Simple Folding Research Articles

Generation of Optical Vortex Arrays Using Single-Element Reversed-Wavefront Folding Interferometer

Optical vortex arrays have been generated using simple, novel, and stable reversed-wavefront folding interferometer. Two new interferometric configurations were used for generating a variety of optical vortex lattices. In the first interferometric configuration one cube beam splitter (CBS) was used in one arm of Mach-Zehnder interferometer for splitting and combining the collimated beam, and one mirror of another arm is replaced by second CBS. At the output of interferometer, three-beam interference gives rise to optical vortex arrays. In second interferometric configuration, a divergent wavefront was made incident on a single CBS which splits and combines wavefronts leading to the generation of vortex arrays due to four-beam interference. It was found that the orientation and structure of the optical vortices can be stably controlled by means of changing the rotation angle of CBS.

Forming a tough shell via an intracellular matrix and cellular junctions in the tail epidermis of Oikopleura dioica (Chordata: Tunicata: Appendicularia)

A postanal tail is a major synapomorphy of the phylum Chordata, which is composed of three subphyla: Vertebrata, Cephalochordata, and Tunicata (Urochordata). Among tunicates, appendicularians are the only group that retains the tail in the adult, and the adult tail functions in locomotion and feeding in combination with a cellulose-based house structure. Given the phylogenetic position of tunicates, the appendicularian adult tail may possess ancestral features of the chordate tail. We assess the ultrastructural development of the tail epidermis of the appendicularian Oikopleura dioica. The epidermis of the larval tail is enclosed by the larval envelope, which is a thin sheet similar to the outer tunic layer of ascidian larvae. The epidermis of the adult tail seems to bear no tunic-like cellulosic integuments, and the tail fin is a simple folding of the epidermis. Every epidermal cell, except for the triangular cells at the edge of the tail fin, has a conspicuous matrix layer of fibrous content in the apical cytoplasm without enclosing membranes. The epidermis of the larval tail does not have a fibrous matrix layer, suggesting the production of the layer during larval development and metamorphosis. Zonulae adhaerentes firmly bind the epidermal cells of the adult tail to one another, and the dense microfilaments lining the cell borders constitute a mechanical support for the cell membranes. The intracellular matrix, cell junctions, and cytoskeletons probably make the tail epidermis a tough, flexible shell supporting the active beating of the oikopleuran adult tail.

Removal of Covalent Heterogeneity Reveals Simple Folding Behavior for P4-P6 RNA

RNA folding landscapes have been described alternately as simple and as complex. The limited diversity of RNA residues and the ability of RNA to form stable secondary structures prior to adoption of a tertiary structure would appear to simplify folding relative to proteins. Nevertheless, there is considerable evidence for long-lived misfolded RNA states, and these observations have suggested rugged energy landscapes. Recently, single molecule fluorescence resonance energy transfer (smFRET) studies have exposed heterogeneity in many RNAs, consistent with deeply furrowed rugged landscapes. We turned to an RNA of intermediate complexity, the P4-P6 domain from the Tetrahymena group I intron, to address basic questions in RNA folding. P4-P6 exhibited long-lived heterogeneity in smFRET experiments, but the inability to observe exchange in the behavior of individual molecules led us to probe whether there was a non-conformational origin to this heterogeneity. We determined that routine protocols in RNA preparation and purification, including UV shadowing and heat annealing, cause covalent modifications that alter folding behavior. By taking measures to avoid these treatments and by purifying away damaged P4-P6 molecules, we obtained a population of P4-P6 that gave near-uniform behavior in single molecule studies. Thus, the folding landscape of P4-P6 lacks multiple deep furrows that would trap different P4-P6 molecules in different conformations and contrasts with the molecular heterogeneity that has been seen in many smFRET studies of structured RNAs. The simplicity of P4-P6 allowed us to reliably determine the thermodynamic and kinetic effects of metal ions on folding and to now begin to build more detailed models for RNA folding behavior.

