Phase-separating RNA-binding proteins form heterogeneous distributions of clusters in subsaturated solutions

Macromolecular phase separation is thought to be one of the processes that drives the formation of membraneless biomolecular condensates in cells. The dynamics of phase separation are thought to follow the tenets of classical nucleation theory, and, therefore, subsaturated solutions should be devoid of clusters with more than a few molecules. We tested this prediction using in vitro biophysical studies to characterize subsaturated solutions of phase-separating RNA-binding proteins with intrinsically disordered prion-like domains and RNA-binding domains. Surprisingly, and in direct contradiction to expectations from classical nucleation theory, we find that subsaturated solutions are characterized by the presence of heterogeneous distributions of clusters. The distributions of cluster sizes, which are dominated by small species, shift continuously toward larger sizes as protein concentrations increase and approach the saturation concentration. As a result, many of the clusters encompass tens to hundreds of molecules, while less than 1% of the solutions are mesoscale species that are several hundred nanometers in diameter. We find that cluster formation in subsaturated solutions and phase separation in supersaturated solutions are strongly coupled via sequence-encoded interactions. We also find that cluster formation and phase separation can be decoupled using solutes as well as specific sets of mutations. Our findings, which are concordant with predictions for associative polymers, implicate an interplay between networks of sequence-specific and solubility-determining interactions that, respectively, govern cluster formation in subsaturated solutions and the saturation concentrations above which phase separation occurs.

Phase separation of RNA-binding proteins with disordered prion-like domains (PLDs) and RNA-binding domains (RBDs) is implicated in the formation and dissolution of membraneless biomolecular condensates such as RNA–protein (RNP) granules (1–9). Macroscopic phase separation is a process whereby a macromolecule in a solvent separates into a dilute, macromolecule-deficient phase that coexists with a dense, macromolecule-rich phase (10, 11). In a binary mixture, the soluble phase, comprising dispersed macromolecules that are well mixed with the solvent, becomes saturated at a concentration designated as c_sat. Above c_sat, for total macromolecular concentrations c_tot that are between the binodal and spinodal, phase separation of full-length RNA-binding proteins and PLDs is thought to follow classical nucleation theory (12–15).In classical nucleation theories, clusters representing incipient forms of the new dense phase form within dispersed phases of supersaturated solutions defined by c_tot > c_sat (16, 17). In the simplest formulation of classical nucleation theory (16–18), the free energy of forming a cluster of radius a is ΔF=−4π3a3Δμρn+4πa2γ. Here, Δµ is the difference in the chemical potential between the one-phase and two-phase regimes (see discussion in SI Appendix), which is negative in supersaturated solutions and positive in subsaturated solutions; ρ_n is the number of molecules per unit volume, and γ is the interfacial tension between dense and dilute phases. At temperature T, in a seed-free solution, the degree of supersaturation s is defined as s≡ΔμRT=ln(ctotcsat), where R is the ideal gas constant. Here, s is positive for c_tot > c_sat, and, as s increases, cluster formation becomes more favorable. Above a critical radius a*, the free energy of cluster formation can overcome the interfacial penalty, and the new dense phase grows in a thermodynamically downhill fashion. Ideas from classical nucleation theory have been applied to analyze and interpret the dynamics of phase separation in supersaturated solutions (12, 13, 15). Classical nucleation theories stand in contrast to two-step nucleation theories that predict the existence of prenucleation clusters in supersaturated solutions (19–22). These newer theories hint at the prospect of there being interesting features in subsaturated solutions, where c_tot < c_sat and s < 0.The subsaturated regime, where s is negative, corresponds to the one-phase regime. Ignoring the interfacial tension, the free energy of realizing clusters with n molecules in subsaturated solutions is: ΔF = –nΔµ. Therefore, the probability P(n) of forming a cluster of n molecules in a subsaturated solution is proportional to exp(sn). Accordingly, the relative probability P(n)/P(1) of forming clusters with n molecules will be exp(s(n – 1)). This quantity, which may be thought of as the concentration of clusters with n molecules, is negligibly small for clusters with more than a few molecules. This is true irrespective of the degree of subsaturation, s. Is this expectation from classical nucleation theories valid? We show here that subsaturated solutions feature a rich distribution of species not anticipated by classical nucleation theories. We report results from measurements of cluster size distributions in subsaturated solutions of phase-separating RNA-binding proteins from the FUS-EWSR1-TAF15 (FET) family. We find that these systems form clusters in subsaturated solutions, and that the cluster sizes follow heavy-tailed distributions. The abundant species are always small clusters. However, as total macromolecular concentration (c_tot) increases, the distributions of cluster sizes shift continuously toward larger values. We discuss these findings in the context of theories for associative polymers (9, 23–30).     

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.     

