scholarly journals Single-Channel Permeability from Markovian Milestoning, Umbrella Sampling, and Voltage Simulations

2021 ◽  
Author(s):  
Yi-Chun Lin ◽  
Yun Luo
Keyword(s):  
Free Energy ◽  
Ion Channel ◽  
Single Channel ◽  
First Passage Time ◽  
Md Simulations ◽  
Passage Time ◽  
Umbrella Sampling ◽  
Advantages And Disadvantages ◽  
Channel Permeability ◽  
Small Conductance

Permeations of ions and small molecules through membrane channels have diverse functions within cells. Various all-atom molecular dynamics (MD) simulations methods have been developed for computing free energy and crossing rate of permeants. However, a systemic comparison across different methods is scarce. Here, using a carbon nanotube as a model of small conductance (~2 pS) ion channel, we systemically compared three classes of MD-based approaches for computing single-channel permeability for potassium ion: equilibrium free energy-based approach using umbrella sampling, rare-even sampling approach using Markovian milestoning, and steady-state approach using applied voltages. The consistent kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. Two solvent boundary conditions are tested for milestoning and yield consistent forward and backward mean first passage time (MFPT). The advantages and disadvantages of each method are discussed, with the focus on the future applications of milestoning in more complex systems.

scholarly journals Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Ran Li ◽  
Kun Zhang ◽  
Jin Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Free Energy ◽  
First Passage Time ◽  
Energy Landscape ◽  
Planck Equation ◽  
Passage Time ◽  
Free Energy Landscape ◽  
De Sitter ◽  
First Passage

Abstract We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.

scholarly journals First-passage times in protein folding: exploring the native-like states vs. overcoming the free energy barrier

2021 ◽  
Author(s):  
Sergei F. Chekmarev
Keyword(s):  
Free Energy ◽  
Protein Folding ◽  
Energy Barrier ◽  
First Passage Time ◽  
Passage Time ◽  
Free Energy Barrier ◽  
Native State ◽  
First Passage ◽  
Single Exponential ◽  
Passage Times

All first-passage time distributions are essentially single-exponential. The first-passage time to reach the native state may be determined by the time to find the native state among native-like ones.

scholarly journals Capturing the Flexibility of a Protein-Ligand Complex: Binding Free Energies from Different Enhanced Sampling Techniques

2020 ◽  
Author(s):  
Sebastian Wingbermühle ◽  
Lars V. Schäfer
Keyword(s):  
Free Energy ◽  
Binding Free Energy ◽  
Md Simulations ◽  
Umbrella Sampling ◽  
Replica Exchange ◽  
Sampling Techniques ◽  
Enhanced Sampling ◽  
Ligand Complex ◽  
Mhc I ◽  
Partial Dissociation

Enhanced sampling techniques are a promising approach to obtain reliable binding free energy profiles for flexible protein-ligand complexes from molecular dynamics (MD) simulations. To put four popular enhanced sampling techniques to a biologically relevant and challenging test, we studied the partial dissociation of an antigenic peptide from the Major Histocompatibility Complex I (MHC I) HLA-B*35:01 to systematically investigate the performance of Umbrella Sampling (US), Replica Exchange with Solute Tempering 2 (REST2), Bias Exchange Umbrella Sampling (BEUS, or replica-exchange umbrella sampling), and well-tempered Metadynamics (MTD). With regard to the speed of sampling and convergence, the peptide-MHC I complex (pMHC I) under study showcases intrinsic strengths and weaknesses of the four enhanced sampling techniques used. We found that BEUS can handle best the sampling challenges that arise from the coexistence of an enthalpically and an entropically stabilized free energy minimum in the pMHC I under study. These findings might be relevant also for other flexible biomolecular systems with competing enthalpically and entropically stabilized minima.<br>

scholarly journals Free Energy Landscapes of Vesicle Fusion by Umbrella Sampling MD Simulations

2013 ◽  
Vol 104 (2) ◽  
pp. 92a ◽  
Author(s):  
Gregory Bubnis ◽  
H.J. Risselada ◽  
Helmut Grubmueller
Keyword(s):  
Free Energy ◽  
Md Simulations ◽  
Vesicle Fusion ◽  
Umbrella Sampling ◽  
Energy Landscapes ◽  
Free Energy Landscapes

scholarly journals Close agreement between deterministic vs. stochastic modeling of first-passage time to vesicle fusion

2021 ◽  
Author(s):  
Victor V Matveev
Keyword(s):  
Close Agreement ◽  
Single Channel ◽  
First Passage Time ◽  
Channel Gating ◽  
Passage Time ◽  
Vesicle Fusion ◽  
Stochastic Simulations ◽  
Mass Action ◽  
First Passage ◽  
Vesicle Exocytosis

Ca2+-dependent cell processes such as neurotransmitter or endocrine vesicle fusion are inherently stochastic due to large fluctuations in Ca2+ channel gating, Ca2+ diffusion and Ca2+ binding to buffers and target sensors. However, prior studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering and sensing, as long as Ca2+ channel gating is not Ca2+-dependent. To understand this result more fully, we present a comparative study complementing prior work, focusing on Ca2+ dynamics downstream of Ca2+ channel gating. Specifically, we compare deterministic (mean-field / mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca2+-bound state of a vesicle fusion sensor, following a brief Ca2+ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ⁓50 Ca2+ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of the fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for the bimolecular Ca2+ binding to buffers and downstream sensor targets. In this case diffusion and buffering effectively decorrelate the state of the Ca2+ sensor from local Ca2+ fluctuations. Thus, fluctuations in the Ca2+ sensor state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value.

