Length dependent folding kinetics of phenylacetylene oligomers: structural characterization of a kinetic trap

Using simulation to study the folding kinetics of 20-mer poly-phenylacetylene (pPA) oligomers, we find a long time scale trapped kinetic phase in the cumulative folding time distribution. This is demonstrated using molecular dynamics to simulate an ensemble of over 100 folding trajectories. The simulation data are fit to a four-state kinetic model which includes the typical folded and unfolded states, along with an intermediate state, and most surprisingly, a kinetically trapped state. Topologically diverse conformations reminiscent of alpha helices, beta turns, and sheets in proteins are observed, along with unique structures in the form of knots. The nonhelical conformations are implicated, on the basis of structural correlations to kinetic parameters, to contribute to the trapped kinetic behavior. The strong solvophobic forces which mediate the folding process and produce a stable helical folded state also serve to overstabilize the nonhelical conformations, ultimately trapping them. From our simulations, the folding time is predicted to be on the order of 2.5-12.5 mus in the presence of the trapped kinetic phase. The folding mechanism for these 20-mer chains is compared with the previously reported folding mechanism for the pPA 12-mer chains. A linear scaling relationship between the chain length and the mean first passage time is predicted in the absence of the trapped kinetic phase. We discuss the major implications of this discovery in the design of self-assembling nanostructures.     

Oligo-Quinolylene–Vinylene Foldamers

Quinoline based aromatic amide foldamers are known to adopt stable folded conformations. We have developed a synthetic approach to produce similar oligomers where all amide bonds, or part of them, have been replaced by an isosteric vinylene group. The results of solution and solid state structural studies show that oligomers exclusively containing vinylene linkages are not well folded, and adopt predominantly flat conformations. In contrast, a vinylene segment flanked by helical oligoamides also folds in a helix, albeit with a slightly lower curvature. The presence of vinylene functions also result in an extension of π-conjugation across the oligomer that may change charge transport properties. Altogether, these results pave the way to foldamers in which both structural control and specific electronic properties may be engineered.     

Helical conformational dynamics and photoisomerism of alternating pyridinedicarboxamide/m-(phenylazo)azobenzene oligomers

Alternating sequences of pyridine-2,6-dicarboxamides and meta-(phenylazo)azobenzenes have been assembled into oligomers composed of four (8) and eight (9) azobenzene linkages. X-ray crystallography confirmed that oligomer 8 adopts a two-turn helical conformation with a helical pitch of approximately 3.4 Angstroms in the solid state. The presence of a two- and four-turn helical conformation of 8 and 9, respectively, in polar and nonpolar solvents was elucidated by the anisotropic upfield shifting of protons located within the helices, NOE enhancements between protons oriented toward the helix interior, and the diastereotopicity of the terminal benzyloxycarbonyl (CBz) methylene protons. (1)H NMR line shape analysis of the CBz methylene hydrogens at the chain ends revealed a dynamic equilibria interconverting M and P helical conformations with energetic barriers (DeltaG) of 11.1 (DeltaS = -19.4 +/- 1.6 cal mol(-1) K(-1); DeltaH = 6.5 +/- 0.4 kcal/mol) for 8 and 13.8 kcal/mol (DeltaS = -6.6 +/- 6.2 cal mol(-1) K(-1); DeltaH = 11.8 +/- 1.8 kcal/mol) for 9. Irradiation of the oligomers with 350 nm light induces an E --> Z isomerization of the azo linkages that decreases in efficacy at longer helix lengths. The suppression of E --> Z isomerization is a consequence of the contrasting behavior of the azo linkages located at the helix termini, which afford Z/E ratios similar to those of model compound 7d, and the internal azo groups, which undergo significantly lower Z/E conversion ratios compared with 7e.     

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.     

