2024] Open
Abstract
Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.
Collapse
Affiliation(s)
- Yutaka Nagahata
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
| | - Masato Kobayashi
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo060-0810, Japan
| | - Mikito Toda
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Faculty Division of Natural Sciences, Nara Women’s University, Nara630-8506, Japan
- Graduate School of Information Science, University of Hyogo, Kobe650-0047, Japan
| | - Satoshi Maeda
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo060-0810, Japan
| | - Tetsuya Taketsugu
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo060-0810, Japan
| | - Tamiki Komatsuzaki
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Suita565-0871, Japan
- The Institute of Scientific and Industrial Research, Osaka University, Ibaraki567-0047, Japan
| |
Collapse
|
3
|
Abstract
Multifunctional systems, such as molecular switches, exhibit multifunnel energy landscapes associated with the alternative functional states. In this contribution the multifunnel organization is decoded from dynamical signatures in the first passage time distribution between reactants and products. Characteristic relaxation rates are revealed by analyzing the kinetics as a function of the observation time scale, which scans the underlying distribution. Extracting the corresponding dynamical signatures provides direct insight into the organization of the molecular energy landscape, which will facilitate a rational design of target functionality. Examples are illustrated for multifunnel landscapes in biomolecular systems and an atomic cluster.
Collapse
|
4
|
Röder K, Wales DJ. The Energy Landscape Perspective: Encoding Structure and Function for Biomolecules. Front Mol Biosci 2022; 9:820792. [PMID: 35155579 PMCID: PMC8829389 DOI: 10.3389/fmolb.2022.820792] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 01/07/2022] [Indexed: 12/02/2022] Open
Abstract
The energy landscape perspective is outlined with particular reference to biomolecules that perform multiple functions. We associate these multifunctional molecules with multifunnel energy landscapes, illustrated by some selected examples, where understanding the organisation of the landscape has provided new insight into function. Conformational selection and induced fit may provide alternative routes to realisation of multifunctionality, exploiting the possibility of environmental control and distinct binding modes.
Collapse
|
5
|
Computer-aided comprehensive explorations of RNA structural polymorphism through complementary simulation methods. QRB DISCOVERY 2022. [PMID: 37529277 PMCID: PMC10392686 DOI: 10.1017/qrd.2022.19] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
While RNA folding was originally seen as a simple problem to solve, it has been shown that the promiscuous interactions of the nucleobases result in structural polymorphism, with several competing structures generally observed for non-coding RNA. This inherent complexity limits our understanding of these molecules from experiments alone, and computational methods are commonly used to study RNA. Here, we discuss three advanced sampling schemes, namely Hamiltonian-replica exchange molecular dynamics (MD), ratchet-and-pawl MD and discrete path sampling, as well as the HiRE-RNA coarse-graining scheme, and highlight how these approaches are complementary with reference to recent case studies. While all computational methods have their shortcomings, the plurality of simulation methods leads to a better understanding of experimental findings and can inform and guide experimental work on RNA polymorphism.
Collapse
|
6
|
RNA Modeling with the Computational Energy Landscape Framework. METHODS IN MOLECULAR BIOLOGY (CLIFTON, N.J.) 2021; 2323:49-66. [PMID: 34086273 DOI: 10.1007/978-1-0716-1499-0_5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The recent advances in computational abilities, such as the enormous speed-ups provided by GPU computing, allow for large scale computational studies of RNA molecules at an atomic level of detail. As RNA molecules are known to adopt multiple conformations with comparable energies, but different two-dimensional structures, all-atom models are necessary to better describe the structural ensembles for RNA molecules. This point is important because different conformations can exhibit different functions, and their regulation or mis-regulation is linked to a number of diseases. Problematically, the energy barriers between different conformational ensembles are high, resulting in long time scales for interensemble transitions. The computational potential energy landscape framework was designed to overcome this problem of broken ergodicity by use of geometry optimization. Here, we describe the algorithms used in the energy landscape explorations with the OPTIM and PATHSAMPLE programs, and how they are used in biomolecular simulations. We present a recent case study of the 5'-hairpin of RNA 7SK to illustrate how the method can be applied to interpret experimental results, and to obtain a detailed description of molecular properties.
Collapse
|
7
|
Röder K. Is the H4 histone tail intrinsically disordered or intrinsically multifunctional? Phys Chem Chem Phys 2021; 23:5134-5142. [PMID: 33624669 DOI: 10.1039/d0cp05405d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The structural versatility of histone tails is one of the key elements in the organisation of chromatin, which allows for the compact storage of genomic information. However, this structural diversity also complicates experimental and computational studies. Here, the potential and free energy landscape for the isolated and bound H4 histone tail are explored. The landscapes exhibit a set of distinct structural ensembles separated by high energy barriers, with little difference between isolated and bound tails. This consistency is a desirable feature that facilitates the formation of transient interactions, which are required for the liquid-like chromatin organisation. The existence of multiple, distinct structures on a multifunnel energy landscape is likely to be associated with multifunctionality, i.e. a set of evolved, distinct functions. Contrasting it with previously reported results for other disordered peptides, this type of landscape may be associated with a conformational selection based binding mechanism. Given the similarity to other systems exhibiting similar multifunnel energy landscapes, the disorder in histone tails might be better described in context of multifunctionality.
