How amide hydrogens exchange in native proteins

Amide hydrogen exchange (HX) is widely used in protein biophysics even though our ignorance about the HX mechanism makes data interpretation imprecise. Notably, the open exchange-competent conformational state has not been identified. Based on analysis of an ultralong molecular dynamics trajectory of the protein BPTI, we propose that the open (O) states for amides that exchange by subglobal fluctuations are locally distorted conformations with two water molecules directly coordinated to the N–H group. The HX protection factors computed from the relative O-state populations agree well with experiment. The O states of different amides show little or no temporal correlation, even if adjacent residues unfold cooperatively. The mean residence time of the O state is ∼100 ps for all examined amides, so the large variation in measured HX rate must be attributed to the opening frequency. A few amides gain solvent access via tunnels or pores penetrated by water chains including native internal water molecules, but most amides access solvent by more local structural distortions. In either case, we argue that an overcoordinated N–H group is necessary for efficient proton transfer by Grotthuss-type structural diffusion.Before the tightly packed and densely H-bonded structure of globular proteins had been established, Hvidt and Linderstrøm-Lang (1) showed that all backbone amide hydrogens of insulin exchange with water hydrogens, implying that all parts of the polypeptide backbone are, at least transiently, exposed to solvent. In the following 60 y, hydrogen exchange (HX), usually monitored by NMR spectroscopy (2) or mass spectrometry (3), has been widely used to study protein folding and stability (4–10), structure (11, 12), flexibility and dynamics (13–15), and solvent accessibility and binding (16, 17), often with single-residue resolution. However, because the exchange mechanism is unclear, HX data from proteins can, at best, be interpreted qualitatively (18–25).Under most conditions, amide HX is catalyzed by hydroxide ions (26, 27) at a rate that is influenced by inductive and steric effects from adjacent side chains (28). For unstructured peptides, HX is a slow process simply because the hydroxide concentration is low. For example, at 25° C and pH 4, HX occurs on a time scale of minutes. Under similar conditions, amides buried in globular proteins exchange on a wide range of time scales, extending up to centuries. HX can only occur if the amide is exposed to solvent, so conformational fluctuations must be an integral part of the HX mechanism (18).Under sufficiently destabilizing conditions HX occurs from the denatured-state ensemble, but under native conditions few amides exchange by such global unfolding (9, 29–31). For example, in bovine pancreatic trypsin inhibitor (BPTI), 8 amides in the core β-sheet exchange by global unfolding under native conditions (7, 32), whereas the remaining 45 amides require less extensive conformational fluctuations. Much of the debate in the protein HX field over the past half-century has concerned the nature of these subglobal fluctuations and their frequency, duration, amplitude, and cooperativity (18–25).According to the standard HX model (18), each amide can exist in a closed (C) state, where exchange cannot occur, or in an open (O) state, where exchange proceeds at a rate k_int. The kinetic scheme for H exchange into D₂O then reads as(N−H)C⇌kclkop(N−H)O→kint(N−D)Oand the measured steady-state HX rate is k_HX = k_op?k_int/(k_op + k_cl + k_int). To make this phenomenological model practically useful, two auxiliary assumptions are needed to disentangle the conformational and intrinsic parts of the process: (i) The conformational fluctuations (k_op and k_cl) are independent of pH, and (ii) HX from the O state proceeds at the same rate as in model peptides with the same neighboring side chains, so that kint=kHX0.Two HX regimes are distinguished with reference to the pH dependence of k_HX (18). If k_HX is constant in some pH range, it follows that k_int ? k_op + k_cl so that k_HX = k_op. In this so-called EX1 limit, the HX experiment measures the opening rate, or the mean residence time (MRT), of the C state, τ_C = 1/k_op. For BPTI, such pH invariance has only been observed for the eight core amides, and then only in a narrow pH interval (32).More commonly, HX experiments are performed in the EX2 limit, where k_int ? k_op + k_cl. Then k_HX = k_int/(κ + 1), where κ ≡ k_cl/k_op = τ_C/τ_O is the protection factor (PF). At equilibrium, the fractional populations, f_C and f_O, and the rates are linked by detailed balance, k_op?f_C = k_cl?f_O, so the PF may also be expressed as κ = f_C/f_O. Clearly, 1/(κ + 1) is the probability of finding the amide in the O state, 1/κ is the C  ?  O equilibrium constant, and β?ΔG = ln?κ is the free energy difference between the O and C states in units of k_B?T ≡ 1/β. The PF can thus be deduced from the HX rates measured (under EX2 conditions) for the amide in the protein and in a model peptide as κ=kHX0/kHX−1.The vast majority of the available protein HX data pertains to the EX2 regime and thus provides no information about the time scales, τ_C and τ_O, of the conformational fluctuations, except for the EX2 bound: 1/τC+1/τO≫kint≈kHX0. In the typical case where kHX≪kHX0, so that τ_C ? τ_O, we therefore only know that τO≪1/kHX0, which is in the millisecond range at pH 9 (EX2 HX data are usually measured at lower pH, where 1/kHX0 is even longer). Our analysis indicates that τ_O is seven orders of magnitude shorter than this upper bound estimate.The HX experiment is unique in probing sparsely populated conformational states with single-residue resolution. However, the physical significance of the PF is obscured by our ignorance about the structure and dynamics of the O state. Several attempts have been made to correlate experimental PFs with physical attributes of the amides, such as solvent contact (33–37), burial depth (38), intramolecular H-bonds (35, 38–40), packing density (38, 41), or electric field (42). Where significant correlations have been found, they suggest that the chosen attribute can serve as a proxy for the propensity for C → O fluctuations. However, whether based on crystal structures or molecular dynamics (MD) trajectories, these studies examined the time-averaged protein structure, which is dominated by the C state and therefore provides little or no information about the nature of the C → O fluctuations.In principle, the O state can be identified from molecular simulations, but this requires extensive conformational sampling because most C → O transitions are exceedingly rare. To date, this approach has been tried only with coarse-grained and/or empirical protein models without explicit solvent (43–45), or for HX from the denatured-state ensemble (46). The recent availability of ultralong MD simulations with realistic force fields opens up new opportunities in the search for the elusive O state. We have thus analyzed the millisecond MD trajectory of fully solvated native BPTI performed by Shaw et al. (47). Fortunately, BPTI is also among the proteins that have been most thoroughly studied by HX experiments.     