Kinetics of Helix‐Handedness Inversion: Folding and Unfolding in Aromatic Amide Oligomers

A series of helically folded oligoamides of 8‐amino‐2‐quinoline carboxylic acid possessing 6, 7, 8, 9, 10 or 16 units are prepared following convergent synthetic schemes. The right‐handed (P) and the left‐handed (M) helical conformers of these oligomers undergo an exchange slow enough to allow their chromatographic separation on a chiral stationary phase. Thus, the M conformer is isolated for each of these oligomers and its slow racemization in hexane/CHCl₃ solutions is monitored at various temperatures using chiral HPLC. The kinetics of racemization at different temperatures in hexane/CHCl₃ (75:25 vol/vol) are fitted to a first order kinetic model to yield the kinetic constant and the Gibbs energy of activation for oligomers having 6, 7, 8, 9, 10 or 16 quinoline units. This energy gives the first quantitative measure of the exceptional stability of the helical conformers of an aromatic amide foldamer with respect to its partly unfolded conformations that occur between an M helix and a P helix. The trend of the Gibbs energy as a function of oligomer length suggests that helix‐handedness inversion does not require a complete unfolding of a helical strand and may instead occur through the propagation of a local unfolding separating two segments of opposite handedness.     

Unravelling Secondary Structure Changes on Individual Anionic Polysaccharide Chains by Atomic Force Microscopy

The structural conformations of the anionic carrageenan polysaccharides in the presence of monovalent salt close to physiological conditions are studied by atomic force microscopy. Iota‐carrageenan undergoes a coil–helix transition at high ionic strength, whereas lambda‐carrageenan remains in the coiled state. Polymer statistical analysis reveals an increase in persistence length from 22.6±0.2 nm in the random coil, to 26.4±0.2 nm in the ordered helical conformation, indicating an increased rigidity of the helical iota‐carrageenan chains. The many decades‐long debated issue on whether the ordered state can exist as single or double helix, is conclusively resolved by demonstrating the existence of a unimeric helix formed intramolecularly by a single polymer chain.     

Foldamer simulations: novel computational methods and applications to poly-phenylacetylene oligomers

We apply several methods to probe the ensemble kinetic and structural properties of a model system of poly-phenylacetylene (pPA) oligomer folding trajectories. The kinetic methods employed included a brute force accounting of conformations, a Markovian state matrix method, and a nonlinear least squares fit to a minimalist kinetic model used to extract the folding time. Each method gave similar measures for the folding time of the 12-mer chain, calculated to be on the order of 7 ns for the complete folding of the chain from an extended conformation. Utilizing both a linear and a nonlinear scaling relationship between the viscosity and the folding time to correct for a low simulation viscosity, we obtain an upper and a lower bound for the approximate folding time within the range 70 ns相似文献   

Crystallization of helical oligomers with chirality selection. I. A molecular dynamics simulation for bare helix

Helical polymers often exhibit pronounced chirality recognition during crystallization. By molecular dynamics simulation, we have already shown that the helical polymers crystallize with or without marked chirality selection depending on structural details of the polymer molecules. We have there classified the helical polymers into two categories: the bare helices made of only backbone atoms which show rather tolerant chirality selection, and the general helices with large side groups showing strict chirality recognition. Polymer crystallization is in general largely hampered and retarded by slow dynamics of the entangled chains, and therefore short helical oligomers are very suitable models for studying the chiral crystallization. We here report on molecular simulations of crystallization in the bare helical oligomer molecules by the use of Monte Carlo and molecular dynamics simulations. First we confirm the low temperature chiral crystal phase and the reversible order-disorder transition. We also observe frequent inversions of the helical sense, and the helix reversal defects propagating along the chains. Then we investigate crystallization from the melt into the chiral crystal phase. We find that the crystallization rate depends very sensitively on the degree of undercooling. The crystallization is found to be the first order transition that conforms well to the traditional picture of crystal growth in small molecules. Even when the crystallization directly into the chiral crystal phase is conducted, marked chirality selections are not observed at the early stage of crystallization; the chains adhere to the crystal surfaces selecting their helical senses rather at random resulting in racemic crystallites. The isothermal crystallization for a sufficiently long time, however, yields lamellar crystals composed of well-developed chiral domains, the growth of which seems to be accomplished through the transition back into the ordered chiral crystal phase.     

