Oscillatory molecular driving force for protein folding at high concentration: a molecular simulation

This paper presents a Langevin dynamics simulation that suggests a novel way to fold protein at high concentration, a fundamental issue in neurodegenerative diseases in vivo and the production of recombinant proteins in vitro. The simulation indicates that the folding of a coarse-grained beta-barrel protein at high concentration follows the "collapse-rearrangement" mechanism but it yields products of various forms, including single proteins in the native, misfolded, and uncollapsed forms and protein aggregates. Misfolded and uncollapased proteins are the "nucleus" of the aggregates that also encapsulate some correctly folded proteins (native proteins). An optimum hydrophobic interaction strength (epsilon*(p)) between the hydrophobic beads of the model protein, which results from a compromise between the kinetics of collapse and rearrangement, is identified for use in increasing the rate of folding over aggregating. Increased protein concentration hinders the structural transitions in both collapse and rearrangement and thus favors aggregation. A new method for protein folding at high concentration is proposed, which uses an oscillatory molecular driving force (epsilon*(p)) to promote the dissociation of aggregates in the low epsilon*(p) regime while promoting folding at a high epsilon*(p). The advantage of this method in enhancing protein folding while depressing aggregation is illustrated by a comparison with the methods based on direct dilution or applying a denaturant gradient.     

Protein folding in a force clamp

Kinetics of folding of a protein held in a force clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations in the end-to-end distance reflect microscopic events during folding. However, the folding scenarios in and out of the force clamp are distinct.     

Ab initio folding of albumin binding domain from all-atom molecular dynamics simulation

Ab initio folding with all-atom model remains to be a difficult task even for small proteins. In this report, we conducted an accumulated 24 mus simulations on the wild type and two mutants of albumin binding domain (ABD) using the AMBER FF03 all-atom force field and a generalized-Born solvation model. Folding events have been observed in multiple trajectories, and the best folded structures achieved root-mean-square deviation (RMSD) of 2.0 A. The folding of this three-helix bundle protein followed a diffusion-collision process, where substantial formation of the individual helices was critical and preceded the global packing. Owing to the difference in the intrinsic helicity, helix I formed faster than the other two helices. The order of the formation of helices II and III varied in different trajectories, indicating heterogeneity of the folding process. The slightly shifted boundaries of the helical segments had direct impact on the global packing, suggesting room for improvement on the simulation force field and solvation model.     

Reversible peptide folding: Dependence on molecular force field used

Temperature‐dependent nuclear magnetic resonance (NMR) and CD spectra of methanol solutions of a β‐heptapeptide have been interpreted in such a way that the secondary structure, a 3₁₄‐helix, is assumed to be stable in a temperature range of between 298 and 393 K. This is in contrast to the results of a 50‐ns molecular dynamics simulation using the GROMOS 96 force field, which found a melting temperature of about 340 K. This discrepancy is addressed by further computational studies using the OPLS‐AA force field. The conformational energetics of N‐formyl‐3‐aminobutanamide in vacuo are obtained using ab initio and density functional quantum‐mechanical calculations at the HF/6‐31G*, B3LYP/6‐31G*, and B3LYP/6‐311+G* levels of theory. The results permit development of torsional parameters for the OPLS‐AA force field that reproduce the conformational energetics of the monomer. By varying the development procedure, three parameter sets are obtained that focus on reproducing either low‐energy or high‐energy conformations. These parameter sets are tested by simulating the reversible folding of the β‐heptapeptide in methanol. The melting temperature of the helix formed (>360 K) is found to be higher than the one obtained from simulations using the GROMOS 96 force field (∼340 K). Differences in the potential energy functions of the latter two force fields are evaluated and point to the origins of the difference in stability. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 774–787, 2000     

Protein folding kinetics: barrier effects in chemical and thermal denaturation experiments

Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.     

