Molecular Mechanism of Self-Assembly of ... - ACS Publications

Subscriber access provided by Gothenburg University Library

Article

Molecular Mechanism of Self-Assembly of Aromatic Oligoamides Into Interlocked Double-Helix Foldamers Dongbo Zhao, Ling Yang, Yigao Yuan, Hanchen Wang, Hao Dong, and Shuhua Li J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b09067 • Publication Date (Web): 11 Oct 2017 Downloaded from http://pubs.acs.org on October 15, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Molecular Mechanism of Self-assembly of Aromatic Oligoamides into Interlocked Double-helix Foldamers Dongbo Zhao1,2, Ling Yang3, Yigao Yuan1, Hanchen Wang1, Hao Dong1,*, Shuhua Li2,* 1

Kuang Yaming Honors School, Nanjing University, 210023, P. R. China; Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, 210023, P. R. China; 3 CAS Key Laboratory of Photochemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China. 2

ABSTRACT: Foldamer, inspired by the structures and functions of biopolymers, is defined as artificial molecular architecture that can fold into a three-dimensional structure in solution, and has been a growing and active field in supramolecular chemistry. Central issue in foldamer science is to understand how the primary sequence of oligomer folds into conformationally ordered structures as well as how individual subunits self-associate into assembly. For duplex structures, these two issues are always interrelated and inseparable with each other. Though the emergence of new foldamer keeps growing, the detailed mechanism remains elusive. Based on an artificially synthesized arylamide oligoamide foldamer with its crystal structure available, we constructed a set of four foldamers with a similar backbone but different substituents, and aimed to dissect the folding and self-association mechanisms of a double-helical foldamer with computations. By using molecular simulations at µs timescale, we observed very consistent processes of the spontaneous self-assembly of two single-helical motifs into an entwined complex. Our results reveal that aggregation of two single-helical motifs driven by extensive π-π interactions is energetically favorable, and that this spontaneous self-assembly proceeds through an ″unwinding-threading-rewinding″ mechanism. The detailed mechanisms about folding and self-assembly in aromatic oligoamide foldamer we present here disclose how the sequence is associated with a well-ordered three-dimensional structure at atomic level, and therefore may have implications for designing new foldamers with versatile functions.

1. INTRODUCTION Biomimetic foldamer research has attracted tremendous attention during the past decades. Despite their molecular diversity, foldamers share some common characteristics that, in general, they could rapidly and spontaneously self-assemble into elaborate three-dimensional structures which could be critical for specific functions. It has uncovered a wide variety of synthetic oligomers with a propensity to fold into various conformations, resembling the folded motifs of biopolymers— helices, linear strands, or turns.1‒3 Since its first synthesis by Hamilton et al.,4 the aromatic amide-based foldamers have expanded various functions in several fields, such as molecular self-assembly and recognition,5‒7 antisense agents in therapeutic spheres,8 cell membranes targeted molecules,9,10 and promoting macro-cyclization.11‒13 Among different architectures, the helical structure is particularly interesting,14‒17 as they are to some extent similar to nucleic acid structures. Therefore, an in-depth understanding of the folding and association mechanism is a prerequisite for a better design of welldefined supramolecular structures formed by foldamers with desired functions. In the literature, extensive studies about single-chain foldamer with computations have been reported. Pande et al. applied markov state models to investigate the folding dynamics of polyphenylacetylene oligomers in different solvents.18‒20 Saven et al. explored the stability of an folded oligo(m-phenylene ethynylene) 18mer helix in water with computer simulations.21 Diezemann et al. has employed forceprobe molecular dynamics to study the unfolding pathways of

peptoids, and peptidic foldamers.12‒24 They suggested that the determining factors are the interplay between the hydrogen bond strength and the backbone rigidity in stabilization of helix conformations. Pophristic et al. carried out systematic studies on arylamide foldamers by using molecular modelling: they investigated the effect of force field parameters on structure properties of foldamers, especially those for the dihedral angles between the amide and aryl groups,25,26 the role of substitution27 and solvent28 for structure stability, the structural preference of foldamer with different aromatic rings as building blocks,29 as well as the binding and release of ligands in the molecular capsules formed by foldamer.30 Recently, they reported a detailed atomistic level description of the handedness inversion mechanism for single-helical arylamide foldamers and found that the simultaneous unfolding and folding of two adjacent aryl-aryl linkages is critical for chiral transformation,31 and further validated their structure design protocol with experiments.32 Nevertheless, the situation becomes more complicated when multiple subunits are involved in self-assembly, as folding/unfolding is invariably coupled with selfassociation/dissociation.33‒37 Acocella et al. calculated a series of stationary points along the intertwining pathway, including minima and transition states, by using molecular mechanics. They identified that the initial insertion is the rate-limiting step, and proposed that the formation of a dimer proceed through a slippage

