The Stability of Protein Secondary Structures in Aqueous Solution

Adiabatic free energy dynamics (AFED) was introduced by Rosso et al. [J. Chem. Phys. 2002, 116, 4389] for computing free energy profiles quickly and accurately using a dynamical adiabatic separation between a set of collective variables or reaction coordinates and the remaining degrees of freedom of a system. This approach has been shown to lead to a significant gain in efficiency versus traditional methods such as umbrella sampling, thermodynamic integration, and free energy perturbation for generating one-dimensional free energy profiles. More importantly, AFED is able to generate multidimensional free energy surfaces efficiently via full sweeps of the surface that rapidly map out the locations of the free energy minima. The most significant drawback to the AFED approach is the need to transform the coordinates into a generalized coordinate system that explicitly contains the collective variables of interest. Recently, Maragliano and Vanden-Eijnden built upon the AFED approach by introducing a set of extended phase-space variables, to which the adiabatic decoupling and high temperature are applied [Chem. Phys. Lett. 2006, 426, 168]. In this scheme, which the authors termed "temperature accelerated molecular dynamics" or TAMD, the need for explicit coordinate transformations is circumvented. The ability of AFED and TAMD to generate free energy surfaces efficiently depends on the thermostatting mechanism employed, since both approaches are inherently nonequilibrium due to the adiabatic decoupling. Indeed, Maragliano and Vanden-Eijnden did not report any direct generation of free energy surfaces within the overdamped Langevin dynamics employed by these authors. Here, we show that by formulating TAMD in a manner that is closer to the original AFED approach, including the generalized Gaussian moment thermostat (GGMT) and multiple time-scale integration, multidimensional free energy surfaces for complex systems can be generated directly from the probability distribution function of the extended phase-space variables. The new TAMD formulation, which we term driven AFED or d-AFED, is applied to compare the conformational preferences of small peptides both in gas phase and in solution for three force fields. The results show that d-AFED/TAMD accurately and efficiently generates free energy surfaces in two collective variables useful for characterizing the conformations, namely, the radius of gyration, R(G), and number of hydrogen bonds, N(H).

Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc.

Is Protein Single Molecule Dynamics under Force Described by Two or More States?

A molecule in a bulk of material is pulled from all the sides whereas a molecule at the surface experiences no pull from the top and is pulled only from the sides and below. Bonding between molecules takes place with lowering of free energy. The bond energies between particles are negative because energy is evolved on bond formation. Therefore, atoms, molecules, or ions on the surface of a liquid or solid possess higher energies than those located in the bulk of the substance. The energy of the surface increases with the increase of the surface area. Hence, the surface free energy can be defined as the energy required to create 1 m2 of new surface. This energy can be expressed in Joule per square meter (or ergs per square cm). As the molecules in solids are rigid, no such effect is realized. Surface free energy is a characteristic property of the liquid phase making a free surface. Since reduction in the surface area reduces the free energy, the surface of the liquid will tend to contract. Liquids tend to form spherical drops because spheres have the least surface area to volume ratio among all geometrical shapes. The tensional force causing the contraction of the free liquid surface is known as surface tension. The surface tension is defined as the force in newtons acting at right angles to a line 1 m long on the surface. The work done in producing 1 m2 of new surface is equivalent to the work done in stretching the surface by 1 m along a 1 m line against the surface tension and this is the surface free energy, σ. Thus, the surface tension σ, newton per meter (Nm−1), is numerically equal to the surface free energy Jm−2. Surface tension is generally used with reference to liquid, whereas surface free energy and interfacial energy are used with reference to liquids and solids, respectively. Solids definitely have surface free energy, but due to their rigid surfaces, they are neither smooth nor free to allow the solid to fill the shape of a container, and therefore, the concept of surface tension is not applicable in solids. Table 6.1 lists the values of surface tension of a few liquids.

The protein folding funnel paradigm suggests that folding and unfolding proceed as directed diffusion in a multidimensional free energy surface where a multitude of pathways can be traversed during the protein's sojourn from initial to final state. However, finding even a single pathway, with the detail chronicling of intermediates, is an arduous task. In this work we explore the free energy surface of unfolding pathway through umbrella sampling, for a small globular α-helical protein chicken-villin headpiece (HP-36) when the melting of secondary structures is induced by adding DMSO in aqueous solution. We find that the unfolding proceeds through the initial separation or melting of aggregated hydrophobic core that comprises of three phenylalanine residues (Phe7, Phe11, and Phe18). This separation is accompanied by simultaneous melting of the second helix. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hydrophobic grooves to stabilize the intermediate states. We identify the configuration of the intermediates and correlate the intermediates with those obtained in our previous works. We also give an estimate of the barriers for different transition states and observe the softening of the barriers with increasing DMSO concentration. We show that higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of a solvent modified, less rugged pathway. The prime outcome of this work is the demonstration that mixed solvents can profoundly transform the nature of the energy landscape and induce unfolding via a modified route. A successful application of Kramer's rate equation correlating the free energy simulation results shows faster rate of unfolding with increasing DMSO concentration. This work perhaps presents the first systematic theoretical study of the effect of a chemical denaturant on the microscopic free energy surface and rates of unfolding of HP-36.