Nature of dynamic gradients,glass formation,and collective effects in ultrathin freestanding films

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of “nanoconfinement effects” on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

Spatially heterogeneous dynamics in glass-forming liquids confined to nanoscale domains (1–7) play a major role in determining the properties of molecular, polymeric, colloidal, and other glass-forming materials (8), including thin films of polymers (9, 10) and small molecules (11–15), small-molecule liquids in porous media (2, 4, 16, 17), semicrystalline polymers (18, 19), polymer nanocomposites (20–22), ionomers (23–25), self-assembled block and layered (26–33) copolymers, and vapor-deposited ultrastable molecular glasses (34–36). Intense interest in this problem over the last 30 y has also been motivated by the expectation that its understanding could reveal key insights concerning the mechanism of the bulk glass transition.Considerable progress has been made for near-interface altered dynamics in thick films, as recently critically reviewed (1). Large amplitude gradients of the structural relaxation time, τ(z,T), converge to the bulk value, τ_bulk(T), in an intriguing double-exponential manner with distance, z, from a solid or vapor interface (13, 37–42). This implies that the corresponding effective activation barrier, F_total(z,T,H) (where H is film thickness), varies exponentially with z, as does the glass transition temperature, T_g (37). Thus the fractional reduction in activation barrier, ε(z,H), obeys the equation ε(z,H)≡1−Ftotal(z,T,H)/Ftotal,bulk(T)=ε0⁡exp(−z/ξF), where F_total,bulk(T) is the bulk temperature-dependent barrier and ξ_F a length scale of modest magnitude. Although the gradient of reduction in absolute activation barriers becomes stronger with cooling, the amplitude of the fractional reduction of the barrier gradient, quantified by ε₀, and the range ξ_F of this gradient, exhibit a weak or absent temperature dependence at the lowest temperatures accessed by simulations (typically with the strength of temperature dependence of ξ_F decreasing rather than increasing on cooling), which extend to relaxation timescales of order 10⁵ ps. This finding raises questions regarding the relevance of critical-phenomena–like ideas for nanoconfinement effects (1). Partially due to this temperature invariance, coarse-grained and all-atom simulations (1, 37, 42, 43) have found a striking empirical fractional power law decoupling relation between τ(z,T) and τ_bulk(T):τ(T,z)τbulk(T)∝(τbulk(T))−ε(z).[1]Recent theoretical analysis suggests (44) that this behavior is consistent with a number of experimental data sets as well (45, 46). Eq. 1 also corresponds to a remarkable factorization of the temperature and spatial location dependences of the barrier:Ftotal(z,T)=[1−ε(z)]Ftotal,bulk(T).[2]This finding indicates that the activation barrier for near-interface relaxation can be factored into two contributions: a z-dependent, but T-independent, “decoupling exponent,” ε(z), and a temperature-dependent, but position-insensitive, bulk activation barrier, F_total,bulk(T). Eq. 2 further emphasizes that ε(z) is equivalent to an effective fractional barrier reduction factor (for a vapor interface), 1−Ftotal(z,T,H)/Ftotal,bulk(T), that can be extracted from relaxation data.In contrast, the origin of “nanoconfinement effects” in thin films, and how much of the rich thick-film physics survives when dynamic gradients from two interfaces overlap, is not well understood. The distinct theoretical efforts for aspects of the thick-film phenomenology (44, 47–50) mostly assume an additive summation of one-interface effects in thin films, thereby ignoring possibly crucial cooperative and whole film finite size confinement effects. If the latter involve phase-transition–like physics as per recent speculations (14, 51), one can ask the following: do new length scales emerge that might be truncated by finite film size? Alternatively, does ultrathin film phenomenology arise from a combination of two-interface superposition of the thick-film gradient physics and noncritical cooperative effects, perhaps in a property-, temperature-, and/or thickness-dependent manner?Here, we answer these questions and establish a mechanistic understanding of thin-film dynamics for the simplest and most universal case: a symmetric freestanding film with two vapor interfaces. We focus on small molecules (modeled theoretically as spheres) and low to medium molecular weight unentangled polymers, which empirically exhibit quite similar alterations in dynamics under “nanoconfinement.” We do not address anomalous phenomena [e.g., much longer gradient ranges (29), sporadic observation of two distinct glass transition temperatures (52, 53)] that are sometimes reported in experiments with very high molecular weight polymers and which may be associated with poorly understood chain connectivity effects that are distinct from general glass formation physics (54–56).We employ a combination of molecular dynamics simulations with a zero-parameter extension to thin films of the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory (57, 58). This theory has previously been shown to predict well both bulk activated relaxation over up to 14 decades (44–46) and the full single-gradient phenomenology in thick films (1). Here, we extend this theory to treat films of finite thickness, accounting for coupled interface and geometric confinement effects. We compare predictions of ECNLE theory to our previously reported (37, 43) and new simulations, which focus on translational dynamics of films comprised of a standard Kremer–Grest-like bead-spring polymer model (see SI Appendix). These simulations cover a wide range of film thicknesses (H, from 4 to over 90 segment diameters σ) and extend to low temperatures where the bulk alpha time is ∼0.1 μs (10⁵ Lennard Jones time units τ_LJ).The generalized ECNLE theory is found to be in agreement with simulation for all levels of nanoconfinement. We emphasize that this theory does not a priori assume any of the empirically established behaviors discovered using simulation (e.g., fractional power law decoupling, double-exponential barrier gradient, gradient flattening) but rather predicts these phenomena based upon interfacial modifications of the two coupled contributions to the underlying activation barrier– local caging constraints and a long-ranged collective elastic field. It is notable that this strong agreement is found despite the fact the dynamical ideas are approximate, and a simple hard sphere fluid model is employed in contrast to the bead-spring polymers employed in simulation. The basic unit of length in simulation (bead size σ) and theory (hard sphere diameter d) are expected to be proportional to within a prefactor of order unity, which we neglect in making comparisons.As an empirical matter, we find from simulation that many features of thin-film behavior can be described to leading order by a linear superposition of the thick-film gradients in activation barrier, that is:ε(z,H)=1−Ftotal(z,T,H)/Ftotal,bulk(T)≈ε0[exp(−z/ξF)+exp(−(H−z)/ξF)],[3]where the intrinsic decay length ξ_F is unaltered from its thick-film value and where ε₀ is a constant that, in the hypothesis of literal gradient additivity, is invariant to temperature and film thickness. We employ this functional form [originally suggested by Binder and coworkers (59)], which is based on a simple superposition of the two single-interface gradients, as a null hypothesis throughout this study: this form is what one expects if no new finite-size physics enters the thin-film problem relative to the thick film.However, we find that the superposition approximation progressively breaks down, and eventually entirely fails, in ultrathin films as a consequence of the emergence of a finite size confinement effect. The ECNLE theory predicts that this failure is not tied to a phase-transition–like mechanism but rather is a consequence of two key coupled physical effects: 1) transfer of surface-induced reduction of local caging constraints into the film, and 2) interfacial truncation and nonadditive modifications of the collective elastic contribution to the activation barrier.     

