Trp Cage Research Articles

Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics.

Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the time scales necessary to capture the structural evolution of biomolecules remains a daunting task. In this work, we present a novel framework to advance simulation time scales by up to 3 orders of magnitude by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müller-Brown potential, the Trp cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations, i.e., collective variables, and can generate, at any instant, all-atom molecular trajectories consistent with the collective variables. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.

Accurate Calculation of Free Energy Changes upon Amino Acid Mutation.

Molecular dynamics based free energy calculations allow for a robust and accurate evaluation of free energy changes upon amino acid mutation in proteins. In this chapter we cover the basic theoretical concepts important for the use of calculations utilizing the non-equilibrium alchemical switching methodology. We further provide a detailed step-by-step protocol for estimating the effect of a single amino acid mutation on protein thermostability. In addition, the potential caveats and solutions to some frequently encountered issues concerning the non-equilibrium alchemical free energy calculations are discussed. The protocol comprises details for the hybrid structure/topology generation required for alchemical transitions, equilibrium simulation setup, and description of the fast non-equilibrium switching. Subsequently, the analysis of the obtained results is described. The steps in the protocol are complemented with an illustrative practical application: a destabilizing mutation in the Trp cage mini protein. The concepts that are described are generally applicable. The shown example makes use of the pmx software package for the free energy calculations using Gromacs as a molecular dynamics engine. Finally,we discuss how the current protocol can readily be adapted to carry out charge-changing or multiple mutations at once, as well aslarge-scale mutational scans.

Atomistic level understanding of the stabilization of protein Trp cage in denaturing and mixed osmolyte solutions

Using replica exchange molecular dynamics simulation technique we report urea-induced denaturation and its counteraction by TMAO (Trimethylamine-N-oxide) of protein Trp cage. We find that in binary solution urea molecules are very much prone to stay nearby the salt bridge. In presence of TMAO, salt bridge is protected from urea molecules. TMAO also prevents hydration of the hydrophobic core of the protein and thus provides counteraction. Emphasizing on the orientational preferences of different aromatic planes reveals that near parallel orientation of Trp6-Trp18 and near perpendicular orientations of Trp6-Trp17 and Trp6-Trp19 have significant contributions towards stabilization. Trp6-Tyr3 pair is more likely to maintain a tilt angle of 25°. These orientational preferences of the planes that are lost in binary urea solution regained significantly in mixed urea/TMAO solutions. We have also found a highly favorable interaction energy between protein and urea contributed from both electrostatic and van der Waals components. Addition of TMAO makes these interactions more unfavorable. Protein solvation behavior and hydrogen bond calculations show that TMAO molecules replace some urea molecules from the surface of the protein. As a result, a reduction in the protein-urea hydrogen bonds is observed when compared to that of binary urea system.

Effects of Trimethylamine-N-Oxide on the Conformation of Peptides and Proteins

To provide insights into the stabilizing mechanisms of trimethylamine-N-oxide (TMAO) on protein structures, we perform all-atom molecular dynamics simulations of peptides and the Trp-cage miniprotein. Effects of TMAO on the charged residues of peptides are found to stabilize compact conformations, whereas effects of TMAO on nonpolar residues lead to peptide swelling. This suggests competing mechanisms of TMAO on proteins which would accounts for swelling of hydrophobic cores and stabilization of charge-charge interactions. These mechanisms are studied from replica exchange molecular dynamics simulations of the Trp cage miniprotein.

Links between the charge model and bonded parameter force constants in biomolecular force fields.