While free energy surfaces are the crux of our understandingofmany chemical and biological processes, their accuracy is generallyunknown. Moreover, many developments to improve their accuracy areoften complicated, limiting their general use. Luckily, several toolsand guidelines are already in place to identify these shortcomings,but they are typically lacking in flexibility or fail to systematicallydetermine how to improve the accuracy of the free energy calculation.To overcome these limitations, this work introduces OGRe, a Pythonpackage for optimal grid refinement in an arbitrary number of dimensions.OGRe is based on three metrics that gauge the confinement, consistency,and overlap of each simulation in a series of umbrella sampling (US)simulations, an enhanced sampling technique ubiquitously adopted toconstruct free energy surfaces for hindered processes. As these threemetrics are fundamentally linked to the accuracy of the weighted histogramanalysis method adopted to generate free energy surfaces from US simulations,they facilitate the systematic construction of accurate free energyprofiles, where each metric is driven by a specific umbrella parameter.This allows for the derivation of a consistent and optimal collectionof umbrellas for each simulation, largely independent of the initialvalues, thereby dramatically increasing the ease-of-use toward accuratefree energy surfaces. As such, OGRe is particularly suited to determinecomplex free energy surfaces with large activation barriers and shallowminima, which underpin many physical and chemical transformationsand hence to further our fundamental understanding of these processes.

The overexpression of aberrantly glycosylated tumor-associated mucin-1 (TA-MUC1) in human cancers makes it a major target for the development of anticancer vaccines derived from synthetic MUC1-(glyco)peptide antigens. However, glycopeptide-based subunit vaccines are weakly immunogenic, requiring adjuvants and/or additional immunopotentiating approaches to generate optimal immune responses. Among these strategies, unimolecular self-adjuvanting vaccine constructs that do not need coadministration of adjuvants or conjugation to carrier proteins emerge as a promising but still underexploited approach. Herein, we report the design, synthesis, immune-evaluation in mice, and NMR studies of new, self-adjuvanting and self-assembling vaccines based on our QS-21-derived minimal adjuvant platform covalently linked to TA-MUC1-(glyco)peptide antigens and a peptide helper T-cell epitope. We have developed a modular, chemoselective strategy that harnesses two distal attachment points on the saponin adjuvant to conjugate the respective components in unprotected form and high yields via orthogonal ligations. In mice, only tri-component candidates but not unconjugated or di-component combinations induced significant TA-MUC1-specific IgG antibodies able to recognize the TA-MUC1 on cancer cells. NMR studies revealed the formation of self-assembled aggregates, in which the more hydrophilic TA-MUC1 moiety gets exposed to the solvent, favoring B-cell recognition. While dilution of the di-component saponin-(Tn)MUC1 constructs resulted in partial aggregate disruption, this was not observed for the more stably-organized tri-component candidates. This higher structural stability in solution correlates with their increased immunogenicity and suggests a longer half-life of the construct in physiological media, which together with the enhanced antigen multivalent presentation enabled by the particulate self-assembly, points to this self-adjuvanting tri-component vaccine as a promising synthetic candidate for further development.

An Evolutionarily Conserved Family of Virion Tail Needles Related to Bacteriophage P22 gp26: Correlation between Structural Stability and Length of the α-Helical Trimeric Coiled Coil

Free energy calculations may provide vital information for studying various chemical and biological processes. Quantum mechanical methods are required to accurately describe interaction energies, but their computations are often too demanding for conformational sampling. As a remedy, level correction schemes that allow calculating high level free energies based on conformations from lower level simulations have been developed. Here, we present a variation of a Monte Carlo (MC) resampling approach in relation to the weighted histogram analysis method (WHAM). We show that our scheme can generate free energy surfaces that can practically converge to the exact one with sufficient sampling, and that it treats cases with insufficient sampling in a more stable manner than the conventional WHAM-based level correction scheme. It can also provide a guide for checking the uncertainty of the level-corrected surface and a well-defined criterion for deciding the extent of smoothing on the free energy surface for its visual improvement. We demonstrate these aspects by obtaining the free energy maps associated with the alanine dipeptide and proton transfer network of the KillerRed protein in explicit water, and exemplify that the MC resampled WHAM scheme can be a practical tool for producing free energy surfaces of realistic systems.