Thermodynamic controls on rates of iron oxide reduction by extracellular electron shuttles

Anaerobic microbial respiration in suboxic and anoxic environments often involves particulate ferric iron (oxyhydr-)oxides as terminal electron acceptors. To ensure efficient respiration, a widespread strategy among iron-reducing microorganisms is the use of extracellular electron shuttles (EES) that transfer two electrons from the microbial cell to the iron oxide surface. Yet, a fundamental understanding of how EES–oxide redox thermodynamics affect rates of iron oxide reduction remains elusive. Attempts to rationalize these rates for different EES, solution pH, and iron oxides on the basis of the underlying reaction free energy of the two-electron transfer were unsuccessful. Here, we demonstrate that broadly varying reduction rates determined in this work for different iron oxides and EES at varying solution chemistry as well as previously published data can be reconciled when these rates are instead related to the free energy of the less exergonic (or even endergonic) first of the two electron transfers from the fully, two-electron reduced EES to ferric iron oxide. We show how free energy relationships aid in identifying controls on microbial iron oxide reduction by EES, thereby advancing a more fundamental understanding of anaerobic respiration using iron oxides.

The use of iron oxides as terminal electron acceptors in anaerobic microbial respiration is central to biogeochemical element cycling and pollutant transformations in many suboxic and anoxic environments (1–6). To ensure efficient electron transfer to solid-phase ferric iron, Fe(III), at circumneutral pH, metal-reducing microorganisms from diverse phylae use dissolved extracellular electron shuttle (EES), including quinones (7–9), flavins (10–16), and phenazines (17–19), to transfer two electrons per EES molecule from the respiratory chain proteins in the outer membrane of the microbial cell to the iron oxide (17, 20, 21). The oxidized EES can diffuse back to the cell surface for rereduction, thereby completing the catalytic redox cycle involving the EES.The electron transfer from the reduced EES to Fe(III) is considered a key step in overall microbial Fe(III) respiration. Several lines of evidence suggest that the free energy of the electron transfer reaction, ΔrG, controls Fe(III) reduction rates (15, 17, 22, 23). For instance, microbial Fe(III) oxide reduction by dissolved model quinones as EES was accelerated only for quinones with standard two-electron reduction potentials, EH,1,20, that fell into a relatively narrow range of −180±80 mV at pH 7 (24). Furthermore, in abiotic experiments, Fe(III) reduction rates by EES decreased with increasing ΔrG that resulted from increasing either EH,1,20 of the EES (25, 26), the concentration of Fe(II) in the system (27), or solution pH (25, 26, 28). However, substantial efforts to relate Fe(III) reduction rates for different EES species, iron oxides, and pH to the EH,1,20 averaged over both electrons transferred from the EES to the iron oxides were only partially successful (25, 28). Reaction free energies of complex redox processes involving the transfer of multiple electrons can readily be calculated using differences in the reduction potentials averaged over all electrons transferred, and this approach is well established in biogeochemistry and microbial ecology. For kinetic considerations, however, the use of averaged reduction potentials is inappropriate.Herein, we posit that rates of Fe(III) reduction by EES instead relate to the ΔrG of the less exergonic first one-electron transfer from the two-electron reduced EES species to the iron oxide, following the general notion that reaction rates scale with reaction free energies (29). Our hypothesis is based on the fact that, at circumneutral to acidic pH and for many EES, the reduction potential of the first electron transferred to the fully oxidized EES to form the one-electron reduced intermediate semiquinone species, EH,1, is lower than the reduction potential of the second electron transferred to the semiquinone to form the fully two-electron reduced EES species, EH,2 [i.e., EH,1<EH,2 (30–33)]. This difference in one-electron reduction potentials implies that the two-electron reduced EES (i.e., the hydroquinone) is the weaker one-electron reductant for Fe(III) as compared to the semiquinone species. We therefore expect that rates of iron oxide reduction relate to the ΔrG of the first electron transferred from the hydroquinone to Fe(III). The ΔrG of this first electron transfer may even be endergonic provided that the two-electron transfer is exergonic.We verified our hypothesis in abiotic model systems by demonstrating that reduction rates of two geochemically important crystalline iron oxides, goethite and hematite, by two-electron reduced quinone- and flavin-based EES over a wide pH range, and therefore thermodynamic driving force for Fe(III) reduction, correlate with the ΔrG of the first electron transferred from the fully reduced EES to Fe(III). We further show that rates of goethite and hematite reduction by EES reported in the literature are in excellent agreement with our rate data when comparing rates on the basis of the thermodynamics of the less exergonic first of the two electron transfers.     