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 10

Figure 1. (A) The primary sequence of the foldamers.41 Different substituents at the terminal, R1, or the middle, R2, of the chain have been studied, which are named as S1-S4. Some rotatable dihedral angles on the left side of the structure labelled as θ1 to θ4 (θ1 = ∠N=C‒N‒C, θ2 = ∠C‒N‒C=N, θ3 = ∠N‒C‒N=C, and θ4 = ∠C=C‒N‒C), and the counterparts on the right side as θ4' to θ1' (θ4' = ∠C‒N‒C‒C, θ3' = ∠C‒N‒C=N, θ2' = ∠N‒C‒N‒C, and θ1' = ∠C‒N‒C=N), all of which are highlighted in yellow. Similarly, aromatic rings on the left side are marked as ring1 to ring4, respectively, the middle one ring5, and those on the right side ring4' to ring1', respectively. (B) Shown is a double-strand helical foldamer S1 (left, space filling mode colored with blue and yellow, respectively) and its monomeric structure (right, stick model in yellow). mechanism.38 Zhang et al. studied the temperature dependent disassembly of the duplex and the quadruplex forms of 7amino-8-ﬂuoro-2-quinoline carboxylic acid.39 A newly published paper reported that the switching between oligomers and dimeric helicates with distinct handedness could be induced by light.40 However, little is known about the dynamic of folding and unfolding of interlocked double-helical foldamer. Inspired by the work of Huc and coworkers, where synthetic aromatic oligoamides (Figure 1A) could either form a double-strand helical structure (Figure 1B) with high stability in solution, or form a single-strand helix that can act as a molecular shuttle to slide along a rod-shaped guest molecule,41 we aim to addressing two critical questions: (i) How stable is the double-strand foldamer with respect to its monomeric form? (ii) How do the two single-strand subunits aggregate into a foldamer? Based on the crystal structure S1 and its analogs S2-S4, we have employed integrated quantum chemical calculations with the generalized energy-based fragmentation (GEBF) method42‒ 44 and molecular dynamics simulations at µs timescale to evaluate the thermodynamic stability of the system S1 where R1 = C(CH3)3 and R2 = F, and to explore the dynamics of selfassembly of two monomeric helices into a double-strand helix for S1-S4. For the first time, we observed the spontaneous self-assembly process of two single-helical motifs into an entwined complex with molecular simulations. We found that the double-helix structure is energetically favorable than the single-strand helix, mainly because of the extensive π-π interactions formed between two subunits, and that spontaneous self-assembly of two monomeric helices into an entwined dimer proceeds through an "unwinding-threading-rewinding"

mechanism. We verified that the back bone amide(CONH)aryl bond is critical for maintaining structure rigidity (for folding) as well as flexibility (for self-assembly). The present work provides mechanistic understanding towards arylamide foldamers by using aromatic rings as building blocks, which is helpful for designing foldamers with novel architectures and functions.

2. COMPUTATIONAL DETAILS 2.1. Quantum Chemical Computations. To figure out why the monomers easily assemble into double-helix foldamers in solution at experimental conditions,41 electronic structure calculations were performed on the experimentally determined structure S1. Due to the large number of atoms in the doublestrand foldamer S1 (444 atoms), the GEBF method as implemented in our low-scaling quantum chemistry (LSQC) program45 was used for all electronic structure calculations. Both the dimer (Figure 2A) and the monomer structures (Figure 2B) were initially taken from the crystal structure (CCDC NO: 797911) and were then fully optimized at the GEBFB3LYP(D3BJ)/6-31G(d)46,47 level with Grimme's empirical dispersion corrections (D3BJ),48 followed by the single point calculations carried out at the GEBF-M06-2X/6-311++G(d,p) level.49 The basis set superposition error (BSSE) was eliminated by the counterpoise method of Boys and Bernardi.50 The implicit conductor-like polarizable continuum model (CPCM)51 was used to take the solvent effect of CHCl3 into account. Frequency calculations also were carried out with the GEBF method to identify the minimum characteristic of each structure, as well as to get the zero-point vibrational corrections to take the contributions from entropy into account. Fi-


Page 3 of 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


nally, we obtained the solution binding free energy via the equation: ∆G = Gdimer – 2Gmonomer + EBSSE + Esol. Based on the molecular dynamics (MD, further described in below) simulations, 200 snapshots were equidistantly selected from well equilibrated trajectory, where solvent molecules within 3 Å of the dimerized foldamer were selected to build molecular clusters. NMR chemical shielding data of these clusters were obtained at the GEBF-B3LYP(D3BJ)/6-311G(d) level by employing the GIAO (gauge-including atomic orbital) approach.52‒54 The detailed GEBF-NMR protocol is given in Ref. 55. The ensemble average of the calculated chemical shielding data was converted to 1H NMR chemical shift by using tetramethylsilane as a reference. For S1, two subunits in the x-ray structure are both in the M configuration. The handedness of the subunit makes it circular dichroism (CD) active. Electronic circular dichroism (ECD) spectra both for the monomer and dimer were performed at the TD-B3LYP(D3BJ)/6-31G(d) level of theory (Figure 2C). All quantum chemical computations were executed by employing the Gaussian 09 package56 and LSQC program.45 2.2. Molecular Dynamics Simulations. To gain insight into the dynamics of folding/unfolding and the mechanisms thereof, classical MD simulations were carried out. The force field parameters for the foldamer were generated with the general Amber force field (GAFF),57 and the partial charges were generated with restraint electrostatic potential (RESP) method.58,59 Though it has been proposed that force field parameters may affect the structural preference of foldamer,25,26 we found that default torsional parameters generated with GAFF could well describe the secondary structure of foldamer in liquid CHCl3 solution in present work, and the calculated binding free energy with force field method is in line with the quantum mechanical result. Therefore, no further parameterization was carried out. Systems with either explicit or implicit solvent model were set up. Firstly, to explore the dynamic stability of the dimerized structure, explicit solvent model was used, and the foldamer was immersed in CHCl3 box (as used in the original experiments41), with the box size of ~ 35 × 55 × 55 Å3, including ~7000 atoms in all of the four systems, where S1 is shown in Figure 3A for illustration. The periodic boundary conditions were used. Long-range electrostatic interactions were computed using the particle mesh Ewald (PME) summation.60 Covalent bonds associated with hydrogen atoms were constrained by the SHAKE algorithm.61 An NPT ensemble was used, with T = 300 K and P = 1 atm. Temperature was controlled with underdamped Langevin simulations of ″virtual″ solvent with the damping coefficient γ = 5 ps−1.62 Pressure was held constant by applying the Langevin piston method.63,64 The systems were equilibrated under harmonic position restraints applied to the foldamer. Starting from 50 kcal·mol−1, the force constant gradually decreased to 0 in 10 ns. After careful equilibration, another 100 ns trajectory was accumulated for the system in explicit solvent CHCl3. In addition, to access the µs timescale in multiple simulations to observe the assembly process, the generalized Born (GBn) implicit solvent model65 was used. The solvent dielectric constant was set to 4.71 to mimic the chloroform solution. Similar protocol was utilized by Huc and coworkers to investigate the encapsulation of small molecule in helical foldamer with molecular simulations.66

