Foldamer dynamics expressed via Markov state models. I. Explicit solvent molecular-dynamics simulations in acetonitrile, chloroform, methanol, and water

In this article, we analyze the folding dynamics of an all-atom model of a polyphenylacetylene (pPA) 12-mer in explicit solvent for four common organic and aqueous solvents: acetonitrile, chloroform, methanol, and water. The solvent quality has a dramatic effect on the time scales in which pPA 12-mers fold. Acetonitrile was found to manifest ideal folding conditions as suggested by optimal folding times on the order of approximately 100-200 ns, depending on temperature. In contrast, chloroform and water were observed to hinder the folding of the pPA 12-mer due to extreme solvation conditions relative to acetonitrile; chloroform denatures the oligomer, whereas water promotes aggregation and traps. The pPA 12-mer in a pure methanol solution folded in approximately 400 ns at 300 K, compared relative to the experimental 12-mer folding time of approximately 160 ns measured in a 1:1 v/v THF/methanol solution. Requisite in drawing the aforementioned conclusions, analysis techniques based on Markov state models are applied to multiple short independent trajectories to extrapolate the long-time scale dynamics of the 12-mer in each respective solvent. We review the theory of Markov chains and derive a method to impose detailed balance on a transition-probability matrix computed from simulation data.     

A conformationally constrained nucleotide analogue controls the folding topology of a DNA g-quadruplex

Guanine-rich DNA and RNA sequences can fold into unique structures known as G-quadruplexes. The structures of G-quadruplexes can be divided into several classes, depending on the parallel or antiparallel nature of the strands and the number of G-rich tracts present in an oligonucleotide. Oligonucleotides with single tracts of guanines form intermolecular parallel tetrameric G-quadruplexes. Oligonucleotides with two tracts of guanosines separated by two or more bases can form both intermolecular antiparallel fold-back dimeric and parallel tetrameric G-quadruplexes, and those with four tracts of guanosines can form both intramolecular parallel and antiparallel structures. Intramolecular G-qaudruplexes can fold into several folding topologies including antiparallel crossover basket, antiparallel chair, and parallel propeller. The ability to control the folding of G-quadruplexes would allow the physical, biochemical, and biological properties of these various folding topologies to be studied. Previously, the known methods to control the folding topology of G-quadruplexes included changing the buffer by varying the mono- and divalent cations that are present, and by changing the DNA sequence. Because the glycosidic bonds in the G-quartets of G-quadruplexes with parallel strands are in the anti conformation, we reasoned that incorporation of nucleoside analogues that prefer the anti conformation of the glycosidic bond into G-rich sequences would increase the preference for parallel G-quadruplex formation. As predicted, by positioning the conformationally constrained nucleotide analogue 2'-O-4'-C-methylene-linked ribonucleotide into specific positions of a DNA G-quadruplex we were able to shift the thermodynamically favored structure of a G-quadruplex from an antiparallel to a parallel structure.     

Folding and Imaging of DNA Nanostructures in Anhydrous and Hydrated Deep‐Eutectic Solvents

There is great interest in DNA nanotechnology, but its use has been limited to aqueous or substantially hydrated media. The first assembly of a DNA nanostructure in a water‐free solvent, namely a low‐volatility biocompatible deep‐eutectic solvent composed of a 4:1 mixture of glycerol and choline chloride (glycholine), is now described. Glycholine allows for the folding of a two‐dimensional DNA origami at 20 °C in six days, whereas in hydrated glycholine, folding is accelerated (≤3 h). Moreover, a three‐dimensional DNA origami and a DNA tail system can be folded in hydrated glycholine under isothermal conditions. Glycholine apparently reduces the kinetic traps encountered during folding in aqueous solvent. Furthermore, folded structures can be transferred between aqueous solvent and glycholine. It is anticipated that glycholine and similar solvents will allow for the creation of functional DNA structures of greater complexity by providing a milieu with tunable properties that can be optimized for a range of applications and nanostructures.     

