Extension Behavior of Helicogenic Polypeptides

Polymer crystallization under external flow

The general aspects of polymer crystallization under external flow, i.e., flow-induced crystallization (FIC) from fundamental theoretical background to multi-scale characterization and modeling results are presented. FIC is crucial for modern polymer processing, such as blowing, casting, and injection modeling, as two-third of daily-used polymers is crystalline, and nearly all of them need to be processed before final applications. For academics, the FIC is intrinsically far from equilibrium, where the polymer crystallization behavior is different from that in quiescent conditions. The continuous investigation of crystallization contributes to a better understanding on the general non-equilibrium ordering in condensed physics. In the current review, the general theories related to polymer nucleation under flow (FIN) were summarized first as a preliminary knowledge. Various theories and models, i.e., coil-stretch transition and entropy reduction model, are briefly presented together with the modified versions. Subsequently, the multi-step ordering process of FIC is discussed in detail, including chain extension, conformational ordering, density fluctuation, and final perfection of the polymer crystalline. These achievements for a thorough understanding of the fundamental basis of FIC benefit from the development of various hyphenated rheometer, i.e., rheo-optical spectroscopy, rheo-IR, and rheo-x-ray scattering. The selected experimental results are introduced to present efforts on elucidating the multi-step and hierarchical structure transition during FIC. Then, the multi-scale modeling methods are summarized, including micro/meso scale simulation and macroscopic continuum modeling. At last, we briefly describe our personal opinions related to the future directions of this field, aiming to ultimately establish the unified theory of FIC and promote building of the more applicable models in the polymer processing.

Energetics and structure of alanine-rich α-helices via adaptive steered molecular dynamics

The energetics and hydrogen bonding profiles of the helix-to-coil transition were found to be an additive property and to increase linearly with chain length, respectively, in alanine-rich α-helical peptides. A model system of polyalanine repeats was used to establish this hypothesis for the energetic trends and hydrogen bonding profiles. Numerical measurements of a synthesized polypeptide Ac-Y(AEAAKA)kF-NH2 and a natural α-helical peptide a2N (1-17) provide evidence of the hypothesis's generality. Adaptive steered molecular dynamics was employed to investigate the mechanical unfolding of all of these alanine-rich polypeptides. We found that the helix-to-coil transition is primarily dependent on the breaking of the intramolecular backbone hydrogen bonds and independent of specific side-chain interactions and chain length. The mechanical unfolding of the α-helical peptides results in a turnover mechanism in which a 310-helical structure forms during the unfolding, remaining at a near constant population and thereby maintaining additivity in the free energy. The intermediate partially unfolded structures exhibited polyproline II helical structure as previously seen by others. In summary, we found that the average force required to pull alanine-rich α-helical peptides in between the endpoints-namely the native structure and free coil-is nearly independent of the length or the specific primary structure.

Single-molecule mechanical unfolding experiments reveal a critical length for the formation of α-helices in peptides

α-Helix is the most predominant secondary structure in proteins and supports many functions in biological machineries. The conformation of the helix is dictated by many factors such as its primary sequence, intramolecular interactions, or the effect of the close environment. Several computational studies have proposed that there is a critical maximum length for the formation of intact compact helical structures, supporting the fact that most intact α-helices in proteins are constituted of a small number of amino acids. To obtain a detailed picture on the formation of α-helices in peptides and their mechanical stability, we have synthesized a long homopolypeptide of about 90 amino acids, poly(γ-benzyl-l-glutamate), and investigated its mechanical behaviour by AFM-based single-molecule force spectroscopy. The characteristic plateaus observed in the force-extension curves reveal the unfolding of a series of small helices (from 1 to 4) of about 20 amino acid residues connected to each other, rather than a long helix of 90 residues. Our results suggest the formation of a tertiary structure made of short helices with kinks, instead of an intact compact helical structure for sequences of more than 20 amino acid residues. To our knowledge, this is the first experimental evidence supporting the concept of a helical critical length previously proposed by several computational studies.