The ff15ipq protein force field is a fixed charge model built by automated tools based on the two charge sets of the implicitly polarized charge method: one set (appropriate for vacuum) for deriving bonded parameters and the other (appropriate for aqueous solution) for running simulations. The duality is intended to treat water-induced electronic polarization with an understanding that fitting data for bonded parameters will come from quantum mechanical calculations in the gas phase. In this study, we compare ff15ipq to two alternatives produced with the same fitting software and a further expanded data set but following more conventional methods for tailoring bonded parameters (harmonic angle terms and torsion potentials) to the charge model. First, ff15ipq-Qsolv derives bonded parameters in the context of the ff15ipq solution phase charge set. Second, ff15ipq-Vac takes ff15ipq's bonded parameters and runs simulations with the vacuum phase charge set used to derive those parameters. The IPolQ charge model and associated protocol for deriving bonded parameters are shown to be an incremental improvement over protocols that do not account for the material phases of each source of their fitting data. Both force fields incorporating the polarized charge set depict stable globular proteins and have varying degrees of success modeling the metastability of short (5-19 residues) peptides. In this particular case, ff15ipq-Qsolv increases stability in a number of α-helices, correctly obtaining 70% helical character in the K19 system at 275 K and showing appropriately diminishing content up to 325 K, but overestimating the helical fraction of AAQAA3 by 50% or more, forming long-lived α-helices in simulations of a β-hairpin, and increasing the likelihood that the disordered p53 N-terminal peptide will also form a helix. This may indicate a systematic bias imparted by the ff15ipq-Qsolv parameter development strategy, which has the hallmarks of strategies used to develop other popular force fields, and may explain some of the need for manual corrections in this force fields' evolution. In contrast, ff15ipq-Vac incorrectly depicts globular protein unfolding in numerous systems tested, including Trp cage, villin, lysozyme, and GB3, and does not perform any better than ff15ipq or ff15ipq-Qsolv in tests on short peptides. We analyze the free energy surfaces of individual amino acid dipeptides and the electrostatic potential energy surfaces of each charge model to explain the differences.

Effects of Trimethylamine-N-oxide on the Conformation of Peptides and its Implications for Proteins.

To provide insights into the stabilizing mechanisms of trimethylamine-N-oxide (TMAO) on protein structures, we perform all-atom molecular dynamics simulations of peptides and the Trp-cage miniprotein. The effects of TMAO on the backbone and charged residues of peptides are found to stabilize compact conformations, whereas effects of TMAO on nonpolar residues lead to peptide swelling. This suggests competing mechanisms of TMAO on proteins, which accounts for hydrophobic swelling, backbone collapse, and stabilization of charge-charge interactions. These mechanisms are observed in Trp cage.

Protein Stability and Unfolding Following Glycine Radical Formation.

Glycine (Gly) residues are particularly susceptible to hydrogen abstraction; which results in the formation of the capto-dative stabilized Cα-centered Gly radical (GLR) on the protein backbone. We examined the effect of GLR formation on the structure of the Trp cage; tryptophan zipper; and the villin headpiece; three fast-folding and stable miniproteins; using all-atom (OPLS-AA) molecular dynamics simulations. Radicalization changes the conformation of the GLR residue and affects both neighboring residues but did not affect the stability of the Trp zipper. The stability of helices away from the radical center in villin were also affected by radicalization; and GLR in place of Gly15 caused the Trp cage to unfold within 1 µs. These results provide new evidence on the destabilizing effects of protein oxidation by reactive oxygen species.

Folding/unfolding of protein Trp cage in aqueous osmolyte solutions under polar confinement

Folding/unfolding processes of the protein Trp cage in presence of osmolytes inside a polar confinement is investigated using replica exchange molecular dynamics (REMD) simulation. A near spherical fullerene like ball consisting of 2940 carbon atoms (charged atoms) is used as a polar confinement. Urea exerts its action profoundly on the protein causing denaturation. Counteraction of TMAO is also observed in ternary solution of urea and TMAO. It is found that TMAO exerts its action in ternary mixed urea–TMAO solution by (i) removing some of the urea–TMAO hydrogen bonds, (ii) preserving the angles and distances between the aromatic planes of the residues Pro17, Pro18 and Pro19 with the indole ring of Trp6 and (iii) retaining the hydrophobic core of the protein Trp cage.