scholarly journals Capturing the Flexibility of a Protein-Ligand Complex: Binding Free Energies from Different Enhanced Sampling Techniques

2020 ◽  
Author(s):  
Sebastian Wingbermühle ◽  
Lars V. Schäfer
Keyword(s):  
Free Energy ◽  
Binding Free Energy ◽  
Md Simulations ◽  
Umbrella Sampling ◽  
Replica Exchange ◽  
Sampling Techniques ◽  
Enhanced Sampling ◽  
Ligand Complex ◽  
Mhc I ◽  
Partial Dissociation

Enhanced sampling techniques are a promising approach to obtain reliable binding free energy profiles for flexible protein-ligand complexes from molecular dynamics (MD) simulations. To put four popular enhanced sampling techniques to a biologically relevant and challenging test, we studied the partial dissociation of an antigenic peptide from the Major Histocompatibility Complex I (MHC I) HLA-B*35:01 to systematically investigate the performance of Umbrella Sampling (US), Replica Exchange with Solute Tempering 2 (REST2), Bias Exchange Umbrella Sampling (BEUS, or replica-exchange umbrella sampling), and well-tempered Metadynamics (MTD). With regard to the speed of sampling and convergence, the peptide-MHC I complex (pMHC I) under study showcases intrinsic strengths and weaknesses of the four enhanced sampling techniques used. We found that BEUS can handle best the sampling challenges that arise from the coexistence of an enthalpically and an entropically stabilized free energy minimum in the pMHC I under study. These findings might be relevant also for other flexible biomolecular systems with competing enthalpically and entropically stabilized minima.<br>

scholarly journals Investigation of Molecular Details of Keap1-Nrf2 Inhibitors Using Molecular Dynamics and Umbrella Sampling Techniques

Molecules ◽  
2019 ◽  
Vol 24 (22) ◽  
pp. 4085 ◽  
Author(s):  
Ashwini Machhindra Londhe ◽  
Changdev Gorakshnath Gadhe ◽  
Sang Min Lim ◽  
Ae Nim Pae
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Binding Free Energy ◽  
Md Simulations ◽  
Binding Pocket ◽  
Umbrella Sampling ◽  
Valuable Insight ◽  
Protein Protein Interaction ◽  
Kelch Domain ◽  
Insight Into

In this study, we investigate the atomistic details of Keap1-Nrf2 inhibitors by in-depth modeling techniques, including molecular dynamics (MD) simulations, and the path-based free energy method of umbrella sampling (US). The protein–protein interaction (PPI) of Keap1-Nrf2 is implicated in several neurodegenerative diseases like cancer, diabetes, and cardiomyopathy. A better understanding of the five sub-pocket binding sites for Nrf2 (ETGE and DLG motifs) inside the Kelch domain would expedite the inhibitor design process. We selected four protein–ligand complexes with distinct co-crystal ligands and binding occupancies inside the Nrf2 binding site. We performed 100 ns of MD simulation for each complex and analyzed the trajectories. From the results, it is evident that one ligand (1VV) has flipped inside the binding pocket, whereas the remaining three were stable. We found that Coulombic (Arg483, Arg415, Ser363, Ser508, and Ser602) and Lennard–Jones (Tyr525, Tyr334, and Tyr572) interactions played a significant role in complex stability. The obtained binding free energy values from US simulations were consistent with the potencies of simulated ligands. US simulation highlight the importance of basic and aromatic residues in the binding pocket. A detailed description of the dissociation process brings valuable insight into the interaction of the four selected protein–ligand complexes, which could help in the future to design more potent PPI inhibitors.

scholarly journals Free energy and stacking of eumelanin nanoaggregates

2021 ◽  
Author(s):  
Sepideh Soltani ◽  
Shahin Sowlati-Hashjin ◽  
Conrard Giresse Tetsassi Feugmo ◽  
Mikko Karttunen
Keyword(s):  
Free Energy ◽  
Density Functional ◽  
Radical Scavenging ◽  
Md Simulations ◽  
Building Blocks ◽  
Umbrella Sampling ◽  
Free Energy Calculations ◽  
Transmission Electron Microscopy Data ◽  
Transmission Electron ◽  
Microscopy Data

AbstractEumelanin, a member of the melanin family, is a black-brown insoluble pigment. It possesses a broad range of properties such as antioxidation, free radical scavenging, photo-protection, and charge carrier transportation. Surprisingly, the exact molecular structure of eumelanin remains undefined. It is, however, generally considered to consist of two main building blocks, 5,6-dihydroxyindole (DHI) and 5,6-dihydroxyindole carboxylic acid (DHICA). We focus on DHI and report, for the first time, a computational investigation of structural properties of DHI eumelanin aggregates in aqueous solutions. First, multi-microsecond molecular dynamics (MD) simulations at different concentrations were performed to investigate aggregation and ordering of tetrameric DHI-eumelanin protomolecules. This was followed by umbrella sampling (US) and density functional theory (DFT) calculations to study the physical mechanisms of stacking. Aggregation occurs through formation of nanoscale stacks and was observed in all systems. Further analyses showed that aggregation and coarsening of the domains is due to decrease in hydrogen bonds between the eumelanins and water; while domains exist, there is no long-range order. The results show non-covalent stacks with and interlayer distance between eumelanin protomolecules being less than 3.5 Å. This is in good agreement with transmission electron microscopy data. Both free energy calculations and DFT revealed strong stacking interactions. The electrostatic potential map provides an explanation and a rationale for the slightly sheared relative orientations and, consequently, for the curved shapes of the nanoscale domains.

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>

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