Alanine Tripeptide Research Articles

Screening Fast-Mode Motion in Collective Variable Discovery for Biochemical Processes.

Collective variables (CVs) describing slow degrees of freedom (DOFs) in biomolecular assemblies are crucial for analyzing molecular dynamics trajectories, creating Markov models and performing CV-based enhanced sampling simulations. While time-lagged independent component analysis (tICA) and its nonlinear successor, time-lagged autoencoder (tAE), are widely used, they often struggle to capture protein dynamics due to interference from random fluctuations along fast DOFs. To address this issue, we propose a novel approach integrating discrete wavelet transform (DWT) with dimensionality reduction techniques. DWT effectively separates fast and slow motion in protein simulation trajectories by decoupling high- and low-frequency signals. Based on the trajectory after filtering out high-frequency signals, which corresponds to fast motion, tICA and tAE can accurately extract CVs representing slow DOFs, providing reliable insights into protein dynamics. Our method demonstrates superior performance in identifying CVs that distinguish metastable states compared to standard tICA and tAE, as validated through analyses of conformational changes of alanine dipeptide and tripeptide and folding of CLN025. Moreover, we show that DWT can be used to improve the performance of a variety of CV-finding algorithms by combining it with Deep-tICA, a cutting-edge CV-finding algorithm, to extract CVs for enhanced-sampling calculations. Given its negligible computational cost and remarkable ability to screen fast motion, we propose DWT as a "free lunch" for CV extraction, applicable to a wide range of CV-finding algorithms.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package.

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Exploration of high dimensional free energy landscapes by a combination of temperature-accelerated sliced sampling and parallel biasing.

Temperature-accelerated sliced sampling (TASS) is an enhanced sampling method for achieving accelerated and controlled exploration of high-dimensional free energy landscapes in molecular dynamics simulations. With the aid of umbrella bias potentials, the TASS method realizes a controlled exploration and divide-and-conquer strategy for computing high-dimensional free energy surfaces. In TASS, diffusion of the system in the collective variable (CV) space is enhanced with the help of metadynamics bias and elevated-temperature of the auxiliary degrees of freedom (DOF) that are coupled to the CVs. Usually, a low-dimensional metadynamics bias is applied in TASS. In order to further improve the performance of TASS, we propose here to use a highdimensional metadynamics bias, in the same form as in a parallel bias metadynamics scheme. Here, a modified reweighting scheme, in combination with artificial neural network is used for computing unbiased probability distribution of CVs and projections of high-dimensional free energy surfaces. We first validate the accuracy and efficiency of our method in computing the four-dimensional free energy landscape for alanine tripeptide in vacuo. Subsequently, we employ the approach to calculate the eight-dimensional free energy landscape of alanine pentapeptide in vacuo. Finally, the method is applied to a more realistic problem wherein we compute the broad four-dimensional free energy surface corresponding to the deacylation of a drug molecule which is covalently complexed with a β-lactamase enzyme. We demonstrate that using parallel bias in TASS improves the efficiency of exploration of high-dimensional free energy landscapes.

Conformation and Metal Cation Binding of Zwitterionic Alanine Tripeptide in Saline Solutions by Infrared Vibrational Spectroscopy and Molecular Dynamics Simulations.

In this work, linear infrared (IR) spectroscopy and molecular dynamics (MD) simulations were used to examine the interaction of different metal cations (Na+, Ca2+, Mg2+, and Zn2+) with backbone (amide C═O) and C-terminal carboxylate (COO-) groups in zwitterionic alanine tripeptide (Ala3) in aqueous solutions with varying saline concentrations. Circular dichroism spectra and MD results suggest that Ala3 is predominantly in polyproline-II (PPII) conformation, whose amide-I and asymmetric carboxylate stretching IR vibration signatures are also supported by quantum-chemistry calculations. The zwitterionic form of Ala3 separates the two amide-I modes in frequency, which are weakly coupled modes, as revealed by two-dimensional IR measurement, and can be used to probe backbone-cation interactions at different scenarios (near charged or neutral chemical groups respectively). Cation concentration-dependent IR frequency red shifts in the amide-I mode are seen for both amide-I modes, whereas blue shifts are also seen in the amide-I mode far from the NH3+ group. The observed spectral changes are discussed from the perspective of the salting-in and salting-out abilities of the cations. In addition, all the metal cations studied here (except Zn2+) can specifically coordinate to the COO- group in bidentate and pseudo-bridging forms simultaneously. For Zn2+, only the pseudo-bridging form exists. Our results shed light on the macroscopic protein salting-in and salting-out phenomena from the perspective of key chemical bonds in peptides.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics.