Selection of G-quadruplex folding topology with LNA-modified human telomeric sequences in K+ solution

G-rich nucleic acid oligomers can form G-quadruplexes built by G-tetrads stacked upon each other. Depending on the nucleotide sequence, G-quadruplexes fold mainly with two topologies: parallel, in which all G-tracts are oriented parallel to each other, or antiparallel, in which one or more G-tracts are oriented antiparallel to the other G-tracts. In the former topology, all glycosidic bond angles conform to anti conformations, while in the latter topology they adopt both syn and anti conformations. It is of interest to understand the molecular forces that govern G-quadruplex folding. Here, we approach this problem by examining the impact of LNA (locked nucleic acid) modifications on the folding topology of the dimeric model system of the human telomere sequence. In solution, this DNA G-quadruplex forms a mixture of G-quadruplexes with antiparallel and parallel topologies. Using CD and NMR spectroscopies, we show that LNA incorporations can modulate this equilibrium in a rational manner and we establish a relationship between incorporation of LNA nucleotides in syn and/or anti positions and the shift of the equilibrium to obtain exclusively the parallel G-quadruplex. The change in topology is driven by a combination of the C3'-endo puckering of LNA nucleotides and their preference for the anti glycosidic conformation. In addition, the parallel LNA-modified G-quadruplexes are thermally stabilised by about 11 °C relative to their DNA counterparts.     

Oligomeric cholates: amphiphilic foldamers with nanometer-sized hydrophilic cavities

The hydroxyl at the C-3 of cholic acid was converted to an amino group, and the resulting amino-functionalized cholic acid was used as a monomer to prepare amide-linked oligomeric cholates. These cholate oligomers fold into helical structures with nanometer-sized hydrophilic internal cavities in solvent mixtures consisting of mostly nonpolar solvents such as carbon tetrachloride or ethyl acetate/hexane and 2-5% of a polar solvent such as methanol or DMSO. The conformations of the foldamers were studied by UV, fluorescence, fluorescence quenching, and fluorescence resonance energy transfer. The nature of the polar/nonpolar solvents and their miscibility strongly influenced the folding reaction. Folding was cooperative, as evidenced by the sigmoidal curves in solvent denaturation experiments. The folded conformers became more stable with an increase in the chain length. The folding/unfolding equilibrium was highly sensitive toward the amount of polar solvent. One percent variation in the solvent composition could change the folding free energies by 0.5-1.4 kcal/mol.     

Viscosity scaling for the glassy phase of protein folding

Although commendable progress has been made in the understanding of the physics of protein folding, a key unresolved issue is whether Kramers' diffusion model of chemical reactions is generally applicable to activated barrier crossing events during folding. To examine the solvent viscosity effect on the folding transition of native-like trapped intermediates, laser flash photolysis has been used to measure the microsecond folding kinetics of a natively folded state of CO-liganded ferrocytochrome c (M-state) in the 1-250 cP range of glycerol viscosity at pH 7.0, 20 degrees C. The single rate coefficient for the folding of the M-state to the native state of the protein (i.e., the M --> N folding process) decreases initially when the solvent viscosity is low (<10 cP), but saturates at higher viscosity, indicating that Kramers model is not general enough for scaling the viscosity dependence of post-transition folding involving glassy dynamics. Analysis based on the Grote-Hynes idea of time dependent friction in conjunction with defect diffusion dynamics can account for the observed non-Kramers scaling.     

Kinetic and thermodynamic control of g-quadruplex folding

A matter of speed: When allowed to fold in a K(+) /poly(ethylene glycol) solution, the guanine?(G)-rich strand of vertebrate telomere DNA forms a parallel/antiparallel G-quadruplex, which is a (3+1) hybrid, within microseconds before slowly transforming into the parallel one within hours. Thus, the conformation that a G-quadruplex initially adopts under physiological conditions may not be the one it adopts at the equilibrium state.     