Collapse
Affiliation(s)
- Konstantin Röder
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
| |
Collapse
|
8
|
Kannan D, Sharpe DJ, Swinburne TD, Wales DJ. Optimal dimensionality reduction of Markov chains using graph transformation. J Chem Phys 2020; 153:244108. [PMID: 33380101 DOI: 10.1063/5.0025174] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Markov chains can accurately model the state-to-state dynamics of a wide range of complex systems, but the underlying transition matrix is ill-conditioned when the dynamics feature a separation of timescales. Graph transformation (GT) provides a numerically stable method to compute exact mean first passage times (MFPTs) between states, which are the usual dynamical observables in continuous-time Markov chains (CTMCs). Here, we generalize the GT algorithm to discrete-time Markov chains (DTMCs), which are commonly estimated from simulation data, for example, in the Markov state model approach. We then consider the dimensionality reduction of CTMCs and DTMCs, which aids model interpretation and facilitates more expensive computations, including sampling of pathways. We perform a detailed numerical analysis of existing methods to compute the optimal reduced CTMC, given a partitioning of the network into metastable communities (macrostates) of nodes (microstates). We show that approaches based on linear algebra encounter numerical problems that arise from the requisite metastability. We propose an alternative approach using GT to compute the matrix of intermicrostate MFPTs in the original Markov chain, from which a matrix of weighted intermacrostate MFPTs can be obtained. We also propose an approximation to the weighted-MFPT matrix in the strongly metastable limit. Inversion of the weighted-MFPT matrix, which is better conditioned than the matrices that must be inverted in alternative dimensionality reduction schemes, then yields the optimal reduced Markov chain. The superior numerical stability of the GT approach therefore enables us to realize optimal Markovian coarse-graining of systems with rare event dynamics.
Collapse
Affiliation(s)
- Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
9
|
Swinburne TD, Kannan D, Sharpe DJ, Wales DJ. Rare events and first passage time statistics from the energy landscape. J Chem Phys 2020; 153:134115. [PMID: 33032418 DOI: 10.1063/5.0016244] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online.
Collapse
Affiliation(s)
- Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
10
|
Neelamraju S, Wales DJ, Gosavi S. Protein energy landscape exploration with structure-based models. Curr Opin Struct Biol 2020; 64:145-151. [DOI: 10.1016/j.sbi.2020.07.003] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Revised: 06/30/2020] [Accepted: 07/15/2020] [Indexed: 12/11/2022]
|
11
|
Röder K, Wales DJ. Improving double-ended transition state searches for soft-matter systems. J Chem Phys 2020; 153:034104. [PMID: 32716181 DOI: 10.1063/5.0011829] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
Transitions between different stable configurations of biomolecules are important in understanding disease mechanisms, structure-function relations, and novel molecular-scale engineering. The corresponding pathways can be characterized efficiently using geometry optimization schemes based on double-ended transition state searches. An interpolation is first constructed between the known states and then refined, yielding a band that contains transition state candidates. Here, we analyze an example where various interpolation schemes lead to bands with a single step transition, but the correct pathway actually proceeds via an intervening, low-energy minimum. We compare a number of different interpolation schemes for this problem. We systematically alter the number of discrete images in the interpolations and the spring constants used in the optimization and test two schemes for adjusting the spring constants and image distribution, resulting in a total of 2760 different connection attempts. Our results confirm that optimized bands are not necessarily a good description of the transition pathways in themselves, and further refinement to actually converge transition states and establish their connectivity is required. We see an improvement in the optimized bands if we employ the adjustment of spring constants with doubly-nudged elastic band and a smaller improvement from the image redistribution. The example we consider is representative of numerous cases we have encountered in a wide variety of molecular and condensed matter systems.
Collapse
Affiliation(s)
- K Röder
- Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW Cambridge, United Kingdom
| | - D J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW Cambridge, United Kingdom
| |
Collapse
|
12
|
Sharpe DJ, Wales DJ. Efficient and exact sampling of transition path ensembles on Markovian networks. J Chem Phys 2020; 153:024121. [DOI: 10.1063/5.0012128] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Daniel J. Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
13
|
Sharpe DJ, Röder K, Wales DJ. Energy Landscapes of Deoxyxylo- and Xylo-Nucleic Acid Octamers. J Phys Chem B 2020; 124:4062-4068. [PMID: 32336100 PMCID: PMC7304908 DOI: 10.1021/acs.jpcb.0c01420] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
![]()
Artificial
analogues of the natural nucleic acids have attracted
interest as a diverse class of information storage molecules capable
of self-replication. In this study, we use the computational potential
energy landscape framework to investigate the structural and dynamical
properties of xylo- and deoxyxylo-nucleic acids (XyNA and dXyNA),
which are derived from their respective RNA and DNA analogues by inversion
of a single chiral center in the sugar moiety of the nucleotides.
