Biomimetic fabrication of 3D structures by spontaneous folding of tapes

This paper describes a biomimetic strategy for the fabrication of 3D structures-including an electrically functional light detector-modeled on the folding of biological macromolecules into globular shapes. The process started by fabricating precursors to 3D, millimeter-sized structures using flexible polymer tapes. These tapes were patterned with metal features supporting liquid solder, crimped into strings of 3D corrugations, and attached to flat polymer tapes to generate linear 3D structures. Capillary interactions between droplets of molten solder on adjacent faces of the crimped tapes resulted in folding of the precursors into quasi-3D and truly 3D structures.     

Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations

Globally RNA folding occurs in multiple stages involving chain compaction and subsequent rearrangement by a number of parallel routes to the folded state. However, the sequence-dependent details of the folding pathways and the link between collapse and folding are poorly understood. To obtain a comprehensive picture of the thermodynamics and folding kinetics we used molecular simulations of coarse-grained model of a pseudoknot found in the conserved core domain of the human telomerase (hTR) by varying both temperature (T) and ion concentration (C). The phase diagram in the [T,C] plane shows that the boundary separating the folded and unfolded state for the finite 47-nucleotide system is relatively sharp, implying that from a thermodynamic perspective hTR behaves as an apparent two-state system. However, the folding kinetics following single C-jump or T-quench is complicated, involving multiple channels to the native state. Although globally folding kinetics triggered by T-quench and C-jump are similar, the kinetics of chain compaction are vastly different, which reflects the role of initial conditions in directing folding and collapse. Remarkably, even after substantial reduction in the overall size of hTR, the ensemble of compact conformations are far from being nativelike, suggesting that the search for the folded state occurs among the ensemble of low-energy fluidlike globules. The rate of unfolding, which occurs in a single step, is faster upon C-decrease compared to a jump in temperature. To identify "hidden" states that are visited during the folding process we performed simulations by periodically interrupting the approach to the folded state by lowering C. These simulations show that hTR reaches the folded state through a small number of connected clusters that are repeatedly visited during the pulse sequence in which the folding or unfolding is interrupted. The results from interrupted folding simulations, which are in accord with non-equilibrium single-molecule folding of a large ribozyme, show that multiple probes are needed to reveal the invisible states that are sampled by RNA as it folds. Although we have illustrated the complexity of RNA folding using hTR as a case study, general arguments and qualitative comparisons to time-resolved scattering experiments on Azoarcus group I ribozyme and single-molecule non-equilibrium periodic ion-jump experiments establish the generality of our findings.     

The self-assembly mechanism of fibril-forming silk-based block copolymers

Triblock copolymers consisting of a silk-based ((Gly-Ala)(3)Gly-Glu) repeat flanked by hydrophilic outer blocks self-assemble into micrometer long fibrils in response to a trigger. Since the exact mechanism of the fibril formation remains unclear, we employ a multiscale modelling approach in combination with rare event simulations to elucidate key processes. Atomistic scale simulations on the silk-based block suggest a mechanism in which a polypeptide prefolded into a β-roll structure docks to the growing end of a fibril through the formation of Glu-Glu sidechain contacts. Subsequently it can slide to the optimal position before water is expelled to form a dry interface between the fibril end and the attaching block copolymer. In addition, we find that the folded state of the silk-based block is further stabilised through interactions with its neighboring block. Templated folding may also play a role in case a partially folded polypeptide attaches. The coarse-grained simulations indicate that the attachment and subsequent sliding is mediated by the hydrophilic flanks in a size dependent manner. The hydrophilic blocks prevent random aggregation and allow growth only at the end of the fibril. Our multiscale approach may be used for other fibril-forming peptides.     

Insertion and assembly of membrane proteins via simulation

Interactions of lipids are central to the folding and stability of membrane proteins. Coarse-grained molecular dynamics simulations have been used to reveal the mechanisms of self-assembly of protein/membrane and protein/detergent complexes for representatives of two classes of membrane protein, namely, glycophorin (a simple alpha-helical bundle) and OmpA (a beta-barrel). The accuracy of the coarse-grained simulations is established via comparison with the equivalent atomistic simulations of self-assembly of protein/detergent micelles. The simulation of OmpA/bilayer self-assembly reveals how a folded outer membrane protein can be inserted in a bilayer. The glycophorin/bilayer simulation supports the two-state model of membrane folding, in which transmembrane helix insertion precedes dimer self-assembly within a bilayer. The simulations also suggest that a dynamic equilibrium exists between the glycophorin helix monomer and dimer within a bilayer. The simulated glycophorin helix dimer is remarkably close in structure to that revealed by NMR. Thus, coarse-grained methods may help to define mechanisms of membrane protein (re)folding and will prove suitable for simulation of larger scale dynamic rearrangements of biological membranes.     