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.     

Low-Reynolds-number,biflagellated Quincke swimmers with multiple forms of motion

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic–electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

In a Newtonian fluid, locomotion of microswimmers requires nonreciprocal body motions (1–3). Bacteria or eukaryotic cells achieve this by beating or rotating their slender hair-like organelles, flagella (4, 5) or cilia (6), powered by molecular motors. Mimicking these organisms, artificial swimmers propelled by rotating helices (7, 8) or whipping filaments (9–12) have been fabricated. They are commonly driven by an external power source such as a magnetic field (7–9, 13, 14), sound (15), light (16, 17), and biological materials (12). However, there are very few electrically powered microswimmers (18–20), although electric fields have been exploited to drive other active systems (21–26) via a phenomenon called Quincke rotation (27).Quincke rotation originates from an electrohydrodynamic instability (28–30). Submerged in a liquid with permittivity εl and conductivity σl, a spherical particle with permittivity εs and electric conductivity σs is polarized under a uniform, steady electric field E→. When the particle is stationary, the induced dipole p→ due to the free charges is parallel or antiparallel to E→ (Fig. 1A): if the particle’s relaxation time τs=εs/σs is shorter than that of the ambient liquid, τl=εl/σl, p→ points in the same direction as E→; when τs>τl, p→ is opposite to E→, which generates an electric torque Γ→Q=p→×E→ that amplifies any angular perturbation. However, due to the resisting viscous torque Γ→μ, the system becomes unstable only when E=|E→| exceeds a threshold Ec. This instability causes the particle to rotate with a constant angular velocity ω:ω=1τEEc2−1,[1]where τ=εs+2εlσs+2σl is the relaxation time of the system (see SI Appendix, SI Text, or refs. 28, 29, 31 for derivation), and the rotational axis can be in any direction perpendicular to E→. During steady-state Quincke rotation, there is a constant angle between p→ and E→ (Fig. 1A), which results in a nonzero Γ→Q.Open in a separate windowFig. 1.Quincke rotation and the experimental setup. (A) Distribution of free charge and the corresponding dipole p→ on a sphere in a uniform, steady electric field E→. The sphere is (Left) stationary, (Middle) stationary, and (Right) rotating with a constant angular velocity ω. (B) A sketch of the biflagellated swimmer. Dashed lines show the roll axis (blue) and pitch axis (green). (C) A schematic illustration of the experimental setup.Recently, a flagellated swimmer in unbounded space driven by Quincke rotation has been proposed theoretically (32, 33). In light of the theory, we built a laboratory prototype, a biflagellated Quincke swimmer composed of a spherical particle and two attached elastic filaments, as shown in Fig. 1B, and systematically studied its behaviors at low Reynolds number (Re<0.3; Materials and Methods). Varying the electric field E→ and the angle between the two filaments, the Quincke swimmers exhibit three distinct forms of motion—two unidirectional rotations, which we call roll and pitch, and a self-oscillatory rotation, due to the balances between the electrical, elastic, and hydrodynamic torques, resulting in distinct trajectories in space. Surprisingly, it was recently reported (34) that spherical bacteria Magnetococcus marinus exhibit a similar pitch motion as our biflagellated artificial swimmers, which is rarely adopted by other microorganisms. Moreover, we found a threshold tail angle that separates the swimmers’ preferred forms of rotation, and within a small range close to this threshold angle, the three forms of motion coexist.     