Sequence-specific binding of m-phenylene ethynylene foldamers to a piperazinium dihydrochloride salt

[reaction: see text] Binding properties of a series of isomeric m-phenylene ethynylene oligomers containing short amide sequences to a piperazinium dihydrochloride salt were investigated by using circular dichroism (CD) measurements. Although these isomeric oligomers exhibited similar helical conformations, high affinity was observed only for one oligomer. This behavior is presumably controlled by the orientation of amino groups of the amide sequence and the folded conformation of the oligomer.     

Encapsulation of small polar guests in molecular apple peels

Three aromatic oligoamides have been prepared that have alternating 1,6-diaminopyridine and 1,6-pyridinedicarboxylic acid units at the center of the sequence and two 8-amino-2-quinolinecarboxylic acid units at each extremity. The three oligomers differ in the number--3, 5, or 7-of pyridine units in the sequence. They were designed to adopt helically folded conformations in solution and in the solid state. The sequence of monomers was chosen so that the diameter of the helix is larger in the center than at each extremity, and hence they resemble helically wrapped apple peels. According to modeling studies, the pyridine units were expected to define a polar hollow within the helix that is large enough to accommodate small polar guests, whereas the quinoline units at each end of the oligomeric sequences were expected to completely cap the hollow and transform the helix cavities into a closed shell that may act as a capsule. Crystallographic studies demonstrate that the oligomers do fold into helices that define a cavity isolated from the surrounding medium in the solid state. Depending on the number of pyridine rings, one or two water molecules are bound within the capsules. The crystal structure of a capsule fragment shows that MeOH can also be hosted by the largest oligomer. Solution NMR studies confirm that binding of water also occurs in solution with the same stoichiometry as observed in the solid state. The capsules have distinct signals depending on whether they are empty, half-full, or full, and these species are in slow exchange on the NMR timescale at low temperature. Indeed, the binding and release of water molecules requires a significant conformational distortion of the helix that slows down these processes. The addition of small polar molecules such as methanol, hydrazine, hydrogen peroxide, or formic acid to the largest capsule leads to the observation of new sets of NMR signals of the capsules that were assigned to complexes with these guests. However, water appears to be the preferred guest.     

Self-assembly of folded m-phenylene ethynylene oligomers into helical columns

Circular dichroism spectroscopy has been used to study the self-assembly of two series of m-phenylene ethynylene oligomers in highly polar solvents. The helical conformation of shorter oligomer lengths was found to be stabilized in aqueous acetonitrile solutions, while longer oligomers began to interact intermolecularly. The intermolecular aggregation of the oligomers in aqueous solutions revealed a chain length dependent association that required the presence of a stable helical conformation. Evidence for intermolecular interactions is provided by Sergeants and Soldiers experiments in which the twist sense bias of a chiral oligomer is transferred to an achiral oligomer.     

alpha and piDL helical states of alternating poly(gamma-benzyl D-L-glutamate) in solution.

As in solid state, strictly alternating poly(gamma-benzyl D-L-glutamate) in solution can adopt two different helical conformations. Besides the alpha helix, a second helical conformation is found at higher temperatures in dioxane and chloroform, the properties of which correspond to that of the piDL4 helix. As the molecules have a finite length a screw sense is favored for both helical forms thus giving rise to optical activity allowing the study of the transconformation by optical rotatory dispersion and circular dichroism besides infrared and dielectric measurements. Thus, as the temperature is raised the equilibria right-left handed alpha helices and alpha-piDL helical forms can be followed. The favored screw senses are determined by the number of interacting side chains for the alpha helix and by the number of hydrogen bonds which are formed in the piDL helical conformation. The side chain-side chain interactions in the alpha helix are experimentally shown to be attractive.     