Structure of human telomeric DNA in crowded solution

G-quadruplex structures formed by DNA at the human telomeres are attractive anticancer targets. Human telomeric sequences can adopt a diverse range of intramolecular G-quadruplex conformations: a parallel-stranded conformation was observed in the crystalline state, while at least four other forms were seen in K(+) solution, raising the question of which conformation is favored in crowded cellular environment. Here, we report the first NMR structure of a human telomeric G-quadruplex in crowded solution. We show that four different G-quadruplex conformations are converted to a propeller-type parallel-stranded G-quadruplex in K(+)-containing crowded solution due to water depletion. This study also reveals the formation of a new higher-order G-quadruplex structure under molecular crowding conditions. Our molecular dynamics simulations of solvent distribution provide insights at molecular level on the formation of parallel-stranded G-quadruplex in environment depleted of water. These results regarding human telomeric DNA can be extended to oncogenic promoters and other genomic G-rich sequences.     

Small change in a G-rich sequence,a dramatic change in topology: new dimeric G-quadruplex folding motif with unique loop orientations

NMR study has shown that DNA oligonucleotide d(G(3)T(4)G(4)) adopts an asymmetric bimolecular G-quadruplex structure in solution. The structure of d(G(3)T(4)G(4))(2) is composed of three G-quartets, overhanging G11 residue and G3, which is part of the loop. Unique structural feature of d(G(3)T(4)G(4))(2) fold is the orientation of the two loops. Thymidine residues T4-T7 form a diagonal loop, whereas T15-T18 form an edge type loop. The G-quadruplex core of d(G(3)T(4)G(4))(2) consists of two stacked G-quartets with syn-anti-anti-anti alternation of dG residues and one G-quartet with syn-syn-anti-anti alternation. Another unusual structural feature of d(G(3)T(4)G(4))(2) is a leap between G19 and G20 over the middle G-quartet and chain reversal between G19 and G20 residues. The presence of one antiparallel and three parallel strands reveals the hitherto unknown G-quadruplex folding motif consisting of antiparallel/parallel strands and diagonal as well as edge type loops. Further examination of the influence of different monovalent cations on the folding of d(G(3)T(4)G(4)) showed that it forms a bimolecular G-quadruplex in the presence of K+, Na+, and NH4+ ions with the same general fold.     

Helical Folding of Conjugated Oligo(phenyleneethynylene): Chain‐Length Dependence,Solvent Effects,and Intermolecular Assembly

As a representative folding system that features a conjugated backbone, a series of monodispersed (o‐phenyleneethynylene)‐alt‐(p‐phenyleneethynylene) (PE) oligomers of varied chain length and different side chains were studied. Molecules with the same backbone but different side‐chain structures were shown to exhibit similar helical conformations in respectively suitable solvents. Specifically, oligomers with dodecyloxy side chains folded into the helical structure in apolar aliphatic solvents, whereas an analogous oligomer with tri(ethylene glycol) (Tg) side chains adopted the same conformation in polar solvents. The fact that the oligomers with the same backbone manifested a similar folded conformation independent of side chains and the nature of the solvent confirmed the concept that the driving force for folding was the intramolecular aromatic stacking and solvophobic interactions. Although all were capable of inducing folding, different solvents were shown to bestow slightly varied folding stability. The chain‐length dependence study revealed a nonlinear correlation between the folding stability with backbone chain length. A critical size of approximately 10 PE units was identified for the system, beyond which folding occurred. This observation corroborated the helical nature of the folded structure. Remarkably, based on the absorption and emission spectra, the effective conjugation length of the system extended more effectively under the folded state than under random conformations. Moreover, as evidenced by the optical spectra and dynamic light‐scattering studies, intermolecular association took place among the helical oligomers with Tg side chains in aqueous solution. The demonstrated ability of such a conjugated foldamer in self‐assembling into hierarchical supramolecular structures promises application potential for the system.     