Unusual magnetotransport in twisted bilayer graphene

We present transport measurements of bilayer graphene with a 1.38^∘ interlayer twist. As with other devices with twist angles substantially larger than the magic angle of 1.1^∘, we do not observe correlated insulating states or band reorganization. However, we do observe several highly unusual behaviors in magnetotransport. For a large range of densities around half filling of the moiré bands, magnetoresistance is large and quadratic. Over these same densities, the magnetoresistance minima corresponding to gaps between Landau levels split and bend as a function of density and field. We reproduce the same splitting and bending behavior in a simple tight-binding model of Hofstadter’s butterfly on a triangular lattice with anisotropic hopping terms. These features appear to be a generic class of experimental manifestations of Hofstadter’s butterfly and may provide insight into the emergent states of twisted bilayer graphene.

The mesmerizing Hofstadter butterfly spectrum arises when electrons in a two-dimensional periodic potential are immersed in an out-of-plane magnetic field. When the magnetic flux Φ through a unit cell is a rational multiple p / q of the magnetic flux quantum Φ0=h/e, each Bloch band splits into q subbands (1). The carrier densities corresponding to gaps between these subbands follow straight lines when plotted as a function of normalized density n/ns and magnetic field (2). Here, n_s is the density of carriers required to fill the (possibly degenerate) Bloch band. These lines can be described by the Diophantine equation (n/ns)=t(Φ/Φ0)+s for integers s and t. In experiments, they appear as minima or zeros in longitudinal resistivity coinciding with Hall conductivity quantized at σxy=te2/h (3, 4). Hofstadter originally studied magnetosubbands emerging from a single Bloch band on a square lattice. In the following decades, other authors considered different lattices (5–7), the effect of anisotropy (6, 8–10), next-nearest-neighbor hopping (11–15), interactions (16, 17), density wave states (9), and graphene moirés (18, 19).It took considerable ingenuity to realize clean systems with unit cells large enough to allow conventional superconducting magnets to reach Φ/Φ0∼1. The first successful observation of the butterfly in electrical transport measurements was in GaAs/AlGaAs heterostructures with lithographically defined periodic potentials (20–22). These experiments demonstrated the expected quantized Hall conductance in a few of the largest magnetosubband gaps. In 2013, three groups mapped out the full butterfly spectrum in both density and field in heterostructures based on monolayer (23, 24) and bilayer (25) graphene. In all three cases, the authors made use of the 2% lattice mismatch between their graphene and its encapsulating hexagonal boron nitride (hBN) dielectric. With these layers rotationally aligned, the resulting moiré pattern was large enough in area that gated structures studied in available high-field magnets could simultaneously approach normalized carrier densities and magnetic flux ratios of 1. Later work on hBN-aligned bilayer graphene showed that, likely because of electron–electron interactions, the gaps could also follow lines described by fractional s and t (26).In twisted bilayer graphene (TBG), a slight interlayer rotation creates a similar-scale moiré pattern. Unlike with graphene–hBN moirés, in TBG there is a gap between lowest and neighboring moiré subbands (27). As the twist angle approaches the magic angle of 1.1^∘ the isolated moiré bands become flat (28, 29), and strong correlations lead to fascinating insulating (30–37), superconducting (31–33, 35–37), and magnetic (34, 35, 38) states. The strong correlations tend to cause moiré subbands within a fourfold degenerate manifold to move relative to each other as one tunes the density, leading to Landau levels that project only toward higher magnitude of density from charge neutrality and integer filling factors (37, 39). This correlated behavior obscures the single-particle Hofstadter physics that would otherwise be present.In this work, we present measurements from a TBG device twisted to 1.38^∘. When we apply a perpendicular magnetic field, a complicated and beautiful fan diagram emerges. In a broad range of densities on either side of charge neutrality, the device displays large, quadratic magnetoresistance. Within the magnetoresistance regions, each Landau level associated with ν=±8,±12,±16,… appears to split into a pair, and these pairs follow complicated paths in field and density, very different from those predicted by the usual Diophantine equation. Phenomenology similar in all qualitative respects appears in measurements on several regions of this same device with similar twist angles and in two separate devices, one at 1.59^∘ and the other at 1.70^∘ (see SI Appendix for details).We reproduce the unusual features of the Landau levels (LLs) in a simple tight-binding model on a triangular lattice with anisotropy and a small energetic splitting between two species of fermions. At first glance, this is surprising, because that model does not represent the symmetries of the experimental moiré structure. We speculate that the unusual LL features we experimentally observe can generically emerge from spectra of Hofstadter models that include the same ingredients we added to the triangular lattice model. With further theoretical work it may be possible to use our measurements to gain insight into the underlying Hamiltonian of TBG near the magic angle.     