Fine Tuning of β‐Peptide Foldamers: a Single Atom Replacement Holds Back the Switch from an 8‐Helix to a 12‐Helix

Cyclic homologated amino acids are important building blocks for the construction of helical foldamers. N‐aminoazetidine‐2‐carboxylic acid (AAzC), an aza analogue of trans‐2‐aminocyclobutanecarboxylic acid (tACBC), displays a strong hydrazino turn conformational feature, which is proposed to act as an 8‐helix primer. tACBC oligomers bearing a single N‐terminal AAzC residue were studied to evaluate the ability of AAzC to induce and support an 8‐helix along the oligopeptide length. While tACBC homooligomers assume a dominant 12‐helix conformation, the aza‐primed oligomers preferentially adopt a stabilized 8‐helix conformation for an oligomer length up to 6 residues. The (formal) single‐atom exchange at the N terminus of a tACBC oligomer thus contributes to the sustainability of the 8‐helix, which resists the switch to a 12‐helix. This effect illustrates atomic‐level programmable design for fine tuning of peptide foldamer architectures.     

From helix to macrocycle: anion-driven conformation control of π-conjugated acyclic oligopyrroles

Anion-responsive pyrrole-based linear receptor oligomers were newly synthesized and their anion-driven dynamic conformation changes were investigated. Phenylene-bridged dimers and a tetramer of dipyrrolyldiketone boron complexes as π-conjugated acyclic anion receptors formed anion-driven helical structures in the solid and solution states. In fact, single-crystal X-ray analyses of the receptor-anion complexes exhibited various helical structures, such as [1+1]- and [1+2]-type single helices and a [2+2]-type double helix according to the lengths of oligomers and the existence of terminal aryl substituents. Anion-binding modes and behaviors of the oligomers in solution state were also examined by (1)H NMR and UV/Vis spectra along with ESI-TOF MS. Differences in the binding modes were observed in the solid and solution states. The oligomers showed augmented anion-binding constants and anion-tunable electronic and optical properties in comparison with the monomer receptor. A negative cooperative effect in the tetramer was observed in the second anion binding of the [1+2]-type single helix due to electrostatic repulsion between two anions captured in the helix. Further, an anion-template coupling reaction from the linear dimer provided a receptor macrocycle, which was obtained as a Cl(-) complex with distinct electronic and optical properties. The macrocycle exhibited extremely high anion-binding constants (>10(10) m(-1) in CH(2)Cl(2)) through multiple hydrogen bonding.     

Flaws in foldamers: conformational uniformity and signal decay in achiral helical peptide oligomers

Although foldamers, by definition, are extended molecular structures with a well-defined conformation, minor conformers must be populated at least to some extent in solution. We present a quantitative analysis of these minor conformers for a series of helical oligomers built from achiral but helicogenic α-amino acids. By measuring the chain length dependence or chain position dependence of NMR or CD quantities that measure screw-sense preference in a helical oligomer, we quantify values for the decay constant of a conformational signal as it passes through the molecular structure. This conformational signal is a perturbation of the racemic mixture of M and P helices that such oligomers typically adopt by the inclusion of an N or C terminal chiral inducer. We show that decay constants may be very low (<1% signal loss per residue) in non-polar solvents, and we evaluate the increase in decay constant that results in polar solvents, at higher temperatures, and with more conformationally flexible residues such as Gly. Decay constants are independent of whether the signal originates from the N or the C terminus. By interpreting the decay constant in terms of the probability with which conformations containing a screw-sense reversal are populated, we quantify the populations of these alternative minor conformers within the overall ensemble of secondary structures adopted by the foldamer. We deduce helical persistence lengths for Aib polymers that allow us to show that in a non-polar solvent a peptide helix, even in the absence of chiral residues, may continue with the same screw sense for approximately 200 residues.     