For the self-assembly of two separate monomers, initially the two helical monomers were randomly placed without perceptible interaction with each other, and 3 µs MD simulations with GB model were accumulated. The simulations were repeated twice for consistency. For the disassembly of the double-strand helical foldamer which is unlikely a spontaneous process, external perturbations were applied to accelerate the conformational change and to generate transition pathway in a predefined direction in conformational space. To be specific, 100 ns steered molecular dynamics (SMD)67 simulations were carried out to separate the two subunits by pulling apart the two carbon atoms on the head group –C(CH3)3 of each chain. A relatively large force constant of 500 kcal· mol−1·Å−1 was used. The simulations were repeated three times for consistency. Along the reaction path determined by SMD, the umbrella sampling technique68 was taken to fully sample the configuration space, ranging from 7 to 91 Å, with a window size of 3.0 Å and a small bias of 0.5 kcal·mol−1·Å–1. A total of 10 µs trajectory was accumulated that each window was fully sampled to get converged free energy profile. The overlap of configuration space sampling of neighboring windows are shown in the Supporting Information Figure S1. The weighted histogram analysis method (WHAM)69 was then employed to calculate the potentials of mean force (PMF) between the initial ″dimerized″ and final ″separated″ states. All MD simulations were carried out by employing the AMBER16 CUDA version.70‒72 To detect the intrinsic motion of the foldamer in solution, principal component analysis (PCA) was conducted (implemented in ProDy73) based on the 100 ns trajectory with explicit solvent model, which was recorded every 100 ps. The first principal component with largest eigenvalue representing the motion of head groups on helices was visualized with Normal Mode Wizard plugin in VMD.74

Figure 2. Structures and ECD spectra of the foldamer S1. Comparison of the optimized structure (in blue) of (A) dimer and (B) 34 monomer with respect to the crystal structure (in red). RMSDs are 0.7 Å and 2.1 Å, respectively. Optimizations were carried out at the GEBF-B3LYP(D3BJ)/6-31G(d) level of theory. Hydrogens are omitted for clarity. (C) ECD spectra for the M- and P-monomer as well as M-dimer, evaluated at the TD-B3LYP(D3BJ)/6-31G(d) level of theory.

3. RESULTS AND DISCUSSION



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.1. Electronic Structure Calculations Indicate that Dimerization is Energetically Preferential. It was determined by

Page 4 of 10

experiments that S1 prefers to form a dimer, and no single helices could be detected in solution at ambient conditions.41

Figure 3. (A) The double-strand foldamer S1 immersed in explicit solvent CHCl3 molecules, where two intertwined chains are in blue and yellow; (B) Time evolution of RMSD for S1 with respect to its crystal structure; (C) Principal component analysis of the 100 ns trajectories of S1 in explicit CHCl3, showing the motions of head groups on both subunits; (D) 1H NMR chemical shift data indicates that protons in the folded state (top panel) of dimer are less exposed than in the extended conformation (bottom panel). Experimental NMR data were shown in parenthesis for comparison.

We then compared the difference between the two forms. The optimized double-strand and one of the two single-strand chains of S1 are shown in Figures 2A & 2B, and the geometry parameters are summarized in Table S1. By using the crystal structure as a reference, the root mean standard deviations (RMSDs) of the optimized dimer and monomer are 0.7 Å and 2.1 Å, respectively. The inter-ring distances are similar in both monomer (intra-subunit) and dimer (inter-chain), though the single-strand helix shrinks to a more compact motif when compared with its structure in the dimeric state. However, the double-strand foldamer has more extensive π-π interactions, as most of the aromatic rings have neighboring rings on both top and bottom. This could be one of the reasons for its high stability, as our previous calculations suggest that π-π stacking interactions could accounts for ~90% of the total stabilization energy in aromatic foldamers.75 The calculated ECD spectra of optimized S1 monomers in both M (left-handed) and P (right-handed) configurations, as well as the optimized dimer (in M configuration), further confirm the contributions from stacking interactions for foldamer stability. As shown in Figure 2C, the ECD spectra of monomers have an intense band calculated at 407 nm, which is attributed to the π-π* excitation, though the structures with opposite handedness have mirror-like images. At the M configuration, the band is red shifted by 46 nm from monomer to dimer at 453 nm, mainly because of the more tight packing after

self-assembly of two helical monomers. Therefore, π-π interactions contribute greatly to the stabilization of the foldamer. For S1, the binding free energy for the two subunits to form a double-strand helix in solution was calculated to be −59.1 kcal·mol−1 in chloroform [at the GEBF-M06-2X/6311++G(d,p) level of theory]. This strongly indicates that the formation of a double-helical foldamer is energetically preferential, which is in accord with the experimentally determined dimerization constant being greater than 106 L·mol−1, suggesting that the double-strand form is predominant in solution at room temperature.75 This entwined dimer allows some aromatic groups to have extensive stacking interactions on both sides, and therefore maximizes the stabilization, and minimizes the entropic cost.76 The entropic contribution to binding was calculated to be 28.9 kcal·mol−1 at 298 K in the present system. Presumably, modification on backbone structure with stacking interactions intact may greatly affect the equilibrium between single- and double-strand forms, as backbone solvation was proposed to be critical for determining folding entropy in protein-like oligomers.77 The calculated dipole moment is 7.4 D for the S1 monomer, in which the F-substituted ring5 contributed significantly to the net dipole. In contrast, the dipole moment for S1 dimer is only 4.7 D, mainly because of the cancellation of the two subunits. Seemingly, the dipole-dipole interaction between two subunits is not the driving force for self-assembly in present