Transient conformational fluctuation of TePixD during a reaction

Knowledge of the dynamical behavior of proteins, and in particular their conformational fluctuations, is essential to understanding the mechanisms underlying their reactions. Here, transient enhancement of the isothermal partial molar compressibility, which is directly related to the conformational fluctuation, during a chemical reaction of a blue light sensor protein from the thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 (TePixD, Tll0078) was investigated in a time-resolved manner. The UV-Vis absorption spectrum of TePixD did not change with the application of high pressure. Conversely, the transient grating signal intensities representing the volume change depended significantly on the pressure. This result implies that the compressibility changes during the reaction. From the pressure dependence of the amplitude, the compressibility change of two short-lived intermediate (I₁ and I₂) states were determined to be +(5.6 ± 0.6) × 10⁻² cm³⋅mol⁻¹⋅MPa⁻¹ for I₁ and +(6.6 ± 0.7)×10⁻² cm³⋅mol⁻¹⋅MPa⁻¹ for I₂. This result showed that the structural fluctuation of intermediates was enhanced during the reaction. To clarify the relationship between the fluctuation and the reaction, the compressibility of multiply excited TePixD was investigated. The isothermal compressibility of I₁ and I₂ intermediates of TePixD showed a monotonic decrease with increasing excitation laser power, and this tendency correlated with the reactivity of the protein. This result indicates that the TePixD decamer cannot react when its structural fluctuation is small. We concluded that the enhanced compressibility is an important factor for triggering the reaction of TePixD. To our knowledge, this is the first report showing enhanced fluctuations of intermediate species during a protein reaction, supporting the importance of fluctuations.Proteins often transfer information through changes in domain–domain (or intermolecular) interactions. Photosensor proteins are an important example. They have light-sensing domains and function by using the light-driven changes in domain–domain interactions (1). The sensor of blue light using FAD (BLUF) domain is a light-sensing module found widely among the bacterial kingdom (2). The BLUF domain initiates its photoreaction by the light excitation of the flavin moiety inside the protein, which changes the domain–domain interaction, causing a quaternary structural change and finally transmitting biological signals (3, 4). It has been an important research topic to elucidate how the initial photochemistry occurring in the vicinity of the chromophore leads to the subsequent large conformation change in other domains, which are generally apart from the chromophore.It may be reasonable to consider that the conformation change in the BLUF domain is the driving force in its subsequent reaction; that is, the change in domain–domain interaction. However, sometimes, clear conformational changes have not been observed for the BLUF domain; its conformation is very similar before and after photo-excitation (5–13). The circular dichroism (CD) spectra of BLUF proteins AppA and PixD from thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 (TePixD) did not change on illumination (5, 13). Similarly, solution NMR studies of AppA and BlrB showed only small chemical shifts on excitation (9, 10). The solution NMR structure of BlrP1 showed a clear change, but this was limited in its C-terminal extension region and not core BLUF (11). Furthermore, the diffusion coefficient (D) of the BLUF domain of YcgF was not changed by photo-excitation (12), although D is sensitive to global conformational changes. These results imply that a minor structural change occurs in the BLUF domain. In such cases, how does the BLUF domain control its interdomain interaction? Recently, a molecular dynamics (MD) simulation on another light-sensing domain, the light-oxygen-voltage (LOV) sensing domain, suggested that fluctuation of the LOV core structure could be a key to understanding the mechanism of information transfer (14–16).Because proteins work at room temperature, they are exposed to thermal fluctuations. The importance of such structural fluctuations for biomolecular reactions has been also pointed out: for example, enzymatic activity (17–20). Experimental detections of such conformation fluctuations using single molecular detection (21) or NMR techniques such as the hydrogen-deuterium (H-D) exchange, relaxation dispersion method, and high-pressure NMR (22–24) have succeeded. However, these techniques could not detect the fluctuation of short-lived transient species. Indeed, single molecule spectroscopy can trace the fluctuation in real time, but it is still rather difficult to detect rapid fluctuations for a short-lived intermediate during a reaction. Therefore, information about the fluctuation of intermediates is thus far limited.A thermodynamic measurement is another way to characterize the fluctuation of proteins. In particular, the partial molar isothermal compressibility [K¯T=−(∂V¯/∂P)T] is essential, because this property is directly linked to the mean-square fluctuations of the protein partial molar volume by 〈(V¯−〈V¯〉)2〉≡〈δV¯2〉=kBTK¯T (25). (Here, <X> means the averaged value of a quantity of X.) Therefore, isothermal compressibility is thought to reflect the structural fluctuation of molecules (26). However, experimental measurement of this parameter of proteins in a dilute solution is quite difficult. Indeed, this quantity has been determined indirectly from the theoretical equation using the adiabatic compressibility of a protein solution, which was determined by the sound velocity in the solution (26–31). Although the relation between volume fluctuations and isothermal compressibility is rigorously correct only with respect to the intrinsic part of the volume compressibility, and not the partial molar volume compressibility (32), we considered that this partial molar volume compressibility is still useful for characterizing the fluctuation of the protein structure including its interacting water molecules. In fact, the relationship between β¯T and the volume fluctuation has been often used to discuss the fluctuation of proteins (17, 26–28), and the strong correlation of β¯T of reactants with the functioning for some enzymes (17, 33, 34) has been reported. These studies show the functional importance of the structural fluctuation represented by β¯T. However, thermodynamic techniques lack time resolution, and it has been impossible to measure the fluctuations of short-lived intermediate species.Recently, we developed a time-resolving method for assessing thermodynamic properties using the pulsed laser induced transient grating (TG) method. Using this method, we thus far succeeded in measuring the enthalpy change (ΔH) (35–38), partial molar volume change (ΔV¯) (12, 35, 37), thermal expansion change (Δα¯th) (12, 37), and heat capacity change (ΔC_p) (36–38) for short-lived species. Therefore, in principle, the partial molar isothermal compressibility change (ΔK¯T) of a short-lived intermediate become observable if we conduct the TG experiment under the high-pressure condition and detect ΔV¯ with varying external pressure.There are several difficulties in applying the traditional high-pressure cell to the TG method to measure thermodynamic parameters quantitatively. The most serious problem is ensuring the quantitative performance of the intensity of TG signals measured under the high-pressure condition. On this point, our group has developed a new high-pressure cell specially designed for TG spectroscopy (39) and overcome this problem. In this paper, by applying this high-pressure TG system to the BLUF protein TePixD, we report the first measurement, to our knowledge, of ΔK¯T of short-lived intermediates to investigate the mechanism underlying signal transmission by BLUF proteins, from the view point of the transient fluctuation.TePixD is a homolog of the BLUF protein PixD, which regulates the phototaxis of cyanobacterium (40) and exists in a thermophilic cyanobacterium Thermocynechococcus elongates BP-1 (Tll0078). TePixD is a relatively small (17 kDa) protein that consists only of the BLUF domain with two extended helices in the C-terminal region. In crystals and solutions, it forms a decamer that consists of two pentameric rings (41). The photochemistry of TePixD is typical among BLUF proteins (42–45); on blue light illumination, the absorption spectrum shifts toward red by about 10 nm within a nanosecond. The absorption spectrum does not change further, and the dark state is recovered with a time constant of ∼5 s at room temperature (40, 43). The spectral red shift was explained by the rearrangement of the hydrogen bond network around the chromophore (6, 46–48). The TG method has revealed the dynamic photoreaction mechanism, which cannot be detected by conventional spectroscopic methods. The TG signal of TePixD (Fig. S1) showed that there are two spectrally silent reaction phases: a partial molar volume expansion with the time constant of ∼40 μs and the diffusion coefficient (D) change with a time constant of ∼4 ms. Furthermore, it was reported that the pentamer and decamer states of TePixD are in equilibrium and that the final photoproduct of the decamer is pentamers generated by its dissociation (13, 49). On the basis of these studies, the reaction scheme has been identified as shown in Fig. 1. Here, I₁ is the intermediate of the spectrally red-shifted species (generated within a nanosecond) and I₂ is the one created on the subsequent volume expansion process of +4 cm³⋅mol⁻¹ (∼40 μs). Furthermore, an experiment of the excitation laser power dependence of its TG signal revealed that the TePixD decamer undergoes the original dissociation reaction when only one monomer in the decamer is excited (50). In this study, we investigated the transient compressibility of the intermediates I₁ and I₂ of the photoreaction of TePixD and found a direct link between their fluctuation and reactivity.Open in a separate windowFig. 1.Schematic illustration of the photoreaction of TePixD. Yellow circles represent the TePixD monomer in the ground state, which constructs the decamer and pentamer states. In the dark state, these two forms are in equilibrium. The excited, spectral red-shifted state of the TePixD monomer is indicated by a red circle. The square represents the I₂ state of the monomer, which is created by the volume expansion process.     

Label-free probe of HIV-1 TAT peptide binding to mimetic membranes

The transacting activator of transduction (TAT) protein plays a key role in the progression of AIDS. Studies have shown that a +8 charged sequence of amino acids in the protein, called the TAT peptide, enables the TAT protein to penetrate cell membranes. To probe mechanisms of binding and translocation of the TAT peptide into the cell, investigators have used phospholipid liposomes as cell membrane mimics. We have used the method of surface potential sensitive second harmonic generation (SHG), which is a label-free and interface-selective method, to study the binding of TAT to anionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-1′-rac-glycerol (POPG) and neutral 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) liposomes. It is the SHG sensitivity to the electrostatic field generated by a charged interface that enabled us to obtain the interfacial electrostatic potential. SHG together with the Poisson–Boltzmann equation yielded the dependence of the surface potential on the density of adsorbed TAT. We obtained the dissociation constants K_d for TAT binding to POPC and POPG liposomes and the maximum number of TATs that can bind to a given liposome surface. For POPC K_d was found to be 7.5 ± 2 μM, and for POPG K_d was 29.0 ± 4.0 μM. As TAT was added to the liposome solution the POPC surface potential changed from 0 mV to +37 mV, and for POPG it changed from −57 mV to −37 mV. A numerical calculation of K_d, which included all terms obtained from application of the Poisson–Boltzmann equation to the TAT liposome SHG data, was shown to be in good agreement with an approximated solution.The HIV type 1 (HIV-1) transacting activator of transduction (TAT) is an important regulatory protein for viral gene expression (1–3). It has been established that the TAT protein has a key role in the progression of AIDS and is a potential target for anti-HIV vaccines (4). For the TAT protein to carry out its biological functions, it needs to be readily imported into the cell. Studies on the cellular internalization of TAT have led to the discovery of the TAT peptide, a highly cationic 11-aa region (protein transduction domain) of the 86-aa full-length protein that is responsible for the TAT protein translocating across phospholipid membranes (5–8). The TAT peptide is a member of a class of peptides called cell-penetrating peptides (CPPs) that have generated great interest for drug delivery applications (ref. 9 and references therein). The exact mechanism by which the TAT peptide enters cells is not fully understood, but it is likely to involve a combination of energy-independent penetration and endocytosis pathways (8, 10). The first step in the process is high-affinity binding of the peptide to phospholipids and other components on the cell surface such as proteins and glycosaminoglycans (1, 9).The binding of the TAT peptide to liposomes has been investigated using a variety of techniques, each of which has its own advantages and limitations. Among the techniques are isothermal titration calorimetry (9, 11), fluorescence spectroscopy (12, 13), FRET (12, 14), single-molecule fluorescence microscopy (15, 16), and solid-state NMR (17). Second harmonic generation (SHG), as an interface-selective technique (18–24), does not require a label, and because SHG is sensitive to the interface potential, it is an attractive method to selectively probe the binding of the highly charged (+8) TAT peptide to liposome surfaces. Although coherent SHG is forbidden in centrosymmetric and isotropic bulk media for reasons of symmetry, it can be generated by a centrosymmetric structure, e.g., a sphere, provided that the object is centrosymmetric over roughly the length scale of the optical coherence, which is a function of the particle size, the wavelength of the incident light, and the refractive indexes at ω and 2ω (25–30). As a second-order nonlinear optical technique SHG has symmetry restrictions such that coherent SHG is not generated by the randomly oriented molecules in the bulk liquid, but can be generated coherently by the much smaller population of oriented interfacial species bound to a particle or planar surfaces. As a consequence the SHG signal from the interface is not overwhelmed by SHG from the much larger populations in the bulk media (25–28).The total second harmonic electric field, E_2ω, originating from a charged interface in contact with water can be expressed as (31–33)E2ω∝∑iχc,i(2)EωEω+∑jχinc,j(2)EωEω+χH2O(3)EωEωΦ,[1]where χc,i(2) represents the second-order susceptibility of the species i present at the interface; χinc,j(2) represents the incoherent contribution of the second-order susceptibility, arising from density and orientational fluctuations of the species j present in solution, often referred to as hyper-Rayleigh scattering; χH2O(3) is the third-order susceptibility originating chiefly from the polarization of the bulk water molecules polarized by the charged interface; Φ is the potential at the interface that is created by the surface charge; and E_ω is the electric field of the incident light at the fundamental frequency ω. The second-order susceptibility, χc,i(2), can be written as the product of the number of molecules, N, at the surface and the orientational ensemble average of the hyperpolarizability α_i⁽²⁾ of surface species i, yielding χc,i(2)=N〈αi(2)〉 (18). The bracket ?? indicates an orientational average over the interfacial molecules. The third term in Eq. 1 depicts a third-order process by which a second harmonic field is generated by a charged interface. This term is the focus of our work. The SHG signal is dependent on the surface potential created by the electrostatic field of the surface charges, often called the χ⁽³⁾ contribution to the SHG signal. The χ⁽³⁾ method has been used to extract the surface charge density of charged planar surfaces and microparticle surfaces, e.g., liposomes, polymer beads, and oil droplets in water (21, 25, 34–39).In this work, the χ⁽³⁾ SHG method is used to explore a biomedically relevant process. The binding of the highly cationic HIV-1 TAT peptide to liposome membranes changes the surface potential, thereby enabling the use of the χ⁽³⁾ method to study the binding process in a label-free manner. Two kinds of liposomes, neutral 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and anionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-1′-rac-glycerol (POPG), were investigated. The chemical structures of TAT, POPC, and POPG lipids are shown in Scheme 1.Open in a separate windowScheme 1.Chemical structures of HIV-1 TAT (47–57) peptide and the POPC and POPG lipids.     