Influence of the conformation of polyethylene on wide-angle neutron scattering patterns

Wide-angle neutron scattering investigations of mixtures of deuterated and nondeuterated chains are well suited to detect sequences of regular adjacent reentry folding of a polymer chain in particular crystallographic directions. It is shown that the diffuse neutron scattering intensity is peaked at large scattering angles for (100) and (010) folding, whereas (110) folding is difficult to detect. Detailed calculations indicate that the position, intensity, and half-width of the diffuse peak depend strongly on the mode of folding as well as on the number of adjacent stems. By a comparison with experimental data adjacent reentry folding in (100) and (010) crystallographic planes with more than five adjacent stems can be excluded. The implications for other folding models containing regular folded chain sequences are discussed.     

Confinement in nanopores can destabilize α-helix folding proteins and stabilize the β structures

Protein folding in confined media has attracted wide attention over the past decade due to its importance in both in vivo and in vitro applications. Currently, it is generally believed that protein stability increases by decreasing the size of the confining medium, if its interaction with the confining walls is repulsive, and that the maximum folding temperature in confinement occurs for a pore size only slightly larger than the smallest dimension of the folded state of a protein. Protein stability in pore sizes, very close to the size of the folded state, has not however received the attention that it deserves. Using detailed, 0.3-ms-long molecular dynamics simulations, we show that proteins with an α-helix native state can have an optimal folding temperature in pore sizes that do not affect the folded-state structure. In contradiction to the current theoretical explanations, we find that the maximum folding temperature occurs in larger pores for smaller α-helices. In highly confined pores the free energy surface becomes rough, and a new barrier for protein folding may appear close to the unfolded state. In addition, in small nanopores the protein states that contain the β structures are entropically stabilized, in contrast to the bulk. As a consequence, folding rates decrease notably and the free energy surface becomes rougher. The results shed light on many recent experimental observations that cannot be explained by the current theories, and demonstrate the importance of entropic effects on proteins' misfolded states in highly confined environments. They also support the concept of passive effect of chaperonin GroEL on protein folding by preventing it from aggregation in crowded environment of biological cells, and provide deeper clues to the α → β conformational transition, believed to contribute to Alzheimer's and Parkinson's diseases. The strategy of protein and enzyme stabilization in confined media may also have to be revisited in the case of tight confinement. For in silico studies of protein folding in confined media, use of non-Go potentials may be more appropriate.     

Ultrafast folding of a computationally designed Trp-cage mutant: Trp2-cage

Miniproteins provide useful model systems for understanding the principles of protein folding and design. These proteins also serve as useful test cases for theories of protein folding, and their small size and ultrafast folding kinetics put them in a regime of size and time scales that is now becoming accessible to molecular dynamics simulations. Previous estimates have suggested the "speed limit" for folding is on the order of 1 mus. Here a computationally designed mutant of the 20-residue Trp-cage miniprotein, Trp2-cage, is presented. The Trp2-cage has greater stability than the parent and folds on the ultrafast time scale of 1 mICROs at room temperature, as determined from infrared temperature-jump experiments.     

Transient tertiary structure formation within the ribosome exit port

The exit tunnel of the ribosome is commonly considered to be sufficiently narrow that co-translational folding can begin only when specific segments of nascent chains are fully extruded from the tunnel. Here we show, on the basis of molecular simulations and comparison with experiment, that the long-range contacts essential for initiating protein folding can form within a nascent chain when it reaches the last 20 ? of the exit tunnel. We further show that, in this "exit port", a significant proportion of native and non-native tertiary structure can form without steric overlap with the ribosome itself, and provide a library of structural elements that our simulations predict can form in the exit tunnel and is amenable to experimental testing. Our results show that these elements of folded tertiary structure form only transiently and are at their midpoints of stability at the boundary region between the inside and the outside of the tunnel. These findings provide a framework for interpreting a range of recent experimental studies of ribosome nascent chain complexes and for understanding key aspects of the nature of co-translational folding.     