Pmx Webserver: A User Friendly Interface for Alchemistry.

With the increase of available computational power and improvements in simulation algorithms, alchemical molecular dynamics based free energy calculations have developed into routine usage. To further facilitate the usability of alchemical methods for amino acid mutations, we have developed a web based infrastructure for obtaining hybrid protein structures and topologies. The presented webserver allows amino acid mutation selection in five contemporary molecular mechanics force fields. In addition, a complete mutation scan with a user defined amino acid is supported. The output generated by the webserver is directly compatible with the Gromacs molecular dynamics engine and can be used with any of the alchemical free energy calculation setup. Furthermore, we present a database of input files and precalculated free energy differences for tripeptides approximating a disordered state of a protein, of particular use for protein stability studies. Finally, the usage of the webserver and its output is exemplified by performing an alanine scan and investigating thermodynamic stability of the Trp cage mini protein. The webserver is accessible at http://pmx.mpibpc.mpg.de.

Effect of nonpolar confinement on protein Trp cage conformation in aqueous osmolyte solutions

Abstract In this article we demonstrate the effects of confinement and osmolytes urea and trimethylamine N-oxide (TMAO) on the conformational behavior of the protein Trp cage using replica exchange molecular dynamics (REMD) simulation. We have used a near spherical nonpolar confinement consisting of 2940 carbon atoms in order to mimic the role of chaperonin unit in protein folding. Encapsulated binary solution of urea exerts denaturing effect on the protein due to favorable direct interaction with the protein. Hydrophobic core of the protein is completely disrupted in the presence of binary urea solution. In ternary solution, presence of TMAO makes protein-urea electrostatic interaction more unfavorable when compared to that for binary urea solution. Encapsulated ternary solution of urea and TMAO provides better protection to the protein conformation than that of without confinement. Confinement reduces the conformational space of the protein which is more pronounced for ternary mixed solution. We have observed that free energy landscapes of the protein are significantly modified when confinement is used in comparison to those without confinement.

A Novel Trp Cage Conformer Revealed by Combining High Pressure NMR and MD Simulations

We have used the tryptophan cage variant Tc5b, a widely used model protein for benchmarking of force fields and water models, to probe pressure effects on proteins using a combination of high pressure 2D proton NMR TOCSY and molecular dynamics simulations. Understanding the key factors of the pressure stability of protein is an essential step towards the development of better force fields and increased predictive power of simulation. We show that results of MD simulations on Tc5b as a function of pressure using the Amber 99sb force field show remarkable agreement with the pressure-dependent NMR data. Pressure perturbation in different solvent conditions yielded novel information on the structural changes in Tc5b induced by pressure. We identified a sub-ensemble in the folded basin that is strongly destabilized by pressure. Hence, most of the pressure effect on Tc5b between 1-2500 bar arises from modulation of the sub-populations of the folded state. The residues observed in the NMR experiments to be strongly affected by pressure coincided precisely with those implicated in the pressure-dependent change in Tc5b secondary structure revealed by the simulations. The relative populations of two folded state conformers, in which the central 3-10 helix and the following bend are inverted, changed upon pressurization, while the total secondary structural content remained the same. These results highlight the existence of significant plasticity in the secondary structure of folded proteins.

Empirical Optimization of Interactions between Proteins and Chemical Denaturants in Molecular Simulations.

Chemical denaturants are the most commonly used perturbation applied to study protein stability and folding kinetics as well as the properties of unfolded polypeptides. We build on recent work balancing the interactions of proteins and water, and accurate models for the solution properties of urea and guanidinium chloride, to develop a combined force field that is able to capture the strength of interactions between proteins and denaturants. We use solubility data for a model tetraglycine peptide in each denaturant to tune the protein-denaturant interaction by a novel simulation methodology. We validate the results against data for more complex sequences: single-molecule Förster resonance energy transfer data for a 34-residue fragment of the globular protein CspTm and photoinduced electron transfer quenching data for the disordered peptides C(AGQ)nW in denaturant solution as well as the chemical denaturation of the mini-protein Trp cage. The combined force field model should aid our understanding of denaturation mechanisms and the interpretation of experiment.

Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.

We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.

Simulations of Chemical Reactions with the Frozen Domain Formulation of the Fragment Molecular Orbital Method

The fully analytic first and second derivatives of the energy in the frozen domain formulation of the fragment molecular orbital (FMO) were developed and applied to locate transition states and determine vibrational contributions to free energies. The development is focused on the frozen domain with dimers (FDD) model. The intrinsic reaction coordinate method was interfaced with FMO. Simulations of IR and Raman spectra were enabled using FMO/FDD by developing the calculation of intensities. The accuracy is evaluated for S(N)2 reactions in explicit solvent, and for the free binding energies of a protein-ligand complex of the Trp cage protein (PDB: 1L2Y ). FMO/FDD is applied to study the keto-enol tautomeric reaction of phosphoglycolohydroxamic acid and the triosephosphate isomerase (PDB: 7TIM ), and the role of amino acid residue fragments in the reaction is discussed.

Dependence of Internal Friction on Native Topology

Apparent internal friction has been identified in the folding rates of several proteins and in the dynamics of unfolded proteins, via their dependence on solvent viscosity. Theoretical and computational studies have attributed this phenomenon, at least in part, to local barrier crossing events, in particular torsion angle isomerizations. However, there are still many systems for which no internal friction has been observed in experiment, and others for which the effect is only weak. Here, we elucidate the origin of this discrepancy by studying a model system whose native state can be either an α-helix or a β-hairpin. Remarkably, we find clear apparent internal friction for the helix, but no evidence of it for the hairpin. These results are consistent with the observation that proteins whose folding rates exhibit internal friction tend to be α-helical. We can explain the difference by examining the occurrence of torsional transitions along the folding coordinate of the hairpin and helix. Finally, we consider the folding of the Trp cage mini protein, whose structure includes both helical and hairpin elements. We obtain two barriers -- the major barrier for formation of the hairpin and a minor barrier for initial helix formation, allowing us to dissect the contribution of internal friction to different parts of the energy landscape. We find a clear signature of internal friction for the helical barrier and, within the uncertainty of our calculation, little internal friction for the hairpin barrier. Our results show how variation of solvent viscosity can be used to probe features of folding mechanisms.

Simulations of Cosolute Effects on Protein's Stability

Cosolutes are small miscible organic molecules that affect the solubility of proteins. Many different kinds of cosolutes have been observed to affect the conformational equilibrium of proteins in solution. Of special consideration are cosolutes that are able to denature (urea), stabilize (TMAO), or prevent aggregation (arginine). We take under consideration a special case of cosolutes termed osmolytes that have a sizable effect on the osmotic pressure of the solution. In particular, we are interested in how simple amino acids (Arg, Pro, Gly) increase the stability and solubility of proteins. We use molecular dynamics simulations to study the interactions of these cosolutes with proteins. The system under study is the mini protein trp cage, simulated in a variety of solutions consisting of different amino acids as cosolutes, in ensembles that are representative of the folded and the unfolded states. We calculate the osmotic pressure to measure the cosolute-cosolute interactions, and the preferential interaction coefficients to further assess the protein-cosolute interactions. These calculations provide information about the interactions of various amino acids with proteins. The calibration and validation with experimental data provide a way of refining force field parameters for modeling proteins in solution.

Rational design of α-helix-stabilized exendin-4 analogues.

