Cell size effects in the molecular dynamics of the intrinsically disordered Aβ peptide

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

Computational Insight into Substrate-Induced Conformational Changes in Methionyl-tRNA Synthetase of Mycobacterium Tuberculosis

Tuberculosis caused by Mycobacterium tuberculosis (M.tb) has killed millions worldwide. Antibiotic resistance leads to the ineffectiveness of the current therapies. Aminoacyl tRNA synthetase (aaRS) class of proteins involved in protein synthesis are promising bacterial targets for developing new therapies. Here, we carried out a systematic comparative study on the aaRS sequences from M.tb and human. We listed important M.tb aaRS that could be explored as potential M.tb targets alongside the detailed conformational space analysis of methionyl-tRNA synthetase (MetRS) in apo- and substrate-bound form, which is among the proposed targets. Understanding the conformational dynamics is central to the mechanistic understanding of MetRS, as the substrate binding leads to the conformational changes causing the reaction to proceed. We performed the most complete simulation study of M.tb MetRS for 6 microseconds (2 systems × 3 runs × 1 microsecond) in the apo and substrate-bound states. Interestingly, we observed differential features, showing comparatively large dynamics for the holo simulations, whereas the apo structures became slightly compact with reduced solvent exposed area. In contrast, the ligand size decreased significantly in holo structures possibly to relax ligand conformation. Our findings correlate with experimental studies, thus validating our protocol. Adenosine monophosphate moiety of the substrate exhibited quite higher fluctuations than the methionine. His21 and Lys54 were found to be the important residues forming prominent hydrogen bond and salt-bridge interactions with the ligand. The ligand-protein affinity decreased during simulations as computed by MMGBSA analysis over the last 500 ns trajectories, which indicates the conformational changes upon ligand binding. These differential features could be further explored for designing new M.tb inhibitors.

Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

The functional role of the hemoglobin-water interface

The interface between hemoglobin (Hb) and its environment, in particular water, is of great physiological relevance. Here, results from in vitro, in vivo, and computational experiments (molecular dynamics simulations) are summarized and put into perspective. One of the main findings from the computations is that the stability of the deoxy, ligand-free T-state (T₀) can be stabilized relative to the deoxy R-state (R₀) only in sufficiently large simulation boxes for the hydrophobic effect to manifest itself. This effect directly influences protein stability and is operative also under physiological conditions. Furthermore, molecular simulations provide a dynamical interpretation of the Perutz model for Hb function. Results from experiments using higher protein concentrations and realistic cellular environments are also discussed. One of the next great challenges for computational studies, which as we show is likely to be taken up in the near future, is to provide a molecular-level understanding of the dynamics of proteins in such crowded environments.

Secondary structure dependence of amyloid-β(1-40) on simulation techniques and force field parameters

Our recent studies revealed that none of the selected widely used force field parameters and molecular dynamics simulation techniques yield structural properties for the intrinsically disordered α-synuclein that are in agreement with various experiments via testing different force field parameters. Here, we extend our studies on the secondary structure properties of the disordered amyloid-β(1-40) peptide in aqueous solution. For these purposes, we conducted extensive replica exchange molecular dynamics simulations and obtained extensive molecular dynamics simulation trajectories from David E. Shaw group. Specifically, these molecular dynamics simulations were conducted using various force field parameters and obtained results are compared to our replica exchange molecular dynamics simulations and experiments. In this study, we calculated the secondary structure abundances and radius of gyration values for amyloid-β(1-40) that were simulated using varying force field parameter sets and different simulation techniques. In addition, the intrinsic disorder propensity, as well as sequence-based secondary structure predisposition of amyloid-β(1-40) and compared the findings with the results obtained from molecular simulations using various force field parameters and different simulation techniques. Our studies clearly show that the epitope region identification of amyloid-β(1-40) depends on the chosen simulation technique and chosen force field parameters. Based on comparison with experiments, we find that best computational results in agreement with experiments are obtained using the a99sb*-ildn, charmm36m, and a99sb-disp parameters for the amyloid-β(1-40) peptide in molecular dynamics simulations without parallel tempering or via replica exchange molecular dynamics simulations.

Recent advances in atomic molecular dynamics simulation of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play important roles in cellular functions. The inherent structural heterogeneity of IDPs makes the high-resolution experimental characterization of IDPs extremely difficult. Molecular dynamics (MD) simulation could provide the atomic-level description of the structural and dynamic properties of IDPs. This perspective reviews the recent progress in atomic MD simulation studies of IDPs, including the development of force fields and sampling methods, as well as applications in IDP-involved protein-protein interactions. The employment of large-scale simulations and advanced sampling techniques allows more accurate estimation of the thermodynamics and kinetics of IDP-mediated protein interactions, and the holistic landscape of the binding process of IDPs is emerging.