For an octameric XyNA sequence and the analogue dXyNA, we observe
facile conformational transitions between a left-handed helix, which
is the free energy global minimum, and a ladder-type structure with
approximately zero helicity. The competing ensembles are better separated
in the dXyNA, making it a more suitable candidate for a molecular
switch, whereas the XyNA exhibits additional flexibility. Both energy
landscapes exhibit greater frustration than we observe in RNA or DNA,
in agreement with the higher degree of optimization expected from
the principle of minimal frustration in evolved biomolecules.
Collapse
Affiliation(s)
- Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Konstantin Röder
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
14
|
Chakraborty D, Chebaro Y, Wales DJ. A multifunnel energy landscape encodes the competing α-helix and β-hairpin conformations for a designed peptide. Phys Chem Chem Phys 2020; 22:1359-1370. [PMID: 31854397 DOI: 10.1039/c9cp04778f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Depending on the amino acid sequence, as well as the local environment, some peptides have the capability to fold into multiple secondary structures. Conformational switching between such structures is a key element of protein folding and aggregation. Specifically, understanding the molecular mechanism underlying the transition from an α-helix to a β-hairpin is critical because it is thought to be a harbinger of amyloid assembly. In this study, we explore the energy landscape for an 18-residue peptide (DP5), designed by Araki and Tamura to exhibit equal propensities for the α-helical and β-hairpin forms. We find that the degeneracy is encoded in the multifunnel nature of the underlying free energy landscape. In agreement with experiment, we also observe that mutation of tyrosine at position 12 to serine shifts the equilibrium in favor of the α-helix conformation, by altering the landscape topography. The transition from the α-helix to the β-hairpin is a complex stepwise process, and occurs via collapsed coil-like intermediates. Our findings suggest that even a single mutation can tune the emergent features of the landscape, providing an efficient route to protein design. Interestingly, the transition pathways for the conformational switch seem to be minimally perturbed upon mutation, suggesting that there could be universal microscopic features that are conserved among different switch-competent protein sequences.
Collapse
Affiliation(s)
- Debayan Chakraborty
- Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, UK.
| | - Yassmine Chebaro
- Department of Integrative Structural Biology, Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), CNRS UMR 7104, INSERM U964, Université de Strasbourg, 67404 Illkirch, France
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, UK.
| |
Collapse
|
15
|
Liu CH, Lee GW, Wu WC, Wang CC. Encapsulating curcumin in ethylene diamine-β-cyclodextrin nanoparticle improves topical cornea delivery. Colloids Surf B Biointerfaces 2019; 186:110726. [PMID: 31862560 DOI: 10.1016/j.colsurfb.2019.110726] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Revised: 11/05/2019] [Accepted: 12/12/2019] [Indexed: 11/26/2022]
Abstract
Curcumin is a powerful scavenger of reactive oxygen species and could prevent the corneal cells from oxidative damage. However, the clinical efficacy of curcumin is limited by its low aqueous solubility and stability, leading to poor bioavailability. β-cyclodextrin, with a hydrophilic surface and a hydrophobic cavity and self-assembling properties, can form inclusion complexes with lipophilic drugs such as curcumin for ocular delivery. We synthesized ethylene diamine (EDA)-modified β-cyclodextrin and prepared the curcumin complexation using the solvent evaporation method. The EDA-β-cyclodextrin provided a better thermodynamic stability and higher complex yield for curcumin complexes, compared to β-cyclodextrin, which were demonstrated on the analysis of their van't Hoff plots and phase solubility diagrams. We characterized EDA-β-cyclodextrin curcumin nanoparticles and determined that the EDA modified β-cyclodextrin is a more suitable carrier than parental β-cyclodextrin, using FT-IR, XRD, TEM, and analyses of solubility and storage stability. In addition, the curcumin-EDA-β-cyclodextrin nanoparticles had better in vitro corneal penetration and 3 -h cumulative flux in a porcine cornea experiment, and displayed an improved biocompatibility, confirmed by the histological examination of porcine corneas and cell viability of bovine corneal epithelial cells. These results together revealed a role of EDA modification in the β-cyclodextrin carrier, including the improvement of curcumin complex formation, thermodynamic properties, cytotoxicity, and the in vitro corneal penetration. The EDA-β-cyclodextrin inclusion can provide curcumin a higher degree of aqueous solubility and corneal permeability.
