scholarly journals The free energy landscape of small peptides as obtained from metadynamics with umbrella sampling corrections

2006 ◽  
Vol 125 (20) ◽  
pp. 204909 ◽  
Author(s):  
Volodymyr Babin ◽  
Christopher Roland ◽  
Thomas A. Darden ◽  
Celeste Sagui
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Umbrella Sampling ◽  
Free Energy Landscape ◽  
Small Peptides

Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Sampling Technique ◽  
Umbrella Sampling ◽  
Energy Simulation ◽  
Nonlinear Dependence ◽  
Free Energy Landscape ◽  
Convergence Criterion ◽  
Base Flipping ◽  
Convergence Behavior

<p>Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for efficient calculation of the free energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of equilibrium umbrella sampling and nonequilibrium stratification is given. The results show that nonequilibrium free energy simulation is able to give similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence behavior determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size. </p>

scholarly journals Free energy landscape for the entire transport cycle of triose-phosphate/phosphate translocator

2017 ◽  
Author(s):  
Mizuki Takemoto ◽  
Yongchan Lee ◽  
Ryuichiro Ishitani ◽  
Osamu Nureki
Keyword(s):  
Free Energy ◽  
Conformational Changes ◽  
Conformational Transition ◽  
Substrate Binding ◽  
Energy Landscape ◽  
Umbrella Sampling ◽  
Free Energy Landscape ◽  
Coupling Mechanism ◽  
Triose Phosphate ◽  
Phosphate Translocator

AbstractSecondary active transporters translocate their substrates using the electrochemical potentials of other chemicals, undergoing large-scale conformational changes. Despite extensive structural studies, the atomic details of the transport mechanism still remain elusive. Here we performed a series of all-atom molecular dynamics simulations of the triose-phosphate/phosphate translocator (TPT), which exports organic phosphates in the chloroplast stroma in strict counter exchange with inorganic phosphate (Pi). Biased sampling methods, including string method and umbrella sampling, successfully reproduced the conformational changes between the inward– and outward-facing states, along with the substrate binding. The free energy landscape of this entire TPT transition pathway demonstrated the alternating access and substrate translocation mechanisms, which revealed Pi is relayed by positively charged residues along the transition pathway. Furthermore, the conserved Glu207 functions as a “molecular switch”, linking the local substrate binding and the global conformational transition. Our results provide atomic-detailed insights into the energy coupling mechanism of antiporter.

Virtual-system-coupled adaptive umbrella sampling to compute free-energy landscape for flexible molecular docking

2015 ◽  
Vol 36 (20) ◽  
pp. 1489-1501 ◽  
Author(s):  
Junichi Higo ◽  
Bhaskar Dasgupta ◽  
Tadaaki Mashimo ◽  
Kota Kasahara ◽  
Yoshifumi Fukunishi ◽  
...  
Keyword(s):  
Free Energy ◽  
Molecular Docking ◽  
Energy Landscape ◽  
Umbrella Sampling ◽  
Free Energy Landscape ◽  
Virtual System

scholarly journals Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

2018 ◽  
Author(s):  
Xiaohui Wang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Sampling Technique ◽  
Umbrella Sampling ◽  
Energy Simulation ◽  
Nonlinear Dependence ◽  
Free Energy Landscape ◽  
Convergence Criterion ◽  
Base Flipping ◽  
Convergence Behavior

<p>Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for efficient calculation of the free energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of equilibrium umbrella sampling and nonequilibrium stratification is given. The results show that nonequilibrium free energy simulation is able to give similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence behavior determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size. </p>

scholarly journals Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Sampling Technique ◽  
Umbrella Sampling ◽  
Energy Simulation ◽  
Nonlinear Dependence ◽  
Free Energy Landscape ◽  
Convergence Criterion ◽  
Base Flipping ◽  
Convergence Behavior

<p>Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for efficient calculation of the free energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of equilibrium umbrella sampling and nonequilibrium stratification is given. The results show that nonequilibrium free energy simulation is able to give similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence behavior determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size. </p>

scholarly journals Exploring the Free Energy Landscape and Thermodynamics of Protein-Protein Association: HIV-1 Integrase Multimerization Induced by an Allosteric Inhibitor