Face-spiral codes in cubic polyhedral graphs with face sizes no larger than 6

According to the face-spiral conjecture, first made in connection with enumeration of fullerenes, a cubic polyhedron can be reconstructed from a face sequence starting from the first face and adding faces sequentially in spiral fashion. This conjecture is known to be false, both for general cubic polyhedra and within the specific class of fullerenes. Here we report counterexamples to the spiral conjecture within the 19 classes of cubic polyhedra with positive curvature, i.e., with no face size larger than six. The classes are defined by triples {p ₃, p ₄, p ₅} where p ₃, p ₄ and p ₅ are the respective numbers of triangular, tetragonal and pentagonal faces. In this notation, fullerenes are the class {0, 0, 12}. For 11 classes, the reported examples have minimum vertex number, but for the remaining 8 classes the examples are not guaranteed to be minimal. For cubic graphs that also allow faces of size larger than 6, counterexamples are common and occur early; we conjecture that every infinite class of cubic polyhedra described by allowed and forbidden face sizes contains non-spiral elements.     

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.     

温控分子动力学研究微管蛋白活性肽链的折叠机制

运用温控和常温分子动力学方法, 研究了微管蛋白活性部位Pep1-28肽链的折叠机制, 总模拟时间为380.0 ns. 对于温控分子动力学, 逐渐降温可以清晰显示Pep1-28肽链的折叠途径, 发生明显折叠的温度约为550 K, 其折叠和去折叠可逆机制为U(>1200 K)←→I1(1200-1000 K)←→I2(800 K)←→I3(600 K)←→I4(450 K)←→F1(400 K)←→F2(300 K), 其中U为去折叠态构象, I1、I2、I3和I4是折叠过程中的四个重要的中间态构象, F1和F2是两个结构相近的折叠态构象. 对于常温(300 K)分子动力学, 其构象转变和折叠过程相当迅速, 很难观察到有效、稳定的中间态构象. 尤其引人注意的是, 其折叠态结构陷入了能量局域极小点, 与温控(300 K)的有较大差异, 两者能量差高达297.53 kJ·mol-1. 可见, 温控分子动力学方法不仅清晰地显示多肽和蛋白质折叠过程的重要中间态构象, 为折叠和去折叠机制提供直接、可靠的依据, 而且还有助于跨越较高的构象能垒, 促使多肽和蛋白质折叠以形成全局能量最低的稳定结构.     

Improved theoretical description of protein folding kinetics from rotations in the phase space of relevant order parameters

A method is introduced to construct a better approximation for the reaction coordinate for protein folding from known order parameters. The folding of a two-state off-lattice alpha helical Go-type protein is studied using molecular dynamics simulations. Folding times are computed directly from simulation, as well as theoretically using an equation derived by considering Brownian-type dynamics for the putative reaction coordinate. Theoretical estimates of the folding time using the number of native contacts (Qn) as a reaction coordinate were seen to differ quite significantly from the true folding time of the protein. By considering the properties of the bimodal free energy surface of this protein as a function of Qn and another relevant coordinate for folding Q (the total number of contacts), we show that by introducing a rotation in the phase space of the order parameters Q and Qn, we can construct a new reaction coordinate q that leads to a fivefold improvement in the estimate of the folding rate. This new coordinate q, resulting from the rotation, lies along the line connecting the unfolded and folded ensemble minima of the free energy map plotted as a function of the original order parameters Q and Qn. Possible reasons for the remaining discrepancy between the folding time computed theoretically and from folding simulations are discussed.     

Temperature dependence of the distribution of the first passage time: results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Gō-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T(opt). The optimal folding temperature T(opt) is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T(opt) and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T(opt) and start to diverge when the temperature is lower than T(opt). The distribution of FPT is close to a log-normal-like distribution at T > or = T(opt). At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.     

Turn-directed folding dynamics of β-hairpin-forming de novo decapeptide Chignolin

Realistic mechanistic pictures of β-hairpin formation, offering valuable insights into some of the key early events in protein folding, are accessible through short designed polypeptides as they allow atomic-level scrutiny through simulations. Here, we present a detailed picture of the dynamics and mechanism of β-hairpin formation of Chignolin, a de novo decapeptide, using extensive, unbiased molecular dynamics simulations. The results provide clear evidence for turn-directed broken-zipper folding and reveal details of turn nucleation and cooperative progression of turn growth, hydrogen-bond formations, and eventual packing of the hydrophobic core. Further, we show that, rather than driving folding through hydrophobic collapse, cross-strand side-chain packing could in fact be rate-limiting as packing frustrations can delay formation of the native hydrophobic core prior to or during folding and even cause relatively long-living misfolded or partially folded states that may nucleate aggregative events in more complex situations. The results support the increasing evidence for turn-centric folding mechanisms for β-hairpin formation suggested recently for GB1 and Peptide 1 based on experiments and simulations but also point to the need for similar examinations of polypeptides with larger numbers of cross-strand hydrophobic residues.     

Is there a unique melting temperature for two-state proteins?