Protein folding invariants

This article discusses the topological invariants associated with an augmented ribbon model of single domain protein. The model is a triple (S, G, J) in S³ where S is a 2-manifold with boundary, G is a circle-with-chords, and J is an arc. The surfaces satisfy an embedding condition called laundry. The invariants are necessary and sufficient conditions for two triples to be equivalent by ambient isotopy. The model describes the native state, the unfolded state, and a unique folding pathway as a single mathematical entity. This may help illuminate some of the remarkable properties of protein. Twist transitions are introduced that allow the surface to pass through itself. A new arithmetic involving the complex numbers is used to represent variable linking numbers.     

Monte Carlo simulation study of melittin: Protein folding and temperature dependence

The tetramerization of melittin, a 26-amino-acid peptide, is considered as a model for protein folding. The Monte Carlo simulation was used to study the folding arrangement of melittin, and the results are compared with the experiment. An acceptance rate of 50% for new configurations is achieved by using ranges of ±0.001 Å for the translations and ±15°C for the rotations. Around 311 K, the folded structure of the protein has the greatest stability; the range from −40 to −80 shows the best ϕ angles for melittin. The final optimized structure of melittin strongly depends on the temperature. The melittin tetramer is found to have a temperature of maximum stability ranging from 35.5 to 43°C.

     

Development of force field parameters for molecular simulation of polylactide

Polylactide is a biodegradable polymer that is widely used for biomedical applications, and it is a replacement for some petroleum based polymers in applications that range from packaging to carpeting. Efforts to characterize and further enhance polylactide based systems using molecular simulations have to this point been hindered by the lack of accurate atomistic models for the polymer. Thus, we present force field parameters specifically suited for molecular modeling of PLA. The model, which we refer to as PLAFF3, is based on a combination of the OPLS and CHARMM force fields, with modifications to bonded and nonbonded parameters. Dihedral angle parameters were adjusted to reproduce DFT data using newly developed CMAP dihedral cross terms, and the model was further adjusted to reproduce experimentally resolved crystal structure conformations, melt density, volume expansivity, and the glass transition temperature of PLA. We recommend the use of PLAFF3 in modeling PLA in its crystalline or amorphous states and have provided the necessary input files required for the publicly available molecular dynamics code GROMACS.     

New force field for molecular simulation of guanidinium-based ionic liquids

An all-atom force field was proposed for a new class of room temperature ionic liquids (RTILs), N,N,N',N'-tetramethylguanidinium (TMG) RTILs. The model is based on the AMBER force field with modifications on several parameters. The refinements include (1) fitting the vibration frequencies for obtaining force coefficients of bonds and angles against the data obtained by ab initio calculations and/or by experiments and (2) fitting the torsion energy profiles of dihedral angles for obtaining torsion parameters against the data obtained by ab initio calculations. To validate the force field, molecular dynamics (MD) simulations at different temperatures were performed for five kinds of RTILs, where TMG acts as a cation and formate, lactate, perchlorate, trifluoroacetate, and trifluoromethylsulfonate act as anions. The predicted densities were in good agreement with the experimental data. Radial distribution functions (RDFs) and spatial distribution functions (SDFs) were investigated to depict the microscopic structures of the RTILs.     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Protein structure and dynamics in ionic liquids. Insights from molecular dynamics simulation studies

We present in this work the first molecular simulation study of an enzyme, the serine protease cutinase from Fusarium solani pisi, in two ionic liquids (ILs): 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) and 1-butyl-3-methylimidazolium nitrate ([BMIM][NO(3)]). We tested different water contents in these ILs at room temperature (298 K) and high temperature (343 K), and we observe that the enzyme structure is highly dependent on the amount of water present in the IL media. We show that the enzyme is preferentially stabilized in [BMIM][PF6] at 5-10% (w/w) (weight of water over protein) water content at room temperature. [BMIM][PF6] renders a more nativelike enzyme structure at the same water content of 5-10% (w/w) as previously found for hexane, and the system displays a similar bell-shape-like dependence with the water content in the IL media. [BMIM][PF6] is shown to increase significantly the protein thermostability at high temperatures, especially at low hydration. Our analysis indicates that the enzyme is less stabilized in [BMIM][NO(3)] relative to [BMIM][PF6] at both temperatures, most likely due to the strong affinity of the [NO(3)]- anion toward the protein main chain. These findings are in accordance with the experimental knowledge for these two ionic liquids. We also show that these ILs "strip off" most of the water from the enzyme surface in a degree similar to that found for polar organic solvents such as acetonitrile, and that the remaining waters at the enzyme surface are organized in many small clusters.     