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Waypoint Graph Generation with Growing Neural Gases for Pathfinding Applications in Molecular Dynamics Simulations

Path planning is a fundamental problem in the fields of autonomous robotics and molecular simulation. A large body of algorithms developed for vision-based robotic motion planning have been successfully applied to molecular pathfinding problems. We present the application of one such technique, the growing neural gas (GNG), an unsupervised machine learning procedure that estimates the optimal topological discretization of a collective variable space of arbitrary dimensionality. The GNG constructs an undirected graph representation of a probability density by utilizing a Hebb-like competitive learning rule, where individual neurons compete to represent different regions of the input space by moving and replicating in response to random samples drawn from the target density. The nodes of the resulting graph correspond to waypoint molecular states and its edges represent the potential transitions between states. Recent developments in autoencoder- and flow-based generative learning procedures have facilitated the unsupervised sampling and discovery of key collective variables in molecular systems, along which free energy differences can be calculated. Applying the GNG to such multidimensional free energy profiles allows for rapid generation of waypoint graphs within the collective variable space, which can be subsequently refined to determine optimal transition paths between selected states of interest. This proposed pipeline enables the unsupervised estimation of minimum free-energy transition paths from an initial molecular structure. We demonstrate our procedure on toy Gaussian-well systems and model molecular systems such as alanine tripeptide and show that the GNG can be a powerful tool for feature space discretization and path planning applications in molecular dynamics simulations.

Specific and non-specific interactions between metal cations and zwitterionic alanine tripeptide in saline solutions reported by the symmetric carboxylate stretching and amide-II vibrations.

The "specific" interaction between metal cations (Na+, Ca2+, Mg2+, and Zn2+) and the charged COO- group, and the "non-specific" interaction between these cations and the peptide backbone of a zwitterionic trialanine (Ala3) in aqueous solutions were examined in detail, using linear infrared (IR) absorptions of the COO- symmetric stretching and the amide-II (mainly the C-N stretching) modes as IR probes. Different IR spectral changes in peak positions and intensities of the two IR probes clearly demonstrate their sensitivities to nearby cation distributions in distance and population. Quantum chemistry calculations and molecular dynamics simulations were used to describe the cation-peptide interaction picture. These combined results suggest that Na+ and Ca2+ tend to bind to the COO- group in the bidentate form, while Mg2+ and Zn2+ tend to bind to the COO- group in the pseudo-bridging form. The results also show that while all three divalent cations indirectly interact with the peptide backbone with large population, Ca2+ and Mg2+ can be sometimes distributed very close to the backbone. Such a non-specific cation interaction can be moderately sensed by the C-N stretching of the amide-II mode when cations approach the polar amide C[double bond, length as m-dash]O group, and is also influenced by the NH3+ charge group located at the N-terminus. The results suggest that the experimentally observed complication of the Hofmeister cation series shall be understood as a combined specific and non-specific cation-peptide interactions.

Mapping saddles and minima on free energy surfaces using multiple climbing strings.

Locating saddle points on free energy surfaces is key in characterizing multistate transition events in complicated molecular-scale systems. Because these saddle points represent transition states, determining minimum free energy pathways to these saddles and measuring their free energies relative to their connected minima are further necessary, for instance, to estimate transition rates. In this work, we propose a new multistring version of the climbing string method in collective variables to locate all saddles and corresponding pathways on free energy surfaces. The method uses dynamic strings to locate saddles and static strings to keep a history of prior strings converged to saddles. Interaction of the dynamic strings with the static strings is used to avoid the convergence to already-identified saddles. Additionally, because the strings approximate curves in collective-variable space, and we can measure free energy along each curve, identification of any saddle's two connected minima is guaranteed. We demonstrate this method to map the network of stationary points in the 2D and 4D free energy surfaces of alanine dipeptide and alanine tripeptide, respectively.

Augmenting Basin-Hopping With Techniques From Unsupervised Machine Learning: Applications in Spectroscopy and Ion Mobility.