Collapse
Affiliation(s)
- Chi-Hsien Liu
- Department of Chemical and Materials Engineering, Chang Gung University, 259, Wen-Hwa First Road, Kwei-Shan, Tao-Yuan, 333, Taiwan; Research Center for Chinese Herbal Medicine and Research Center for Food and Cosmetic Safety, College of Human Ecology, Chang Gung University of Science and Technology, 261, Wen-Hwa First Road, Taoyuan, Taiwan; Department of Chemical Engineering, Ming Chi University of Technology, 84, Gung-Juan Road, New Taipei City, Taiwan; Department of Ophthalmology, Chang Gung Memorial Hospital, 5, Fu-Hsing Street, Taoyuan, Taiwan.
| | - Guan-Wei Lee
- Graduate Institute of Biomedical Engineering, Chang Gung University, 259, Wen-Hwa First Road, Kwei-Shan, Tao-Yuan 333, Taiwan
| | - Wei-Chi Wu
- Department of Ophthalmology, Chang Gung Memorial Hospital, 5, Fu-Hsing Street, Taoyuan, Taiwan; College of Medicine, Chang Gung University, 259, Wen-Hwa First Road, Taoyuan, Taiwan
| | - Chun-Chao Wang
- Institute of Molecular Medicine & Department of Medical Science, National Tsing Hua University, 101, Kuang-Fu Road, Hsinchu, Taiwan
| |
Collapse
|
16
|
Sharpe DJ, Wales DJ. Identifying mechanistically distinct pathways in kinetic transition networks. J Chem Phys 2019; 151:124101. [DOI: 10.1063/1.5111939] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniel J. Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
17
|
Chakraborty D, Wales DJ. Dynamics of an adenine-adenine RNA conformational switch from discrete path sampling. J Chem Phys 2019; 150:125101. [DOI: 10.1063/1.5070152] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Debayan Chakraborty
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
18
|
Röder K, Joseph JA, Husic BE, Wales DJ. Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201800175] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Konstantin Röder
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - Jerelle A. Joseph
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - Brooke E. Husic
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - David J. Wales
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| |
Collapse
|
19
|
Li X, Li S, Wang Z, Yang X, Yan Z. A Frank-Kasper polyhedral structure of 17-atom vanadium clusters. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.08.024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
20
|
Klimavicz JS, Röder K, Wales DJ. Energy Landscapes of Mini-Dumbbell DNA Octanucleotides. J Chem Theory Comput 2018; 14:3870-3876. [PMID: 29792700 DOI: 10.1021/acs.jctc.8b00262] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Single-stranded DNA structures play a significant role in biological systems, in particular during replication, translation, and DNA repair. Tracts of simple repetitive DNA are associated with slipped-strand mispairing, which can lead to genetic diseases. Recent NMR studies of TTTA and CCTG repeats have shown that these sequences form mini-dumbbells (MDBs), leading to frameshift mutations. Here we explore the energy landscapes of (CCTG)2 and (TTTA)2, which are currently the smallest known molecules to form MDBs. While (CCTG)2 MDBs are stable, (TTTA)2 exhibits numerous other structures with lower energies. A key factor identified in the stabilization of MDB structures is the bonding strength between residues 1 and 4, and 5 and 8.
Collapse
Affiliation(s)
- James S Klimavicz
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom.,Department of Entomology , Iowa State University , Ames , Iowa 50011 , United States
| | - Konstantin Röder
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom
| | - David J Wales
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom
| |
Collapse
|
21
|
Abstract
A general formulation for constructing addressable atomic clusters is introduced, based on one or more reference structures. By modifying the well depths in a given interatomic potential in favour of nearest-neighbour interactions that are defined in the reference(s), the potential energy landscape can be biased to make a particular permutational isomer the global minimum. The magnitude of the bias changes the resulting potential energy landscape systematically, providing a framework to produce clusters that should self-organise efficiently into the target structure. These features are illustrated for small systems, where all the relevant local minima and transition states can be identified, and for the low-energy regions of the landscape for larger clusters. For a 55-particle cluster, it is possible to design a target structure from a transition state of the original potential and to retain this structure in a doubly addressable landscape. Disconnectivity graphs based on local minima that have no direct connections to a lower minimum provide a helpful way to visualise the larger databases. These minima correspond to the termini of monotonic sequences, which always proceed downhill in terms of potential energy, and we identify them as a class of biminimum. Multiple copies of the target cluster are treated by adding a repulsive term between particles with the same address to maintain distinguishable targets upon aggregation. By tuning the magnitude of this term, it is possible to create assemblies of the target cluster corresponding to a variety of structures, including rings and chains.