Dynamic rupture initiation and propagation in a fluid-injection laboratory setup with diagnostics across multiple temporal scales

Fluids are known to trigger a broad range of slip events, from slow, creeping transients to dynamic earthquake ruptures. Yet, the detailed mechanics underlying these processes and the conditions leading to different rupture behaviors are not well understood. Here, we use a laboratory earthquake setup, capable of injecting pressurized fluids, to compare the rupture behavior for different rates of fluid injection, slow (megapascals per hour) versus fast (megapascals per second). We find that for the fast injection rates, dynamic ruptures are triggered at lower pressure levels and over spatial scales much smaller than the quasistatic theoretical estimates of nucleation sizes, suggesting that such fast injection rates constitute dynamic loading. In contrast, the relatively slow injection rates result in gradual nucleation processes, with the fluid spreading along the interface and causing stress changes consistent with gradually accelerating slow slip. The resulting dynamic ruptures propagating over wetted interfaces exhibit dynamic stress drops almost twice as large as those over the dry interfaces. These results suggest the need to take into account the rate of the pore-pressure increase when considering nucleation processes and motivate further investigation on how friction properties depend on the presence of fluids.

The close connection between fluids and faulting has been revealed by a large number of observations, both in tectonic settings and during human activities, such as wastewater disposal associated with oil and gas extraction, geothermal energy production, and CO₂ sequestration (1–11). On and around tectonic faults, fluids also naturally exist and are added at depths due to rock-dehydration reactions (12–15) Fluid-induced slip behavior can range from earthquakes to slow, creeping motion. It has long been thought that creeping and seismogenic fault zones have little to no spatial overlap. Nonetheless, growing evidence suggests that the same fault areas can exhibit both slow and dynamic slip (16–19). The existence of large-scale slow slip in potentially seismogenic areas has been revealed by the presence of transient slow-slip events in subduction zones (16, 18) and proposed by studies investigating the physics of foreshocks (20–22).Numerical and laboratory modeling has shown that such complex fault behavior can result from the interaction of fluid-related effects with the rate-and-state frictional properties (9, 14, 19, 23, 24); other proposed rheological explanations for complexities in fault stability include combinations of brittle and viscous rheology (25) and friction-to-flow transitions (26). The interaction of frictional sliding and fluids results in a number of coupled and competing mechanisms. The fault shear resistance τres is typically described by a friction model that linearly relates it to the effective normal stress σ^n via a friction coefficient f:τres=f σ^n=f (σn−p),[1]where σn is the normal stress acting across the fault and p is the pore pressure. Clearly, increasing pore pressure p would reduce the fault frictional resistance, promoting the insurgence of slip. However, such slip need not be fast enough to radiate seismic waves, as would be characteristic of an earthquake, but can be slow and aseismic. In fact, the critical spatial scale h* for the slipping zone to reach in order to initiate an unstable, dynamic event is inversely proportional to the effective normal stress (27, 28) and hence increases with increasing pore pressure, promoting stable slip. This stabilizing effect of increasing fluid pressure holds for both linear slip-weakening and rate-and-state friction; it occurs because lower effective normal stress results in lower fault weakening during slip for the same friction properties. For example, the general form for two-dimensional (2D) theoretical estimates of this so-called nucleation size, h*, on rate-and-state faults with steady-state, velocity-weakening friction is given by:h*=(μ*DRS)/[F(a,b)(σn−p)],[2]where μ*=μ/(1−ν) for modes I and II, and μ*=μ for mode III (29); DRS is the characteristic slip distance; and F(a, b) is a function of the rate-and-state friction parameters a and b. The function F(a, b) depends on the specific assumptions made to obtain the estimate: FRR(a,b)=4(b−a)/π (ref. 27, equation 40) for a linearized stability analysis of steady sliding, or FRA(a,b)=[π(b−a)2]/2b, with a/b>1/2 for quasistatic crack-like expansion of the nucleation zone (ref. 30, equation 42).Hence, an increase in pore pressure induces a reduction in the effective normal stress, which both promotes slip due to lower frictional resistance and increases the critical length scale h*, potentially resulting in slow, stable fault slip instead of fast, dynamic rupture. Indeed, recent field and laboratory observations suggest that fluid injection triggers slow slip first (4, 9, 11, 31). Numerical modeling based on these effects, either by themselves or with an