Evolutionary algorithms such as the basin-hopping (BH) algorithm have proven to be useful for difficult non-linear optimization problems with multiple modalities and variables. Applications of these algorithms range from characterization of molecular states in statistical physics and molecular biology to geometric packing problems. A key feature of BH is the fact that one can generate a coarse-grained mapping of a potential energy surface (PES) in terms of local minima. These results can then be utilized to gain insights into molecular dynamics and thermodynamic properties. Here we describe how one can employ concepts from unsupervised machine learning to augment BH PES searches to more efficiently identify local minima and the transition states connecting them. Specifically, we introduce the concepts of similarity indices, hierarchical clustering, and multidimensional scaling to the BH methodology. These same machine learning techniques can be used as tools for interpreting and rationalizing experimental results from spectroscopic and ion mobility investigations (e.g., spectral assignment, dynamic collision cross sections). We exemplify this in two case studies: (1) assigning the infrared multiple photon dissociation spectrum of the protonated serine dimer and (2) determining the temperature-dependent collision cross-section of protonated alanine tripeptide.

Free energy calculations of alanine tripeptide in explicit water using temperature accelerated sliced sampling

Free energy calculations of alanine tripeptide in explicit water using temperature accelerated sliced sampling

Free energy reaction root mapping of alanine tripeptide in water

ABSTRACTWe have investigated the free energy surface of alanine tripeptide in water. To elucidate the secondary structure of the amide chain, information on the free energy surface with explicit water at room temperature, and the multidimensional reaction coordinates are required. We studied the minimum free energy paths (MFEPs) connecting reactants, transition structures (TS) and products. To solve this problem, we used the free energy reaction root mapping (FERRMap) method. This is an automated search method to find MFEPs by using umbrella integration and the scaled hypersphere search method. We calculated the four-dimensional free energy surface for alanine tripeptide in water using FERRMap and found 61 equilibrium structures (EQ) connected by 133 TS points. After elucidating the MFEP network, we analysed the structures of the EQ points and the MFEPs connecting beta-sheet structures and beta-turn structures or left-handed helix structures.

Automated Search of Minimum Free-Energy Path by Umbrella Integration.

The free-energy landscape is an important factor for understanding the conformational equilibria of chemical reactions, and many techniques have been developed to calculate the potential of the mean force. Unfortunately, these methods require a previous knowledge of the system for calculations because the results depend on the reaction coordinates. In this study, we combine the scaled hypersphere search method with the umbrella integration method to obtain the transition states on free-energy landscapes and minimum-free-energy paths (MFEPs). With this approach, the MFEP connections between known and unknown equilibrium points are constructed without the prior knowledge of the free-energy landscape. The problem of reaction coordinates can be solved by using a multidimensional, fully automated interrogation of MFEPs for acquiring the potential of mean force. The efficiency of the proposed method is demonstrated by applying it to alanine dipeptide and alanine tripeptide. © 2018 Wiley Periodicals, Inc.

Milieu-Initiated Inversion of the Aqueous Polyproline II/β Propensity in the Alanine Tripeptide: Aggregation Origin of the Onset of Amyloid Formation.

Extending our earlier analogous study of the alanine dipeptide (ADP), we have now analyzed the effect of the external environment on the polyproline II (P) and β relative energies, the P/β propensity, of the alanine tripeptide (ATP). Ab initio calculations of ATP(H2O)19 and ATP(H2O)19(HCl) exhibit the same propensity inversion as in ADP: in the pure water case the PP conformation is favored while the addition of the HCl molecule results in the ββ conformation being of lower energy. A comparison, following an intermediate insertion and departure of an HCl molecule, shows that the energy of a hydrogen-bonded (H2O)19βATP::βATP(H2O)19 structure is lower than that of the sum of two separate PP systems, i.e., that the aggregated state of the peptide is favored. This arises from the basic physical response to their total environmental influences. Questions about quantitative results from molecular dynamics simulations, obviously needed to analyze longer chains and other side chains, are addressed via rigid water calculations. The desirability of basing studies of amyloid formation on our proposed alternative milieu-folding paradigm is discussed.

Reinforced dynamics for enhanced sampling in large atomic and molecular systems.

