Energy Landscape Analysis Research Articles

MEPSA: minimum energy pathway analysis for energy landscapes.

From conformational studies to atomistic descriptions of enzymatic reactions, potential and free energy landscapes can be used to describe biomolecular systems in detail. However, extracting the relevant data of complex 3D energy surfaces can sometimes be laborious. In this article, we present MEPSA (Minimum Energy Path Surface Analysis), a cross-platform user friendly tool for the analysis of energy landscapes from a transition state theory perspective. Some of its most relevant features are: identification of all the barriers and minima of the landscape at once, description of maxima edge profiles, detection of the lowest energy path connecting two minima and generation of transition state theory diagrams along these paths. In addition to a built-in plotting system, MEPSA can save most of the generated data into easily parseable text files, allowing more versatile uses of MEPSA's output such as the generation of molecular dynamics restraints from a calculated path. MEPSA is freely available (under GPLv3 license) at: http://bioweb.cbm.uam.es/software/MEPSA/ CONTACT: pagomez@cbm.csic.es. Supplementary data are available at Bioinformatics online.

High-resolution free energy landscape analysis of protein folding.

The free energy landscape can provide a quantitative description of folding dynamics, if determined as a function of an optimally chosen reaction coordinate. The profile together with the optimal coordinate allows one to directly determine such basic properties of folding dynamics as the configurations of the minima and transition states, the heights of the barriers, the value of the pre-exponential factor and its relation to the transition path times. In the present study, we review the framework, in particular, the approach to determine such an optimal coordinate, and its application to the analysis of simulated protein folding dynamics.

Folding or misfolding: the choice of β-hairpin.

Proteins fold through complex inter-residue interactions which are mutually supportive and cooperatively lead to thermodynamically favorable native structures. Competing (misfolded) structures, however, could exist, which might affect the thermodynamic and kinetic properties of folded structure. Running long-time REMD simulations on two β-structured polypeptides, the present study identifies the folded and (less populated) competing misfolded states of β-hairpins. Of particular interest is a one-residue shifted misfolded state which has been often seen in previous reports. The folding and misfolding pathways are then energetically characterized by free energy landscape analysis, indicating that the folding and misfolding of β-hairpin are parallel pathways and a protein's selection of following which pathway is a consequence of the competition between the formation of alterable turn configurations and cross-strand hydrophobic interactions. Proteins possessing high percentage of hydrophobic residues introduce strong cross-strand hydrophobic interactions which stabilize the native structural elements in the folding pathway, leading to low possibility of misfolding. The present study provides novel insights into the origin of sequence-dependent β-hairpin misfolding "hidden" behind experimentally detectable β-hairpin folding, suggesting the direction for the structure design of β-structured protein.

Structural perspective of ARHI mediated inhibition of STAT3 signaling: An insight into the inactive to active transition of ARHI and its interaction with STAT3 and importinβ

ARHI, a putative tumor suppressor protein with unique 32 amino acid extension in the N-terminal region, differs from oncogenes Ras and Rap, negatively regulates STAT3 signaling and inhibits the migration of ovarian cancer cells. ARHI associates directly with STAT3, also forms complex with importinβ, and prevents formation of RanGTPase–importinβ complex, which is essential for transporting STAT3 into the nucleus. Hence, the structural aspects pertaining to ARHI mediated inhibition of STAT3 translocation can provide hints on the regulation of STAT3 signaling mechanism. Accordingly, in the present study, the structure of ARHI was predicted and its transition from inactive to active state studied using MD simulations and free energy landscape analysis. The transition of ARHI is marked by the movement of switch I region towards γ-phosphate of GTP, in addition, the hydrophobic interaction between N-terminal helix and switch II region of ARHI accounts for its low intrinsic GTPase activity. Further, the protein–protein interaction studies reveal that the residues of N-terminal helix, effector domain, P-loop and G box motif of ARHI actively form polar and non-polar interaction with NTD of STAT3 and make them compact thereby rendering STAT3 inaccessible for Ran–importinβ mediated translocation. On the other hand, ARHI competes with RanGTPase and interacts with importinβ via basic–acidic patch interaction, which leads to inhibition of STAT3 translocation. The interacting residues involved for this structural mechanism would be instrumental in designing inhibitors for STAT3, which mimics ARHI thereby leading to the suppression of cancer cell growth.