Collapse
Affiliation(s)
- David J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
22
|
Joseph JA, Röder K, Chakraborty D, Mantell RG, Wales DJ. Exploring biomolecular energy landscapes. Chem Commun (Camb) 2018; 53:6974-6988. [PMID: 28489083 DOI: 10.1039/c7cc02413d] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The potential energy landscape perspective provides both a conceptual and a computational framework for predicting, understanding and designing molecular properties. In this Feature Article, we highlight some recent advances that greatly facilitate structure prediction and analysis of global thermodynamics and kinetics in proteins and nucleic acids. The geometry optimisation procedures, on which these calculations are based, can be accelerated significantly using local rigidification of selected degrees of freedom, and through implementations on graphics processing units. Results of progressive local rigidification are first summarised for trpzip1, including a systematic analysis of the heat capacity and rearrangement rates. Benchmarks for all the essential optimisation procedures are then provided for a variety of proteins. Applications are then illustrated from a study of how mutation affects the energy landscape for a coiled-coil protein, and for transitions in helix morphology for a DNA duplex. Both systems exhibit an intrinsically multifunnel landscape, with the potential to act as biomolecular switches.
Collapse
Affiliation(s)
- Jerelle A Joseph
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
| | - Konstantin Röder
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
| | - Debayan Chakraborty
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK. and Department of Chemistry, The University of Texas at Austin, 24th Street Stop A5300, Austin, TX 78712, USA
| | - Rosemary G Mantell
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
| |
Collapse
|
23
|
Curtis F, Li X, Rose T, Vázquez-Mayagoitia Á, Bhattacharya S, Ghiringhelli LM, Marom N. GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction. J Chem Theory Comput 2018; 14:2246-2264. [PMID: 29481740 DOI: 10.1021/acs.jctc.7b01152] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the implementation of GAtor, a massively parallel, first-principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy minima, including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re-ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. The experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with P1̅ symmetry and a scaffold packing motif, which has not been reported previously.
Collapse
Affiliation(s)
- Farren Curtis
- Department of Physics , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Xiayue Li
- Google , Mountain View , California 94030 , United States.,Department of Materials Science and Engineering , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Timothy Rose
- Department of Materials Science and Engineering , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Álvaro Vázquez-Mayagoitia
- Argonne Leadership Computing Facility , Argonne National Laboratory , Lemont , Illinois 60439 , United States
| | - Saswata Bhattacharya
- Department of Physics , Indian Institute of Technology Delhi , Hauz Khas , New Delhi 110016 , India
| | - Luca M Ghiringhelli
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6 , 14195 , Berlin , Germany
| | - Noa Marom
- Department of Physics , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States.,Department of Materials Science and Engineering , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States.,Department of Chemistry , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| |
Collapse
|
24
|
Abstract
The complex conformational change from B-DNA to Z-DNA requires inversion of helix-handedness. Multiple degrees of freedom are intricately coupled during this transition, and formulating an appropriate reaction coordinate that captures the underlying complexity would be problematic. In this contribution, we adopt an alternative approach, based on the potential energy landscape perspective, to construct a kinetic transition network. Microscopic insight into the B → Z transition is provided in terms of geometrically defined discrete paths consisting of local minima and the transition states that connect them. We find that the inversion of handedness can occur via two competing mechanisms, either involving stretched intermediates, or a B-Z junction, in agreement with previous predictions. The organisation of the free energy landscape further suggests that this process is likely to be slow under physiological conditions. Our results represent a key step towards decoding the more intriguing features of the B → Z transition, such as the role of ionic strength and negative supercoiling in reshaping the landscape.
Collapse
Affiliation(s)
- Debayan Chakraborty
- Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, UK.
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, UK.
| |
Collapse
|
25
|
Taylor JN, Pirchi M, Haran G, Komatsuzaki T. Deciphering hierarchical features in the energy landscape of adenylate kinase folding/unfolding. J Chem Phys 2018; 148:123325. [DOI: 10.1063/1.5016487] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. Nicholas Taylor
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-Ku, Sapporo 001-0020, Japan
| | | | - Gilad Haran
- Weizmann Institute of Science, Rehovot 76100, Israel
| | - Tamiki Komatsuzaki
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-Ku, Sapporo 001-0020, Japan
- Graduate School of Life Science, Hokkaido University, Sapporo 001-0020, Japan
| |
Collapse
|
26
|
Bouvier B, Cézard C. Impact of iron coordination isomerism on pyoverdine recognition by the FpvA membrane transporter of Pseudomonas aeruginosa. Phys Chem Chem Phys 2017; 19:29498-29507. [PMID: 29082401 DOI: 10.1039/c7cp04529h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Pyoverdines, the primary siderophores of Pseudomonas bacteria, scavenge the iron essential to bacterial life in the outside medium and transport it back into the periplasm. Despite their relative simplicity, pyoverdines feature remarkably flexible recognition characteristics whose origins at the atomistic level remain only partially understood: the ability to bind other metals than ferric iron, the capacity of outer membrane transporters to recognize and internalize noncognate pyoverdines from other pseudomonads… One of the less examined factors behind this polymorphic recognition lies in the ability for pyoverdines to bind iron with two distinct chiralities, at the cost of a conformational switch. Herein, we use free energy simulations to study how the stereochemistry of the iron chelating groups influences the structure and dynamics of two common pyoverdines and impacts their recognition by the FpvA membrane transporter of P. aeruginosa. We show that conformational preferences for one metal binding chirality over the other, observed in solution depending on the nature of the pyoverdine, are canceled out by the FpvA transporter, which recognizes both chiralities equally well for both pyoverdines under study. However, FpvA discriminates between pyoverdines by altering the kinetics of stereoisomer interconversion. We present structural causes of this intriguing recognition mechanism and discuss its possible significance in the context of the competitive scavenging of iron.