Understanding the kinetic mechanism of RNA single base pair formation

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model.RNAs perform critical cellular functions at the level of gene expression and regulation (1–4). RNA functions are determined not only by RNA structure or structure motifs [e.g., tetraloop hairpins (5, 6)] but also by conformational distributions and dynamics and kinetics of conformational changes. For example, riboswitches can adopt different conformations in response to specific conditions of the cellular environment (7, 8). Understanding the kinetics, such as the rate and pathways for the conformational changes, is critical for deciphering the mechanism of RNA function (9–19). Extensive experimental and theoretical studies on RNA folding kinetics have provided significant insights into the kinetic mechanism of RNA functions (19–36). However, due to the complexity of the RNA folding energy landscape (37–46) and the limitations of experimental tools (47–55), many fundamental problems, including single base flipping and base pair formation and fraying, remain unresolved. These unsolved fundamental problems have hampered our ability to resolve other important issues, such as RNA hairpin and larger structure folding kinetics. Several key questions remain unanswered, such as whether the hairpin folding is rate-limited by the conformational search of the native base pairs, whose formation leads to fast downhill folding of the whole structure, or by the breaking of misfolded base pairs before refolding to the native structure (18, 19, 54–73).Motivated by the need to understand the basic steps of nucleic acids folding, Hagan et al. (74) performed forty-three 200-ps unfolding trajectories at 400 K and identified both on- and off-pathway intermediates and two dominant unfolding pathways for a terminal C-G base pair in a DNA duplex. In one of the pathways, base pairing and stacking interactions are broken concomitantly, whereas in the other pathway, base stacking is broken after base pairing is disrupted. Furthermore, the unfolding requires that the Cyt diffuse away from the pairing Gua to a distance such that the C-G hydrogen bond cannot reform easily. More recently, Colizzi and Bussi (75) performed molecular dynamics (MD) pulling simulations for an RNA duplex and construct free energy landscape from the pulling simulation. The simulation showed that the base pair opening reaction starts with the unbinding of the 5′-base, followed by the unbinding of the 3′-base (i.e., the 5′-base is less stable than the 3′-base). These previous unfolding simulations offered significant insights into the pathways and transition states. However, as shown below, several important issues remain.One intriguing problem is the rate model for base pairing. There are currently three main types of models. In the first type of model, the barrier ΔG+‡ for closing a base pair is dominated by the entropic cost ΔS for positioning the nucleotides to the base-paired configuration and the barrier ΔG−‡ for opening a base pair is the enthalpic cost ΔH for disrupting the hydrogen bonds and base stacking interactions (18, 59, 60). In the second type of model, ΔG+‡ is the net free energy change for base pairing ΔG = ΔH ? TΔS and ΔG−‡ is zero (76, 77). In the third type of model, ΔG±‡=±ΔG/2 is used (78). In addition to the above three main types, other models, such as more sophisticated hybrid rate models, have been proposed (29).In this paper, we report a hybrid method (see Fig. 1) to investigate the single base pairing process. In contrast to the previous simulations for temperature- or force-induced unfolding reactions, we directly model the folding process here (i.e., the base pair closing process). Specifically, we use MD simulations to identify the conformational clusters. Based on the network of the conformational clusters as a reduced conformational ensemble, we apply kinetic Monte Carlo (KMC) and master equation (ME) methods to elucidate the detailed roles of base pairing and stacking interactions, as well as the roles of water and ions (79–82). The study reveals previously unidentified kinetics pathways, misfolded states, and rate-limiting steps. A clear understanding of the microscopic details of the elementary kinetic move is a prerequisite for further rigorous study of large-scale RNA kinetic studies. The method described here may provide a feasible way to develop a rate model for the base pair/stack-based kinetic move set. Furthermore, the mechanism of RNA single base folding may provide useful insights into many biologically significant processes, such as nucleotide flipping (83) in helicases and base pair fraying (84) (as the possible first step for nucleic duplex melting in nucleic acid enzymatic processes).Open in a separate windowFig. 1.(A) Folding of a single nucleotide (G1, red) from the unfolded (Left) to the native folded (Right) state. (B) Exhaustive sampling for the (discrete) conformations of the G1 nucleotide (Right) through enumeration of the torsion angles (formed by the blue bonds). (C) Schematic plot shows the trajectories on the energy landscape (depicted with two reaction coordinates for clarity) explored by the MD simulations. The lines, open circles, and hexagons denote the trajectories; the initial states; and the (centroid structures of the) clusters, respectively. (D) Conformational network based on six clusters. (E) The rmsds to the different clusters provide information about the structural changes in a MD trajectory.     

Electrostatics-driven shape transitions in soft shells

Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we investigate charged elastic shells that do not exchange material with their environment, such as elastic membranes formed in emulsions or synthetic nanocontainers. We find that by decreasing the salt concentration or increasing the total charge on the shell’s surface, the spherical symmetry is broken, leading to the formation of ellipsoids, discs, and bowls. Shape changes are accompanied by a significant lowering of the electrostatic energy and a rise in the surface area of the shell. To substantiate our simulation findings, we show analytically that a uniformly charged disc has a lower Coulomb energy than a sphere of the same volume. Further, we test the robustness of our results by including the effects of charge renormalization in the analysis of the shape transitions and find the latter to be feasible for a wide range of shell volume fractions.Biological matter in cells is often compartmentalized by elastic membranes that take various shapes such as blood cell membranes, organelles, and viral capsids. These biomembranes are highly optimized to perform specific functions. A key focus of current biomedical technologies is to engineer synthetic materials that can match the performance and structural sophistication displayed by natural entities. Mimicking key physical features of biomembranes, including shape, size, and flexibility, is a crucial step toward the design of such synthetic biomaterials (1). Recent findings also indicate that the shape of a drug-carrier nanoparticle directly influences the amount and efficiency of drug delivery (2–5). The shape and deformability of soft materials such as colloids, emulsions, hydrogels, or micelles play an important role in determining their usefulness in various technological applications as well (6–9). For example, colloidal self-assembly is governed to a large extent by the shape of individual colloids (6, 10, 11). Similarly, controlling the shape and size of reverse micelles is of key importance in their use as solvent extraction systems for removing rare earth metals from aqueous solutions or as templates for nanoparticle synthesis (12–15).Shape transformations in materials are engineered via chemically induced modifications (10, 11) or using techniques such as photoswitching of membrane properties (16) and controlled evaporation of the enclosed solvent (17). However, generating desired material shapes with precision and manipulating them with relative ease at the nanoscale has been a challenge (6). From the theoretical standpoint, much attention has been focused on finding the low-energy conformations of flexible materials, modeled often as soft elastic membranes, in the hope of suggesting superior experimental systems that can enable the design of nanostructures (18–20). Examples include the exploration of shape transitions driven by topological defects (21–23) or compression (24), and the study of low-energy conformations of multicomponent shells (18, 25–27).Changing the shape of an elastic shell entails bending and stretching it, and the associated energy costs form the components of the elastic free energy of the shell (28). However, when the shell is charged, it is possible to compensate for the increase in elastic energy associated with the shape deformation if the latter is accompanied with a significant lowering of the electrostatic free energy (29–33). Previous studies on charged soft membranes mainly focused on mapping a charged elastic shell to an uncharged elastic shell with charge-renormalized elastic parameters (34–39). In the case of charged nanoshells, electrostatic screening length is comparable to the shell dimensions, and the surface-charge density can assume high values. As a result, shell models where Coulomb interactions are included explicitly are needed (29, 30). Using such models, it has been shown that an ionic shell, where positive and negative charges populate the surface, lowers its energy by taking an icosahedral shape with the same surface area (29). In this work, we find that a uniformly charged, spherical elastic shell, when constrained to maintain the enclosed volume, can lower its free energy by deforming into smooth structures such as ellipsoids, discs, and bowls (Fig. 1). We show that the transition to these nonspherical shapes can be driven by varying environmental properties such as the electrolyte concentration in the surrounding solvent.Open in a separate windowFig. 1.Snapshots of minimum-energy conformations of charged elastic nanoshells for three different bending rigidities κ = 1, 5, and 10 (columns from left to right). In each column the electrolyte concentration c (M) decreases (rows from top to bottom) as c = 1, 0.1, 0.05, and 0.005. Different colors suggest different concentration values, with red being the highest c under study and purple corresponding to the lowest c. As the concentration is lowered, the range of electrostatic interactions is increased, leading to the variation in the shape of the nanoshell. We find that for the concentration range under investigation, softer shells tend to form bowl-like structures, wheras more rigid vesicles form ellipsoidal and disc-like shapes. All of the above nanostructures have the same total surface charge and volume, fixed to values associated with the spherical conformation.To include the nonlinear coupling between the shape of the shell and its electrostatic response self-consistently, we study the charged soft nanoshells numerically. We model the charged shell by a set of discrete points placed on a spherical membrane, forming a mesh consisting of vertices, edges, and faces (Fig. S1), recognizing that in the limit of large number of vertices the discretized elastic membrane recovers the physics of the associated continuum model (see Materials and Methods for details). The uniform surface-charge density is simulated by assigning every vertex with the same charge. We work with elastic parameters such that the uncharged shell assumes a spherical shape at equilibrium. We allow only the deformations that preserve the shell’s total volume, the latter being chosen to be that of the uncharged conformation. Our model is applicable to monolayers, such as emulsions or reverse micelles where nanodroplets of oil or water are surrounded by properly polymerized charged surfactant molecules, and also to incompressible bilayer systems and nanocontainers that do not exchange material with their environment. In the following sections, we provide evidence that this minimum model reproduces various shapes observed experimentally. Furthermore, we test the validity of this electrostatic model and associated simulation results by providing analytical solutions in limiting cases, namely by computing the electrostatic energy of oblate spheroidal shells and comparing it with that of a sphere of the same volume in salt-free conditions. Effects of ion condensation are then included via a two-state model to derive the renormalized charge on the spherical and spheroidal shells to test the robustness of our results.Using the discretization of the continuum expression for the elastic energy introduced in ref. 21, we write the free energy ? associated with the discretized shell asℱ[{ri}]=κ2∑l∈E|nl,1−nl,2|2+k2R2∑l∈E(|rl,1−rl,2|−al)2+lBz22∑i,j∈Ve−|ri−rj|λD|ri−rj|,[1]where ? is measured in units of k_BT. Here T is the room temperature and k_B is the Boltzmann constant. We make the free energy dimensionless by defining κ=κ˜/kBT, where κ˜ is proportional to the bending rigidity κ_b of the continuum model, and k=k˜R2/kBT, with k˜ being proportional to the 2D Young’s modulus Y of the continuous elastic membrane, and R is the spherical shell radius. We use the dimensionless bending rigidity κ and the spring constant k as the scale for bending and stretching energies respectively. In Eq. 1, E and V denote the set of all edges and vertices respectively, and r_i is the position vector of the ith vertex. The first term on the right-hand side is the bending energy with n_l,1 and n_l,2 being the normal vectors to the faces adjacent to edge l. The second term is the stretching energy with r_l,1 and r_l,2 being the position vectors of the vertices corresponding to the edge l, and a_l is the rest length of edge l. The last term is the (dimensionless) electrostatic energy of the model membrane. We consider an aqueous environment inhabiting electrolyte whose presence is taken into consideration implicitly, leading to screened Coulomb interactions between each vertex pair. Here, l_B denotes the Bjerrum length in water, λ_D is the Debye length, and z is a dimensionless charge associated with each vertex. We assume a uniform dielectric to simplify the computations, thus ignoring any induced charge effects.As is evident from Eq. 1, the free energy ? is a function of the set of vertex position vectors {r_i} which also parametrizes the shape of the shell. The equilibrium shape of the shell is the one that corresponds to the minimum of ? subject to constraint of fixed enclosed volume. We perform this constrained free-energy minimization using a molecular dynamics (MD)-based simulated annealing procedure, details of which are provided in Materials and Methods.     