An α-helix mimetic oligopyridylamide, ADH-31, modulates Aβ42 monomer aggregation and destabilizes protofibril structures: insights from molecular dynamics simulations

Alzheimer's disease (AD), an epidemic growing worldwide due to no effective medical aid available in the market, is a neurological disorder. AD is known to be directly associated with the toxicity of amyloid-β (Aβ) aggregates. In search of potent inhibitors of Aβ aggregation, Hamilton and co-workers reported an α-helix mimetic, ADH-31, which acts as a powerful antagonist of Aβ42 aggregation. To identify the key interactions between protein-ligand complexes and to gain insights into the inhibitory mechanism of ADH-31 against Aβ42 aggregation, molecular dynamics (MD) simulations were performed in the present study. The MD simulations highlighted that ADH-31 showed distinct binding capabilities with residues spanning from the N-terminal to the central hydrophobic core (CHC) region of Aβ42 and restricted the conformational transition of the helix-rich structure of Aβ42 into another form of secondary structures (coil/turn/β-sheet). Hydrophobic contacts, hydrogen bonding and π-π interaction contribute to the strong binding between ADH-31 and Aβ42 monomer. The Dictionary of Secondary Structure of Proteins (DSSP) analysis highlighted that the probability of helical content increases from 38.5% to 50.2% and the turn content reduces from 14.7% to 6.2% with almost complete loss of the β-sheet structure (4.5% to 0%) in the Aβ42 monomer + ADH-31 complex. The per-residue binding free energy analysis demonstrated that Arg5, Tyr10, His14, Gln15, Lys16, Val18, Phe19 and Lys28 residues of Aβ42 are responsible for the favourable binding free energy in Aβ42 monomer + ADH-31 complex, which is consistent with the 2D HSQC NMR of the Aβ42 monomer that depicted a change in the chemical shift of residues spanning from Glu11 to Phe20 in the presence of ADH-31. The MD simulations highlighted the prevention of sampling of amyloidogenic β-strand conformations in Aβ42 trimer in the presence of ADH-31 as well as the ability of ADH-31 to destabilize Aβ42 trimer and protofibril structures. The lower binding affinity between Aβ42 trimer chains in the presence of ADH-31 highlights the destabilization of the Aβ42 trimer structure. Overall, MD results highlighted that ADH-31 inhibited Aβ42 aggregation by constraining Aβ peptides into helical conformation and destabilized Aβ42 trimer as well as protofibril structures. The present study provides a theoretical insight into the atomic level details of the inhibitory mechanism of ADH-31 against Aβ42 aggregation as well as protofibril destabilization and could be implemented in the structure-based drug design of potent therapeutic agents for AD.

Current Challenges and Limitations in the Studies of Intrinsically Disordered Proteins in Neurodegenerative Diseases by Computer Simulations

Experiments face challenges in the analysis of intrinsically disordered proteins in solution due to fast conformational changes and enhanced aggregation propensity. Computational studies complement experiments, being widely used in the analyses of intrinsically disordered proteins, especially those positioned at the centers of neurodegenerative diseases. However, recent investigations - including our own - revealed that computer simulations face significant challenges and limitations themselves. In this review, we introduced and discussed some of the scientific challenges and limitations of computational studies conducted on intrinsically disordered proteins. We also outlined the importance of future developments in the areas of computational chemistry and computational physics that would be needed for generating more accurate data for intrinsically disordered proteins from computer simulations. Additional theoretical strategies that can be developed are discussed herein.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.

Water Dynamics Around Proteins: T- and R-States of Hemoglobin and Melittin

The water dynamics, as characterized by the local hydrophobicity (LH), is investigated for tetrameric hemoglobin (Hb) and dimeric melittin. For the T₀ to R₀ transition in Hb, it is found that LH provides additional molecular-level insight into the Perutz mechanism, i.e., the breaking and formation of salt bridges at the α₁/β₂ and α₂/β₁ interface is accompanied by changes in LH. For Hb in cubic water boxes with 90 and 120 Å edge length it is observed that following a decrease in LH as a consequence of reduced water density or change of water orientation at the protein/water interface the α/β interfaces are destabilized; this is a hallmark of the Perutz stereochemical model for the T to R transition in Hb. The present work thus provides a dynamical view of the classical structural model relevant to the molecular foundations of Hb function. For dimeric melittin, earlier results by Cheng and Rossky [ Nature 1998, 392, 696-699] are confirmed and interpreted on the basis of LH from simulations in which the protein structure is frozen. For the flexible melittin dimer, the changes in the local hydration can be as much as 30% greater than for the rigid dimer, reflecting the fact that protein and water dynamics are coupled.

How Does the Mono-Triazole Derivative Modulate Aβ42 Aggregation and Disrupt a Protofibril Structure: Insights from Molecular Dynamics Simulations