Collapse
Affiliation(s)
- Benjamin Bouvier
- Laboratoire de Glycochimie, des Antimicrobiens et des Agroressources, CNRS UMR7378/Université de Picardie Jules Verne, 10 rue Baudelocque, 80039 Amiens Cedex, France.
| | | |
Collapse
|
27
|
Cragnolini T, Chakraborty D, Šponer J, Derreumaux P, Pasquali S, Wales DJ. Multifunctional energy landscape for a DNA G-quadruplex: An evolved molecular switch. J Chem Phys 2017; 147:152715. [DOI: 10.1063/1.4997377] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tristan Cragnolini
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Debayan Chakraborty
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jiří Šponer
- Institute of Biophysics, Academy of Sciences of the Czech Republic, Královopolská 135, 612 65 Brno, Czech Republic
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, IBPC 13 Rue Pierre et Marie Curie, 75005 Paris, France
- Institut Universitaire de France, Boulevard Saint-Michel, 75005 Paris, France
| | - Samuela Pasquali
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, IBPC 13 Rue Pierre et Marie Curie, 75005 Paris, France
| | - David J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
28
|
Rossi K, Baletto F. The effect of chemical ordering and lattice mismatch on structural transitions in phase segregating nanoalloys. Phys Chem Chem Phys 2017; 19:11057-11063. [DOI: 10.1039/c7cp01397c] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
We elucidate the effect of lattice mismatch and chemical ordering on structural transitions in bimetallic nanoalloys.
Collapse
|
29
|
Koorehdavoudi H, Bogdan P. A Statistical Physics Characterization of the Complex Systems Dynamics: Quantifying Complexity from Spatio-Temporal Interactions. Sci Rep 2016; 6:27602. [PMID: 27297496 PMCID: PMC4906350 DOI: 10.1038/srep27602] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2016] [Accepted: 05/20/2016] [Indexed: 12/28/2022] Open
Abstract
Biological systems are frequently categorized as complex systems due to their capabilities of generating spatio-temporal structures from apparent random decisions. In spite of research on analyzing biological systems, we lack a quantifiable framework for measuring their complexity. To fill this gap, in this paper, we develop a new paradigm to study a collective group of N agents moving and interacting in a three-dimensional space. Our paradigm helps to identify the spatio-temporal states of the motion of the group and their associated transition probabilities. This framework enables the estimation of the free energy landscape corresponding to the identified states. Based on the energy landscape, we quantify missing information, emergence, self-organization and complexity for a collective motion. We show that the collective motion of the group of agents evolves to reach the most probable state with relatively lowest energy level and lowest missing information compared to other possible states. Our analysis demonstrates that the natural group of animals exhibit a higher degree of emergence, self-organization and complexity over time. Consequently, this algorithm can be integrated into new frameworks to engineer collective motions to achieve certain degrees of emergence, self-organization and complexity.