SOD1 aggregation in ALS mice shows simplistic test tube behavior

A longstanding challenge in studies of neurodegenerative disease has been that the pathologic protein aggregates in live tissue are not amenable to structural and kinetic analysis by conventional methods. The situation is put in focus by the current progress in demarcating protein aggregation in vitro, exposing new mechanistic details that are now calling for quantitative in vivo comparison. In this study, we bridge this gap by presenting a direct comparison of the aggregation kinetics of the ALS-associated protein superoxide dismutase 1 (SOD1) in vitro and in transgenic mice. The results based on tissue sampling by quantitative antibody assays show that the SOD1 fibrillation kinetics in vitro mirror with remarkable accuracy the spinal cord aggregate buildup and disease progression in transgenic mice. This similarity between in vitro and in vivo data suggests that, despite the complexity of live tissue, SOD1 aggregation follows robust and simplistic rules, providing new mechanistic insights into the ALS pathology and organism-level manifestation of protein aggregation phenomena in general.So far, the difficulty to experimentally measure protein aggregation in live tissue has focused many researchers to infer mechanistic details of neurodegenerative disease from molecular studies in vitro. An important outcome of this in vitro development is the establishment of rational protocols for quantitative assessment of protein aggregation data (1–4), which now start to consolidate our view of what is happening (5). Protein aggregation follows general and simplistic rules dictated by the amino acid sequence. However, the sheer number of competing aggregation sites within a typical protein chain (6) makes the process intrinsically malleable and dependent on experimental conditions (7). The nagging concern is then to what extent these already complex in vitro data are transferable to the even more complex situation in vivo? Here, we shed light on this question by comparing directly in vitro aggregation kinetics with corresponding data from transgenic mice using a recently developed in vivo quantification strategy based on antibodies (8). Our model system is the aggregation of superoxide dismutase 1 (SOD1) associated with the motor neuron disease ALS (8) (Fig. 1). A key feature of this system is that the immature apoSOD1 monomer, which is also implicated as a precursor in human pathology (9–12), needs to be globally unfolded to fibrillate in vitro (7) (Fig. 1). This simplistic behavior presents the experimental advantage that the fibrillation kinetics of apoSOD1 show simple dependence on structural stability (13, 14):ΔGD−N=−RTlnKD−N=−RTln[N][D],[1]where N is the soluble native structure, and D is the aggregation-competent unfolded state. Accordingly, it has been shown that the in vitro fibrillation of apoSOD1 displays the characteristic fingerprint of fragmentation-assisted growth (15) with a square root dependence on [D] (7), consistent with the requirement of sample agitation to expedite the reaction (1–4, 10). Analogous fibrillation behavior is found for β2-microglobulin (2), yeast prions Sup35 (16) and Ure2p (17), insulin (18), WW domain (19), TI 127 (20), and α-synuclein (21). The main difference between these proteins seems to be that some are intrinsically disordered and constantly aggregation-competent by lacking the ability to hide sticky sequence material by folding. In this study, we see that this simplistic in vitro behavior also translates to the more complex conditions in live tissue: the survival times of ALS mice expressing SOD1 variants of different stabilities are directly correlated with the in vivo levels of globally unfolded protein. Also, spinal cords of mice expressing the human SOD1 mutation G93A show exponential buildup of SOD1 aggregates with a square root dependence on log[D] indistinguishable from the fibrillation kinetics observed in agitated test tubes. The data raise fundamental questions about not only the striking resemblance between mouse and test tube aggregation but also, the apparent differences with human ALS pathology, which seems to have less ordered progression. Clues to the latter, however, are hinted in data from homozygous D90A mice showing two strains of structurally distinct SOD1 aggregates.Open in a separate windowFig. 1.SOD1 aggregation in vitro and in ALS mice. (A) Aggregation of SOD in test tubes yields fibrillar structures similar to those of other proteins (7). (B) Immunohistochemistry of the ventral horn in the terminal hSOD1^G93A mouse showing characteristics of aggresomes (44). (C) Competition between SOD1 folding and fibrillation in vitro, where elongation occurs by unfolded monomers through an encounter complex (7). The question that we ask is how do the in vitro and in vivo aggregations compare mechanistically. (D) Agitation-induced fibrillation in vitro with representative data from an SOD1 mutant in 0 (blue) and 5 M (red) urea with the associated statistics of τ_1/2 for repeated measures. To account for this statistical variation, we use the distribution average (Table S1). (E) Log plot of ν_max vs. τ_1/2 for all individual measures in this study showing uniform behavior of the various SOD1 mutants and a slope of one characteristic for exponential growth (1–4). ALS-associated SOD1 mutations examined in ALS mice (red) (Table S1), other ALS-associated mutations (blue) (Table S1), and SOD1 control mutations (black) (Table S1).     

From the Cover: Folding pathway of a multidomain protein depends on its topology of domain connectivity

How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N- and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N- and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant.Topology of protein conformation, or the spatial arrangement of structural units and the chain connectivity among them, is a key determinant of the folding mechanisms of proteins (1–5). However, predicting a folding pathway is a subtle problem when a protein comprises multiple regions of cooperative structure formation (i.e., foldons or domains). Given that a protein has n such cooperative regions and each region tends to show a two-state–like structural transition between ordered and disordered states, the protein as a whole can have 2ⁿ conformation states and multiple folding routes passing through them are allowed. The statistical weights of these folding routes should be determined both by the interactions among structural regions and the strength of cooperativity within individual regions (6). When multiple competitive routes coexist, the observed folding pathway of an ensemble of molecules should be a superposition of these routes, and the dominant folding pathway should be flexibly changed by changing the solution conditions or by mutations. The multiplicity and flexibility of pathways are important, even for small single-domain proteins like ribosomal protein S6 (7, 8), and are evident for proteins that have repeating structures (9–13). For proteins comprising multiple domains (14), the multiplicity of possible folding pathways is significant. The relative importance among 2ⁿ conformation states in the folding process in proteins with n independently foldable domains should be determined by length, structure (13), the topological connectivity of linkers between domains (3), and the interactions at the interface between domains (3, 15, 16). Fig. 1A shows an example protein for the case n = 2.Open in a separate windowFig. 1.Examples of two-domain proteins with different topological complexities. (A) Human γD-crystallin (PDB ID: 1HK0), which has two independently foldable domains connected by a single linker. (B) DHFR (PDB ID: 1rx1), which is topologically more complex, comprising two domains, DLD (blue) and ABD (pink). DLD is a discontinuous domain comprising the N- and C-terminal parts of the chain, and ABD and DLD are connected by two linkers. The positions of linkers are designated by red arrows.The above mechanism for determining folding intermediates and pathways of multidomain proteins is not applicable when domains have mutually correlated folding tendencies. In particular, the correlation between domains may be significant in a topologically complex protein, which has a domain comprising multiple discontinuous parts of a chain. For example, consider one domain, a discontinuous domain, consisting of residues 1 ≤ i ≤ N₁ and N₂ ≤ i ≤ N, and another domain, a continuous domain, consisting of residues N₁ < i < N₂. Because there is a tendency that the continuous parts of the chain form “islands” of ordered structures (17, 18) and that these continuous parts of a sequence can be the nuclei for folding, the discontinuous domain may not be an independent folding unit, but may depend on the continuous domain. In this paper, we theoretically analyze the problem of how a folding pathway is selected in multidomain proteins that have a discontinuous domain by using Escherichia coli dihydrofolate reductase (DHFR) as an example and compare it with its circular permutant that consists only of continuous domains.As shown in Fig. 1B, DHFR is a 159-residue α/β protein consisting of two domains: a discontinuous loop domain (DLD) (residues 1–37 and 107–159) and an adenosine-binding domain (ABD) (residues 38–106). Because DLD does not include a single contiguous region of the chain, but rather includes separate N- and C-terminal parts, the structural ordering of DLD can be correlated with the structural ordering of ABD. As a model protein, DHFR has been intensively investigated (19–29), which has resulted in a picture that DHFR folds along the following pathway:U→τ7I6→τ6I5→τ5IHF→τ1,…,τ4{N}.[1]Here I₆ is an intermediate exhibiting heterogeneous compactness with DLD being only partially compacted but ABD attaining a native-like compactness (19). I₆ appeared in τ₇ < 35?μs after folding was initiated from the unfolded state (U). During τ₆ ～ 550?μs, further structural development was observed both in ABD and in DLD (19), which led to I₅ in which the secondary structures were reasonably formed (20–22) and two subsets of hydrogen-bonding networks were formed in ABD and DLD (23). During τ₅ ～ 200 ms, structures of ABD and DLD were further organized, which led to the hyperfluorescent intermediate state, I_HF, consisting of four substates, I₁, …, I₄, which matured through four parallel pathways on timescales of τ₁, …, τ₄ = 1 ? 100 s to reach the four native conformers, collectively denoted by {N} in Eq. 1 (24–27). It is plausible that the slow process (several hundred seconds) during the τ₁ ? τ₄ phases is due to intense “internal friction” (30–32) in the glassy dynamics of conformation (33), including formation/disruption of nonnative contacts, the effects of proline isomerization, and the cis–trans isomerization of Gly95 and Gly96. Apart from this complexity during the last phase, the folding scheme in Eq. 1 can be regarded as a hierarchical assembly of structures that begins from the ordering of each domain at the early phase of τ₇ and proceeds to the formation of the whole protein during the later phase of τ₅ (19). Therefore, the questions are the mechanisms for how such a sequential pathway is realized in DHFR and how the topological complexity of DHFR affects the pathway selection.     