Clinical studies have identified that abnormal self-assembly of amyloid-β (Aβ) peptide into toxic fibrillar aggregates is associated with the pathology of Alzheimer's disease (AD). The most acceptable therapeutic approach to stop the progression of AD is to inhibit the formation of β-sheet-rich structures. Recently, we designed and evaluated a series of novel mono-triazole derivatives 4(a-x), where compound 4v was identified as the most potent inhibitor of Aβ₄₂ aggregation and disaggregates preformed Aβ₄₂ fibrils significantly. Moreover, 4v strongly averts the Cu²⁺-induced Aβ₄₂ aggregation and disaggregates the preformed Cu²⁺-induced Aβ₄₂ fibrils, halts the generation of reactive oxygen species, and shows neuroprotective effects in SH-SY5Y cells. However, the underlying molecular mechanism of inhibition of Aβ₄₂ aggregation by 4v and disaggregation of preformed Aβ₄₂ fibrils remains obscure. In this work, molecular dynamics (MD) simulations have been performed to explore the conformational ensemble of the Aβ₄₂ monomer and a pentameric protofibril structure of Aβ₄₂ in the presence of 4v. The MD simulations highlighted that 4v binds preferentially at the central hydrophobic core region of the Aβ₄₂ monomer and chains D and E of the Aβ₄₂ protofibril. The dictionary of secondary structure of proteins analysis indicated that 4v retards the conformational conversion of the helix-rich structure of the Aβ₄₂ monomer into the aggregation-prone β-sheet conformation. The binding free energy calculated by the molecular mechanics Poisson-Boltzmann surface area method revealed an energetically favorable process with ΔG _binding = -44.9 ± 3.3 kcal/mol for the Aβ₄₂ monomer-4v complex. The free energy landscape analysis highlighted that the Aβ₄₂ monomer-4v complex sampled conformations with significantly higher helical contents (35 and 49%) as compared to the Aβ₄₂ monomer alone (17%). Compound 4v displayed hydrogen bonding with Gly37 (chain E) and π-π interactions with Phe19 (chain D) of the Aβ₄₂ protofibril. Further, the per-residue binding free energy analysis also highlighted that Phe19 (chain D) and Gly37 (chain E) of the Aβ₄₂ protofibril showed the maximum contribution in the binding free energy. The decreased binding affinity and residue-residue contacts between chains D and E of the Aβ₄₂ protofibril in the presence of 4v indicate destabilization of the Aβ₄₂ protofibril structure. Overall, the structural information obtained through MD simulations indicated that 4v stabilizes the native helical conformation of the Aβ₄₂ monomer and persuades a destabilization in the protofibril structure of Aβ₄₂. The results of the study will be useful in the rational design of potent inhibitors against amyloid aggregation.

Common mechanism of thermostability in small α- and β-proteins studied by molecular dynamics

Protein thermostability is important to evolution, diseases, and industrial applications. Proteins use diverse molecular strategies to achieve stability at high temperature, yet reducing the entropy of unfolding seems required. We investigated five small α-proteins and five β-proteins with known, distinct structures and thermostability (T_m ) using multi-seed molecular dynamics simulations at 300, 350, and 400 K. The proteins displayed diverse changes in hydrogen bonding, solvent exposure, and secondary structure with no simple relationship to T_m . Our dynamics were in good agreement with experimental B-factors at 300 K and insensitive to force-field choice. Despite the very distinct structures, the native-state (300 + 350 K) free-energy landscapes (FELs) were significantly broader for the two most thermostable proteins and smallest for the three least stable proteins in both the α- and β-group and with both force fields studied independently (tailed t-test, 95% confidence level). Our results suggest that entropic ensembles stabilize proteins at high temperature due to reduced entropy of unfolding, viz., ΔG = ΔH - TΔS. Supporting this mechanism, the most thermostable proteins were also the least kinetically stable, consistent with broader FELs, typified by villin headpiece and confirmed by specific comparison to a mesophilic ortholog of Thermus thermophilus apo-pyrophosphate phosphohydrolase. We propose that molecular strategies of protein thermostabilization, although diverse, tend to converge toward highest possible entropy in the native state consistent with the functional requirements. We speculate that this tendency may explain why many proteins are not optimally structured and why molten-globule states resemble native proteins so much.

Impact of the Astaxanthin, Betanin, and EGCG Compounds on Small Oligomers of Amyloid Aβ40 Peptide

There is experimental evidence that the astaxanthin, betanin, and epigallocatechin-3-gallate (EGCG) compounds slow down the aggregation kinetics and the toxicity of the amyloid-β (Aβ) peptide. How these inhibitors affect the self-assembly at the atomic level remains elusive. To address this issue, we have performed for each ligand atomistic replica exchange molecular dynamic (REMD) simulations in an explicit solvent of the Aβ_11-40 trimer from the U-shape conformation and MD simulations starting from Aβ_1-40 dimer and tetramer structures characterized by different intra- and interpeptide conformations. We find that the three ligands have similar binding free energies on small Aβ₄₀ oligomers but very distinct transient binding sites that will affect the aggregation of larger assemblies and fibril elongation of the Aβ₄₀ peptide.

Interactions of a multifunctional di-triazole derivative with Alzheimer's Aβ42monomer and Aβ42protofibril: a systematic molecular dynamics study

The molecular dynamics simulations results highlighted that the multi-target-directed ligand6nstabilizes the native α-helix conformation of the Aβ₄₂monomer and induces a sizable destabilization in the Aβ₄₂protofibril structure.

Cryo-temperature effects on membrane protein structure and dynamics

Cryo-electron structures revolutionize biology, yet cooling effects are unclear. Using a simulation protocol of hot, cold, and rapidly cooled γ-secretase we identify cryo-contraction and modes relevant to Aβ production and cryo-analysis in general.