Critical energy density of O(n) models in d = 3

A relation between O(n) models and Ising models has been recently conjectured (Casetti et al 2011 Phys. Rev. Lett. 106 057208). Such a relation, inspired by an energy landscape analysis, implies that the microcanonical density of states of an O(n) spin model on a lattice can be effectively approximated in terms of the density of states of an Ising model defined on the same lattice and with the same interactions. Were this relation exact, it would imply that the critical energy densities of all the O(n) models (i.e. the average values per spin of the O(n) Hamiltonians at their respective critical temperatures) should be equal to that of the corresponding Ising model. It is therefore worth investigating how different the critical energies are and how this difference depends on n.We compare the critical energy densities of O(n) models in three dimensions in some specific cases: the O(1) or Ising model, the O(2) or XY model, the O(3) or Heisenberg model, the O(4) model and the O(∞) or spherical model, all defined on regular cubic lattices and with ferromagnetic nearest-neighbor interactions. The values of the critical energy density in the n = 2, n = 3 and n = 4 cases are derived through a finite-size scaling analysis of data produced by means of Monte Carlo simulations on lattices with up to 1283 sites. For n = 2 and n = 3 the accuracy of previously known results has been improved. We finally derive an interpolation formula showing that the difference between the critical energy densities of O(n) models and that of the Ising model is smaller than 1% if n < 8 and never exceeds 3% for any n.

The Pathway for O2 Diffusion inside CotA Laccase and Possible Implications on the Multicopper Oxidases Family.

Laccases and multicopper oxidases (MCOs) oxidize a wide range of organic compounds while reducing O2 to water, enabling numerous biotechnological applications. It is still unknown how O2 reaches the internalized catalytic center of MCOs where it gets reduced, despite a proposed channel inferred from X-ray crystallography structures. Herein, an alternative new pathway is found through the use of a combination of free energy calculations (implicit ligand sampling), landscape analysis, and Markov modeling. The reported pathway is shown to be the one mostly contributing to O2 reaching the catalytic center. This pathway is considered in light of the whole MCO family, and a relation to the protonation state of a structurally conserved acidic residue right above the center is advanced.

Atomic Mobility in a Polymer Glass after Shear and Thermal Cycles

Molecular dynamics simulations and energy landscape analyses are carried out to study the atomic mobility of a polymer glass during the physical aging process that follows shear and thermal cycles. The mobility is characterized by the fraction of atoms moving more than their diameter in a given time interval. The mobility is enhanced after a shear or thermal cycle, and this enhancement decays with time. These mobility results are related to the position of the system on the energy landscape, as characterized by the average energy of the energy minima visited by the system; the mobility over longer time scales increases with the average energy of the energy minima visited, but the mobility over shorter time scales does not show a correlation with this average energy. From these results, we conclude that barriers separating metabasins composed of proximate energy minima, rather than barriers between individual energy minima, control the physical aging process. We also show that, after some finite time, the mobility following shear and thermal cycle appears to behave similarly to the mobility without perturbations; however, the system is at different regions of the energy landscape in these two cases, which implies that mobility alone does not characterize the state of the system.

Energy landscape analysis of native folding of the prion protein yields the diffusion constant, transition path time, and rates

Protein folding is described conceptually in terms of diffusion over a configurational free-energy landscape, typically reduced to a one-dimensional profile along a reaction coordinate. In principle, kinetic properties can be predicted directly from the landscape profile using Kramers theory for diffusive barrier crossing, including the folding rates and the transition time for crossing the barrier. Landscape theory has been widely applied to interpret the time scales for protein conformational dynamics, but protein folding rates and transition times have not been calculated directly from experimentally measured free-energy profiles. We characterized the energy landscape for native folding of the prion protein using force spectroscopy, measuring the change in extension of a single protein molecule at high resolution as it unfolded/refolded under tension. Key parameters describing the landscape profile were first recovered from the distributions of unfolding and refolding forces, allowing the diffusion constant for barrier crossing and the transition path time across the barrier to be calculated. The full landscape profile was then reconstructed from force-extension curves, revealing a double-well potential with an extended, partially unfolded transition state. The barrier height and position were consistent with the previous results. Finally, Kramers theory was used to predict the folding rates from the landscape profile, recovering the values observed experimentally both under tension and at zero force in ensemble experiments. These results demonstrate how advances in single-molecule theory and experiment are harnessing the power of landscape formalisms to describe quantitatively the mechanics of folding.

Transition Path Times for Nucleic Acid Folding Determined from Energy-Landscape Analysis of Single-Molecule Trajectories

The duration of structural transitions in biopolymers is only a fraction of the time spent searching diffusively over the configurational energy landscape. We found the transition time, τ(TP), and the diffusion constant, D, for DNA and RNA folding using energy landscapes obtained from single-molecule trajectories under tension in optical traps. DNA hairpins, RNA pseudoknots, and a riboswitch all had τ(TP)~10 μs and D~10(-13-14) m(2)/s, despite widely differing unfolding rates. These results show how energy-landscape analysis can be harnessed to characterize brief but critical events during folding reactions.