Life history effects on the molecular clock of autosomes and sex chromosomes

One of the foundational results in molecular evolution is that the rate at which neutral substitutions accumulate on a lineage equals the rate at which mutations arise. Traits that affect rates of mutation therefore also affect the phylogenetic “molecular clock.” We consider the effects of sex-specific generation times and mutation rates in species with two sexes. In particular, we focus on the effects that the age of onset of male puberty and rates of spermatogenesis have likely had in hominids (great apes), considering a model that approximates features of the mutational process in mammals, birds, and some other vertebrates. As we show, this model can account for a number of seemingly disparate observations: notably, the puzzlingly low X-to-autosome ratios of substitution rates in humans and chimpanzees and differences in rates of autosomal substitutions among hominine lineages (i.e., humans, chimpanzees, and gorillas). The model further suggests how to translate pedigree-based estimates of human mutation rates into split times among extant hominoids (apes), given sex-specific life histories. In so doing, it largely bridges the gap reported between estimates of split times based on fossil and molecular evidence, in particular suggesting that the human–chimpanzee split may have occurred as recently as 6.6 Mya. The model also implies that the “generation time effect” should be stronger in short-lived species, explaining why the generation time has a major influence on yearly substitution rates in mammals but only a subtle one in human pedigrees.Most of our inferences about species split times on short phylogenetic timescales rely on the neutral molecular clock. According to the neutral theory, the number of substitutions K that accumulate in a lineage over T years (e.g., since the split from another species) is K=(u¯/G¯)T, where u¯ and G¯ are the average mutation rate per generation and average generation time, respectively (1). Inferring split times therefore requires estimates of the yearly mutation rate u¯/G¯ on the lineage in question. Such estimates generally derive from securely dated fossils on other lineages or from measurements of mutation rates in extant species (2–5). Using these estimates for dating thus necessitates an understanding of the way that yearly mutation rates may change over time.Neutral substitution patterns in mammals offer some insights. Variation in yearly mutation rates on phylogenetic timescales can be assessed by comparing the number of neutral substitutions along two branches leading from a common ancestor to extant species. These comparisons show marked variation in yearly rates on autosomes. For example, there are 50% fewer substitutions on the human branch compared with rodents (6) and 25% fewer compared with baboons, with more moderate differences among hominine lineages (6–9). The average yearly rates are also negatively correlated with generation times (and their correlates) in extant mammals, leading to the notion of a “generation time effect” on the molecular clock (6, 10, 11).Neutral substitutions rates vary not only among taxa but also between sex chromosomes and autosomes. For brevity, we consider the relative rates on X and autosomes, but these considerations extend naturally to Y (or ZW). Because autosomes spend the same number of generations in both sexes, whereas the X spends twice as many generations in females, rates of neutral substitutions on autosomes reflect a greater relative contribution of male mutations than on the X. In a wide range of taxa, neutral substitutions rates on autosomes are greater than on the X (or lower than on the Z), suggesting a male biased contribution to yearly mutation rates (12). Moreover, observed X-to-autosome ratios are extremely variable, ranging between 0.76 and 0.9 in hominids and up to 1.0 in surveyed mammals, indicating that the degree of male bias itself varies greatly on phylogenetic timescales (12, 13).Our current understanding of mutation can help tie these observations together (5). Pedigree studies in humans and chimpanzees establish that most mutations are paternal in origin and that the paternal but not the maternal contribution increases strongly with age (4, 14). This has long been thought to be true because germ-cell division is arrested before birth in females but proceeds continuously postpuberty in males (5, 15–17). The same reasoning may extend to mammals, birds, and other vertebrate taxa in which oogenesis ceases before birth or hatching (18–20). These considerations suggest that maternal and paternal generation times should affect the molecular clock differently. They also imply that the age of puberty in males and the rate of spermatogenic germ cell divisions should affect yearly mutation rates (5). The variation observed among closely related extant species indicates that these parameters change over phylogenetic timescales. Here we ask how such changes would affect the molecular clock on X and autosomes.     

Quinary structure modulates protein stability in cells

Protein quinary interactions organize the cellular interior and its metabolism. Although the interactions stabilizing secondary, tertiary, and quaternary protein structure are well defined, details about the protein–matrix contacts that comprise quinary structure remain elusive. This gap exists because proteins function in the crowded cellular environment, but are traditionally studied in simple buffered solutions. We use NMR-detected H/D exchange to quantify quinary interactions between the B1 domain of protein G and the cytosol of Escherichia coli. We demonstrate that a surface mutation in this protein is 10-fold more destabilizing in cells than in buffer, a surprising result that firmly establishes the significance of quinary interactions. Remarkably, the energy involved in these interactions can be as large as the energies that stabilize specific protein complexes. These results will drive the critical task of implementing quinary structure into models for understanding the proteome.The inside of cells is packed with macromolecules whose concentrations reach 300–400 g/L (1). Compared with the ideal (dilute) environments conventionally used to study proteins, crowding inside cells can significantly alter the biophysical landscape of proteins, including their equilibrium thermodynamic stability (2–6). Experimental and computational efforts establish that crowding effects arise from a combination of short-range (steric) repulsions and longer-range (often called soft) interactions between macromolecules (7–13). Despite a growing number of in-cell protein studies (2–6), there is no quantitative information about the energetics of quinary interactions.Amide proton exchange experiments have been used for more than 50 y to measure equilibrium protein stability, defined as the Gibbs free energy required to open the protein and expose individual backbone amide protons to solvent, ΔGop°′ (14). For the B1 domain of protein G (GB1), ΔGop°′ equals −RTln(k_obs/k_uns), where R is the gas constant, T is the absolute temperature, k_obs is the observed rate of exchange, and k_uns is the rate in an unstructured peptide (6). We know that the cytoplasm does not affect k_uns (15). Most importantly, we know that for exchange under these conditions ΔGop°′ approximates the free energy required to denature the protein, ΔGden°′ (6). Therefore, these experiments provide a thermodynamically rigorous measure of equilibrium global protein stability. Using this information, we quantified the stability of GB1 at the residue level in Escherichia coli (6) via NMR-detected backbone amide hydrogen/deuterium exchange (16).Thermodynamic cycles (17) can be used to quantify the energetics of interactions between proteins in specific protein complexes (17, 18) and between side chains in globular proteins (19, 20). Briefly, the individual effects of two single-site amino acid changes are compared with the combined effect of both mutations. If the sites interact, the sum of the contributions from the single-site changes will not equal the contribution from the double mutant. The difference between the two values measures the strength of the interaction.We realized that transferring a variant (“var”) from buffer (“buff”) to cells (“cell”) is analogous to making a second mutation to the protein (Fig. 1 and SI Appendix, Fig. S1). Discrepancies in the horizontal (and vertical) sides of Fig. 1 define the free energy (δΔΔGint°′) associated with quinary interactions. Differences in the residue-level stability change caused by the mutation (ΔΔGop,mut°′) in cells and in buffer are used to calculate δΔΔGop,int°′:δΔΔGint°′=(ΔGcell,var°′−ΔGcell,WT°′)−(ΔGbuff,var°′−ΔGbuff,WT°′)=ΔΔGmut,cell°′−ΔΔGmut,buff°′=ΔΔGcell,var°′−ΔΔGcell,WT°′.A negative value of δΔΔGint°′ indicates the introduction of an attractive interaction (relative to WT) upon transferring the mutant from buffer to cells.Open in a separate windowFig. 1.Thermodynamic cycle used to quantify quinary interactions.     

Fragile charge order in the nonsuperconducting ground state of the underdoped high-temperature superconductors

The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa₂Cu₃O6+δ. Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa₂Cu₄O₈, which reveals similar Fermi surface properties to YBa₂Cu₃O6+δ, despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa₂Cu₃O6+δ. Fermi surface reconstruction in YBa₂Cu₄O₈ is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations.The normal state of the underdoped copper oxide superconductors has proven to be even more perplexing than the d-wave superconducting state in these materials. At high temperatures in zero magnetic fields, the normal state of the underdoped cuprates comprises an unconventional Fermi surface of truncated “Fermi arcs” in momentum space, which is referred to as the pseudogap state (1). At low temperatures in high magnetic fields, quantum oscillations reveal the nonsuperconducting ground state in various families of underdoped hole-doped copper oxide superconductors to comprise small Fermi surface pockets (2–15). These small Fermi pockets in YBa₂Cu₃O6+δ have been identified as nodal electron pockets (2, 3, 11, 16, 17) originating from Fermi surface reconstruction associated with charge order measured by X-ray diffraction (18–20), ultrasound (21), nuclear magnetic resonance (22), and optical reflectometry (23). However, various aspects of the underlying charge order and the associated Fermi surface reconstruction remain obscure. A central question pertains to the origin of this charge order, curious features of which include a short correlation length in zero magnetic field that grows with increasing magnetic field and decreasing temperature (20). It is crucial to understand the nature of this ground-state order that is related to the high-temperature pseudogap state and delicately balanced with the superconducting ground state. Here, we shed light on the nature of this state by performing extended magnetic field, temperature, and tilt angle-resolved quantum oscillation experiments in the stoichiometric copper oxide superconductor YBa₂Cu₄O₈ (24). This material with double CuO chains has fixed oxygen stoichiometry, making it a model system to study. YBa₂Cu₄O₈ avoids disorder associated with the fractional oxygen stoichiometry in the YBa₂Cu₃O6+δ chains, which has been shown by microwave conductivity to be the dominant source of weak-limit (Born) scattering (25).Intriguingly, we find magnetic field- and angle-dependent signatures of quantum oscillations in YBa₂Cu₄O₈ (13, 14) that are very similar to those in YBa₂Cu₃O6+δ, indicating a similar nodal Fermi surface that arises from Fermi surface reconstruction by charge order with orthogonal wave vectors (16). However, the same X-ray diffraction measurements that show a Bragg peak characteristic of charge order in YBa₂Cu₃O6+δ for a range of hole dopings from 0.084≤p≤0.164 (19, 20, 26) have, thus far, not revealed a Bragg peak in the case of YBa₂Cu₄O₈ (19). We suggest that charge order enhanced by applied magnetic fields reconstructs the Fermi surface in YBa₂Cu₄O₈, whereas charge order is revealed even in zero magnetic fields in YBa₂Cu₃O6+δ because of pinning by increased disorder from oxygen vacancies.     