Protonation/deprotonation effects on the stability of the Trp-cage miniprotein

The Trp-cage miniprotein is a 20 amino acid peptide that exhibits many of the properties of globular proteins. In this protein, the hydrophobic core is formed by a buried Trp side chain. The folded state is stabilized by an ion pair between aspartic acid and an arginine side chain. The effect of protonating the aspartic acid on the Trp-cage miniprotein folding/unfolding equilibrium is studied by explicit solvent molecular dynamics simulations of the protein in the charged and protonated Asp9 states. Unbiased Replica Exchange Molecular Dynamics (REMD) simulations, spanning a wide temperature range, are carried out to the microsecond time scale, using the AMBER99SB forcefield in explicit TIP3P water. The protein structural ensembles are studied in terms of various order parameters that differentiate the folded and unfolded states. We observe that in the folded state the root mean square distance (rmsd) from the backbone of the NMR structure shows two highly populated basins close to the native state with peaks at 0.06 nm and 0.16 nm, which are consistent with previous simulations using the same forcefield. The fraction of folded replicas shows a drastic decrease because of the absence of the salt bridge. However, significant populations of conformations with the arginine side chain exposed to the solvent, but within the folded basin, are found. This shows the possibility to reach the folded state without formation of the ion pair. We also characterize changes in the unfolded state. The equilibrium populations of the folded and unfolded states are used to characterize the thermodynamics of the system. We find that the change in free energy difference due to the protonation of the Asp amino acid is 3 kJ mol(-1) at 297 K, favoring the charged state, and resulting in ΔpK(1) = 0.5 units for Asp9. We also study the differences in the unfolded state ensembles for the two charge states and find significant changes at low temperature, where the protonated Asp side chain makes multiple hydrogen bonds to the protein backbone.     

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.     

Molecular dynamics simulation of folding of a short helical peptide with many charged residues

A molecular dynamics simulation of the folding of conantokin-T (con-T), a short helical peptide with 5 helical turns of 21 amino acids with 10 charged residues, was carried out to examine folding pathways for this peptide and to predict the folding rate. In the 18 trajectories run at 300 K, 16 trajectories folded, with an averaged folding time of approximately 50 ns. Two trajectories did not fold in up to 200 ns simulation. The folded structure in folded trajectories is in good agreement with experimental structure. An analysis of the trajectories showed that, at the beginning of a few nanoseconds, helix formation started from residues 5-9 with assistance of a hydrophobic clustering involving Tyr5, Met8, and Leu9. The peptide formed a U-shape mainly due to charge-charge interactions between charged residues at the N- and C-terminus segments. In the next approximately 10 ns, several nonnative charge-charge interactions were broken and nonnative Gla10-Lys18 (this denotes a salt bridge between Gal10 and Lys18) and/or Gla10-Lys19 interactions appeared more frequently in this folding step and the peptide became a fishhook J-shape. From this structure, the peptide folded to the folded state in 7 of all 16 folded trajectories in approximately 15 ns. Alternatively, in approximately 30 ns, the con-T went to a conformation in an L-shape with 4 helical turns and a kink at the Arg13 and Gla14 segment in the other 9 trajectories. Con-T in the L-shape then required another approximately 15 ns to fold into the folded state. In addition, in overall folding times, the former 7 trajectories folded faster with the total folding times all shorter than 45 ns, while the latter 9 trajectories folded at a time longer than 45 ns, resulting in an average folding time of approximately 50 ns. Two major folding intermediates found in 2 nonfolded trajectories are stabilized by charge clusters of 5 and 6 charged residues, respectively. With inclusion of friction and solvent-solvent interactions, which were ignored in the present GB/SA solvation model, the folding time obtained above should be multiplied by a factor of 1.25-1.7 according to a previous, similar simulation study. This results in a folding time of 65-105 ns, slightly shorter than the folding time of 127 ns for an alanine-based peptide of the same length. This suggests that the energy barrier of folding for this type of peptides with many charged residues is slightly lower than alanine-based helical peptides by less than 1 kcal/mol.     