Exendin-4 (Ex4) is a potent glucagon-like peptide-1 receptor agonist, a drug regulating the plasma glucose level of patients suffering from type 2 diabetes. The molecule's poor solubility and its readiness to form aggregates increase the likelihood of unwanted side effects. Therefore, we designed Ex4 analogues with improved structural characteristics and better water solubility. Rational design was started from the parent 20-amino acid, well-folded Trp cage (TC) miniprotein and involved the step-by-step N-terminal elongation of the TC head, resulting in the 39-amino acid Ex4 analogue, E19. Helical propensity coupled to tertiary structure compactness was monitored and quantitatively analyzed by electronic circular dichroism and nuclear magnetic resonance (NMR) spectroscopy for the 14 peptides of different lengths. Both (15)N relaxation- and diffusion-ordered NMR measurements were established to investigate the inherent mobility and self-association propensity of Ex4 and E19. Our designed E19 molecule has the same tertiary structure as Ex4 but is more helical than Ex4 under all studied conditions; it is less prone to oligomerization and has preserved biological activity. These conditions make E19 a perfect lead compound for further drug discovery. We believe that this structural study improves our understanding of the relationship between local molecular features and global physicochemical properties such as water solubility and could help in the development of more potent Ex4 analogues with improved pharmacokinetic properties.

Robustness in Protein Folding Revealed by Thermodynamics Calculations

Long-range intraprotein interactions play important roles in protein folding. In the present study, we use two variants of the B domain of protein A (BdpA F14W/G30A and BdpA_ds) and two variants of the Trp cage (TC5b_P1 and TC5b_P2) as models to investigate how long-range hydrophobic interactions affect protein tertiary and secondary structures. The mutation of the selected residues (BdpA F14W/G30A) or the change in the sequence order of Helix1 and Helix2 (BdpA_ds) changes detailed hydrophobic interactions. However, this change does not alter the global three-helix-bundle structure of BdpA and the overall shape of the folding free-energy landscape. It does affect the formation and stability of individual secondary structures. Similarly, the addition of an extra segment to the C-terminus of Trp-cage increases the number of long-range hydrophobic interactions without making any significant change of the native structure of Trp-cage. These results show the robustness of the overall protein folding, where rather large sequence changes exert significant influences on secondary but not tertiary structures.

Simulation Studies of Protein Folding/Unfolding Equilibrium under Polar and Nonpolar Confinement

We study the equilibrium folding/unfolding thermodynamics of a small globular miniprotein, the Trp cage, that is confined to the interior of a 2 nm radius fullerene ball. The interactions of the fullerene surface are changed from nonpolar to polar to mimic the interior of the GroEL/ES chaperonin that assists proteins to fold in vivo. We find that nonpolar confinement stabilizes the folded state of the protein due to the effects of volume reduction that destabilize the unfolded state and also due to interactions with the fullerene surface. For the Trp cage, polar confinement has a net destabilizing effect that results from the stabilizing confinement and the competitive exclusion effect that keeps the protein away from the surface hydration shell and stronger interactions between charged side chains in the protein and the polar surface that compete against the formation of an ion pair that stabilizes the protein folded state. We show that confinement effects due to volume reduction can be overcome by sequence-specific interactions of the protein side chains with the encapsulating surface. This study shows that there is a complex balance among many competing effects that determine the mechanism of GroEL chaperonin in enhancing the folding rate of polypeptide inside its cavity.

Four Small Puzzles That Rosetta Doesn't Solve

A complete macromolecule modeling package must be able to solve the simplest structure prediction problems. Despite recent successes in high resolution structure modeling and design, the Rosetta software suite fares poorly on small protein and RNA puzzles, some as small as four residues. To illustrate these problems, this manuscript presents Rosetta results for four well-defined test cases: the 20-residue mini-protein Trp cage, an even smaller disulfide-stabilized conotoxin, the reactive loop of a serine protease inhibitor, and a UUCG RNA tetraloop. In contrast to previous Rosetta studies, several lines of evidence indicate that conformational sampling is not the major bottleneck in modeling these small systems. Instead, approximations and omissions in the Rosetta all-atom energy function currently preclude discriminating experimentally observed conformations from de novo models at atomic resolution. These molecular “puzzles” should serve as useful model systems for developers wishing to make foundational improvements to this powerful modeling suite.