2020 ◽  
Author(s):  
C. Tse ◽  
L. Wickstrom ◽  
M. Kvaratskhelia ◽  
E. Gallicchio ◽  
R. Levy ◽  
...  
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Critical Role ◽  
Configurational Entropy ◽  
Umbrella Sampling ◽  
Free Energy Landscape ◽  
Drug Induced ◽  
Protein Association ◽  
Hiv 1

AbstractWe report the free energy landscape and thermodynamics of the protein-protein association responsible for the drug-induced multimerization of HIV-1 integrase (IN). Allosteric HIV-1 integrase inhibitors (ALLINIs) promote aberrant IN multimerization by bridging IN-IN intermolecular interactions. However, the thermodynamic driving forces and kinetics of the multimerization remain largely unknown. Here we explore the early steps in the IN multimerization by using umbrella sampling and unbiased molecular dynamics simulations in explicit solvent. In direct simulations, the two initially separated dimers spontaneously associate to form near-native complexes that resemble the crystal structure of the aberrant tetramer. Most strikingly, the effective interaction of the protein-protein association is very short-ranged: the two dimers associate rapidly within tens of nanoseconds when their binding surfaces are separated by d ≤ 4.3 Å (less than two water diameters). Beyond this distance, the oligomerization kinetics appears to be diffusion controlled with a much longer association time. The free energy profile also captured the crucial role of ALLINI in promoting multimerization, and explained why several CTD mutations are remarkably resistant to the drug-induced multimerization. The results also show that at small separation the protein-protein binding process contains two consecutive phases with distinct thermodynamic signatures. First, inter-protein water molecules are expelled to the bulk resulting in a small increase in entropy, as the solvent entropy gain from the water release is nearly cancelled by the loss of side chain entropies as the two proteins approach each other. At shorter distances, the two dry binding surfaces adapt to each other to optimize their interaction energy at the expense of further protein configurational entropy loss. While the binding interfaces feature clusters of hydrophobic residues, overall, the protein-protein association in this system is driven by enthalpy and opposed by entropy.Statement of SignificanceElucidating the energetics and thermodynamic aspects of protein-protein association is important for understanding this fundamental biophysical process. This study provided a more complete physical picture of the protein-protein association responsible for the drug-induced HIV-1 integrase multimerization. The results captured the critical role of the inhibitor, and accounted for the effects of mutations on the protein association. Remarkably, the effective range of the protein-protein attractive funnel is found to be very short, at less than two layers of water, despite the fact that the two binding partners carry opposite net charges. Lastly, entropy/enthalpy decomposition shows that the solvent release from the inter-protein region into the bulk is more than offset by the loss of the solute configurational entropy due to complexation.

scholarly journals Exploring the aggregation free energy landscape of the amyloid-β protein (1–40)

2016 ◽  
Vol 113 (42) ◽  
pp. 11835-11840 ◽  
Author(s):  
Weihua Zheng ◽  
Min-Yeh Tsai ◽  
Mingchen Chen ◽  
Peter G. Wolynes
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Amyloid Β ◽  
Umbrella Sampling ◽  
Coarse Grained ◽  
Free Energy Landscape ◽  
Amyloid Β Protein ◽  
Hydrophobic Core ◽  
Β Protein ◽  
Β Sheets

A predictive coarse-grained protein force field [associative memory, water-mediated, structure, and energy model for molecular dynamics (AWSEM)-MD] is used to study the energy landscapes and relative stabilities of amyloid-β protein (1–40) in the monomer and all of its oligomeric forms up to an octamer. We find that an isolated monomer is mainly disordered with a short α-helix formed at the central hydrophobic core region (L17-D23). A less stable hairpin structure, however, becomes increasingly more stable in oligomers, where hydrogen bonds can form between neighboring monomers. We explore the structure and stability of both prefibrillar oligomers that consist of mainly antiparallel β-sheets and fibrillar oligomers with only parallel β-sheets. Prefibrillar oligomers are polymorphic but typically take on a cylindrin-like shape composed of mostly antiparallel β-strands. At the concentration of the simulation, the aggregation free energy landscape is nearly downhill. We use umbrella sampling along a structural progress coordinate for interconversion between prefibrillar and fibrillar forms to identify a conversion pathway between these forms. The fibrillar oligomer only becomes favored over its prefibrillar counterpart in the pentamer where an interconversion bottleneck appears. The structural characterization of the pathway along with statistical mechanical perturbation theory allow us to evaluate the effects of concentration on the free energy landscape of aggregation as well as the effects of the Dutch and Arctic mutations associated with early onset of Alzheimer’s disease.

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