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2-xTe3

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a “Dirac-mass gap” in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r) ∝ n(r) is confirmed throughout and exhibits an electron–dopant interaction energy J* = 145 meV·nm². These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.That the surface states of 3D topological insulators (TIs) exhibit a “massless” Dirac spectrum E(k) = ?vk?σ with spin-momentum locking and protected by time-reversal symmetry is now firmly established. Opening a gap in this spectrum is key to the realization of several extraordinary new types of electronic phenomena. The prevalent approach to opening this “Dirac-mass gap” is to dope the materials with magnetic atoms (1–6). A plethora of new physics is then predicted, including σ_xy = ±e²/h quantum anomalous Hall effects (QAHE) (7, 8), topological surface-state magneto-electric effects (9–12), related magneto-optical Kerr and Faraday rotations (10, 13, 14), axionic-like electrodynamics (15, 16), and even E-field induced magnetic monopoles (17, 18). As yet, none of these phenomena except the QAHE (19–22) have been detected, and the QAHE itself is poorly understood because σ_xy = ±e²/h is observed only at temperatures far below 1 K.Interactions between the TI surface electrons and the magnetic dopant atoms at random surface locations r_i can be represented theoretically by a Hamiltonian of the type H_DA = ?J^?∑^?S_i · sδ(r ? r_i). Here S_i (s) is the spin of each dopant (surface-state carrier) measured in units of ?, and J^? is their exchange-interaction energy scale. In the simple case of a homogenous ferromagnetic state with magnetization parallel to the surface normal z^, the Hamiltonian becomes H = ?J^?n₀S_zσ₃/2, where n₀ is the average 2D dopant-atom density and S_z the magnitude of the z component of the dopant spin. Such interactions should open a Zeeman-like energy gap of magnitude Δ = J^?M_z/2μ_B( ≡ mv²), where M_z = n₀S_zμ_B is the homogeneous z^-aligned magnetization, m is the Dirac mass, and v is the Fermi velocity. The resulting surface-state dispersion is given by E±(k)=ED±(ℏv)2k2+Δ2, where E_D is the Dirac point of the ungapped bands measured relative to the surface-state Fermi energy E_F, and Δ is the Dirac-mass gap. Angle-resolved photoemission studies provide good evidence that high densities of magnetic dopant atoms generate a ferromagnetic state and open such energy gaps in TI materials (23, 24). Nevertheless, theoretical studies of dopant effects (1–6) have raised several fundamental issues about the atomic-scale phenomenology of ferromagnetic TIs that can be resolved only by direct electronic structure visualization experiments. First, what effect (if any) does the random distribution of dopant atoms have on the formation and homogeneity of the ferromagnetic state? Second, and perhaps most importantly, what are the consequences of any nanoscale disorder in the ferromagnetism for spatial arrangements of the Dirac-mass gap? Finally, if such Dirac-mass disorder existed, how would it influence the all-important transport characteristics of the surface states? A detailed atomic-scale understanding of the actual physical arrangements of ferromagnetic TI surface states in the presence of magnetic dopant atoms is required to address these issues.     

A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate

We report the observation of coherent circulation in a macroscopic Bose–Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.Ring condensates, analogous to superconducting rings, have received much attention lately (1–9); among other predictions, a ring condensate allows the possibility of macroscopic superposition of states with different circulation. A ring condensate is topologically distinct from a condensate in a simply connected region.With the advance of the field of polariton condensates in the past few years, it is a natural step to create a condensate ring in a microcavity polariton system. The polariton system allows direct, nondestructive observation of the momentum distribution, energy distribution, and spatial distribution of the particles as well as direct measurement of the coherence properties through interferometry. To make a macroscopic ring requires macroscopic transport distances as well as macroscopic coherence length. Macroscopic coherence has been achieved with polaritons with coherent motion over tens of micrometers with lifetimes of 10–20 ps (10, 11) and coherent motion over hundreds of micrometers with lifetimes of 150–200 ps (12–14). One advantage of the long-lifetime polariton systems is that the polaritons can move well away from the laser spot where they are generated, so that the laser can be viewed as a simple source term and does not interact with the condensate. General reviews of previous polariton work with shorter transport distances are in refs. 15–19.The polaritons can be viewed as photons that have been given a small effective mass of the order of 10^?4 times the mass of a vacuum electron and repulsive interactions, which are about 10⁴ times stronger than the typical χ⁽³⁾ nonlinearities of photons in solids. The effective mass comes from the dispersion of the photons in a planar cavity, ℏω=ℏc(k∥2+k⊥)1/2, where k_⊥ is fixed by the width of the cavity, which implies that ℏω≃E0+ℏ2k∥2/2meff with m_eff = ?k_⊥/c for low k_∥. There are two circular polarization modes of the cavity photons corresponding to m = ±1 for the projection of the angular momentum on the z axis perpendicular to the plane. The strong interactions between photons are generated by mixing the photon states with a sharp excitonic resonance in a semiconductor inside the cavity, so that the photons pick up a fraction of the exciton–exciton interaction. Although their interactions are much stronger than the interactions of typical photons in a solid medium, the polaritons are still in the weakly interacting Bose gas regime.The structure for these experiments is a planar cavity, in which the mirrors are distributed Bragg reflectors of AlAs/AlGaAs and the exciton medium consists of GaAs/AlGaAs quantum wells embedded in this cavity. This structure has the same design as that used in previous experiments, which allows coherent transport of polaritons over hundreds of micrometers in the 2D plane of the cavity (12–14). Recent measurements (14) give the cavity lifetime as 135 ps, which corresponds to a polariton lifetime of 200 ps or more. Although this lifetime may seem to be short compared with atoms evaporating from an optical trap on timescales of seconds, the polariton lifetime is sufficient for them to interact many times with each other. In these long-lifetime polariton systems, the ratio of lifetime in the trap to the particle–particle collision time can be of the order of 500:1, comparable with the ratio for cold atom condensates.The lifetime of the polaritons and the strength of the interaction between the polaritons can be tuned by varying the energy difference between the photon states and the exciton states (known as the “detuning”), which leads to a varying degree of mixing of the photons and excitons. Because the planar cavity has a wedge that gives a gradient of cavity width, we can tune the strength of the polariton–polariton interactions simply by choosing different locations on the sample with different cavity width. There is a tradeoff in how much excitonic interaction character to give to the polaritons. Fewer interactions (more photon-like) allow long transport length, whereas more interactions allow better thermalization of the polariton gas through collisions and longer population lifetime.     

An alcohol-sensing site in the calcium- and voltage-gated,large conductance potassium (BK) channel

Ethanol alters BK (slo1) channel function leading to perturbation of physiology and behavior. Site(s) and mechanism(s) of ethanol–BK channel interaction are unknown. We demonstrate that ethanol docks onto a water-accessible site that is strategically positioned between the slo1 calcium-sensors and gate. Ethanol only accesses this site in presence of calcium, the BK channel’s physiological agonist. Within the site, ethanol hydrogen-bonds with K361. Moreover, substitutions that hamper hydrogen bond formation or prevent ethanol from accessing K361 abolish alcohol action without altering basal channel function. Alcohol interacting site dimensions are approximately 10.7 × 8.6 × 7.1 Å, accommodating effective (ethanol-heptanol) but not ineffective (octanol, nonanol) channel activators. This study presents: (i) to our knowledge, the first identification and characterization of an n-alkanol recognition site in a member of the voltage-gated TM6 channel superfamily; (ii) structural insights on ethanol allosteric interactions with ligand-gated ion channels; and (iii) a first step for designing agents that antagonize BK channel-mediated alcohol actions without perturbing basal channel function.Alcohol (ethyl alcohol, ethanol) is a psychoactive agent that has been overwhelmingly consumed by mankind across cultures and civilizations. Alcohol actions on central nervous system (CNS) physiology and behavior are largely independent of beverage type but due to ethanol itself (1). Ethanol alters cell excitability by modifying function of transmembrane (TM) ion channel proteins, including K⁺ channels. These channels constitute the most heterogeneous and extensive group of ion channels, its members belonging to TM2, TM4, and TM6 protein superfamilies. Within this myriad of proteins, several K⁺ channels have been shown to modify behavior in response to acute exposure to ethanol concentrations that reach the CNS and other excitable tissues during alcohol drinking (2–5). However, with the sole exception of the TM2, G protein-regulated inward rectifier K⁺ (GIRK) channel (6), there is no structural information on ethanol-K⁺ channel protein interacting sites currently available.Voltage/Ca²⁺-gated, large conductance K⁺ channels (BK), which are members of the TM6 voltage-gated ion channel superfamily, constitute major mediators of alcohol actions in excitable tissues. Acute exposure to ethanol levels reached in CNS during alcohol intoxication alters BK-mediated currents and thus, elicits widespread and profound modifications in physiology and behavior. In rodent models, acute ethanol exposure leads to reduced vasopressin, oxytocin and growth hormone release with consequent perturbation in physiology and behavior (7), altered firing rates in nucleus accumbens (8) and dorsal root ganglia neurons (9), and alcohol-induced cerebral artery constriction (10, 11). Moreover, studies in both mammals and invertebrate models demonstrate that ethanol targeting of neuronal BK is involved in development of alcohol tolerance and dependence (12–16). Although the physiological and behavioral consequences of ethanol disruption of BK function have been well documented, it remains unknown whether alcohol modification of BK function results from drug interaction with a defined recognition site(s) in a protein target vs. physical perturbation of the proteolipid environment where the BK protein resides. Thus, location and structural characteristics of the ethanol-recognition site(s), as well as nature of chemical bonds between ethanol and functional target that lead to modification of BK function, remain unknown.Ethanol-induced regulation of BK channels is fine-tuned by many factors, including the BK channel-forming slo1 protein (α subunit) isoform (17) and its modification by phosphorylation (18), BK channel accessory (β) subunits (11), the channel-activating ionic ligand (Cai2+) (19) and the lipid microenvironment around the BK protein complex (20). However, ethanol perturbation of BK function is sustained when the slo1 protein is probed with the alcohol in cell-free membrane patches (19–21) or after protein reconstitution into artificial lipid bilayers (22). We recently demonstrated that perturbation of slo1 function by ethanol concentrations reached in blood during alcohol intoxication does not extend to Na⁺-gated slo2 and pH-gated slo3 channels, which are phylogenetically and structurally related to slo1. However, ethanol sensitivity does extend to a prokaryotic K⁺ channel from Methanobacterium thermoautotrophicum (MthK) (23), a TM2 ion channel that shares basic Cai2+-driven gating mechanisms with slo1 (24). Collectively, these studies lead us to hypothesize that ethanol-recognition site(s) involved in alcohol modification of BK current exists in the slo1 cytosolic Cai2+-sensing tail domain (CTD).Based on crystallographic data of the slo1 CTD and primary alignment of slo1-related ion channels that share ethanol sensitivity, we first identified eight putative ethanol recognition regions in the slo1 CTD. Using computational modeling, point amino acid substitutions and electrophysiology, we identified a distinct pocket as the ethanol-recognition site that leads to alcohol modification of BK current. This site has a few common characteristics of alcohol-binding protein sequences (25), yet presents features that differ from those of the alcohol site described in GIRK (6). In opposition to GIRK currents, which can be potentiated by alcohol in absence of G proteins (6), ethanol modulation of BK currents is dependent on the presence of Cai2+ (19). Our data strongly suggest that ethanol access to the newly identified BK ethanol-recognition site depends on the Cai2+ levels associated with the slo1 CTD. Thus, current data not only provide a structural basis for understanding Cai2+–alcohol allosterism on BK channels but could render structural insights on other ligand-gated channels that are activated by ethanol in presence of their natural ligand (26–30). Finally, present data document that the newly identified site plays a critical role in BK channel sensitivity to long-chain alkanols and explain the reported chain length differential sensitivity (“cutoff”) of linear n-alkanols to modify BK current (31).Identification of a distinct alcohol-sensing site in BK channels opens the door for rational design of pharmaceuticals to counteract widespread effects of alcohol intoxication in the body without altering basal BK channel function. Because this site is present in human BK protein ({"type":"entrez-protein","attrs":{"text":"AAA92290.1","term_id":"758791","term_text":"AAA92290.1"}}AAA92290.1), it is possible that genetic, epigenetic or other modifications of the alcohol-sensing site in BK channels could contribute to differential sensitivity to alcohol intoxication in humans. In addition, considering that individuals with low alcohol sensitivity are prone to developing heavy drinking (32), an altered profile of alcohol-sensing site on BK channels might be included as a potential predictor, along with other targets, for developing alcohol preference.     