Page 5 of 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


system, as the direction of dipole in each monomer is perpendicular to its helix axis (Figure S2). However, it does help the aggregation of two subunits, as described below. 3.2. Molecular Dynamic Simulations Show that the Double-Helical Duplex S1 is Stable in Chloroform. Experimentally, the helical structure was proposed to be stable in chloroform solution, as characterized by the nuclear magnetic resonance (NMR) spectroscopy measurement.41 To explore the stability of the double-strand foldamer S1 in solution, a total of 100 ns classical MD simulations was performed under an NPT ensemble at P = 1 atm and T = 300 K (Figure 3A) after careful equilibration, where the density of the system is 1.46 g·cm−3, close to that of liquid CHCl3 (1.48 g·cm−3). The structure of the double-strand foldamer S1 has relatively small fluctuations over time, and the average RMSD of the foldamer is 3.0 Å (Figure 3B), indicating that the double-helical structure could be well maintained, though it becomes more flexible when it is immersed in solution, while the close packing in crystal structure makes it more rigid. Structure ensemble of the trajectory provides information for foldamer dynamics. Presumably the trajectory obtained from aforementioned 100 ns simulations was long enough to capture the equilibrated dynamics of the foldamer. Therefore, the principal component analysis of MD trajectories was carried out to detect the global, correlated motions of the system, which may have functional significance.78 The mode with largest eigenvalue from PCA shows that the aromatic rings at both helix terminus have a tendency to flip away from tight packing by rotating the amide(CONH)-aryl bond (Figure 3C), irrespective of the conjugation between amide and aromatic groups. In contrast, mainly due to the repulsive electrostatic potential between amide carbonyl and nitrogen in ortho position on aromatic ring, the amide(NHCO)-aryl bond in present system can only adopt the anti but not the syn conformation, and therefore its rotation is restricted. This has implications for the conformational change of the double-helical structure that the unwinding originates from the intrinsic dynamics of the backbone, and is likely to occur firstly at helix terminus and then transmit along the strand. Similar trend was observed in both single α- and β-helices, where the unfolding happens from the termini to the center.22 Compared to the central building blocks in helix, the terminal segment is more exposed to the environment, and is more susceptible to the local fluctuations associated with thermal energy, resulting in more frequent opening motions. We further calculated the 1H NMR chemical shifts of the foldamer S1 at the GEBF-B3LYP(D3BJ)/6-311G(d) level of theory, with a total number of 200 frames equidistantly selected from the MD simulation trajectory, as shown in Figure 3D. The prominent peak at 0.6 ppm corresponds to the H atoms in the -C(CH3)3 group at both ends of the foldamer; lying in the middle of the NMR spectra are two peaks stemming from H atoms in the -iOBu group; the peak lies somewhere in the vicinity of 6.8 ppm originating from the aromatic backbone H atoms. Therefore, the stability of the foldamer in solution is further confirmed by spectroscopic evidence. It should be noted that, our calculations are in good agreement with the experimentally determined NMR spectrum.41 We further calculated the 1H NMR of the foldamer structure when it is fully unfolded to stay in an extended state (we will discuss this unfolded structure later). About 1 ppm downfield shift for all protons

was observed, indicating that the hydrogen atoms are less exposed in the folded state. As it is not easy to define a simple or collective reaction coordinates to describe the transition between the double-strand foldamer and its single-strand subunits, we designed an artificial disassembly pathway for S1, driven by external forces, to explore the associated free energy change. A biased force was applied to pull the head tert-butyl groups of each chain, and the reaction coordinate is defined as the distance between them (Figure 4). Briefly speaking, the entwined two subunits gradually lose contact in the dissociation process. More details about the artificial dissociation pathway could be found in Figure S4. The PMF shows that the dissociation process along the reaction coordinate is energetically unfavorable: the disassembly is accompanied by a continuous increase in free energy up to ~60 kcal·mol−1 until the two ″head″ tert-butyl groups being separated by ~70 Å. The presence of a ″platform″ indicates that the two chains are still entangled with weak interactions when the reaction ordinate is less than 84 Å. After that, the PMF drops to –53.7 kcal·mol−1, mainly due to the rewinding of each strand into helical motifs. It is worthy to mention that, though this artificial pathway does not correspond to a real disassembly process, the free energy difference of 53.7 kcal·mol−1, obtained with the classical force field method, between the double-strand foldamer and its single-strand subunits illustrates the relative stability between the two states. And more importantly, it is in accordance with our quantum chemical computations of the dimerization energy in chloroform (–59.1 kcal·mol−1). As shown in the above PMF profile, the free energy continues to increase before two subunits in S1 getting fully separated, indicating that refolding is plausible. To test this hypothesis, we explore the self-assembly process with unbiased MD simulations, as described below.

Figure 4. Potential of mean force of a designed disassembly process from a double-strand helical foldamer to two single-strand helices. The reaction coordinate is defined as the distance between head tert-butyl groups of each chain (highlighted with red dashed-line circles), which were pulled apart with external force along the reaction coordinate.

3.3. The Spontaneous Assembly of Two Subunits into an Entwined Dimer at µs Timescale through an “UnwindingThreading-Rewinding” Mechanism. Given the large dimerization constant determined experimentally, and the calculated energy difference between the double- and single-strand helices, we then explore the spontaneous self-assembly of two separate monomers into a double-strand helix. Four different



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

systems, S1-S4, with a similar backbone but different substituents at either middle or terminal were studied. Starting with

Page 6 of 10

two helical monomers that are randomly placed without

Figure 5. Self-assembly process of S1: two single-strand subunits into a double-strand helix through an “unwinding-threading-rewinding” mechanism. (A-I) Representative configurations taken from a 3 µs MD simulation for the self-assembly process, with time labelled underneath. Starting with configuration (A), the host and the guest subunits approach each other to form complex (B). Both subunits form partially unwound configurations at (C) so that the guest subunit M2 could insert into the cavity of the host M1. Then the double-strand helix is gradually formed by M2 threading along the helix axis of M1, with multiple intermediate states (D) to (H). At (I), the double-strand foldamer is finally formed by rewinding of the two strands to complete the self-assembly. Aromatic rings on both subunits are shown in space-filling model, but with different colors: those on M1 are in yellow, except for the ring-2', which is highlighted in magenta as it is used as the reference for tracing the conformational change during the self-assembly; on M2, ring1 to ring4 are in dark blue, ring5 in cyan, and ring4' to ring1' in light blue.