Organophilic, Superparamagnetic, and Reversibly Thermoresponsive Silica-Polypeptide Core-Shell Particles

Particles with a superparamagnetic cobalt inner core, silica outer core, and covalently bound homopolypeptide shell were investigated under thermal and magnetic stimuli. The homopolypeptide was poly(ε-carbobenzyloxy-l-lysine), PCBL, which is known to exhibit a thermoreversible coil ⇔ helix transition when dissolved as a pure polymer in m-cresol. Tethering to a core particle did not prevent PCBL from undergoing this conformational transition, as confirmed by dynamic light scattering and optical rotation, but the transition was broadened compared to that of the untethered polymer. The Co@SiO₂-PCBL hybrid particles retained the superparamagnetic properties of the cobalt inner nougat. Indeed, some response remains even after aging for >5 years. The aged PCBL shell also preserved its responsiveness to temperature, although differences in the shape of the size vs temperature transition curve were observed compared to the freshly made particles. A reversible coil ⇔ helix transition for a particle-bound polypeptide in a pure organic solvent is rare. In addition to providing a convenient tool for characterizing coil ⇔ helix transitions for surface-bound polypeptides without interference from pH or the strong ionic forces that dominate behavior in aqueous systems, the Co@SiO₂-PCBL/m-cresol system may prove useful in studies of the effect of shell polymer conformation on colloid interactions. The stability of the magnetic core and polypeptide shell suggest a long shelf life for Co@SiO₂-PCBL, which can, in principle, be deprotected to yield positively charged Co@SiO₂-poly(l-lysine) particles for possible transfection or antimicrobial applications or chained magnetically to produce responsive poly(colloids).

Molecular basis of the mechanical hierarchy in myomesin dimers for sarcomere integrity

Myomesin is one of the most important structural molecules constructing the M-band in the force-generating unit of striated muscle, and a critical structural maintainer of the sarcomere. Using molecular dynamics simulations, we here dissect the mechanical properties of the structurally known building blocks of myomesin, namely α-helices, immunoglobulin (Ig) domains, and the dimer interface at myomesin's 13th Ig domain, covering the mechanically important C-terminal part of the molecule. We find the interdomain α-helices to be stabilized by the hydrophobic interface formed between the N-terminal half of these helices and adjacent Ig domains, and, interestingly, to show a rapid unfolding and refolding equilibrium especially under low axial forces up to ∼ 15 pN. These results support and yield atomic details for the notion of recent atomic-force microscopy experiments, namely, that the unique helices inserted between Ig domains in myomesin function as elastomers and force buffers. Our results also explain how the C-terminal dimer of two myomesin molecules is mechanically outperforming the helices and Ig domains in myomesin and elsewhere, explaining former experimental findings. This study provides a fresh view onto how myomesin integrates elastic helices, rigid immunoglobulin domains, and an extraordinarily resistant dimer into a molecular structure, to feature a mechanical hierarchy that represents a firm and yet extensible molecular anchor to guard the stability of the sarcomere.

An energetic model for macromolecules unfolding in stretching experiments

We propose a simple approach, based on the minimization of the total (entropic plus unfolding) energy of a two-state system, to describe the unfolding of multi-domain macromolecules (proteins, silks, polysaccharides, nanopolymers). The model is fully analytical and enlightens the role of the different energetic components regulating the unfolding evolution. As an explicit example, we compare the analytical results with a titin atomic force microscopy stretch-induced unfolding experiment showing the ability of the model to quantitatively reproduce the experimental behaviour. In the thermodynamic limit, the sawtooth force-elongation unfolding curve degenerates to a constant force unfolding plateau.