Collapse
Affiliation(s)
- Hana Koorehdavoudi
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
| | - Paul Bogdan
- Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2560, USA
| |
Collapse
|
30
|
Nagahata Y, Maeda S, Teramoto H, Horiyama T, Taketsugu T, Komatsuzaki T. Deciphering Time Scale Hierarchy in Reaction Networks. J Phys Chem B 2015; 120:1961-71. [DOI: 10.1021/acs.jpcb.5b09941] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yutaka Nagahata
- Graduate
School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
| | - Satoshi Maeda
- Department
of Chemistry, Faculty of Science, Hokkaido University, Kita 10,
Nishi 8, Kita-ku, Sapporo 060-0810, Japan
| | - Hiroshi Teramoto
- Graduate
School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
- Molecule
and Life Nonlinear Sciences Laboratory, Research Institute for Electronic
Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Takashi Horiyama
- Graduate
School of Science and Engineering, Saitama University, Shimo-Ookubo
255, Sakura-ku, Saitama 338-8570, Japan
| | - Tetsuya Taketsugu
- Department
of Chemistry, Faculty of Science, Hokkaido University, Kita 10,
Nishi 8, Kita-ku, Sapporo 060-0810, Japan
| | - Tamiki Komatsuzaki
- Graduate
School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
- Molecule
and Life Nonlinear Sciences Laboratory, Research Institute for Electronic
Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| |
Collapse
|
31
|
Pavan L, Rossi K, Baletto F. Metallic nanoparticles meet metadynamics. J Chem Phys 2015; 143:184304. [DOI: 10.1063/1.4935272] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Affiliation(s)
- L. Pavan
- Physics Department, King’s College London, London WC2R 2LS, United Kingdom
| | - K. Rossi
- Physics Department, King’s College London, London WC2R 2LS, United Kingdom
| | - F. Baletto
- Physics Department, King’s College London, London WC2R 2LS, United Kingdom
| |
Collapse
|
32
|
Yildirim I, Chakraborty D, Disney MD, Wales DJ, Schatz GC. Computational investigation of RNA CUG repeats responsible for myotonic dystrophy 1. J Chem Theory Comput 2015; 11:4943-58. [PMID: 26500461 PMCID: PMC4606397 DOI: 10.1021/acs.jctc.5b00728] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2015] [Indexed: 01/02/2023]
Abstract
Despite the importance of the knowledge of molecular hydration entropy (ΔShyd) in chemical and biological processes, the exact calculation of ΔShyd is very difficult, because of the complexity in solute–water interactions. Although free-energy perturbation (FEP) methods have been employed quite widely in the literature, the poor convergent behavior of the van der Waals interaction term in the potential function limited the accuracy and robustness. In this study, we propose a new method for estimating ΔShyd by means of combining the FEP approach and the scaled particle theory (or information theory) to separately calculate the electrostatic solute–water interaction term (ΔSelec) and the hydrophobic contribution approximated by the cavity formation entropy (ΔScav), respectively. Decomposition of ΔShyd into ΔScav and ΔSelec terms is found to be very effective with a substantial accuracy enhancement in ΔShyd estimation, when compared to the conventional full FEP calculations. ΔScav appears to dominate over ΔSelec in magnitude, even in the case of polar solutes, implying that the major contribution to the entropic cost for hydration comes from the formation of a solvent-excluded volume. Our hybrid scaled particle theory and FEP method is thus found to enhance the accuracy of ΔShyd prediction by effectively complementing the conventional full FEP method.
Collapse
Affiliation(s)
- Ilyas Yildirim
- Department
of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
- Department
of Chemistry, University of Cambridge, Cambridge, United Kingdom CB2 1EW
| | - Debayan Chakraborty
- Department
of Chemistry, University of Cambridge, Cambridge, United Kingdom CB2 1EW
| | - Matthew D. Disney
- Department
of Chemistry, The Scripps Research Institute, Jupiter, Florida 33458, United States
| | - David J. Wales
- Department
of Chemistry, University of Cambridge, Cambridge, United Kingdom CB2 1EW
| | - George C. Schatz
- Department
of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| |
Collapse
|
33
|
Chekmarev SF. Equilibration of Protein States: A Time Dependent Free-Energy Disconnectivity Graph. J Phys Chem B 2015; 119:8340-8. [PMID: 26068182 DOI: 10.1021/acs.jpcb.5b04336] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The process of equilibration of protein states in a three-stranded antiparallel β-sheet miniprotein is studied using a time-dependent free energy disconnectivity graph. To determine the rates of transitions, the molecular dynamics simulation results of a recent work (Kalgin, I. V.; J. Phys. Chem. B 2013, 117, 6092) are employed. The vertices of the graph are the free energies of characteristic states of the protein, and the edges are the transition state free energies. To determine the latter, the "complete" partition function (Eyring, 1935) is used, which includes the translational partition function corresponding to the ballistic motion of the system along the reaction coordinate. The distance along the reaction coordinate that enters the translational partition function is taken to be proportional to the observation time and thus measures the number of representative points that cross the transition state surface during given time. As the time increases, the free energy barriers between the clusters of characteristic conformations (native-like, helical, and β-sheet conformations of different degree of organization) decrease and (local) equilibrium between the clusters is established. With time, these clusters are grouped into larger clusters, extending the equilibrium to a larger portion of protein states.