perceptible interactions, we observed quite consistent results that in each system the two single helices gradually moved close to each other and eventually self-assembled into a double helix in 3 µs MD simulations. As the aggregation process for all the 4 systems resembles each other, we focus on S1. More details about S2-S4 can be found in SI. By examining the trajectory, we identify an ʺunwindingthreading-rewindingʺ mechanism, and describe it in details as below. For clarity, ʺmonomer Yʺ is demoted as MY where Y= 1 or 2, and ʺringX of monomer Yʺ as ringX(MY) where X=1, 2, 3, 4 or 5. Initially, the two helical monomers, M1 (host subunit) and M2 (guest subunit), were separated with no interaction (Figure 5A). After free diffusion within 0.1 µs, they approached close enough and piled up in similar orientation to form tight packing. It should be noted that at the interface between the two helical monomers, θ1' on M1 and θ1 on M2 flipped by 180º, so that the bulky tert-butyl group will not impede the stacking between two monomers (Figure 5B). After relaxation for ~1.8 µs in MD simulations, the two monomers partially unwound the helical structures near the interface. To be more specific, M1 rotated its θ2' from 180º to 90º, and ring1'(M1) and ring2'(M1), the two peripheral 2,6pyridinedicarboxamide units at tail, moved away from the helical axis. Therefore one turn of M1's helical structure with a relatively narrow diameter was broken and the central cavity

at the interior of the double-helix with a wider diameter was then accessible to M2 (Figure 5C). In the meantime, M2 rotated its θ1 by 90º, so that the bulky tert-butyl group and the outermost ring1(M2) were parallel to the principal axis of the helix. Consequently, M2 inserted its bulky head group into the cavity of M1 and was anchored there, as a couple of hydrogen bond interactions were formed between F atoms on M1 and H atoms on the tert-butyl of M2 (Figure 6A). In fact, the anchoring role of F atoms was found to be critical during the initial stage of the self-assembly, as shown in Figure 6B. The fluoroaromatic group has increased local dipole moment, therefore is better to stabilize the tert-butyl group than the unsubstituted one. The M2, the guest subunit, was not trapped at this configuration, but rather, ring1(M2) could further enter into the cavity of the host M1. The driving force for this insertion mainly comes from the π-π stacking at the intact interface between the two subunits, which makes the tight packing between the two. This intermediate structure was mainly stabilized by forming hydrogen bond interactions between the pyridine ring and amide group (Figure 5D).The insertion of the bulky tert-butyl head group and ring1(M2) anchored M2 at the interior of M1, so that the rest part of M2 can gradually form intertwined interactions with M1 after long time relaxation. The threading motion could easily be tracked by monitoring the location of the freely moving segment ring2'(M1). Occa-


Page 7 of 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


sionally this ring intercalated with M2, and formed sandwich configuration with aromatic ring2(M2) and ring4'(M2) by using both sides (Figure 5E). Then the aggregation followed a simple threading mechanism, that M2 spiraled long the helix axis of M1, further intercalated into M1, so that ring2'(M1) switched to the second sandwich configuration with ring3(M2) at the top and ring3'(M2) at the bottom (Figure 5F). In the meantime, the head group of M2 got flattened, and formed partial packing with the head of M1. After that, M2 continued to move along the helical path, and consequently ring2'(M1) formed the third sandwich configuration with ring4(M2) at the top and ring2'(M2) at the bottom (Figure 5G). Meantime, ring3(M2) and ring2(M2) also formed sandwich configurations with M1 individually. As M2 kept moving, the ring2'(M1) jumped to form the fourth sandwich configuration with ring5(M2) at the top and ring1'(M2) at the bottom (Figure 5H). Up to this stage, the double-strand helix was almost formed, though both ends of the subunits were still open. And ring2'(M1) only had stacking interaction with ring4'(M2) at the top (Figure 5I), resembling the double-strand foldamer structure.41 The termini of the two subunits experienced extensive conformational change in another 1 µs, mainly because of the local fluctuations associated with thermal energy. Rewinding of the two strands completed the self-assembly.

4. CONCLUSIONS In this work, we explored the self-assembly processes of two single-strand helices into an entangled double-strand helical aromatic foldamer with molecular modelling. Our results reveal that the spontaneous formation of the foldamer, driven by extensive π-π interactions, proceeds through an ″unwinding- threading-rewinding″ mechanism, which is energetically favorable, as confirmed by both quantum mechanical calculations and MD simulations. The detailed mechanism about folding and self-assembly in aromatic oligoamide foldamer we present here discloses how the sequence is associated with the well-ordered three-dimensional structure at atomic level, and therefore may have implications for designing new foldamers with versatile functions.

ASSOCIATED CONTENT Supporting Information. Umbrella sampling for each window, dipole moment of dimer and monomer, and details about the designed disassembly process, and the self-assembly processes of S2-S4. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *[email protected]; *[email protected].

ACKNOWLEDGMENT

Figure 6. The fluoroaromatic group on the host subunit stabilizes the guest subunit by anchoring it bulky tert-butyl group. (A) Shown here is a representative structure when M2 (shown in lines model, except for the head tert-butyl group which is highlighted in stick model) just inserted into the cavity of M1 (in paperchain model), where all methyl groups at the head of M2 formed hydrogen bonding with F atoms on M1. (B) Hydrogen bond distances between each of the three F atoms on M1 (in red, green and blue, respectively) with the nearest H on methyl group of M2. After relaxation for ~1.8 µs in MD simulations, the tert-butyl group of M2 inserted into M1, accompanied by the formation of multiple F···H interactions, therefore stabilized the complex.

It is worthwhile noting that, the abovementioned selfassembly process for S1 are reproducible, as similar scenarios were found in two independent simulations. More interestingly, this mechanism was adopted by S2-S4 as well (Figure S4), except for that the terminal groups do not insert into the central cavity but staying at the periphery of the complex during the threading. This is mainly because of the lack of favorable stacking interactions between terminal group and the cavity in these three systems. In contrast, as shown in Figures 5C and 6A, the terminal tert-butyl group on one subunit in S1 inserted into the pore of the other subunit before threading, due to the presence of extensive stabilization in the cavity. Therefore, not only the backbone but also the sidechain groups may have profound impacts on the self-assembly of foldamers.