additional stabilizing effect of shear-layer dilatancy and the associated drop in fluid pressure, have been successful in capturing a number of properties of slow-slip events observed on natural faults and in field fluid-injection experiments (14, 24, 32–34). However, understanding the dependence of the fault response on the specifics of pore-pressure increase remains elusive. Several studies suggest that the nucleation size can depend on the loading rate (35–38), which would imply that the nucleation size should also depend on the rate of friction strength change and hence on the rate of change of the pore fluid pressure. The dependence of the nucleation size on evolving pore fluid pressure has also been theoretically investigated (39). However, the commonly used estimates of the nucleation size (Eq. 2) have been developed for faults under spatially and temporally uniform effective stress, which is clearly not the case for fluid-injection scenarios. In addition, the friction properties themselves may change in the presence of fluids (40–42). The interaction between shear and fluid effects can be further affected by fault-gauge dilation/compaction (40, 43–45) and thermal pressurization of pore fluids (42, 46–48).Recent laboratory investigations have been quite instrumental in uncovering the fundamentals of the fluid-faulting interactions (31, 45, 49–57). Several studies have indicated that fluid-pressurization rate, rather than injection volume, controls slip, slip rate, and stress drop (31, 49, 57). Rapid fluid injection may produce pressure heterogeneities, influencing the onset of slip. The degree of heterogeneity depends on the balance between the hydraulic diffusion rate and the fluid-injection rate, with higher injection rates promoting the transition from drained to locally undrained conditions (31). Fluid pressurization can also interact with friction properties and produce dynamic slip along rate-strengthening faults (50, 51).In this study, we investigate the relation between the rate of pressure increase on the fault and spontaneous rupture nucleation due to fluid injection by laboratory experiments in a setup that builds on and significantly develops the previous generations of laboratory earthquake setup of Rosakis and coworkers (58, 59). The previous versions of the setup have been used to study key features of dynamic ruptures, including sub-Rayleigh to supershear transition (60); rupture directionality and limiting speeds due to bimaterial effects (61); pulse-like versus crack-like behavior (62); opening of thrust faults (63); and friction evolution (64). A recent innovation in the diagnostics, featuring ultrahigh-speed photography in conjunction with digital image correlation (DIC) (65), has enabled the quantification of the full-field behavior of dynamic ruptures (66–68), as well as the characterization of the local evolution of dynamic friction (64, 69). In these prior studies, earthquake ruptures were triggered by the local pressure release due to an electrical discharge. This nucleation procedure produced only dynamic ruptures, due to the nearly instantaneous normal stress reduction.To study fault slip triggered by fluid injection, we have developed a laboratory setup featuring a hydraulic circuit capable of injecting pressurized fluid onto the fault plane of a specimen and a set of experimental diagnostics that enables us to detect both slow and fast fault slip and stress changes. The range of fluid-pressure time histories produced by this setup results in both quasistatic and dynamic rupture nucleation; the diagnostics allows us to capture the nucleation processes, as well as the resulting dynamic rupture propagation. In particular, here, we explore two injection techniques: procedure 1, a gradual, and procedure 2, a sharp fluid-pressure ramp-up. An array of strain gauges, placed on the specimen’s surface along the fault, can capture the strain (translated into stress) time histories over a wide range of temporal scales, spanning from microseconds to tens of minutes. Once dynamic ruptures nucleate, an ultrahigh-speed camera records images of the propagating ruptures, which are turned into maps of full-field displacements, velocities, and stresses by a tailored DIC) analysis. One advantage of using a specimen made of an analog material, such as poly(methyl meth-acrylate) (PMMA) used in this study, is its transparency, which allows us to look at the interface through the bulk and observe fluid diffusion over the interface. Another important advantage of using PMMA is that its much lower shear modulus results in much smaller nucleation sizes h* than those for rocks, allowing the experiments to produce both slow and fast slip in samples of manageable sizes.We start by describing the laboratory setup and the diagnostics monitoring the pressure evolution and the slip behavior. We then present and discuss the different slip responses measured as a result of slow versus fast fluid injection and interpret our measurements by using the rate-and-state friction framework and a pressure-diffusion model.     