Collapse
Affiliation(s)
- Sergei F Chekmarev
- †Institute of Thermophysics, SB RAS, 630090 Novosibirsk, Russia.,‡Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia
| |
Collapse
|
34
|
Chebaro Y, Ballard AJ, Chakraborty D, Wales DJ. Intrinsically disordered energy landscapes. Sci Rep 2015; 5:10386. [PMID: 25999294 PMCID: PMC4441119 DOI: 10.1038/srep10386] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Accepted: 04/10/2015] [Indexed: 12/19/2022] Open
Abstract
Analysis of an intrinsically disordered protein (IDP) reveals an underlying multifunnel structure for the energy landscape. We suggest that such 'intrinsically disordered' landscapes, with a number of very different competing low-energy structures, are likely to characterise IDPs, and provide a useful way to address their properties. In particular, IDPs are present in many cellular protein interaction networks, and several questions arise regarding how they bind to partners. Are conformations resembling the bound structure selected for binding, or does further folding occur on binding the partner in a induced-fit fashion? We focus on the p53 upregulated modulator of apoptosis (PUMA) protein, which adopts an α-helical conformation when bound to its partner, and is involved in the activation of apoptosis. Recent experimental evidence shows that folding is not necessary for binding, and supports an induced-fit mechanism. Using a variety of computational approaches we deduce the molecular mechanism behind the instability of the PUMA peptide as a helix in isolation. We find significant barriers between partially folded states and the helix. Our results show that the favoured conformations are molten-globule like, stabilised by charged and hydrophobic contacts, with structures resembling the bound state relatively unpopulated in equilibrium.
Collapse
Affiliation(s)
- Yassmine Chebaro
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW
| | - Andrew J Ballard
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW
| | - Debayan Chakraborty
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW
| |
Collapse
|
35
|
Deng DM, Chang CH. Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks. J Chem Phys 2015; 142:184103. [PMID: 25978879 DOI: 10.1063/1.4919952] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.
Collapse
Affiliation(s)
- De-Ming Deng
- Institute of Physics, National Chiao Tung University, Hsinchu 300, Taiwan
| | - Cheng-Hung Chang
- Institute of Physics, National Chiao Tung University, Hsinchu 300, Taiwan
| |
Collapse
|
36
|
Abstract
Phosphorene is a new 2D atomic material, and we document a drastic reduction of its electronic gap when under a conical shape. Furthermore, geometry determines the properties of 2D materials, and we introduce discrete differential geometry to study them. This geometry arises from particle/atomic positions; it is not based on a parametric continuum, and it applies across broad disciplinary lines. Lattice kirigami, ultralight metamaterials, polydisperse aggregates, ceramic nanolattices, and 2D atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene––a new 2D atomic material––in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its nonplanar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2D material. We also classify other 2D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse 2D structures while bypassing common descriptions of shape that are based from a parametric continuum.
Collapse
|
37
|
Pietropaolo A, Wang Y, Nakano T. Predicting the Switchable Screw Sense in Fluorene-Based Polymers. Angew Chem Int Ed Engl 2015. [DOI: 10.1002/ange.201411313] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
|
38
|
Pietropaolo A, Wang Y, Nakano T. Predicting the switchable screw sense in fluorene-based polymers. Angew Chem Int Ed Engl 2015; 54:2688-92. [PMID: 25641571 DOI: 10.1002/anie.201411313] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2014] [Revised: 12/09/2014] [Indexed: 11/05/2022]
Abstract
A chirality-switching free-energy landscape was reconstructed on a 43-mer of poly(9,9-dioctylfluoren-2,7-diyl) (PDOF). The simulations were conducted on amorphous silica surface as well as in the vacuum phase for a single chain or for a group of sixteen chains. The achiral-to-chiral transition occurs only on amorphous silica (activation free-energy 35 kcal mol(-1) ), where the enantiomeric (homochiral) basins are detected. This was supported by the experiments where effective chirality induction to PDOF using circularly polarized light (CPL) was attained only for a film deposited on a quartz glass and not for a solution or a suspension. These results indicate that interactions of PDOF with amorphous silica play a crucial role in chirality switching. Importance of chain assembling was also indicated. Theoretical ECD spectra of the enantiomeric basins containing a 51 helix reproduce the experimental spectra.
Collapse
Affiliation(s)
- Adriana Pietropaolo
- Dipartimento di Scienze della Salute, Università di Catanzaro, Viale Europa, 88100 Catanzaro (Italy).
| | | | | |
Collapse
|
39
|
Chakraborty D, Collepardo-Guevara R, Wales DJ. Energy Landscapes, Folding Mechanisms, and Kinetics of RNA Tetraloop Hairpins. J Am Chem Soc 2014; 136:18052-61. [DOI: 10.1021/ja5100756] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Debayan Chakraborty
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | | - David J. Wales
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
40
|
Cameron MK. Metastability, spectrum, and eigencurrents of the Lennard-Jones-38 network. J Chem Phys 2014; 141:184113. [PMID: 25399138 DOI: 10.1063/1.4901131] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.
Collapse
Affiliation(s)
- Maria K Cameron
- Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015, USA
| |
Collapse
|