A biophysical protein folding model accounts for most mutational fitness effects in viruses

Fitness effects of mutations fall on a continuum ranging from lethal to deleterious to beneficial. The distribution of fitness effects (DFE) among random mutations is an essential component of every evolutionary model and a mathematical portrait of robustness. Recent experiments on five viral species all revealed a characteristic bimodal-shaped DFE featuring peaks at neutrality and lethality. However, the phenotypic causes underlying observed fitness effects are still unknown and presumably, are thought to vary unpredictably from one mutation to another. By combining population genetics simulations with a simple biophysical protein folding model, we show that protein thermodynamic stability accounts for a large fraction of observed mutational effects. We assume that moderately destabilizing mutations inflict a fitness penalty proportional to the reduction in folded protein, which depends continuously on folding free energy (ΔG). Most mutations in our model affect fitness by altering ΔG, whereas based on simple estimates, ~10% abolish activity and are unconditionally lethal. Mutations pushing ΔG > 0 are also considered lethal. Contrary to neutral network theory, we find that, in mutation/selection/drift steady state, high mutation rates (m) lead to less stable proteins and a more dispersed DFE (i.e., less mutational robustness). Small population size (N) also decreases stability and robustness. In our model, a continuum of nonlethal mutations reduces fitness by ~2% on average, whereas ~10-35% of mutations are lethal depending on N and m. Compensatory mutations are common in small populations with high mutation rates. More broadly, we conclude that interplay between biophysical and population genetic forces shapes the DFE.

Identification of Multiple Folding Pathways of Monellin Using Pulsed Thiol Labeling and Mass Spectrometry

Protein folding reactions often display multiexponential kinetics of changes in intrinsic optical signals, as a manifestation of heterogeneity, either on one folding pathway or on multiple folding pathways. Delineating the origin of this heterogeneity is difficult because different coexisting structural forms of a protein cannot be easily distinguished by optical probes. In this study, the complex folding reaction of single-chain monellin has been investigated using a pulsed thiol labeling (SX) methodology in conjunction with mass spectrometry, which measures the kinetics of burial of a cysteine side chain thiol during folding. Because it can directly distinguish between unfolded and folded molecules and can measure the disappearance of the former during folding, the pulsed SX methodology is an ideal method for investigating whether multiple pathways are operative during folding. The kinetics of burial of the C42 thiol of monellin was observed to follow biexponential kinetics. To determine whether this was because the fast phase leads to the partial protection of the thiol group in all the molecules or to complete protection in only a fraction of the molecules, the duration and intensity of the labeling pulse were varied. The observation that the extent of labeling did not vary with the duration of the pulse cannot be explained by a simple sequential folding mechanism. Two parallel folding pathways are shown to be operative, with one leading to the formation of thiol-protective structure more rapidly than the other.

ABC of molecular origami

Arranging polymers into well-defined shapes endows them with specific properties; but although it is routinely achieved in nature, accurate origami has proved challenging with synthetic polymers. A surprisingly simple folding strategy has now been described.

Bacterial proteins fold faster than eukaryotic proteins with simple folding kinetics

Protein domain frequency and distribution among kingdoms was statistically analyzed using the SCOP structural database. It appeared that among chosen protein domains with the best resolution, eukaryotic proteins more often belong to α-helical and β-structural proteins, while proteins of bacterial origin belong to α/β structural class. Statistical analysis of folding rates of 73 proteins with known experimental data revealed that bacterial proteins with simple kinetics (23 proteins) exhibit a higher folding rate compared to eukaryotic proteins with simple folding kinetics (27 proteins). Analysis of protein domain amino acid composition showed that the frequency of amino acid residues in proteins of eukaryotic and bacterial origin is different for proteins with simple and complex folding kinetics.

Is Stoichiometry-Driven Protein Folding Getting Out of Thermodynamic Control?

conditions is fundamental to describing their functions at molecular level. Sig-nificant advances in theory, experiment and simulation have been achieved (1), making it possible to solve the three mostly focused aspects of protein folding problems (2):(i) The thermodynamic question of how a native structure results from inter-atomic forces acting on an amino acid sequence - the folding code; (ii) The kinetic problem of how a native structure can fold so fast - the folding rate;(iii) The computational problem of how to predict the native structure of a protein from its amino acid sequence – the protein structure prediction. The views on protein folding have evolved from simple force-driven folding (3),

Column-Parallel Correlated Multiple Sampling Circuits for CMOS Image Sensors and Their Noise Reduction Effects

For low-noise complementary metal-oxide-semiconductor (CMOS) image sensors, the reduction of pixel source follower noises is becoming very important. Column-parallel high-gain readout circuits are useful for low-noise CMOS image sensors. This paper presents column-parallel high-gain signal readout circuits, correlated multiple sampling (CMS) circuits and their noise reduction effects. In the CMS, the gain of the noise cancelling is controlled by the number of samplings. It has a similar effect to that of an amplified CDS for the thermal noise but is a little more effective for 1/f and RTS noises. Two types of the CMS with simple integration and folding integration are proposed. In the folding integration, the output signal swing is suppressed by a negative feedback using a comparator and one-bit D-to-A converter. The CMS circuit using the folding integration technique allows to realize a very low-noise level while maintaining a wide dynamic range. The noise reduction effects of their circuits have been investigated with a noise analysis and an implementation of a 1Mpixel pinned photodiode CMOS image sensor. Using 16 samplings, dynamic range of 59.4 dB and noise level of 1.9 e− for the simple integration CMS and 75 dB and 2.2 e− for the folding integration CMS, respectively, are obtained.

High-resolution angle-resolved photoemission spectroscopy study of the electronic structure ofEuFe2As2

We report the high-resolution angle-resolved photoemission spectroscopy studies of electronic structure of ${\text{EuFe}}_{2}{\text{As}}_{2}$. The paramagnetic state data are found to be consistent with density-functional calculations. In the antiferromagnetic ordering state of Fe, our results show that the band splitting, folding, and hybridization evolve with temperature, which cannot be explained by a simple folding picture. Detailed measurements reveal that a tiny electron Fermi pocket and a tiny hole pocket are formed near $(\ensuremath{\pi},\ensuremath{\pi})$ in the $(0,0)\ensuremath{-}(\ensuremath{\pi},\ensuremath{\pi})$ direction, which qualitatively agree with the results of quantum oscillations, considering ${k}_{z}$ variation in Fermi surface. Furthermore, no noticeable change within the energy resolution is observed across the antiferromagnetic transition of ${\text{Eu}}^{2+}$ ordering, suggesting weak coupling between Eu sublattice and FeAs sublattice.

Experimental evidence for a frustrated energy landscape in a three-helix-bundle protein family

Energy landscape theory is a powerful tool for understanding the structure and dynamics of complex molecular systems, in particular biological macromolecules1. The primary sequence of a protein defines its free energy landscape, and thus determines the folding pathway and the rate constants of folding and unfolding, as well as its native structure. Theory has shown that roughness in the energy landscape will lead to slower folding1, but derivation of detailed experimental descriptions of this landscape is challenging. Simple folding models2,3 show that folding is significantly influenced by chain entropy; proteins where the contacts are local fold fast, due to the low entropy cost of forming stabilising, native contacts during folding4,5. For some protein families, stability is also a determinant of folding rate constants6. Where these simple metrics fail to predict folding behaviour it is probable that there are features in the energy landscape that are unusual. Such general observations cannot explain the folding behaviour of the R15, R16 and R17 domains of α-spectrin. R15 folds ~3000 times faster than its homologues, although they have similar structures, stabilities and, as far as can be determined, transition state stabilities7-10. Here we show that landscape roughness (internal friction) is responsible for the slower folding and unfolding of R16 and R17. We use chimeric domains to demonstrate that this internal friction is a property of the core, and suggest that frustration in the landscape of the slow folding spectrin domains may be due to mis-docking of the long helices during folding. Although theoretical studies have suggested that rugged landscapes will result in slower folding, this is the first time that such a phenomenon has been shown experimentally to directly influence the folding kinetics of a “normal” protein with a significant energy barrier – one which folds on a relatively slow ms-s timescale.

Competition between native topology and nonnative interactions in simple and complex folding kinetics of natural and designed proteins

We compared folding properties of designed protein Top7 and natural protein S6 by using coarse-grained chain models with a mainly native-centric construct that accounted also for nonnative hydrophobic interactions and desolvation barriers. Top7 and S6 have similar secondary structure elements and are approximately equal in length and hydrophobic composition. Yet their experimental folding kinetics were drastically different. Consistent with experiment, our simulated folding chevron arm for Top7 exhibited a severe rollover, whereas that for S6 was essentially linear, and Top7 model kinetic relaxation was multiphasic under strongly folding conditions. The peculiar behavior of Top7 was associated with several classes of kinetic traps in our model. Significantly, the amino acid residues participating in nonnative interactions in trapped conformations in our Top7 model overlapped with those deduced experimentally. These affirmations suggest that the simple ingredients of native topology plus sequence-dependent nonnative interactions are sufficient to account for some key features of protein folding kinetics. Notably, when nonnative interactions were absent in the model, Top7 chevron rollover was not correctly predicted. In contrast, nonnative interactions had little effect on the quasi linearity of the model folding chevron arm for S6. This intriguing distinction indicates that folding cooperativity is governed by a subtle interplay between the sequence-dependent driving forces for native topology and the locations of favorable nonnative interactions entailed by the same sequence. Constructed with a capability to mimic this interplay, our simple modeling approach should be useful in general for assessing a designed sequence's potential to fold cooperatively.

Natural and artificial RNAs occupy the same restricted region of sequence space

Different chemical and mutational processes within genomes give rise to sequences with different compositions and perhaps different capacities for evolution. The evolution of functional RNAs may occur on a "neutral network" in which sequences with any given function can easily mutate to sequences with any other. This neutral network hypothesis is more likely if there is a particular region of composition that contains sequences that are functional in general, and if many different functions are possible within this preferred region of composition. We show that sequence preferences in active sites recovered by in vitro selection combine with biophysical folding rules to support the neutral network hypothesis. These simple active-site specifications and folding preferences obtained by artificial selection experiments recapture the previously observed purine bias and specific spread along the GC axis of naturally occurring aptamers and ribozymes isolated from organisms, although other types of RNAs, such as miRNA precursors and spliceosomal RNAs, that act primarily through complementarity to other amino acids do not share these preferences. These universal evolved sequence features are therefore intrinsic in RNA molecules that bind small-molecule targets or catalyze reactions.

The prolyl isomerase domain of PpiD fromEscherichia colishows a parvulin fold but is devoid of catalytic activity

PpiD is a periplasmic folding helper protein of Escherichia coli. It consists of an N-terminal helix that anchors PpiD in the inner membrane near the SecYEG translocon, followed by three periplasmic domains. The second domain (residues 264-357) shows homology to parvulin-like prolyl isomerases. This domain is a well folded, stable protein and follows a simple two-state folding mechanism. In its solution structure, as determined by NMR spectroscopy, it resembles most closely the first parvulin domain of the SurA protein, which resides in the periplasm of E. coli as well. A previously reported prolyl isomerase activity of PpiD could not be reproduced when using improved protease-free peptide assays or assays with refolding proteins as substrates. The parvulin domain of PpiD interacts, however, with a proline-containing tetrapeptide, and the binding site, as identified by NMR resonance shift analysis, colocalized with the catalytic sites of other parvulins. In its structure, the parvulin domain of PpiD resembles most closely the inactive first parvulin domain of SurA, which is part of the chaperone unit of this protein and presumably involved in substrate recognition.

Unconventional electronic reconstruction in undoped(Ba,Sr)Fe2As2across the spin density wave transition

Through a systematic high-resolution angle-resolved photoemission study of the iron pnictide compounds $(\text{Ba},\text{Sr}){\text{Fe}}_{2}{\text{As}}_{2}$, we show that the electronic structures of these compounds are significantly reconstructed across the spin density wave transition, which cannot be described by a simple folding scenario of conventional density wave ordering. Moreover, we find that LDA calculations with an incorporated suppressed magnetic moment of $0.5{\ensuremath{\mu}}_{\text{B}}$ can match well the details in the reconstructed electronic structure, suggesting that the nature of magnetism in the pnictides is more itinerant than local, while the origin of suppressed magnetic moment remains an important issue for future investigations.

Vibration and Flutter Characteristics of a Folding Wing

Studies are presented that characterize the dynamic aeroelastic aspects of a morphing aircraft design concept. The notion of interest is a folding wing design resulting in large-scale wing area changes. A finite element approach is used to investigate the sensitivity of natural frequencies and flutter instabilities to the wing position (e.g., fold angle), actuator stiffness, and vehicle weight. Sensitivities in these areas drive design requirements and raise flight envelope awareness issues. The study is presented in two parts as a comparison between two models of varying complexity. A simple folding wing model, based on the Goland wing, is analyzed and results are compared with a built-up structural model of the proposed full scale morphing vehicle.

Experimental determination of the band structure of photonic crystals of colloidal silica spheres

A photonic band structure of colloidal crystals of silica spheres is analytically determined by a band model with three fitting parameters: the sphere size, the effective refractive index, and the band-gap. Optical properties of the crystals annealed at various temperatures were characterized by a procedure similar to X-ray diffraction technique, and the width of photonic band-gap measured from the transmission spectra experimentally servers as an additional check on the validation of the model. The photonic band structures defined by the band-gap, the refractive index, and the Brillouin zone are obviously superior to the use of the Bragg's expression involving simple zone folding.

A designed protein as experimental model of primordial folding

How do proteins accomplish folding during early evolution? Theoretically the mechanism involves the selective stabilization of the native structure against all other competing compact conformations in a process that involves cumulative changes in the amino acid sequence along geological timescales. Thus, an evolved protein folds into a single structure at physiological temperature, but the conformational competition remains latent. For natural proteins such competition should emerge only near cryogenic temperatures, which places it beyond experimental testing. Here, we introduce a designed monomeric miniprotein (FSD-1ss) that within biological temperatures (330-280 K) switches between simple fast folding and highly complex conformational dynamics in a structurally degenerate compact ensemble. Our findings demonstrate the physical basis for protein folding evolution in a designed protein, which exhibits poorly evolved or primordial folding. Furthermore, these results open the door to the experimental exploration of primitive folding and the switching between alternative protein structures that takes place in evolutionary branching points and prion diseases, as well as the benchmarking of de novo design methods.

Dynamics of one-state downhill protein folding.

The small helical protein BBL has been shown to fold and unfold in the absence of a free energy barrier according to a battery of quantitative criteria in equilibrium experiments, including probe-dependent equilibrium unfolding, complex coupling between denaturing agents, characteristic DSC thermogram, gradual melting of secondary structure, and heterogeneous atom-by-atom unfolding behaviors spanning the entire unfolding process. Here, we present the results of nanosecond T-jump experiments probing backbone structure by IR and end-to-end distance by FRET. The folding dynamics observed with these two probes are both exponential with common relaxation times but have large differences in amplitude following their probe-dependent equilibrium unfolding. The quantitative analysis of amplitude and relaxation time data for both probes shows that BBL folding dynamics are fully consistent with the one-state folding scenario and incompatible with alternative models involving one or several barrier crossing events. At 333 K, the relaxation time for BBL is 1.3 micros, in agreement with previous folding speed limit estimates. However, late folding events at room temperature are an order of magnitude slower (20 micros), indicating a relatively rough underlying energy landscape. Our results in BBL expose the dynamic features of one-state folding and chart the intrinsic time-scales for conformational motions along the folding process. Interestingly, the simple self-averaging folding dynamics of BBL are the exact dynamic properties required in molecular rheostats, thus supporting a biological role for one-state folding.

The basal chordate amphioxus as a simple model for elucidating developmental mechanisms in vertebrates

This review examines the basal chordate, amphioxus, as a simple model for providing insights into the development and evolution of the vertebrates, with which it shares many features, including a pharynx perforated with gill slits, a dorsal nerve cord, segmented muscles, and a notochord. Conversely, amphioxus is simpler than vertebrates in lacking neural crest and paired cephalic sensory organs. Amphioxus embryos are less derived than those of vertebrates, because it lacks large quantities of yolk and/or extra-embryonic tissues. Embryogenesis involves only a simple folding of tissue layers. In addition, the amphioxus genome lacks the large-scale gene duplications of vertebrates. However, in spite of the comparative simplicity of amphioxus, its developmental mechanisms are proving to be highly conserved with those of vertebrates. Thus, studies of amphioxus development can shed light on similar, but more complex, development of vertebrates. Such studies are especially interesting for their insights into the genetic basis of craniofacial birth defects in humans.