A new approach for efficiently exploring the configuration space and computing the free energy of large atomic and molecular systems is proposed, motivated by an analogy with reinforcement learning. There are two major components in this new approach. Like metadynamics, it allows for an efficient exploration of the configuration space by adding an adaptively computed biasing potential to the original dynamics. Like deep reinforcement learning, this biasing potential is trained on the fly using deep neural networks, with data collected judiciously from the exploration and an uncertainty indicator from the neural network model playing the role of the reward function. Parameterization using neural networks makes it feasible to handle cases with a large set of collective variables. This has the potential advantage that selecting precisely the right set of collective variables has now become less critical for capturing the structural transformations of the system. The method is illustrated by studying the full-atom explicit solvent models of alanine dipeptide and tripeptide, as well as the system of a polyalanine-10 molecule with 20 collective variables.

Machine learning molecular dynamics for the simulation of infrared spectra.

Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects - typically neglected by conventional quantum chemistry approaches - we base our machine learning strategy on ab initio molecular dynamics simulations. While these simulations are usually extremely time consuming even for small molecules, we overcome these limitations by leveraging the power of a variety of machine learning techniques, not only accelerating simulations by several orders of magnitude, but also greatly extending the size of systems that can be treated. To this end, we develop a molecular dipole moment model based on environment dependent neural network charges and combine it with the neural network potential approach of Behler and Parrinello. Contrary to the prevalent big data philosophy, we are able to obtain very accurate machine learning models for the prediction of infrared spectra based on only a few hundreds of electronic structure reference points. This is made possible through the use of molecular forces during neural network potential training and the introduction of a fully automated sampling scheme. We demonstrate the power of our machine learning approach by applying it to model the infrared spectra of a methanol molecule, n-alkanes containing up to 200 atoms and the protonated alanine tripeptide, which at the same time represents the first application of machine learning techniques to simulate the dynamics of a peptide. In all of these case studies we find an excellent agreement between the infrared spectra predicted via machine learning models and the respective theoretical and experimental spectra.

Parallel β-Sheet Structure of Alanine Tetrapeptide in the Solid State As Studied by Solid-State NMR Spectroscopy.

The structural analysis of alanine oligopeptides is important for understanding the crystalline region in silks from spiders and wild silkworms and also the mechanism of cellular toxicity of human diseases arising from expansion in polyalanine sequences. The atomic-level structures of alanine tripeptide and tetrapeptide with antiparallel β-sheet structures (AP-Ala3 and AP-Ala4, respectively) together with alanine tripeptide with parallel β-sheet structures (P-Ala3) have been determined, but alanine tetrapeptide with a parallel β-sheet structure (P-Ala4) has not been reported yet. In this article, first, we established the preparation protocol of P-Ala4 from more stable AP-Ala4. Second, complete assignments of the (13)C, (15)N, and (1)H solid-state NMR spectra were performed with (13)C- and (15)N-labeled Ala4 samples using several solid-state NMR techniques. Then, the structural constraints were obtained, for example, the amide proton peaks of P-Ala4 in the (1)H double-quantum magic-angle spinning NMR spectrum were heavily overlapped and observed at about 7.4 ppm, which was a much higher field than that of 8.7-9.1 ppm observed for AP-Ala4, indicating that the intermolecular hydrogen-bond lengths across strands (N-H···O═C) were considerably longer for P-Ala4, that is, 2.21-2.34 Å, than those reported for AP-Ala4, that is, 1.8-1.9 Å. The structural model was proposed for P-Ala4 by NMR results and MD calculations.

Adapting DFT+U for the Chemically Motivated Correction of Minimal Basis Set Incompleteness.

Recent algorithmic and hardware advances have enabled the application of electronic structure methods to the study of large-scale systems such as proteins with O(10(3)) atoms. Most such methods benefit greatly from the use of reduced basis sets to further enhance their speed, but truly minimal basis sets are well-known to suffer from incompleteness error that gives rise to incorrect descriptions of chemical bonding, preventing minimal basis set use in production calculations. We present a strategy for improving these well-known shortcomings in minimal basis sets by selectively tuning the energetics and bonding of nitrogen and oxygen atoms within proteins and small molecules to reproduce polarized double-ζ basis set geometries at minimal basis set cost. We borrow the well-known +U correction from the density functional theory community normally employed for self-interaction errors and demonstrate its power in the context of correcting basis set incompleteness within a formally self-interaction-free Hartree-Fock framework. We tune the Hubbard U parameters for nitrogen and oxygen atoms on small-molecule tautomers (e.g., cytosine), demonstrate the applicability of the approach on a number of amide-containing molecules (e.g., formamide, alanine tripeptide), and test our strategy on a 10 protein test set where anomalous proton transfer events are reduced by 90% from RHF/STO-3G to RHF/STO-3G+U, bringing the latter into quantitative agreement with RHF/6-31G* results. Although developed with the study of biological molecules in mind, this empirically tuned U approach shows promise as an alternative strategy for correction of basis set incompleteness errors.