Contribution of charged groups to the enthalpic stabilization of the folded states of globular proteins

In this paper we use the results from all-atom molecular dynamics (MD) simulations of proteins and peptides to assess the individual contribution of charged atomic groups to the enthalpic stability of the native state of globular proteins and investigate how the distribution of charged atomic groups in terms of solvent accessibility relates to protein enthalpic stability. The contributions of charged groups is calculated using a comparison of nonbonded interaction energy terms from equilibrium simulations of charged amino acid dipeptides in water (the "unfolded state") and charged amino acids in globular proteins (the "folded state"). Contrary to expectation, the analysis shows that many buried, charged atomic groups contribute favorably to protein enthalpic stability. The strongest enthalpic contributions favoring the folded state come from the carboxylate (COO(-)) groups of either Glu or Asp. The contributions from Arg guanidinium groups are generally somewhat stabilizing, while N(+)(3) groups from Lys contribute little toward stabilizing the folded state. The average enthalpic gain due to the transfer of a methyl group in an apolar amino acid from solution to the protein interior is described for comparison. Notably, charged groups that are less exposed to solvent contribute more favorably to protein native-state enthalpic stability than charged groups that are solvent exposed. While solvent reorganization/release has favorable contributions to folding for all charged atomic groups, the variation in folded state stability among proteins comes mainly from the change in the nonbonded interaction energy of charged groups between the unfolded and folded states. A key outcome is that the calculated enthalpic stabilization is found to be inversely proportional to the excess charge density on the surface, in support of an hypothesis proposed previously.     

Probing the complete folding trajectory of a DNA hairpin using dual beam fluorescence fluctuation spectroscopy

The conformational fluctuations of dye-quencher labeled DNA hairpin molecules in aqueous solution were investigated using dual probe beam fluorescence fluctuation spectroscopy. The measurements revealed the flow and diffusion times of the DNA molecules through two spatially offset optical probe regions, the absolute and relative concentrations of each conformational substate of the DNA, and the kinetics of the DNA hairpin folding and unfolding reactions in the 1 micros to 10 ms time range. A DNA hairpin containing a 21-nucleotide polythymine loop and a 4-base pair stem exhibited double exponential relaxation kinetics, with time constants of 84 and 393 micros. This confirms that folding and melting of the DNA hairpin structure is not a two state process but proceeds by way of metastable intermediate states. The fast time constant corresponds to formation and unfolding of an intermediate, and the slow time constant is due to formation and disruption of the fully base-paired stem. This is consistent with a previous study of a similar DNA hairpin with a 5-base pair stem, in which the fast reaction was attributed to the fluctuations of an intermediate DNA conformation [J. Am. Chem. Soc. 2006, 128, 1240-1249]. In that case, reactions involving the native conformation could not be observed directly due to the limited observation time range of the fluorescence correlation spectroscopy experiment. The intermediate states of the DNA hairpins are suggested to be due to a collapsed ensemble of folded hairpins containing various partially folded or misfolded conformations.     

Energetic basis of human telomeric DNA folding into G-quadruplex structures

Recent theoretical studies performed on the folding/unfolding mechanism of the model telomeric human DNA, 5'-AGGGTTAGGGTTAGGGTTAGGG-3' (Tel22), have indicated that in the presence of K(+) ions Tel22 folds into two hybrid G-quadruplex structures characterized by one double and two reversal TTA loops arranged in a different way. They predicted a new unfolding pathway from the initial mixture of hybrid G-quadruplexes via the corresponding intermediate triplex structures into the final, fully unfolded state. Significantly, no experimental evidence supporting the suggested pathway has been reported. In the current work, we performed a comprehensive global thermodynamic analysis of calorimetric (DSC, ITC) and spectroscopic (CD) data obtained on monitoring the folding/unfolding of Tel22 induced by changes of temperature and K(+) concentration. We show that unfolding of Tel22 may be described as a monomolecular equilibrium three-state process that involves thermodynamically distinguishable folded (F), intermediate (I), and unfolded (U) state. Considering that calorimetric methods cannot distinguish between energetically similar G-quadruplex or triplex conformations predicted by the theoretical model one can conclude that our results represent the first experimental support of the suggested unfolding/folding mechanism of Tel22. This conclusion is confirmed by the fact that the estimated number of K(+) ions released upon each unfolding step in our thermodynamic model agrees well with the corresponding values predicted by the theoretical model and that the observed changes in enthalpy, entropy, and heat capacity accompanying the F → I and I → U transitions can be reasonably explained only if the intermediate state I is considered to be a triplex structural conformation.     