From the Cover: Subsecond dopamine fluctuations in human striatum encode superposed error signals about actual and counterfactual reward

In the mammalian brain, dopamine is a critical neuromodulator whose actions underlie learning, decision-making, and behavioral control. Degeneration of dopamine neurons causes Parkinson’s disease, whereas dysregulation of dopamine signaling is believed to contribute to psychiatric conditions such as schizophrenia, addiction, and depression. Experiments in animal models suggest the hypothesis that dopamine release in human striatum encodes reward prediction errors (RPEs) (the difference between actual and expected outcomes) during ongoing decision-making. Blood oxygen level-dependent (BOLD) imaging experiments in humans support the idea that RPEs are tracked in the striatum; however, BOLD measurements cannot be used to infer the action of any one specific neurotransmitter. We monitored dopamine levels with subsecond temporal resolution in humans (n = 17) with Parkinson’s disease while they executed a sequential decision-making task. Participants placed bets and experienced monetary gains or losses. Dopamine fluctuations in the striatum fail to encode RPEs, as anticipated by a large body of work in model organisms. Instead, subsecond dopamine fluctuations encode an integration of RPEs with counterfactual prediction errors, the latter defined by how much better or worse the experienced outcome could have been. How dopamine fluctuations combine the actual and counterfactual is unknown. One possibility is that this process is the normal behavior of reward processing dopamine neurons, which previously had not been tested by experiments in animal models. Alternatively, this superposition of error terms may result from an additional yet-to-be-identified subclass of dopamine neurons.Dopamine is an essential neuromodulator whose presence is required for normal learning, decision-making, and behavioral control (1, 2) and whose absence or dysfunction is associated with a variety of disease states including Parkinson’s disease, schizophrenia, addiction, and depression (3–7). Experiments in animal models support the hypothesis that changes in dopamine release at target neural structures encode reward prediction errors (RPEs) (the difference between actual and expected outcomes) important for learning and value-based decision-making (1, 8–12). In support of this claim, direct recordings of spike activity in mesencephalic dopaminergic neurons in nonhuman primates demonstrate that these neurons encode prediction errors in future reward delivery (8–10, 13, 14) and they may also encode other computations relevant for reward-guided actions (1, 15–17). However, action potential production in brainstem dopaminergic neurons can only be part of the story because activity in parent axons must be converted to changes in neurotransmitter release at synaptic terminals to have any impact on downstream neural systems (1, 18). There have been no direct measurements of dopamine release in human striatum that tests these ideas directly. In a large cohort of human subjects (n = 17), we tested the hypothesis that subsecond fluctuations in dopamine delivery to the human striatum encode RPEs generated during a sequential choice task.Our measurements of dopamine release are made in patients undergoing deep brain stimulating (DBS)-electrode implantation for the treatment of Parkinson’s disease. This patient population provides a unique and important window of opportunity to investigate dopamine’s role in human brain function. Parkinson’s disease symptoms are treated with dopamine replacement therapies, and yet we know nothing about how rapid (subsecond) dopamine concentration changes contribute to their symptoms or changes in their decision-making abilities. The opportunity to measure dopamine release with subsecond temporal resolution in the brains of humans with Parkinson’s disease is an opportunity to learn about fundamental processes in human brain function as well as an opportunity to assess dopamine signaling in a patient population whose primary treatment is focused on replacing function lost as dopamine neurons degenerate.Participants (n = 17) in these experiments performed a simple, yet engaging, sequential investment game (Fig. 1 and refs. 19–21) while dopamine measurements with subsecond temporal resolution were made in the striatum (n = 14 in the caudate and n = 3 in the putamen). Participants were offered participation after they were deemed candidates for deep brain-stimulating electrode implantation (22, 23). The research protocol was explained to the participants verbally, and they were provided a written consent form, as required by dual-institutional review board (IRB)-approved protocols at Wake Forest University Health Sciences and Virginia Tech Carilion Research Institute. Patients thus indicated that they understood the research protocol and provided written informed consent to proceed with the research procedure.Open in a separate windowFig. 1.Investment game. (A) Participants played a sequential-choice game during surgery using button boxes (Left) and a visual display (Right). For each patient, bet size adjustments (e.g., increase bet or decrease bet) and the decision to submit one’s answer were performed with button boxes. (B) Investment game (19, 21): participants view a graphical depiction of the market price history (red trace), their current portfolio value (bottom left box), and their most recent outcome (bottom right box) to decide and submit investment decisions (bets) using a slider bar in 10% increments (bottom center). Bet sizes were limited to 0–100% (in 10% increments) of the participant’s portfolio—no shorting of the market was allowed. During an experiment, a participant played 6 markets with 20 decisions made per market. (C) Timeline of events during a single round of the investment game.The sequential investment game (Fig. 1 and refs. 19–21) consists of 120 investment decisions. On each trial (t), this game requires participants to use button boxes to adjust and submit an investment [bet (b_t), where bet sizes could range from 0% to 100% of the participants portfolio, in 10% increments], after which, participants experience a gain or loss (participant return) equal to the bet size times the fractional change in the market price [market return (r) at time t: rt= Δptpt, where p is the market price and the participant return (i.e., gain or loss) at time t is equal to b_tr_t]. Previous work used this task and functional magnetic resonance imaging to demonstrate that RPEs and CPEs over gains are tracked by blood oxygenation level-dependent (BOLD) responses in the striatum (19, 20). These reports also demonstrated at the behavioral level that humans use counterfactual information over choices that “might have been made” and RPE information over choices that were actually made to make their next choice (19, 20).     

Activation of cyclic electron flow by hydrogen peroxide in vivo

Cyclic electron flow (CEF) around photosystem I is thought to balance the ATP/NADPH energy budget of photosynthesis, requiring that its rate be finely regulated. The mechanisms of this regulation are not well understood. We observed that mutants that exhibited constitutively high rates of CEF also showed elevated production of H₂O₂. We thus tested the hypothesis that CEF can be activated by H₂O₂ in vivo. CEF was strongly increased by H₂O₂ both by infiltration or in situ production by chloroplast-localized glycolate oxidase, implying that H₂O₂ can activate CEF either directly by redox modulation of key enzymes, or indirectly by affecting other photosynthetic processes. CEF appeared with a half time of about 20 min after exposure to H₂O₂, suggesting activation of previously expressed CEF-related machinery. H₂O₂-dependent CEF was not sensitive to antimycin A or loss of PGR5, indicating that increased CEF probably does not involve the PGR5-PGRL1 associated pathway. In contrast, the rise in CEF was not observed in a mutant deficient in the chloroplast NADPH:PQ reductase (NDH), supporting the involvement of this complex in CEF activated by H₂O₂. We propose that H₂O₂ is a missing link between environmental stress, metabolism, and redox regulation of CEF in higher plants.In oxygenic photosynthesis, linear electron flow (LEF) is the process by which light energy is captured to drive the extraction of electrons and protons from water and transfer them through a system of electron carriers to reduce NADPH. LEF is coupled to proton translocation into the thylakoid lumen, generating an electrochemical gradient of protons (Δμ~H+) or proton motive force (pmf). The pmf drives the synthesis of ATP to power the reactions of the Calvin–Benson–Bassham (CBB) cycle and other essential metabolic processes in the chloroplast. The pmf is also a key regulator of photosynthesis in that it activates the photoprotective q_E response to dissipate excess light energy and down-regulates electron transfer by controlling the rate of oxidation of plastoquinol at the cytochrome b₆f complex (b₆f), thus preventing the buildup of reduced intermediates (1, 2).LEF results in the transfer or deposition into the lumen of three protons for each electron transferred through PSII, plastoquinone (PQ), b₆f, plastocyanin, and photosystem I (PSI) to ferredoxin (Fd). The synthesis of one ATP is thought to require the passage of 4.67 protons through the ATP synthase, so that LEF should produce a ratio of ATP/NADPH of about 1.33; this ratio is too low to sustain the CBB cycle or supply ATP required for translation, protein transport, or other ATP-dependent processes (3). In addition, the relative demands for ATP and NADPH can change dramatically depending on environmental, developmental, and other factors, leading to rapid energy imbalances that require dynamical regulation of ATP/NADPH balance.Several alternative electron flow pathways in the chloroplast have been proposed to augment ATP production, thus balancing the ATP/NADPH budget of the chloroplast (2, 3). Perhaps the most important and complicated of these pathways is cyclic electron flow around photosystem I (CEF), in which electron flow from the acceptor side of PSI is shunted back into the PQ pool, generating additional pmf that can power ATP production without net NADPH production. There are several proposed CEF pathways that may operate under different conditions or in different species (reviewed in refs. 2 and 3). In higher-plant chloroplasts, the most studied routes of CEF are the antimycin A-sensitive pathway, which involves a complex of two CEF-related proteins, PGR5 (Proton Gradient Regulation 5) and PGRL1 (PGR5-like 1), directly reducing the quinone pool (4–7), the respiratory complex I analog, the NADPH dehydrogenase (NDH) complex (8–10), which oxidizes Fd or NAD(P)H to reduce plastoquinone (8, 11), and through the Q_i site of b₆f (12, 13). Different CEF mechanisms seem to operate in other species. In Chlamydomonas, for example, CEF seems to be conducted by a supercomplex of PSI, b₆f, and the PGRL1 protein (14, 15), and the involvement of PGR5 has recently been described as important for CEF under hypoxia (16, 17).Regardless of the mechanism of CEF, the overall process must be well regulated to properly balance the production of ATP to match the demands of metabolism. The mechanism of this regulation is not known, but many general models have been proposed. Perhaps the most widely cited regulatory model is the antenna state transition, which was previously shown to be correlated with activation of CEF in Chlamydomonas reinhardtii (14, 18) and favor the formation of the PSI–b₆f supercomplex (14). However, it was recently shown that state transitions are not required for CEF activation, supporting models that include redox control (15–17, 19–22). Other possible regulatory mechanisms include sensing of ATP/ADP ratios (23, 24), the redox status of NAD(P)H or Fd (25), various CBB metabolic intermediates (reviewed in ref. 26), calcium signaling (15, 27), phosphorylation of CEF-related proteins (27), and the reactive oxygen species H₂O₂ (26–29).One possibility is that CEF may be at least partly regulated by H₂O₂ (26), which is produced by the light reactions of photosynthesis and already known to regulate other cellular processes such as plant growth, development, and defense (30–32). Based on in vitro studies, it was previously proposed that H₂O₂ could activate CEF or chlororespiration by modifying the NDH complex (27). It has also been shown that H₂O₂ can increase the expression of the NDH complex (29) and may further affect the accumulation of photosynthetic metabolites, indirectly activating CEF (26). Consistent with this possibility, H₂O₂ is a well-documented signaling molecule (33), possibly through its ability to oxidize thiols (34, 35). Furthermore, H₂O₂ is expected to be produced under many conditions that initiate CEF [e.g., under a deficit of ATP, when electrons should accumulate in the PSI acceptor pools, leading to superoxide production that can be converted to H₂O₂ by superoxide dismutase (36)].This study aims to test the hypothesis that CEF can be initiated in vivo by H₂O₂ using a combination of in vivo spectroscopy and genetic modifications to selectively and rapidly initiate H₂O₂ production in the chloroplast.     