Evaluation of force fields for molecular simulation of polyhedral oligomeric silsesquioxanes

Polyhedral oligomeric silsesquioxanes (POSS) are nanometer-size molecules suitable for the production of organic-inorganic nanocomposite materials. These organic-inorganic nano-building blocks show promise for enabling the production of polymeric materials of exceptional mechanical properties as well as novel composite materials. While the experimental studies of these materials have rapidly evolved in the past decade, their theoretical investigation is still in its infancy. Toward the validation of force fields for the molecular simulation of POSS-containing systems, we present the charge-transfer reactive (CTR) force field for the molecular simulation of polyhedral oligomeric silsesquioxane (POSS) molecules and compare the ability of this, and several force fields taken from the literature, to predict the thermophysical properties of POSS-containing systems. The literature force fields compared include the universal force field (UFF) and the COMPASS and Hybrid-COMPASS force fields. Predictions from molecular dynamics simulations of the structural parameters (unit cell vectors), melting temperature, and FT-IR spectra of crystals of POSS monomers are presented. The POSS monomers investigated are octahydride, octamethyl, and octapropyl POSS. Predicted quantities are compared to experimental results where available and provide molecular-level physical insight into several aspects of the behavior of POSS molecules. While all the force fields tested perform reasonably well, our results indicate that the Hybrid-COMPASS and CTR force fields predict structural properties that are in good agreement with experimental data.     

The protein folding transition state: insights from kinetics and thermodynamics

We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4相似文献   

Protein folding through kinetic discrimination

Proteins fold on a micros-ms time scale. However, the number of possible conformations of the polypeptide backbone is so large that random sampling would not allow the protein to fold within the lifetime of the universe, the Levinthal paradox. We show here that a protein chain can fold efficiently with high fidelity if on average native contacts survive longer than non-native ones, that is, if the dissociation rate constant for breakage of a contact is lower for native than for non-native interactions. An important consequence of this finding is that no pathway needs to be specified for a protein to fold. Instead, kinetic discrimination among formed contacts is a sufficient criterion for folding to proceed to the native state. Successful protein folding requires that productive contacts survive long enough to obtain a certain level of probability that other native contacts form before the first interacting unit dissociates. If native contacts survive longer than non-native ones, this prevents misfolding and provides the folding process with directionality toward the native state. If on average all contacts survive equally long, the protein chain is deemed to fold through random search through all possible conformations (i.e., the Levinthal paradox). A modest degree of cooperativity among the native contacts, that is, decreased dissociation rate next to neighboring contacts, shifts the required ratio of dissociation rates into a realistic regime and makes folding a stochastic process with a nucleation step. No kinetic discrimination needs to be invoked in regards to the association process, which is modeled as dependent on the diffusion rate of chain segments.     

Graphic rule for non-steady-state enzyme kinetics and protein folding kinetics

When going more deeply into the principles of enzyme action as well as protein folding, one is often confronted with transient process systems. Based on the recent progress in graphic methods of enzyme kinetics, in this article a graphic rule is described, which can be used to deal with transient processes occurring in both enzyme-catalyzed reaction systems and protein folding systems. Introducing the graphic method to nonsteady-state systems can raise the efficiency of the calculations and provide an intuitive picture, helping the analysis of the mechanisms concerned. For instance, using the current graphic rule, one can immediately write out the phase concentrations of enzyme species or protein folding states. Calculation work such as setting up differential equations, making Laplace transformations, and expanding determinants, which is both tedious and liable to error, is completely avoided. The mathematical proof of the non-steady-state graphic rule is given in the appendix.Presented at the Symposium on Applied Graph Theory and Discrete Mathematics in Chemistry held at the University of Saskatchewan, Saskatoon, Canada, September 12-14, 1991, in honor of Professor Frank Harary on the occasion of his 70th birthday.     

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.     

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.