Sensitivity enhanced (14)N/(14)N correlations to probe inter-beta-sheet interactions using fast magic angle spinning solid-state NMR in biological solids.

(14)N/(14)N correlations are vital for structural studies of solid samples, especially those in which (15)N isotopic enrichment is challenging, time-consuming and expensive. Although (14)N nuclei have high isotopic abundance (99.6%), there are inherent difficulties in observing (14)N/(14)N correlations due to limited resolution and sensitivity related to: (i) low (14)N gyromagnetic ratio (γ), (ii) large (14)N quadrupolar couplings, (iii) integer (14)N spin quantum number (I = 1), and (iv) very weak (14)N-(14)N dipolar couplings. Previously, we demonstrated a proton-detected 3D (14)N/(14)N/(1)H correlation experiment at fast magic angle spinning (MAS) on l-histidine·HCl·H2O utilizing a through-bond (J) and residual dipolar-splitting (RDS) based heteronuclear multiple quantum correlation (J-HMQC) sequence mediated through (1)H/(1)H radio-frequency driven recoupling (RFDR). As an extension of our previous work, in this study we show the utility of dipolar-based HMQC (D-HMQC) in combination with (1)H/(1)H RFDR mixing to obtain sensitivity enhanced (14)N/(14)N correlations in more complex biological solids such as a glycyl-l-alanine (Gly-l-Ala) dipeptide, and parallel (P) and antiparallel (AP) β-strand alanine tripeptides (P-(Ala)3 and AP-(Ala)3, respectively). These systems highlight the mandatory necessity of 3D (14)N/(14)N/(1)H measurements to get (14)N/(14)N correlations when the amide proton resonances are overlapped. Moreover, the application of long selective (14)N pulses, instead of short hard ones, is shown to improve the sensitivity. Globally, we demonstrate that replacing J-scalar with dipolar interaction and hard- with selective-(14)N pulses allows gaining a factor of ca. 360 in experimental time. On the basis of intermolecular NH/NH distances and (14)N quadrupolar tensor orientations, (14)N/(14)N correlations are effectively utilized to make a clear distinction between the parallel and antiparallel arrangements of the β-strands in (Ala)3 through the observation of inter-β-sheet correlations.

Oscillatory Diffusion and Second-Order Cyclostationarity in Alanine Tripeptide from Molecular Dynamics Simulation.

Molecular dynamics (MD) simulation distinctly describes motions of biomolecules at high resolution and can potentially be used to explain allosteric mechanism in subcellular processes. Statistical methods are necessary to realize this potential because MD simulations generate a large volume of data and because the analysis is never efficient, objective, or thorough without using appropriate statistical approaches. Tracing the flow of information within a biomolecule requires not only a description of an overall mechanism but also a multiscale statistical description from atomic interactions to the overall mechanism. The foundation of this multiscale description, in general, is a measure of correlation between motions of atoms or residues, as reflected by dynamic cross-correlation, Pearson correlation, or mutual information. However, these correlations can be inadequate because they assume wide sense stationarity, which means that the instantaneous average and correlation of a particular property are time-independent. Consequently, these measures of correlation cannot account for correlation between motions of different frequencies, since frequency implies oscillation and variation over time. Here, we characterize the nonstationarity in the form of pure oscillatory instantaneous variance in the signed dihedral angular accelerations (SDAA) along the main chain of alanine tripeptide in MD simulations by power spectrum, corrected squared envelope spectrum (CSES), and cross-CSES. This oscillation has a physical interpretation of an oscillatory diffusion. The fraction of this oscillation in all motions is as high as about 40% at some frequencies. This shows that oscillatory instantaneous variance exists in the SDAA and that significant correlation may not be accounted for in current correlation analysis. This oscillation is also found to transmit between dihedral angles. These results could have implications in the understanding of the dynamics of biomolecules.

Theoretical investigation on nearsightedness of finite model and molecular systems based on linear response function analysis.

We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r′), decays rapidly for the distance, |r−r′|. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems’ counterparts, H2, He22+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems.