Two-state Behavior Research Articles

Peptide Folding Using Multiscale Coarse-Grained Models

The multiscale coarse-graining (MS-CG) method has been previously used to describe the equilibrium properties of peptides. The present study reveals that MS-CG models of alpha-helical polyalanine and the beta-hairpin V 5PGV 5 possess the capacity to efficiently refold in simulations initiated from unfolded configurations. The MS-CG peptides exhibit free energy landscapes that are funneled toward folded configurations and two-state folding behavior, consistent with the known characteristics of small, rapidly folding peptides. Moreover, the models demonstrate enhanced sampling capabilities when compared to systems with full atomic detail. The significance of these observations with respect to the theoretical basis of the MS-CG approach is discussed. The MS-CG peptides were used to reconstruct atomically detailed configurations in order to evaluate the extent to which MS-CG ensembles embody all-atom peptide free energy landscapes. Ensembles obtained from these reconstructed configurations display good agreement with the all-atom simulation data used to generate the MS-CG models and also corroborate the presence of features observed in the MS-CG peptide free energy landscapes. These findings suggest that MS-CG models may be of significant utility in the study of peptide folding.

Effects of Excluded Volume upon Protein Stability in Covalently Cross-Linked Proteins with Variable Linker Lengths

To explore the effects of molecular crowding and excluded volume upon protein stability, we used a series of cross-linking reagents with nine different single-cysteine mutants of staphylococcal nuclease to make covalently linked dimers. These cross-linkers ranged in length from 10.5 to 21.3 A, compelling separations which would normally be found only in the most concentrated protein solutions. The stabilities of the dimeric proteins and monomeric controls were determined by guanidine hydrochloride and thermal denaturation. Dimers with short linkers tend to exhibit pronounced three-state denaturation behavior, as opposed to the two-state behavior of the monomeric controls. Increasing linker length leads to less pronounced three-state behavior. The three-state behavior is interpreted in a three-state model where cross-linked native protein dimer, N-N, interconverts in a two-state transition with a dimer where one protein subunit is denatured, N-D. The remaining native protein in turn can denature in another two-state transition to a state, D-D, in which both tethered proteins are denatured. Three-state behavior is best explained by excluded volume effects in the denatured state. For many dimers, linkers longer than 17 A removed most three-state character. This sets a limit on the flexibility and size of the denatured state. Notably, in contradiction to theoretical predictions, these cross-linked dimers were not stabilized. The failure of these predictions is possibly due to neglect of the alteration in hydrophobic exposure that accompanies any significant reduction in the conformational space of the denatured state.

The folding transition state theory in simple model systems

We present the results of an exact analysis of several model free energy landscapes of aprotein to clarify the notion of the transition state and the physical meaning of theϕ values determined in protein engineering experiments. We argue that a proper searchstrategy for the transition state in more realistic models should involve identification of acommon part of various methods. Two of the models considered involve explicitconformations instead of just points on the free energy axis. These models are minimalisticas they are endowed only with five or 36 states to enumerate folding paths and to identifythe transition state easily. Even though they display much of the two-state behavior, theϕ values are found not to correspond to the conformation of the transition state.

Single-molecule nonequilibrium periodic Mg 2+ -concentration jump experiments reveal details of the early folding pathways of a large RNA

The evolution of RNA conformation with Mg(2+) concentration ([Mg(2+)]) is typically determined from equilibrium titration measurements or nonequilibrium single [Mg(2+)]-jump measurements. We study the folding of single RNA molecules in response to a series of periodic [Mg(2+)] jumps. The 260-residue catalytic domain of RNase P RNA from Bacillus stearothermophilus is immobilized in a microfluidic flow chamber, and the RNA conformational changes are probed by fluorescence resonance energy transfer (FRET). The kinetics of population redistribution after a [Mg(2+)] jump and the observed connectivity of FRET states reveal details of the folding pathway that complement and transcend information from equilibrium or single-jump measurements. FRET trajectories for jumps from [Mg(2+)] = 0.01 to 0.1 mM exhibit two-state behavior whereas jumps from 0.01 mM to 0.4 mM exhibit two-state unfolding but multistate folding behavior. RNA molecules in the low and high FRET states before the [Mg(2+)] increase are observed to undergo dynamics in two distinct regions of the free energy landscape separated by a high barrier. We describe the RNA structural changes involved in crossing this barrier as a "hidden" degree of freedom because the changes do not alter the detected FRET value but do alter the observed dynamics. The associated memory prevents the populations from achieving their equilibrium values at the end of the 5- to 10-sec [Mg(2+)] interval, thereby creating a nonequilibrium steady-state condition. The capability of interrogating nonequilibrium steady-state RNA conformations and the adjustable period of [Mg(2+)]-jump cycles makes it possible to probe regions of the free energy landscape that are infrequently sampled in equilibrium or single-jump measurements.

Folding of the αΙΙ-spectrin SH3 domain under physiological salt conditions

The SH3 domain has often been used as a model for protein folding due to its typical two-state behaviour. However, recent experimental data at low pH as well as molecular dynamic simulations have indicated that the folding process of SH3 probably is more complicated, and may involve intermediate states. Using both kinetic and equilibrium measurements we have obtained evidence that under native-like conditions the folding of the spectrin SH3 domain does not follow a classic two-state behaviour. The curvature we observed in the Chevron plots is a strong indication of a non-linear activation energy relationship due to the presence of high-energy intermediates. In addition, circular dichroism measurements indicated that refolding after thermal denaturation did not follow the same pattern as thermal unfolding but rather implied less cooperativity and that the refolding transition increased with increasing protein concentration. Further, NMR experiments indicated that upon refolding the SH3 domain gave rise to more than one conformation. Therefore, our results suggest that the folding of the SH3 domain of αII-spectrin does not follow a classical two-state process under high-salt conditions and neutral pH. Heterogeneous folding pathways, which can include folding intermediates as well as misfolded intermediates, might give a more reasonable insight into the folding behaviour of the αII-spectrin SH3 domain.

Thermodynamics and kinetics of a Gō proteinlike heteropolymer model with two-state folding characteristics

We present results of Monte Carlo computer simulations of a coarse-grained hydrophobic-polar Gō-like heteropolymer model and discuss thermodynamic properties and kinetics of an exemplified heteropolymer, exhibiting two-state folding behavior. It turns out that general, characteristic folding features of realistic proteins with a single free-energy barrier can also be observed in this simplified model, where the folding transition is primarily driven by the hydrophobic force.

Domain-wall induced magneto-resistive memory in ferromagnetic (Ga, Mn)As nanostructures

Novel magneto-resistive memory effect is demonstrated, which appears in lithographically patterned Y-shaped, three-terminal nanostructures, consisting of three nanowires joined in one point, formed in the epitaxial layer of a ferromagnetic (Ga,Mn)As semiconductor. The effect, in which the zero-field resistance of a pair of nanowires depends on the direction of the previously applied magnetic field, results from a rearrangement of magnetic domain walls, contributing an extra resistance, between different pairs of nanowires in the structure. Two-state behaviour of the nanostructure resistance provides its usefulness for applications in non-volatile memory devices.

Sequence-Dependent Variations Associated with H2A/H2B Depletion of Nucleosomes

Mechanisms that can alter nucleosome structure to enhance DNA accessibility are of great interest because of their potential involvement in genomic processes. One such mechanism is H2A/H2B release from nucleosomes; it occurs in vivo and is involved in the in vitro activities of several transcription-associated complexes. Using fluorescence approaches based on Förster resonance energy transfer, we previously detected sequence-dependent structure/stability variations between 5S and two types of promoter nucleosomes (from yeast GAL10 or mouse mammary tumor virus promoters). Those variations included differing responses when nucleosomes were diluted to concentrations (sub-nM) known to produce H2A/H2B loss. Here, we show that treatment of these same three types of nucleosomes with the histone chaperone yNAP-1, which causes H2A/H2B release from nucleosomes in vitro, produces the same differential Förster resonance energy transfer responses, again demonstrating sequence-dependent variations associated with conditions that produce H2A/H2B loss. Single-molecule population data indicate that DNA dynamics on the particles produced by diluting nucleosomes to sub-nM concentrations follow two-state behavior. Rate information (determined by fluorescence correlation spectroscopy) suggests that these dynamics are enhanced in MMTV-B or GAL10 compared to 5S particles. Taken together, the results indicate that H2A/H2B loss has differing effects on 5S compared to these two promoter nucleosomes and the differences reflect sequence-dependent structure/stability variations in the depleted particles.

Up and down states

Operationally, up and down states refer to the observation that neurons have two preferred subthreshold membrane potentials, both subthreshold for action potential generation. The most common method of detecting these states is the so-called all-points histogram (Cowan and Wilson, 1994; Wilson and Kawaguchi, 1996; Pare et al., 1998). This method, borrowed from the study of single channel currents, plots the frequency of occurrence of various values of membrane potential for every point in a digitized record. Figure 1 shows a typical example for a striatal spiny neuron, and for a cortical pyramidal cell in layer V, recorded simultaneously. The histogram to the left of each one shows the amount of time the cell spends at each value of membrane potential. Both cells toggle between two preferred membrane potentials, one very hyperpolarized (Down state), and one more depolarized (Up state). In both cells, the Up state is only a few millivolts from the action potential threshold. Usually, membrane potential fluctuations around the Up state are of higher amplitude, whereas the Down state is relatively free of noise. Figure 1 Up and down states. Up and Down states have been most often studied in animals anesthetized with urethane or other anesthetics that induce slow coherent oscillations in the cortex similar to those seen during sleep or anesthesia (e.g. Steriade et al., 1993; Steriade et al., 2001; Mahon et al., 2006; Destexhe et al. 2007). Because of this, Up and Down states are sometimes used as a synonym for slow oscillations. That usage is avoided here, and, Up and Down states will refer only to the set of cellular and network properties that causes neurons to respond to synaptic input in a two-state manner. These cellular properties arise from ionic conductances that are always present in the cell, and can continue to influence cellular activity in other circumstances not associated with slow oscillations. For example, much of the work on Up and Down states has been obtained in tissue slices, which are neither anethetized nor asleep, and often not showing any slow oscillations. Neurons may exhibit two-state behavior because of their intrinsic properties, or because they are in a network that imposes it on them, or both, and may be expressed as a part of a variety of activity states.

Point Mutations in Membrane Proteins Reshape Energy Landscape and Populate Different Unfolding Pathways

Using single-molecule force spectroscopy, we investigated the effect of single point mutations on the energy landscape and unfolding pathways of the transmembrane protein bacteriorhodopsin. We show that the unfolding energy barriers in the energy landscape of the membrane protein followed a simple two-state behavior and represent a manifestation of many converging unfolding pathways. Although the unfolding pathways of wild-type and mutant bacteriorhodopsin did not change, indicating the presence of same ensemble of structural unfolding intermediates, the free energies of the rate-limiting transition states of the bacteriorhodopsin mutants decreased as the distance of those transition states to the folded intermediate states decreased. Thus, all mutants exhibited Hammond behavior and a change in the free energies of the intermediates along the unfolding reaction coordinate and, consequently, their relative occupancies. This is the first experimental proof showing that point mutations can reshape the free energy landscape of a membrane protein and force single proteins to populate certain unfolding pathways over others.

Residue-Specific pKa Determination of Lysine and Arginine Side Chains by Indirect 15N and 13C NMR Spectroscopy: Application to apo Calmodulin

Electrostatic interactions in proteins can be probed experimentally through determination of residue-specific acidity constants. We describe here triple-resonance NMR techniques for direct determination of lysine and arginine side-chain protonation states in proteins. The experiments are based on detection of nonexchangeable protons over the full range of pH and temperature and therefore are well suited for pKa determination of individual amino acid side chains. The experiments follow the side-chain 15Nzeta (lysine) and 15Nepsilon or 13Czeta (arginine) chemical shift, which changes due to sizable changes in the heteronuclear electron distribution upon (de)protonation. Since heteronuclear chemical shifts are overwhelmed by the charge state of the amino acid side chain itself, these methods supersede 1H-based NMR in terms of accuracy, sensitivity, and selectivity. Moreover, the 15Nzeta and 15Nepsilon nuclei may be used to probe changes in the local electrostatic environment. Applications to three proteins are described: apo calmodulin, calbindin D9k, and FKBP12. For apo calmodulin, residue-specific pKa values of lysine side chains were determined to fall between 10.7 and 11.2 as a result of the high net negative charge on the protein surface. Ideal two-state titration behavior observed for all lysines indicates the absence of significant direct charge interactions between the basic residues. These results are compared with earlier studies based on chemical modification.

P31 comet Blocks Mad2 Activation through Structural Mimicry

The status of spindle checkpoint signaling depends on the balance of two opposing dynamic processes that regulate the highly unusual two-state behavior of Mad2. In mitosis, a Mad1-Mad2 core complex recruits cytosolic Mad2 to kinetochores through Mad2 dimerization and converts Mad2 to a conformer amenable to Cdc20 binding, thereby facilitating checkpoint activation. p31(comet) inactivates the checkpoint through binding to Mad1- or Cdc20-bound Mad2, thereby preventing Mad2 activation and promoting the dissociation of the Mad2-Cdc20 complex. Here, we report the crystal structure of the Mad2-p31(comet) complex. The C-terminal region of Mad2 that undergoes rearrangement in different Mad2 conformers is a major structural determinant for p31(comet) binding, explaining the specificity of p31(comet) toward Mad1- or Cdc20-bound Mad2. p31(comet) adopts a fold strikingly similar to that of Mad2 and binds at the dimerization interface of Mad2. Thus, p31(comet) exploits the two-state behavior of Mad2 to block its activation by acting as an "anti-Mad2."

Planar Hall Effect in Ferromagnetic (Ga,Mn)As/GaAs Superlattices

The planar Hall effect was used for investigation of magnetic anisotropy in short period (Ca,Mn)As/CaAs superlattices epitaxially grown on (001) oriented GaAs substrate. The results confirmed the existence of low-temperature magneto crystalline anisotropy in the superlattices with the easy magnetic axes directed along the two in-plane (100) directions. Attention is paid to the two-state behaviour of the planar Hall resistance at zero magnetic field that provides its usefulness for applications in non-volatile memory devices.

Influence of metal ions on folding pathway and conformational stability of bovine serum albumin

In order to understand the effects of metal ions on the structural stability of proteins, urea-induced unfolding transition of bovine serum albumin (BSA) in the presence of different kinds of metal ions (Zn 2+, Ca 2+, Cd 2+ and Co 2+) are characterized by far-UV circular dichroism (CD) and fluorescence spectra. Under neutral condition, there is a significant deviation of the unfolding transition curves of free protein by fluorescence and CD spectra. However, the unfolding curves of fluorescence and CD spectra turn to be coincident in the presence of Ca 2+ or Cd 2+ ions, indicating that the tertiary and secondary structures of BSA unfold simultaneously, i.e. a cooperative two-state behavior, while the deviation of them is enhanced in the presence of Zn 2+ or Co 2+ ions, suggesting that the unfolding remains a three-state behavior. Our results provide evidence that the metal ions alter the urea-induced unfolding pathway of BSA. Furthermore, the change of free energy (Δ G), the midpoint of chemical denaturation ( C m) and the solvent-exposed surface ( m) during the urea-induced unfolding process have also been obtained to characterize the effects of metal ions on the conformational stability of BSA.

Probing the cytochrome c′ folding landscape

The folding kinetics of R. palustris cytochrome c′ (cyt c′) have been monitored by heme absorption and native Trp72 fluorescence at pH 5. The Trp72 fluorescence burst signal suggests early compaction of the polypeptide ensemble. Analysis of heme transient absorption spectra reveals deviations from two-state behavior, including a prominent slow phase that is accelerated by the prolyl isomerase cyclophilin. A nonnative proline configuration (Pro21) likely interferes with the formation of the helical bundle surrounding the heme.