Photon gating in four-dimensional ultrafast electron microscopy

Ultrafast electron microscopy (UEM) is a pivotal tool for imaging of nanoscale structural dynamics with subparticle resolution on the time scale of atomic motion. Photon-induced near-field electron microscopy (PINEM), a key UEM technique, involves the detection of electrons that have gained energy from a femtosecond optical pulse via photon–electron coupling on nanostructures. PINEM has been applied in various fields of study, from materials science to biological imaging, exploiting the unique spatial, energy, and temporal characteristics of the PINEM electrons gained by interaction with a “single” light pulse. The further potential of photon-gated PINEM electrons in probing ultrafast dynamics of matter and the optical gating of electrons by invoking a “second” optical pulse has previously been proposed and examined theoretically in our group. Here, we experimentally demonstrate this photon-gating technique, and, through diffraction, visualize the phase transition dynamics in vanadium dioxide nanoparticles. With optical gating of PINEM electrons, imaging temporal resolution was improved by a factor of 3 or better, being limited only by the optical pulse widths. This work enables the combination of the high spatial resolution of electron microscopy and the ultrafast temporal response of the optical pulses, which provides a promising approach to attain the resolution of few femtoseconds and attoseconds in UEM.In ultrafast electron microscopy (UEM) (1–3), electrons generated by photoemission at the cathode of a transmission electron microscope are accelerated down the microscope column to probe the dynamic evolution of a specimen initiated by an ultrafast light pulse. The use of femtosecond lasers to generate the electron probe and excite the specimen has made it possible to achieve temporal resolution on the femtosecond time scale, as determined by the cross-correlation of the optical and electron pulses. One important method in the UEM repertoire is photon-induced near-field electron microscopy (PINEM) (4, 5), in which the dynamic response detected by the electron probe is the pump-induced charge density redistribution in nanoscale specimens (6).Photon–electron coupling is the basic building block of PINEM, which takes place in the presence of nanostructures when the energy-momentum conservation condition is satisfied (4, 5). This coupling leads to inelastic gain/loss of photon quanta by electrons in the electron packet, which can be resolved in the electron energy spectrum (5, 7, 8). This spectrum consists of discrete peaks, spectrally separated by multiples of the photon energy (n?ω), on the higher and lower energy sides of the zero loss peak (ZLP) (4) (Fig. 1). The development of PINEM enables the visualization of the spatiotemporal dielectric response of nanostructures (9), visualization of plasmonic fields (4, 5) and their spatial interferences (10), imaging of low atomic number nanoscale materials (11), characterization of ultrashort electron packets (12, 13), and imaging of different biological structures (14).Open in a separate windowFig. 1.Concept of photon gating in 4D electron microscopy. (A) The microscope column with one electron (dark blue) and two optical (red) pulses focused onto the specimen. The wavefunctions of the three pulses are schematically shown at the top. One optical pulse is coincident with the electron pulse at the specimen to generate a PINEM signal. The resulting light blue PINEM pulse is sliced out from other electrons for detection as an energy spectrum, an image, or a diffraction signal (see the text). The second optical pulse initiates the dynamics to be probed. (B) Electron energy spectrum generated at the specimen plane when optical and electron pulses arrive simultaneously. The gain energy range is shaded light blue. (C) Illustration for the temporal pulse sequence, two optical and one electron pulse for ultrafast time-resolved PINEM measurements.As shown by Park et al. (5), the PINEM intensity (I_PINEM) is given by the square modulus of the field integral F˜0 (i.e., IPINEM∝|F˜0|2), in the weak interaction limit. The near field of a nanoparticle leads to the scattering of the electron packet, which can be treated rigorously using the Schrödinger equation/Mie scattering theory. It follows that PINEM images the object and displays its field characteristics depending on its shape, the polarization and wavelength of optical excitation, and the width of pulses used. For a spherical nanoparticle, the field integral at point (x, y) in the specimen plane is simplified to give (6)F˜0≈−iE˜0⁡cos⁡ϕχs 23 a3(Δk)2K[Δkb],[1]where E˜0 is the electric field amplitude of the incident light, ? the light polarization angle, a the particle radius, b=x2+y2 the impact parameter, K the modified Bessel function of the second type, Δk the momentum change of the electron, and χ_s = 3(ε ? 1)/(ε + 2), where χ_s is the material susceptibility and ε the dielectric function.In previous studies of the parameters in Eq. 1, only E˜0 was time dependent. The PINEM intensity, at a given point in space, was a function only of the time delay between the optical and electron pulses, providing, for the pulse lengths currently used, a cross-correlation profile when this delay was scanned across the time of temporal coincidence, or t = 0 (4, 5, 9, 13). Hitherto, PINEM has not been used to study the ultrafast dynamics of matter. Here, we follow the strategy of using the PINEM gain electrons generated by a first optical pulse, whose delay relative to the electron pulse is maintained at t = 0, to probe dynamics initiated by introduction of a second optical pulse on the specimen, as proposed theoretically in ref. 15. By this approach, we were able to optically gate the electron pulse (i.e., create an electron pulse that only lasts for the duration of the optical pulse) and achieve significant enhancement of the temporal resolution (see the second paragraph below).The concept of the experiment is illustrated by Fig. 1A, in which the electron pulse in blue and one optical pulse (P₁) in red are shown arriving at the specimen plane simultaneously. Interaction between photon and electron in the presence of the specimen “slices out” the light blue pulse of gain electrons, which are separated from all other electrons by energy dispersion or filtering to be detected according to microscope settings in spectroscopy, imaging, or diffraction mode, as illustrated schematically at the bottom of the column. Note, it is possible to obtain PINEM diffraction, but this is not the subject of this paper. A second, or pump, optical pulse (P₂) is shown below the specimen, having already triggered the dynamics of interest. A series of time axes is plotted in Fig. 1C showing examples of characteristic sequences of pulse arrival times at the specimen plane during the experiment, with the pump arrival defining the zero of time.A striking feature of this technique that was alluded to above is the potential for high temporal resolution, unlimited by the electron pulse duration, because the optical pulse acts as a temporal gate for a longer electron pulse. In the weak interaction limit, the duration of the pulse of PINEM electrons emulates that of the optical pulse that created it (15), as clearly shown in Fig. 1A. When these photon-gated electrons are used to probe dynamics triggered by a second ultrafast optical pulse, the time resolution is determined by the cross-correlation of the two optical pulses. This paves the way for the realization of attosecond electron microscopy, as done in all-optical spectroscopy (16) but with the spatial resolution being that of atomic motions. As suggested in Fig. 1A, we envisage the use of the photon-gated electron pulses, in imaging or in diffraction mode, for the study of a variety of optically initiated material processes, either of the nanostructure or of its surrounding media.The PINEM signal can be directly monitored to detect changes in any of the specimen optical or physical properties expressed in Eq. 1. Here, we demonstrate the use of the time-resolved PINEM technique where it is shown that the photoinduced dielectric response of VO₂—which is strongly related to the lattice symmetry (17)—manifests itself in a change in PINEM intensity. We relate the changes in optical properties of the polycrystalline VO₂ nanoparticles to the phase transition dynamics from initial (monoclinic) insulator phase to (tetragonal) metal phase, the subject of numerous previous studies.Vanadium dioxide has been discussed as an active metamaterial (18) and one of the best candidates for solid-state ultrafast optical switches in photonics applications (19, 20) due to its unique structural photoinduced phase transition behavior (21). This phase transition has been examined by investigating the change in the heat capacity through thermal excitation (22, 23), whereas its ultrafast dynamics has been studied by optical spectroscopy (24, 25), THz spectroscopy (26, 27), X-ray diffraction (28, 29), ultrafast electron crystallography (30), and electron microscopy (31).