Helix formation in the polymer brush

This work considers the physics of a brush formed by polymers capable of undergoing a helix-coil transition. A self-consistent field approximation for strongly stretched polymer chains is used in combination with a lattice model of the interaction energy in helix-coil mixtures. Crowding-induced chain stretching stabilizes helix formation at moderate tethering densities while high tethering density causes sufficiently strong stretching to unravel segments of the helix, resulting in distinct layers of monomer density and helical content. Compared to a random-coil brush at low-to-moderate tethering density, a helicogenic brush is less resistant to compression in the direction perpendicular to stretching due to easy alignment of helices and fewer unfavorable interactions between helical segments. At higher tethering density, the abovementioned stretch-induced decrease in helical content resists further compression. The proposed model is useful for understanding an emerging class of biomaterials that utilize helix-forming polymer brushes to induce shape changes or to stabilize biofunctional helical peptide sequences.

Competition for hydrogen-bond formation in the helix-coil transition and protein folding

The problem of the helix-coil transition of biopolymers in explicit solvents, such as water, with the ability for hydrogen bonding with a solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds. The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress, or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure and underscores the advantage of pulling experiments for studies of DNA. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.

Free energies and forces in helix-coil transition of homopolypeptides under stretching

We show here that constant velocity steered molecular dynamics (SMD) simulations of alpha-helices in a vacuum present a well defined plateau in the force-extension relationship for homopolypeptides having more than (approximately) twenty residues. With the processes being far away from equilibrium, the energies strongly depend on the stretching velocity. Importantly, for a given velocity variation, the energy variation depends also on the helix sequence. Additionally, our observations show that homopolypeptides made of ten different amino acids (Ala, Cys, Gln, Ile, Leu, Met, Phe, Ser, Thr and Val) present a linear helix-coil transition.

Stretching of a single-stranded DNA: evidence for structural transition

Recent experiments have shown that the force-extension (F-x) curve for single-stranded DNA (ssDNA) consisting only of adenine [poly(dA)] is significantly different from thymine [poly(dT)]. Here, we show that the base stacking interaction is not sufficient to describe the F-x curves as seen in the experiments. A reduction in the reaction coordinate arising from the formation of helix at low forces and an increase in the distance between consecutive phosphates of unstacked bases in the stretched state at high force in the proposed model qualitatively reproduce the experimentally observed features. The multistep plateau in the F-x curve is a signature of structural change in ssDNA.

Structure and aggregation of a helix-forming polymer

We have studied the competition between helix formation and aggregation for a simple polymer model. We present simulation results for a system of two such polymers, examining the potential of mean force, the balance between intermolecular and intramolecular interactions, and the promotion or disruption of secondary structure brought on by the proximity of the two molecules. In particular, we demonstrate that proximity between two such molecules can stabilize secondary structure. However, for this model, observed secondary structure is not stable enough to prevent collapse of the system into an unstructured globule.

Stretching of homopolymeric RNA reveals single-stranded helices and base-stacking

We have found strong supporting evidence for the helical structures of single-stranded nucleic acids by stretching individual molecules of polyadenylic acid [poly(A)] and polycytidylic acid [poly(C)]. Analyzing the force versus extension data using a two-state elastic model in which random-coil domains alternate with rigid helical domains allows one to extract the thermodynamic and structural properties. In addition, it also yields moderate to low cooperativity of the helix-coil transition for poly(A) and poly(C), respectively.

Helical structures from an isotropic homopolymer model

We present Monte Carlo simulation results for square-well homopolymers at a series of bond lengths. Although the model contains only isotropic pairwise interactions, under appropriate conditions this system shows spontaneous chiral symmetry breaking, where the chain exists in either a left- or a right-handed helical structure. We investigate how this behavior depends upon the ratio between bond length and monomer radius.