Thermal unfolding (or folding) in many proteins occurs in an apparent two-state manner, suggesting that only two states, unfolded and folded, are populated. At the melting temperature, Tm, the two states coexist. Using lattice models with side chains we show that individual residues become structured at temperatures that deviate from Tm, which implies that partially folded conformations make substantial contribution to thermodynamic properties of two-state proteins. We also find that the folding cooperativity for a given residue is linked to its accessible surface area. These results are consistent with the experiments on GCN4-like zipper peptide, which showed that local melting temperatures differ from Tm. Analysis of thermal unfolding of six proteins shows that deltaT/Tm approximately N(-1), where deltaT is the transition width and N is the number of residues. This scaling allows us to conclude that, when corrected for finite size effects, folding cooperativity can be captured using coarse grained models.     

Folding processes of the B domain of protein A to the native state observed in all-atom ab initio folding simulations

Reaching the native states of small proteins, a necessary step towards a comprehensive understanding of the folding mechanisms, has remained a tremendous challenge to ab initio protein folding simulations despite the extensive effort. In this work, the folding process of the B domain of protein A (BdpA) has been simulated by both conventional and replica exchange molecular dynamics using AMBER FF03 all-atom force field. Started from an extended chain, a total of 40 conventional (each to 1.0 micros) and two sets of replica exchange (each to 200.0 ns per replica) molecular dynamics simulations were performed with different generalized-Born solvation models and temperature control schemes. The improvements in both the force field and solvent model allowed successful simulations of the folding process to the native state as demonstrated by the 0.80 A C(alpha) root mean square deviation (RMSD) of the best folded structure. The most populated conformation was the native folded structure with a high population. This was a significant improvement over the 2.8 A C(alpha) RMSD of the best nativelike structures from previous ab initio folding studies on BdpA. To the best of our knowledge, our results demonstrate, for the first time, that ab initio simulations can reach the native state of BdpA. Consistent with experimental observations, including Phi-value analyses, formation of helix II/III hairpin was a crucial step that provides a template upon which helix I could form and the folding process could complete. Early formation of helix III was observed which is consistent with the experimental results of higher residual helical content of isolated helix III among the three helices. The calculated temperature-dependent profile and the melting temperature were in close agreement with the experimental results. The simulations further revealed that phenylalanine 31 may play critical to achieve the correct packing of the three helices which is consistent with the experimental observation. In addition to the mechanistic studies, an ab initio structure prediction was also conducted based on both the physical energy and a statistical potential. Based on the lowest physical energy, the predicted structure was 2.0 A C(alpha) RMSD away from the experimentally determined structure.     

Version of zones and zigzag structure in icosahedral fullerenes and icosadeltahedra

A circuit of faces in a polyhedron is called a zone if each face is attached to its two neighbors by opposite edges. (For odd-sized faces, each edge has a left and a right opposite partner.) Zones are called alternating if, when odd faces (if any) are encountered, left and right opposite edges are chosen alternately. Zigzag (Petrie) circuits in cubic (= trivalent) polyhedra correspond to alternating zones in their deltahedral duals. With these definitions, a full analysis of the zone and zigzag structure is made for icosahedral centrosymmetric fullerenes and their duals. The zone structure provides hypercube embeddings of these classes of polyhedra which preserve all graph distances (subject to a scale factor of 2) up to a limit that depends on the vertex count. These embeddings may have applications in nomenclature, atom/vertex numbering schemes, and in calculation of distance invariants for this subclass of highly symmetric fullerenes and their deltahedral duals.     

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.     

Backbone-rigidified oligo(m-phenylene ethynylenes)

Oligo(m-phenylene ethynylenes) (oligo(m-PE)) with backbones rigidified by intramolecular hydrogen bonds were found to fold into well-defined conformations. The localized intramolecular hydrogen bond involves a donor and an acceptor from two adjacent benzene rings, respectively, which enforces globally folded conformations on these oligomers. Oligomers with two to seven residues have been synthesized and characterized. The persistence of the intramolecular hydrogen bonds and the corresponding curved conformations were established by ab initio and molecular mechanics calculations, 1D and 2D (1)H NMR spectroscopy, and UV spectroscopy. Pentamer 5, hexamer 6, and heptamer 7 adopt well-defined helical conformations. Such a backbone-based conformational programming should lead to molecules whose conformations are resilient toward structural variation of the side groups. These m-PE oligomers have provided a new approach for achieving folded unnatural oligomers under conditions that are otherwise unfavorable for previously described, solvent-driven folding of m-PE foldamers. Stably folded structures based on the design principle described here can be developed and may find important applications.     

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

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