This work was supported by the Natural Science Foundation of Jiangsu Province (Grant No. SBK2015041570), the National Natural Science Foundation of China (Grant Nos. 21333004, 21361140376 and 21673110), the ″Specially-Appointed Professors by Universities in Jiangsu Province″ program, and the ″Fundamental Research Funds for the Central Universities″. Part of the calculations were performed using computational resources on an IBM Blade cluster system from the High Performance Computing Center (HPCC) of Nanjing University and the Shenzhen Supercomputer Center (SSC, China).

REFERENCES (1) Yashima, E.; Ousaka, N.; Taura, D.; Shimomura, K.; Ikai, T.; Maeda, K. Supramolecular Helical Systems: Helical Assemblies of Small Molecules, Foldamers, and Polymers with Chiral Amplification and Their Functions, Chem. Rev. 2016, 116, 13752−13990. (2) Zhang, D. W.; Zhao, X.; Hou, J. L.; Li, Z. T. Aromatic Amide Foldamers: Structures, Properties, and Functions, Chem. Rev. 2012, 112, 5271−5316. (3) Goodman, C. M.; Choi, S.; Shandler, S.; DeGrado, W. F. Foldamers as versatile frameworks for the design and evolution of function, Nat. Chem. Biol. 2007, 3, 252−262. (4) Hamuro, Y.; Geib, S. J.; Hamilton, A. D. Novel Molecular Scaffolds: Formation of Helical Secondary Structure in a Family of Oligoanthranilamides, Angew. Chem. Int. Ed. 1994, 33, 446−448. (5) Lautrette, G.; Wicher, B.; Kauffmann, B.; Ferrand, Y.; Huc, I. Iterative Evolution of an Abiotic Foldamer Sequence for the Recognition of Guest Molecules with Atomic Precision, J. Am. Chem. Soc. 2016, 138, 10314−10322. (6) Chandramouli, N.; Ferrand, Y.; Lautrette, G.; Kauffmann, B.; Mackereth, C. D.; Laguerre, M.; Dubreuil, D.; Huc, I. Iterative design of a helically folded aromatic oligoamide sequence for the selective encapsulation of fructose, Nat. Chem. 2015, 7, 334−341. (7) Delsuc, N.; Massip, S.; Leger, J. M.; Kauffmann, B.; Huc, I. Relative Helix-Helix Conformations in Branched Aromatic Oligoamide Foldamers, J. Am. Chem. Soc. 2011, 133, 3165−3172.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(8) Wahlestedt, C.; Salmi, P.; Good, L.; Kela, J.; Johnsson, T.; Hokfelt, T.; Broberger, C.; Porreca, F.; Lai, J.; Ren, K.; Ossipov, M.; Koshkin, A.; Jakobsen, N.; Skouv, J.; Oerum, H.; Jacobsen, M. H.; Wengel, J. Potent and nontoxic antisense oligonucleotides containing locked nucleic acids, Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 5633−5638. (9) Jeon, H. G.; Jung, J. Y.; Kang, P.; Choi, M. G.; Jeong, K. S. Folding-Generated Molecular Tubes Containing One-Dimensional Water Chains, J. Am. Chem. Soc. 2016, 138, 92−95. (10) Xin, P.; Zhu, P.; Su, P.; Hou, J. L.; Li, Z. T. Hydrogen Bonded Helical Hydrazide Oligomers and Polymer That Mimic the Ion Transport of Gramicidin A, J. Am. Chem. Soc. 2014, 136, 13078−13081. (11) Feng, W.; Yamato, K.; Yang, L.; Ferguson, J. S.; Zhong, L.; Zou, S.; Yuan, L.; Zeng, X. C.; Gong, B. Efficient Kinetic Macrocyclization, J. Am. Chem. Soc. 2009, 131, 2629−2637. (12) Zhu, Y. Y.; Li, C.; Li, G. Y.; Jiang, X. K.; Li, Z. T. HydrogenBonded Aryl Amide Macrocycles: Synthesis, Single-Crystal Structures, and Stacking Interactions with Fullerenes and Coronene, J. Org. Chem. 2008, 73, 1745−1751. (13) Berni, E.; Dolain, C.; Kauffmann, B.; Leger, J. M.; Zhan, C.; Huc, I. Expanding the Registry of Aromatic Amide Foldamers: Folding, Photochemistry and Assembly Using Diaza-anthracene Units, J. Org. Chem. 2008, 73, 2687−2694. (14) Shang, J.; Gan, Q.; Dawson, S. J.; Rosu, F.; Jiang, H.; Ferrand, Y.; Huc, I. Self-Association of Aromatic Oligoamide Foldamers into Double Helices in Water, Org. Lett. 2014, 16, 4992−4995. (15) Zhang, P.; Zhang, L.; Wang, H.; Zhang, D. W.; Li, Z. T. Helical folding of an arylamide polymer in water and organic solvents of varying polarity, Polym. Chem. 2015, 6, 2955−2961. (16) Guo, R.; Zhang, L.; Wang, H.; Zhang, D. W.; Li, Z. T. Hydrophobically driven twist sense bias of hollow helical foldamers of aromatic hydrazide polymers in water, Polym. Chem. 2015, 6, 2382−2385. (17) Wu, C. F.; Li, Z. M.; Xu, X. N.; Zhao, Z. X.; Zhao, X.; Wang, R. X.; Li, Z. T. Folding-Induced Folding: The Assembly of Aromatic Amide and 1,2,3-Triazole Hybrid Helices, Chem. Eur. J. 2014, 20, 1418−1426. (18) Elmer, S. P.; Pande, V. S. Foldamer simulations: Novel computational methods and applications to poly-phenylacetylene oligomers, J. Chem. Phys. 2004, 121, 12760. (19) Elmer, S. P.; Park, S.; Pande, V. S. Foldamer dynamics expressed via Markov state models. I. Explicit solvent moleculardynamics simulations in acetonitrile, chloroform, methanol, and water, J. Chem. Phys. 2005, 123, 114902. (20) Elmer, S. P.; Park, S.; Pande, V. S. Foldamer dynamics expressed via Markov state models. II. State space decomposition, J. Chem. Phys. 2005, 123, 114903. (21) Lee, O.-S.; Saven, J. G. Simulation Studies of a Helical mPhenylene Ethynylene Foldamer, J. Phys. Chem. B 2004, 108, 11988−11994. (22) Uribe, L.; Gauss, J.; Diezemann, G. J. Phys. Chem. B Determining Factors for the Unfolding Pathway of Peptides, Peptoids, and Peptidic Foldamers, 2016, 120, 10433−10441. (23) Uribe, L.; Jaschonek, S.; Gauss, J.; Diezemann, G. Mechanical unfolding pathway of a model β-peptide foldamer, J. Chem. Phys. 2015, 142, 204901. (24) Uribe, L.; Gauss, J.; Diezemann, G. Comparative Study of the Mechanical Unfolding Pathways of α- and β-Peptides, J. Phys. Chem. B 2015, 119, 8313−8320. (25) Liu, Z.; Teslja, A.; Pophristic, V. An ab initio Molecular Orbital Study of Intramolecular Hydrogen Bonding in Ortho-Substituted Arylamides: Implications for the Parameterization of Molecular Mechanics Force Fields, J. Comput. Chem. 2011, 32, 1846−1858. (26) Pophristic, V.; Vemparala, S.; Ivanov, I.; Liu, Z.; Klein, M. L.; DeGrado, W. F. Controlling the shape and flexibility of arylamides: A combined ab initio, ab initio molecular dynamics, and classical molecular dynamics study, J. Phys. Chem. B 2006, 110, 3517−3526. (27) Galan, J. F.; Brown, J.; Wildin, J. L.; Liu, Z.; Liu, D.; Moyna, G.; Pophristic, V. Intramolecular Hydrogen Bonding in ortho-