The Y22W/Q33Y/G46,48A mutant of the protein lambda6-85 folds in a few microseconds at room temperature. We find that its folding kinetics are probe-dependent under a strong bias toward the native state, a new signature for downhill folding. The IR- and fluorescence-detected relaxation time scales converge when the native bias is removed by raising the temperature, recovering activated two-state folding. Langevin dynamics simulations on one- and 2D free energy surfaces tunable from two-state to downhill folding reproduce the difference between the IR and fluorescence experiments, as well as the temperature and viscosity trends. In addition, the 2D surface reproduces the stretched exponential dynamics that we fit to the glucose solution experimental data at short times. Nonexponential dynamics at <10 micros is a signature either for local free energy minima along the reaction coordinate ("longitudinal roughness"), or for folding on a higher-dimensional free energy surface ("transverse roughness").

Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad, and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad, and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories. © 2016 Wiley Periodicals, Inc.

A peptide fragment corresponding to the third helix of Staphylococcus Aureus protein A, domain B, was chosen to study the effect of the main-chain direction upon secondary structure formation and stability, applying the retro-enantio concept. For this purpose, two peptides consisting of the native (Ln) and reversed (Lr) sequences were synthesized and their conformational preferences analysed by CD and NMR spectroscopy. A combination of CD and NMR data, such as molar ellipcitity. NOE connectivities, H alpha and NH chemical shifts, 3J alpha N coupling constants and amide temperature coefficients indicated the presence of nascent helices for both Ln and Lr in water, stabilized upon addition of the fluorinated solvents TFE and HFIP. Helix formation and stabilization appeared to be very similar in both normal and retro peptides, despite the unfavourable charge-macrodipole interactions and bad N-capping in the retro peptide. Thus, these helix stabilization factors are not a secondary structure as determined for this specific peptide. In general, the synthesis and confirmational analysis of peptide pairs with opposite main-chain directions, normal and retro peptides, could be useful in the determination of secondary structure stabilization factors dependent on the direction.

We used UV resonance Raman (UVRR) spectroscopy to quantitatively correlate the peptide bond AmIII3 frequency to its Psi Ramachandran angle and to the number and types of amide hydrogen bonds at different temperatures. This information allows us to develop a family of relationships to directly estimate the Psi Ramachandran angle from measured UVRR AmIII3 frequencies for peptide bonds (PBs) with known hydrogen bonding (HB). These relationships ignore the more modest Phi Ramachandran angle dependence and allow determination of the Psi angle with a standard error of +/-8 degrees , if the HB state of a PB is known. This is normally the case if a known secondary structure motif is studied. Further, if the HB state of a PB in water is unknown, the extreme alterations in such a state could additionally bias the Psi angle by +/-6 degrees . The resulting ability to measure Psi spectroscopically will enable new incisive protein conformational studies, especially in the field of protein folding. This is because any attempt to understand reaction mechanisms requires elucidation of the relevant reaction coordinate(s). The Psi angle is precisely the reaction coordinate that determines secondary structure changes. As shown elsewhere (Mikhonin et al. J. Am. Chem. Soc. 2005, 127, 7712), this correlation can be used to determine portions of the energy landscape along the Psi reaction coordinate.

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.

Accurately computing the free energy for biological processes like protein folding or protein-ligand association remains a challenging problem. Both describing the complex intermolecular forces involved and sampling the requisite configuration space make understanding these processes innately difficult. Herein, we address the sampling problem using a novel methodology we term "movable type". Conceptually it can be understood by analogy with the evolution of printing and, hence, the name movable type. For example, a common approach to the study of protein-ligand complexation involves taking a database of intact drug-like molecules and exhaustively docking them into a binding pocket. This is reminiscent of early woodblock printing where each page had to be laboriously created prior to printing a book. However, printing evolved to an approach where a database of symbols (letters, numerals, etc.) was created and then assembled using a movable type system, which allowed for the creation of all possible combinations of symbols on a given page, thereby, revolutionizing the dissemination of knowledge. Our movable type (MT) method involves the identification of all atom pairs seen in protein-ligand complexes and then creating two databases: one with their associated pairwise distant dependent energies and another associated with the probability of how these pairs can combine in terms of bonds, angles, dihedrals and non-bonded interactions. Combining these two databases coupled with the principles of statistical mechanics allows us to accurately estimate binding free energies as well as the pose of a ligand in a receptor. This method, by its mathematical construction, samples all of configuration space of a selected region (the protein active site here) in one shot without resorting to brute force sampling schemes involving Monte Carlo, genetic algorithms or molecular dynamics simulations making the methodology extremely efficient. Importantly, this method explores the free energy surface eliminating the need to estimate the enthalpy and entropy components individually. Finally, low free energy structures can be obtained via a free energy minimization procedure yielding all low free energy poses on a given free energy surface. Besides revolutionizing the protein-ligand docking and scoring problem this approach can be utilized in a wide range of applications in computational biology which involve the computation of free energies for systems with extensive phase spaces including protein folding, protein-protein docking and protein design.