A mechanistic insight into the amyloidogenic structure of hIAPP peptide revealed from sequence analysis and molecular dynamics simulation

A collective approach of sequence analysis, phylogenetic tree and in silico prediction of amyloidogenecity using bioinformatics tools have been used to correlate the observed species-specific variations in IAPP sequences with the amyloid forming propensity. Observed substitution patterns indicate that probable changes in local hydrophobicity are instrumental in altering the aggregation propensity of the peptide. In particular, residues at 17th, 22nd and 23rd positions of the IAPP peptide are found to be crucial for amyloid formation. Proline25 primarily dictates the observed non-amyloidogenecity in rodents. Furthermore, extensive molecular dynamics simulation of 0.24μs have been carried out with human IAPP (hIAPP) fragment 19–27, the portion showing maximum sequence variation across different species, to understand the native folding characteristic of this region. Principal component analysis in combination with free energy landscape analysis illustrates a four residue turn spanning from residue 22 to 25. The results provide a structural insight into the intramolecular β-sheet structure of amylin which probably is the template for nucleation of fibril formation and growth, a pathogenic feature of type II diabetes.

How Deformation Enhances Mobility in a Polymer Glass

Molecular dynamics simulations and energy landscape analyses are carried out for a realistic model of glassy polystyrene under shear deformation. Deformation enhances the atomic mobility, as quantified by the van Hove function. The enhanced mobility is shown to arise from two mechanisms: First, active deformation continually reduces barriers for hopping events, and the importance of this mechanism is modulated by the rate of thermally activated transitions between adjacent energy minima. Second, deformation moves the system to higher-energy regions of the energy landscape, characterized by lower barriers. Both mechanisms enhance the dynamics during deformation, and the second mechanism is also relevant after deformation has ceased. Furthermore, neither mechanism on its own could be expected to correlate all mobility data.

Lifetime statistics of quantum chaos studied by a multiscale analysis

In a series of pump and probe experiments, we study the lifetime statistics of a quantum chaotic resonator when the number of open channels is greater than one. Our design embeds a stadium billiard into a two dimensional photonic crystal realized on a silicon-on-insulator substrate. We calculate resonances through a multiscale procedure that combines energy landscape analysis and wavelet transforms. Experimental data is found to follow the universal predictions arising from random matrix theory with an excellent level of agreement.

Density of states of continuous and discrete spin models: a case study

A relation between O(n) lattice spin models and Ising models defined on the same lattice was recentlyput forward (Casetti et al 2011 Phys. Rev. Lett. 106 057208). Such a relation,inspired by an energy landscape analysis, implies that the density of states of anO(n) spin model on a lattice can be effectively approximated, at least close to the phasetransition, in terms of the density of states of an Ising model defined on the same latticeand with the same interactions. In this paper we show that such a relation exactlyholds, albeit in a slightly modified form, in the special cases of the mean-fieldXY model and theone-dimensional XY model. We also discuss the possible consequences of this result for the generalcase.

Substrate Binding in Lactate Dehydrogenase: A Story Told by Conformational Sampling and Energy Landscape Analysis

Lactate Dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate with concomitant interconversion of NADH and NAD+. Due to the widespread presence in a variety of organisms, LDH has been served as a general model for studying the catalytic mechanism of enzymes. Extensive IR spectroscopic studies by Callender et al. have revealed complex conformational sub-states for different substrate binding to LDH in mesophilic and thermophilic organisms. To facilitate the elucidation of the underling mechanism of LDH enzyme reaction, molecular dynamics simulation approaches were applied to study the conformational dynamics of mesophilic LDH in complex with substrate or its mimics. The functionally important motions were characterized by conformational sampling. To determine the relationship between protein stability, flexibility, and catalytic activity, thermophilic LDH enzyme will be further investigated. The energy landscape within the Michaelis complex will be explored. The computational study in connection with the experimental findings will shed new light on the mechanism of enzyme dynamics and function.

Backbone conformational preferences of an intrinsically disordered protein in solution