Page 8 of 10

Substituted Arylamide Oligomers: A Computational and Experimental Study of ortho-Fluoroand ortho-Chloro-Nmethylbenzamides, J. Phys. Chem. B 2009, 113, 12809−12815. (28) Liu, Z.; Remsing, R. C.; Liu, D.; Moyna, G.; Pophristic, V. Hydrogen Bonding in ortho-Substituted Arylamides: The Influence of Protic Solvents, J. Phys. Chem. B 2009, 113, 7041−7044. (29) Galan, J. F.; Tang, C. N.; Chakrabarty, S.; Liu, Z.; Moyna, G.; Pophristic, V. Conformational preferences of furan- and thiophenebased arylamides: a combined computational and experimental study, Phys. Chem. Chem. Phys. 2013, 15, 11883−11892. (30) Abramyan, A. M.; Liu, Z.; Pophristic, V. Mechanistic and dynamic insights into ligand encapsulation by helical arylamide foldamers, Phys. Chem. Chem. Phys. 2014, 16, 20406−20410. (31) Abramyan, A. M.; Liu, Z.; Pophristic, V. Helix handedness inversion in arylamide foldamers: elucidation and free energy profile of a hopping mechanism, Chem. Commun. 2016, 52, 669−672. (32) Liu, Z.; Hu, X.; Abramyan, A. M.; Meszaros, A.; Csekei, M.; Kotschy, A.; Huc, I.; Pophristic, V. Computational Prediction and Rationalization, and Experimental Validation of Handedness Induction in Helical Aromatic Oligoamide Foldamers, Chem. Eur. J. 2017, 23, 1−12. (33) Berl, V.; Huc, I.; Khoury, R. G.; Krische, M. J.; Lehn, J.-M. Interconversion of single and double helices formed from synthetic molecular strands, Nature, 2000, 407, 720−723. (34) Ferrand, Y.; Gan, Q.; Kauffmann, B.; Jiang, H.; Huc, I. Template-Induced Screw Motions within an Aromatic Amide Foldamer Double Helix, Angew. Chem. Int. Ed. 2011, 50, 7572−7575. (35) Baptiste, B.; Zhu, J.; Haldar, D.; Kauffmann, B.; Léger, J.-M.; Huc, I. Hybridization of Long Pyridine-Dicarboxamide Oligomers into Multi-Turn Double Helices: Slow Strand Association and Dissociation, Solvent Dependence, and Solid State Structures, Chem. Asian J. 2010, 5, 1364–1375. (36) Gan, Q.; Ferrand, Y.; Chandramouli, N.; Kauffmann, B.; Aube, C.; Dubreuil, D.; Huc, I. Identification of a Foldaxane Kinetic Byproduct during Guest Induced Single to Double Helix Conversion, J. Am. Chem. Soc. 2012, 134, 15656–15659. (37) Berni, E.; Kauffmann, B.; Bao, C.; Lefeuvre, J.; Bassani, D. M.; Huc, I. Assessing the Mechanical Properties of a Molecular Spring, Chem. Eur. J. 2007, 13, 8463–8469. (38) Acocella, A.; Venturini, A.; Zerbetto, F. Pyridinedicarboxamide Strands Form Double Helices via an Activated Slippage Mechanism, J. Am. Chem. Soc. 2004, 126, 2362–2367. (39) Zhang, B.; Yuan, T.; Jiang, H.; Lei, M. Molecular Dynamics Simulations on the Stability and Assembly Mechanisms of Quadruple and Double Helical Aromatic Amide Foldamers, J. Phys. Chem. B 2009, 113, 10934–10941. (40) Zhao, D.; van Leeuwen, T.; Cheng, J.; Feringa, B. L. Dynamic control of chirality and self-assembly of double-stranded helicates with light, Nat. Chem. 2017, 9, 250−256. (41) Gan, Q.; Ferrand, Y.; Bao, C.; Kauffmann, B.; Grélard, A.; Jiang, H.; Huc, I. Helix-Rod Host-Guest Complexes with Shuttling Rates Much Faster than Disassembly, Science 2011, 331, 1172−1175. (42) Li, S.; Li, W.; Ma, J. Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates, Acc. Chem. Res. 2014, 47, 2712−2720. (43) Li, W.; Li, S.; Jiang, Y. Generalized Energy-Based Fragmentation Approach for Computing the Ground-State Energies and Properties of Large Molecules, J. Phys. Chem. A 2007, 111, 2193−2199. (44) Li, S.; Li, W.; Fang, T. An Efficient Fragment-Based Approach for Predicting the Ground-State Energies and Structures of Large Molecules, J. Am. Chem. Soc. 2005, 127, 7215−7226. (45) Li, W.; Chen, C.; Zhao, D.; Li, S. LSQC: Low Scaling Quantum Chemistry Program, Int. J. Quantum Chem. 2015, 115, 641−646. (46) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 1993, 98, 5648−5652. (47) Lee, C.; Yang, W.; Parr, R. G. Development of the ColleSalvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 1988, 37, 785. (48) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion


Page 9 of 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 2010, 132, 154104. (49) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 2008, 120, 215−241. (50) Boys, S. F.; Bernardi, F. D. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors, Mol. Phys. 1970, 19, 553−566. (51) Barone, V.; Cossi, M. Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model, J. Phys. Chem. A 1998, 102, 1995−2001. (52) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. A comparison of models for calculating nuclear magnetic resonance shielding tensors, J. Chem. Phys. 1996, 104, 5497−5509. (53) Wolinski, K.; Hinton, J. F.; Pulay, P. Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations, J. Am. Chem. Soc. 1990, 112, 8251−8260. (54) Ditchfield, R. Self-consistent perturbation theory of diamagnetism I. A gauge-invariant LCAO method for N.M.R. chemical shifts, Mol. Phys. 1974, 27, 789−807. (55) Zhao, D.; Song, R.; Li, W.; Ma, J.; Dong, H.; Li, S. Accurate Prediction of NMR Chemical Shifts in Macromolecular and Condensed-phase Systems with the Generalized Energy-based Fragmentation Method, J. Chem. Theory Comput. 2017, DOI: 10.1021/acs.jctc.7b00380. (56) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski J.; Fox, D. J. Gaussian, Inc., Wallingford CT, 2013. (57) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general amber force field, J. Comput. Chem. 2004, 25, 1157−1174. (58) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Kollmann, P. A. Application of RESP charges to calculate conformational energies, hydrogen bond energies, and free energies of solvation, J. Am. Chem. Soc. 1993, 115, 9620−9631. (59) Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A wellbehaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model, J. Phys. Chem. 1993, 97, 10269−10280. (60) Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems, J. Chem. Phys. 1993, 98, 10089−10092. (61) Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. Numerical integration of the cartesian equations of motion of a system with con-

straints: molecular dynamics of n-alkanes, J. Comput. Phys. 1977, 23, 327−341. (62) Adelman, S.; Doll, J. Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids, J. Chem. Phys. 1976, 64, 2375−2388. (63) Feller, S. E.; Zhang, Y.; Pastor, R. W.; Brooks, B. R. Constant pressure molecular dynamics simulation: The Langevin piston method, J. Chem. Phys. 1995, 103, 4613−4621. (64) Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant pressure molecular dynamics algorithms, J. Chem. Phys. 1994, 101, 4177−4189. (65) Delsuc, N.; Kawanami, T.; Lefeuvre, J.; Shundo, A.; Ihara, H.; Takafuji, M.; Huc, I. Kinetics of Helix-Handedness Inversion: Folding and Unfolding in Aromatic Amide Oligomers, ChemPhysChem 2008, 9, 1882−1890. (66) Ferrand, Y.; Chandramouli, N.; Kendhale, A. M.; Aube, C.; Kauffmann, B.; Grelard, A.; Laguerre, M.; Dubreuil, D.; Huc, I. Identification of a Foldaxane Kinetic Byproduct during Guest Induced Single to Double Helix Conversion, J. Am. Chem. Soc. 2012, 134, 11282−11288. (67) Isralewitz, B.; Gao, M.; Schulten, K. Steered molecular dynamics and mechanical functions of proteins, Curr. Opin. Struct. Biol. 2001, 11, 224−230. (68) Torrie, G. M.; Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling, J. Comput. Phys. 1977, 23, 187−199. (69) Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. THE weighted histogram analysis method for freeenergy calculations on biomolecules. I. The method, J. Comput. Chem. 1992, 13, 1011−1021. (70) Salomon-Ferrer, R.; Götz, A. W.; Poole, D.; Le Grand, S.; Walker, R. C. Routine microsecond molecular dynamics simulations with AMBER - Part II: Particle Mesh Ewald, J. Chem. Theory Comput. 2013, 9, 3878−3888. (71) Salomon-Ferrer, R.; Case, D. A.; Walker, R. C. An overview of the Amber biomolecular simulation package, WIREs Com-put. Mol. Sci. 2013, 3, 198−210. (72) Götz, A. W.; Williamson, M. J.; Xu, D.; Poole, D.; Le Grand, S.; Walker, R. C. Routine microsecond molecular dynamics simulations with AMBER - Part I: Generalized Born, J. Chem. Theory Comput. 2012, 8, 1542−1555. (73) Bakan, A.; Meireles, L. M.; Bahar, I. ProDy: Protein Dynamics Inferred from Theory and Experiments, Bioinformatics 2011, 27, 1575−1577. (74) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics, J. Mol. Graphics 1996, 14, 33−38. (75) Dong, H.; Hua, S.; Li, S. Understanding the Role of Intra- and Inter-molecular Interactions in the Formation of Single- and DoubleHelical Structures of Aromatic Oligoamides: A Computational Study, J. Phys. Chem. A 2009, 113, 1335−1342. (76) Huc, I. Aromatic Oligoamide Foldamers, Eur. J. Org. Chem. 2004, 2004, 17−29. (77) Reinert, Z. E.; Horne, W. S. Folding thermodynamics of protein-like oligomers with heterogeneous backbones, Chem. Sci. 2014, 5, 3325−3330. (78) Bahar, I.; Lezon, T. R.; Bakan, A.; Shrivastava, I. H. Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins, Chem. Rev. 2010, 110, 1463−1497.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 10

TOC Graphic


10

Molecular Mechanism of Self-Assembly of ... - ACS Publications

Recommend Documents