New insights into the effect of molecular crowding environment induced by dimethyl sulfoxide on the conformation and stability of G-quadruplex

Various structures of G-quadruplex in biosystems play an important role in different diseases and are often regulated by a variety of molecular crowding environments induced by internal and even external factors (e.g., a solvent). Dimethyl sulfoxide (DMSO), a universal solvent, has been widely used in biological studies and for drug therapy, but little is known regarding its effect on G-quadruplex structure and stability. Here, we report the influence of molecular crowding environment induced by DMSO on the conformation and stability of G-quadruplex structure. We show that the G-quadruplex-forming sequences such as human telomeric sequence, which may have diverse conformations in different environments, tend to convert their topologies to parallel structures under the molecular crowding stimulated by DMSO. Moreover, DMSO can increase the stability of the parallel and antiparallel topologies, especially the parallel G-quadruplex sequence c-kit, but not the hybrid topologies. Further analysis of c-kit using the CD and NMR technique, combined with the unique structural characteristics of c-kit, reveals that the crowding, dehydration and interaction of DMSO are conductive to the formation and stability of the parallel G-quadruplex. The present study suggests that, DMSO, a common solvent used in DNA experiments, may have a nonnegligible influence on the structure and stability of G-quadruplex.     

Concepts and misconcepts in the analysis of simple kinetics of protein folding

Unusually simple two-state kinetics characterizes the folding of a number of small proteins possessing a variety secondary structures. This limits dramatically the number of experimentally resolvable parameters that may characterize this process and also suggests the possibility to describe it based on simple theories borrowed from the field of ordinary chemical reactions. An attempt is made to critically evaluate the basic concepts, which are in the background of this approach. We demonstrate their limitations, which may cast doubt on the interpretation of experimental data. It is shown also that, in contrast to provisions of transition state theory, the simple kinetics of protein folding does not correlate with folded state stability or with the size of the folding unit. Moreover, the folding kinetics exhibits anomalous dependence on temperature and pressure and surprisingly strong dependence on solvent viscosity. The possible role in folding of fluctuations, relaxations and gradient dynamics is discussed. Being overlooked or underestimated, these mechanisms may determine the rate and specificity of the process.     

Estimation of protein folding rate from Monte Carlo simulations and entropy capacity

The problem of protein self-organization is one of the most important problems of molecular biology nowadays. Despite the recent success in the understanding of general principles of protein folding, details of this process are yet to be elucidated. Moreover, the prediction of protein folding rates has its own practical value due to the fact that aggregation directly depends on the rate of protein folding. The time of folding has been calculated for 67 proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native states using a Monte Carlo model where each residue is considered to be either folded as in the native state or completely disordered. The times of folding for 67 proteins which reach the native state within the limit of 10(8) Monte Carlo steps are in a good correlation with the experimentally measured folding rate at the mid-transition point (the correlation coefficient is -0.82). Theoretical consideration of a capillarity model for the process of protein folding demonstrates that the difference in the folding rate for proteins sharing more spherical and less spherical folds is the result of differences in the conformational entropy due to a larger surface of the boundary between folded and unfolded phases in the transition state for proteins with more spherical fold. The capillarity model allows us to predict the folding rate at the same level of correlation as by Monte Carlo simulations. The calculated model entropy capacity (conformational entropy per residue divided by the average contact energy per residue) for 67 proteins correlates by about 78% with the experimentally measured folding rate at the mid-transition point.     

Conformational Dynamics of DNA G-Quadruplex in Solution Studied by Kinetic Capillary Electrophoresis Coupled On-line with Mass Spectrometry

Invited for this months cover is the group of Prof. Maxim V. Berezovski. The cover picture shows the two-dimensional separation of unfolded (green) and folded (red) forms of G-quadruplex (GQ) DNA. The first dimension is kinetic capillary electrophoresis (KCE) separation of unfolded and folded DNA with different K⁺ concentrations in solution; the second dimension is ion mobility mass spectrometry separation of DNA conformers in the gas phase. DNA folding into a compact GQ structure is mediated by K⁺ ions. For more details, see the Full Paper on p. 58 ff.