Simple method for the preparation of DNA-poly(o-methoxyaniline) hybrid: structure, morphology, and uncoiling of poly(o-methoxyaniline) on the DNA surface

The DNA-poly(o-methoxyaniline) (POMA) hybrid is prepared by mixing aqueous solutions of POMA [emeraldine salt (ES), doping level [Cl]/[N] = 0.52] and sodium salt of DNA (Na-DNA) and is then freeze-dried after 4 days. Three different compositions (WDNA = 0.25, 0.5, and 0.75, WDNA is the weight fraction of DNA) of the hybrids are prepared. The SEM pictures show a gradation in morphology; for example, for WDNA = 0.75, fibrils are present but, at lower DNA concentration, a fibrillar network structure of the hybrid is observed. The circular dichroism (CD) spectra of the hybrid solutions indicate unchanged DNA conformation and WAXS patterns indicate intact crystal structure of DNA in the hybrid. The UV-vis spectra suggest no denaturation of DNA during the blending process. The UV-vis spectra of the hybrids in aqueous medium show a gradual red shift of the pi band to polaron band transition with time. The plots of these wavelengths with time are sigmoidal, indicating the autocatalytic nature of the process. With an increase in the temperature, the rate of the red shift of the above peak is faster. Arrhenius analysis of the rate (1/tau700 where tau700 is the time required to reach the absorption maximum at the wavelength 700 nm) yields straight lines for the three hybrid compositions with activation energy values of 13-15 kcal/mol. These values are almost equal to the activation energy values of conformational transition of other polymers, supporting the red shift in UV-vis spectra occurs from conformational transition. DNA offers a surface where POMA gets adsorbed and the stable conformational transition resulting in the uncoiling of the POMA chain occurs through repulsive interaction among bound radical cations of POMA (ES) on the DNA surface. The conductivity of the hybrids is on the order of 10(-6) S/cm, and the I-V characteristic curves indicate the semiconducting nature of the hybrids.

Mechanically induced helix-coil transition in biopolymer networks

The quasi-equilibrium evolution of the helical fraction occurring in a biopolymer network (gelatin gel) under an applied stress has been investigated by observing modulation in its optical activity. Its variation with the imposed chain extension is distinctly nonmonotonic and corresponds to the transition of initially coiled strands to induced left-handed helices. The experimental results are in qualitative agreement with theoretical predictions of helices induced on chain extension. This new effect of mechanically stimulated helix-coil transition has been studied further as a function of the elastic properties of the polymer network: crosslink density and network aging.

Induced helicity in biopolymer networks under stress

By combining dynamic mechanical and optical measurements in probing the internal structure of a biopolymer network (gelatin gel), we studied the quasi-equilibrium evolution of helical content as a function of the applied stress. Assuming that the net optical activity is proportional to the concentration of secondary helices of collagen chains, and assuming that affine mechanical deformation, we find a nonmonotonic relationship between the helical domains and an imposed deformation. The results are in qualitative agreement with theoretical predictions of alpha-helices induced by chain end-to-end stretching, and give a consistent picture of mechanically stimulated helix-coil transition in networks of denatured polypeptides.

Nonlinear elasticity of an alpha -helical polypeptide

We study a minimal extension of the wormlike chain model to describe polypeptides having alpha-helical secondary structure. In this model the presence or absence of secondary structure enters as a scalar variable that controls the local chain bending modulus. Using this model we compute the extensional compliance of an alpha-helix under tensile stress, the bending compliance of the molecule under externally imposed torques, and the nonlinear interaction of such torques and forces on the molecule. We find that, due to coupling of the "internal" secondary structure variables to the conformational degrees of freedom of the polymer, the molecule has a highly nonlinear response to applied stress and force couples. In particular we demonstrate a sharp lengthening transition under applied force and a buckling transition under applied torque. Finally, we speculate that the inherent bistability of the molecule may underlie protein conformational change in vivo.

Effects of stacking on the configurations and elasticity of single-stranded nucleic acids

Stacking interactions in single-stranded nucleic acids give rise to configurations of an annealed rod-coil multiblock copolymer. Theoretical analysis identifies the following resulting signatures for long homopolynucleotides: a nonmonotonic dependence of size on temperature, the corresponding effects on cyclization and a plateau in the extension force law. Explicit numerical results for polydeoxyadenylate [poly(dA)] and polyriboadenylate [poly(rU)] are presented.