We have performed a 4-μs molecular dynamics simulation to investigate the native conformational preferences of the intrinsically disordered kinase-inducible domain (KID) of the transcription factor CREB in solution. There is solid experimental evidence showing that KID does not possess a bound-like structure in solution; however, it has been proposed that coil-to-helix transitions upon binding to its binding partner (CBP) are template-driven. While these studies indicate that IDPs possess a bias towards the bound structure, they do not provide direct evidence on the time-dependent conformational preferences of IDPs in atomic detail. Our simulation captured intrinsic conformational characteristics of KID that are in good agreement with experimental data such as a very small percentage of helical structure in its segment α(B) and structural disorder in solution. We used dihedral principal component analysis dPCA to map the conformations of KID in the microsecond timescale. By using principal components as reaction coordinates, we further constructed dPCA-based free energy landscapes of KID. Analysis of the free energy landscapes showed that KID is best characterized as a conformational ensemble of rapidly interconverting conformations. Interestingly, we found that despite the conformational heterogeneity of the backbone and the absence of substantial secondary structure, KID does not randomly sample the conformational space in solution: analysis of the (Φ, Ψ) dihedral angles showed that several individual residues of KID possess a strong bias toward the helical region of the Ramachandran plot. We suggest that the intrinsic conformational preferences of KID provide a bias toward the folded state without having to populate bound-like conformations before binding. Furthermore, we argue that these conformational preferences do not represent actual structural constraints which drive binding through a single pathway, which allows for specific interactions with multiple binding partners. Based on this evidence, we propose that the backbone conformational preferences of KID provide a thermodynamic advantage for folding and binding without negatively affecting the kinetics of binding. We further discuss the relation of our results to previous studies to rationalize the functional implications of the conformational preferences of IDPs, such as the optimization of structural disorder in protein-protein interactions. This study illustrates the importance in obtaining atomistic information of intrinsically disordered proteins in real time to reveal functional features arising from their complex conformational space.

The Protein Folding Mechanism Revealed by the Folding Free Energy Landscape Analysis and Denaturation Simulations

α-helix and β-hairpin are the two principal secondary structures in proteins. A large number of experimental and theoretical kinetics and thermodynamics studies of the folding and unfolding of α-helix and β-hairpin structured polypeptides and proteins have been performed. Different theoretical models have been proposed to explain their folding mechanisms. Inconsistencies exist among the various models, which essentially reflect the different understanding of how individual structural elements affect the folding process and stability of protein structures. The present review mainly summarizes our recent simulation studies of the structure stability, folding and unfolding (denaturation) mechanism of various α-helix bundle and β-structure systems. Keywords: Protein folding, Free energy landscape analysis, Molecular dynamics simulation, α-helix bundle, hydrophobic, Urea Denaturation, Helix, mutation, replica

The Protein Folding Mechanism Revealed by the Folding Free Energy Landscape Analysis and Denaturation Simulations

α-helix and β-hairpin are the two principal secondary structures in proteins. A large number of experimental and theoretical kinetics and thermodynamics studies of the folding and unfolding of α-helix and β-hairpin structured polypeptides and proteins have been performed. Different theoretical models have been proposed to explain their folding mechanisms. Inconsistencies exist among the various models, which essentially reflect the different understanding of how individual structural elements affect the folding process and stability of protein structures. The present review mainly summarizes our recent simulation studies of the structure stability, folding and unfolding (denaturation) mechanism of various α-helix bundle and β-structure systems.

2PS010 負荷存在下におけるアクチン-ミオシンVI相互作用の自由エネルギーランドスケープ解析(日本生物物理学会第50回年会(2012年度))

2PS010 負荷存在下におけるアクチン-ミオシンVI相互作用の自由エネルギーランドスケープ解析(日本生物物理学会第50回年会(2012年度))

The Fast-Folding Mechanism of Villin Headpiece Subdomain Studied by Multiscale Distributed Computing.

The fast-folding mechanism of a 35-residue mini-protein, villin headpiece subdomain (HP35), was investigated using folding free energy landscape analysis with the multiscale free energy landscape calculation method (MSFEL). A major and a minor folding pathway were deduced from the folding free energy landscape. In the major folding pathway, the formation of helices II and III was the rate-limiting step in the transition to an intermediate state, triggered by the folding of the PLWK motif. HP35 then folds into the native structure through the formation of the hydrophobic core located at the center of the three-helix bundle. Mutations in the motif and hydrophobic core that suppressed folding into the native state drastically changed the folding free energy landscape compared to the wild type protein. In the minor folding pathway, nucleation of the hydrophobic core preceded formation of the motif.

Phase transitions in simplified models with long-range interactions

We study the origin of phase transitions in several simplified models with long-range interactions. For the self-gravitating ring model, we are unable to observe a possible phase transition predicted by Nardini and Casetti [Phys. Rev. E 80, 060103R (2009).] from an energy landscape analysis. Instead we observe a sharp, although without any nonanalyticity, change from a core-halo to a core-only configuration in the spatial distribution functions for low energies. By introducing a different class of solvable simplified models without any critical points in the potential energy we show that a behavior similar to the thermodynamics of the ring model is obtained, with a first-order phase transition from an almost homogeneous high-energy phase to a clustered phase and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features for the simplified models and show that the first-order phase transition comes from the maximization of the entropy of the system as a function of energy and an order parameter, as previously discussed by Hahn and Kastner [Phys. Rev. E 72, 056134 (2005); Eur. Phys. J. B 50, 311 (2006)], which seems to be the main mechanism causing phase transitions in long-range interacting systems.