Probing the folding intermediate of Rd‐apocyt b562 by protein engineering and infrared T‐jump

Small proteins often fold in an apparent two-state manner with the absence of detectable early-folding intermediates. Recently, using native-state hydrogen exchange, intermediates that exist after the rate-limiting transition state have been identified for several proteins. However, little is known about the folding kinetics from these post-transition intermediates to their corresponding native states. Herein, we have used protein engineering and a laser-induced temperature-jump (T-jump) technique to investigate this issue and have applied it to Rd-apocyt b(562) , a four-helix bundle protein. Previously, it has been shown that Rd-apocyt b(562) folds via an on-pathway hidden intermediate, which has only the N-terminal helix unfolded. In the present study, a double mutation (V16G/I17A) in the N-terminal helix of Rd-apocyt b(562) was made to further increase the relative population of this intermediate state at high temperature by selectively destabilizing the native state. In the circular dichroism thermal melting experiment, this mutant showed apparent two-state folding behavior. However, in the T-jump experiment, two kinetic phases were observed. Therefore, these results are in agreement with the idea that a folding intermediate is populated on the folding pathway of Rd-apocyt b(562) . Moreover, it was found that the exponential growth rate of the native state from this intermediate state is roughly (25 microsec)(-1) at 65 degrees C.

Protein folding kinetics: barrier effects in chemical and thermal denaturation experiments.

Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.

Secondary structure length as a determinant of folding rate of proteins with two‐ and three‐state kinetics

We present a simple method for determining the folding rates of two- and three-state proteins from the number of residues in their secondary structures (secondary structure length). The method is based on the hypothesis that two- and three-state foldings share a common pattern. Three-state proteins first condense into metastable intermediates, subsequent forming of alpha-helices, turns, and beta-sheets at slow rate-limiting step. The folding rate of such proteins anticorrelate with the length of these beta-secondary structures. It is also assumed that in two-state folding, rapidly folded alpha-helices and turns may facilitate formation of fleeting unobservable intermediates and thus show two-state behavior. There is an inverse relationship between the folding rate and the length of beta-sheets and loops. Our study achieves 94.0 and 88.1% correlations with folding rates determined experimentally for 21 three- and 38 two-state proteins, respectively, suggesting that protein-folding rates are determined by the secondary structure length. The kinetic kinds are selected on the basis of a competitive formation of hydrophobic collapse and alpha-structure in early intermediates.

Effect of force on mononucleosomal dynamics

Using single-molecule optical-trapping techniques, we examined the force-induced dynamic behavior of a single nucleosome core particle. Our experiments using the DNA construct containing the 601 nucleosome-positioning sequence revealed that the nucleosome unravels in at least two major stages. The first stage, which we attributed to the unraveling of the first DNA wrap around the histone octamer, could be mechanically induced in a reversible manner, and when kept at constant force within a critical force range, exhibited two-state hopping behavior. From the hopping data, we determined the force-dependent equilibrium constant and rates for opening/closing of the outer wrap. Our investigation of the second unraveling event at various loading rates, which we attributed to the inner DNA wrap, revealed that this unraveling event cannot be described as a simple two-state process. We also looked at the behavior of the mononucleosome in a high-salt buffer, which revealed that the outer DNA wrap is more sensitive to changes in the ionic environment than the inner DNA wrap. These findings are needed to understand the energetics of nucleosome remodeling.

Insights into Allosteric Control of Vinculin Function from Its Large Scale Conformational Dynamics

Vinculin is an important constituent of both cell-cell and cell-matrix junctions, where it plays crucial roles in the regulation of cell adhesion and migration. When activated, it mediates the linkage between cadherins (cell-cell) or integrins (cell-matrix) and the actin cytoskeleton through interactions with various proteins. The activation of vinculin requires structural conversions from an autoinhibited conformation to the "open" conformations in which the occluded binding sites of its different ligands become exposed, while the structural dynamics underlying the vinculin activation remains largely unknown. Here we report the first computational study of large scale conformational dynamics of full-length vinculin. We find that the "holding" and "releasing" motions between vinculin tail and pincer-like structure formed by first three domains of vinculin are the dominant motions near the native state of vinculin, indicating that an inherent flexibility of vinculin has a large influence on its allostery. We also find a cooperative dissociation between the head and tail domains of vinculin with increasing temperature in both thermodynamic and kinetic simulations, implying that vinculin may function as an allosteric switch in response to external signals. We show that the kinetics of vinculin unfolding exhibits specific sequential patterns, suggesting that a sophisticated interplay between domains may synergistically contribute to vinculin activation. We further find that the interaction between vinculin-binding site peptide from talin and vinculin significantly destabilizes the intramolecular head-tail interactions, suggesting a direct role of talin binding in vinculin activation.