Helical Folding Competing with Unfolded Aggregation in Phenylene Ethynylene Foldamers

The folding and aggregation behavior of a pair of oligo(phenylene ethynylene) (OPE) foldamers are investigated by means of UV/Vis absorption and circular dichroism spectroscopy. With identical OPE backbones, two foldamers, 1 with alkyl side groups and 2 with triethylene glycol side chains, manifest similar helical conformations in solutions in n‐hexane and methanol, respectively. However, disparate and competing folding and aggregation processes are observed in alternative solvents. In cyclohexane, oligomer 1 initially adopts the helical conformation, but the self‐aggregation of unfolded chains, as a minor component, gradually drives the folding–unfolding transition eventually to the unfolded aggregate state completely. In contrast, in aqueous solution (CH₃OH/H₂O) both folded and unfolded oligomer 2 appear to undergo self‐association; aggregates of the folded chains are thermodynamically more stable. In solutions with a high H₂O content, self‐aggregation among unfolded oligomers is kinetically favored; these oligomers very slowly transform into aggregates of helical structures with greater thermodynamic stability. The folded–unfolded conformational switch thus takes place with the free (nonaggregated) molecules, and the very slow folding transition is due to the low concentration of molecularly dispersed oligomers.     

Helical aromatic oligoamides: reliable, readily predictable folding from the combination of rigidified structural motifs

Factors responsible for the folding of aromatic oligoamides with backbones rigidified by local three-center H-bonds were investigated. The stability of the three-center H-bonds was quantified by the half-lives of amide proton-deuterium exchange reactions, which show that the three-center H-bonds were largely intact at room temperature in the oligomer examined. This result is consistent with our current and previous 2D NMR studies. The overall helical conformation of nonamer 1 was found by variable-temperature NOESY studies to be dynamic. As temperature rose, the end-to-end NOEs rapidly disappeared, while the amide side chain NOEs were still readily detectable, corresponding to the "breath" and stretching of the helix by slightly twisting the local H-bonded rings. Based on the simple repetition of the same structural motif and local conformational preference, undecamer 2 was found to fold into well-defined helical conformation. The predictability of the folding of these backbone-rigidified aromatic oligoamides was demonstrated by a simple modeling method using structural parameters from oligomers with known crystal structures. The reliability and generality of the modeling methods were shown by the excellent agreement between the modeled structures corresponding to 1 and 2 and data from NOESY studies.     

Molecular dynamics simulations of helix-forming, amine-functionalized m-poly(phenyleneethynylene)s

We present here the results of all-atom and united-atom molecular dynamics (MD) simulations that were used to examine the folding behavior of an amine-functionalized m-poly(phenyleneethynylene) (m-PPE) oligomer in aqueous environment. The parallelized GROMACS MD simulation code and OPLS force field were used for multiple MD simulations of m-PPE oligomers containing 24 phenyl rings in extended, coiled and helix conformations separately in water to determine the minimum energy conformation of the oligomer in aqueous solvent and what interactions are most important in determining this structure. Simulation results showed that the helix is the preferred minimum energy conformation of a single oligomer in water and that Lennard-Jones interactions are the dominant forces for the stabilization of the helix. In addition, these solvophobic interactions are strong enough to maintain the helix conformation at temperatures up to 523 K.     

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.     

Hydrogen bonding and the conformations of poly(alkyl acrylamides)

The conformations of poly(alkyl acrylamide) oligomers in nonpolar solvents were studied using molecular dynamics techniques. Poly(methyl acrylamide) was found to collapse to a globule-like conformation at low temperatures; however, excluded volume effects inhibited the collapse of poly(octadecyl acrylamide). A high density of structured units, characterized by a trans-gauche-trans-trans-gauche-trans torsional sequence along the backbone, was noted in all simulations. Such units were found to create a particularly stable set of intramolecular hydrogen bonds. An oligomer constructed with these stable units was found to have significantly lower minimized energy than both the all-trans and the helical backbone conformations. The constructed conformation had lower Coulomb energy (more hydrogen bonds) than the all-trans conformation and lower dihedral energy (less backbone distortion) than the helical conformation. The propensity for poly(octadecyl acrylamide) to form hydrogen bonds introduced significant disorder into the orientation of the alkyl side chains. This disorder would inhibit crystallization and restrict the ability of such polymers to form epitaxial seeds for nucleating paraffin crystals.