Magnetoelastic standing waves induced in UO2 by microsecond magnetic field pulses

Magnetoelastic dilatometry of the piezomagnetic antiferromagnet UO₂ was performed via the fiber Bragg grating method in magnetic fields up to 150 T generated by a single-turn coil setup. We show that in microsecond timescales, pulsed-magnetic fields excite mechanical resonances at temperatures ranging from 10 to 300 K, in the paramagnetic as well as within the robust antiferromagnetic state of the material. These resonances, which are barely attenuated within the 100-µs observation window, are attributed to the strong magnetoelastic coupling in UO₂ combined with the high crystalline quality of the single crystal samples. They compare well with mechanical resonances obtained by a resonant ultrasound technique and superimpose on the known nonmonotonic magnetostriction background. A clear phase shift of π in the lattice oscillations is observed in the antiferromagnetic state when the magnetic field overcomes the piezomagnetic switch field Hc=−18 T. We present a theoretical argument that explains this unexpected behavior as a result of the reversal of the antiferromagnetic order parameter at Hc.

The antiferromagnetic (AFM) insulator uranium dioxide UO₂ has been the subject of extensive research during the last decades predominantly due to its widespread use as nuclear fuel in commercial power reactors (1). Besides efforts to understand the unusually poor thermal conductivity of UO₂, which impacts its performance as nuclear fuel (2), a recent magnetostriction study in pulsed magnetic fields up to 92 T uncovered linear magnetostriction in UO₂ (3), a hallmark of piezomagnetism.Piezomagnetism is characterized by the induction of a magnetic polarization by application of mechanical strain, which, in the case of UO₂, is enabled by broken time-reversal symmetry in the 3-k AFM structure that emerges below TN=30.8 K (4–7) and is accompanied by a Jahn–Teller distortion of the oxygen cage (8–11). This also leads to a complex hysteretic magnetoelastic memory behavior where magnetic domain switching occurs at fields around ±18 T at T=2.5 K. Interestingly, the very large applied magnetic fields proved unable to suppress the AFM state that sets in at TN (3). These earlier results provide direct evidence for the unusually high energy scale of spin-lattice interactions and call for further studies in higher magnetic fields.Here we present axial magnetostriction data obtained in a UO₂ single crystal in magnetic fields to 150 T. These ultrahigh fields were produced by single-turn coil pulsed resistive magnets (12, 13) and applied along the [111] crystallographic axis at various temperatures between 10 K and room temperature. At all temperatures, we observe a dominant negative magnetostriction proportional to H² accompanied by unexpectedly strong oscillations that establish a mechanical resonance in the sample virtually instantly upon delivery of the 102 T/μs pulsed magnetic field rate of change. The oscillations are long-lasting due to very low losses and match mechanical resonances obtained with a resonant ultrasound spectroscopy (RUS) technique (14). Mechanical resonances were suggested to explain anomalies in magnetostriction measurements during single-turn pulses (15, 16); however, their potential to elucidate magnetic dynamics was not explored so far. When the sample is cooled below room temperature, the frequencies soften, consistent with observations in studies of the UO₂ elastic constant c₄₄ as a function of temperature (17, 18).In the AFM state, i.e., T<30.8 K, the characteristic magnetic field sign switch in our single-turn coil magnet (a feature of destructive magnets) results in applied field values in excess of the UO₂ AFM domain switch field of Hc≈−18 T. This field sign switch exposes yet another unexpected result, namely, a π (180°) phase shift in the magnetoelastic oscillations. We use a driven harmonic oscillator and an analytical model to shed light on the origin of the observed phase shift.     

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.     

Coupled CH4 production and oxidation support CO2 supersaturation in a tropical flood pulse lake (Tonle Sap Lake,Cambodia)

Carbon dioxide (CO₂) supersaturation in lakes and rivers worldwide is commonly attributed to terrestrial–aquatic transfers of organic and inorganic carbon (C) and subsequent, in situ aerobic respiration. Methane (CH₄) production and oxidation also contribute CO₂ to freshwaters, yet this remains largely unquantified. Flood pulse lakes and rivers in the tropics are hypothesized to receive large inputs of dissolved CO₂ and CH₄ from floodplains characterized by hypoxia and reducing conditions. We measured stable C isotopes of CO₂ and CH₄, aerobic respiration, and CH₄ production and oxidation during two flood stages in Tonle Sap Lake (Cambodia) to determine whether dissolved CO₂ in this tropical flood pulse ecosystem has a methanogenic origin. Mean CO₂ supersaturation of 11,000 ± 9,000 μatm could not be explained by aerobic respiration alone. ¹³C depletion of dissolved CO₂ relative to other sources of organic and inorganic C, together with corresponding ¹³C enrichment of CH₄, suggested extensive CH₄ oxidation. A stable isotope-mixing model shows that the oxidation of ¹³C depleted CH₄ to CO₂ contributes between 47 and 67% of dissolved CO₂ in Tonle Sap Lake. ¹³C depletion of dissolved CO₂ was correlated to independently measured rates of CH₄ production and oxidation within the water column and underlying lake sediments. However, mass balance indicates that most of this CH₄ production and oxidation occurs elsewhere, within inundated soils and other floodplain habitats. Seasonal inundation of floodplains is a common feature of tropical freshwaters, where high reported CO₂ supersaturation and atmospheric emissions may be explained in part by coupled CH₄ production and oxidation.

Globally, most lakes and rivers are supersaturated with dissolved carbon dioxide (CO₂) relative to the atmosphere, highlighting their outsized role in transferring and transforming terrestrial carbon (C) (1–3). Terrestrial–aquatic transfers of C can include CO₂ dissolved in terrestrial ground and surface waters (3–6), dissolved inorganic carbon (DIC) from carbonate weathering (7, 8), or organic C from various sources that is subsequently respired in lakes and rivers (9, 10). Initially, oceanic export was thought to be the only fate for terrestrial–aquatic transfers of C, but a growing body of research on sediment burial of organic C and CO₂ emissions from freshwaters prompted the “active pipe” revision to this initial set of assumptions (11). Although freshwaters are now recognized as focal points for transferring and transforming C on the landscape, most of this research has been conducted within temperate freshwaters (2, 11, 12). Few studies focus on the mechanisms of CO₂ supersaturation in tropical lakes and rivers, with most conducted in just one watershed, the Amazon (4, 13–15).CO₂ supersaturation within tropical freshwaters is likely influenced by their unique flood pulse hydrology. The canonical flood pulse concept hypothesizes that annual flooding of riparian land will lead to organic C mobilization and respiration (16). Partial pressures of CO₂ (pCO₂) have been measured in excess of 44,000 μatm in the Amazon River (13), 16,000 μatm in the Congo River (17), and 12,000 μatm in the Lukulu River (17). Richey et al. (13), Borges et al. (18), and Zuidgeest et al. (17) have each shown that that riverine pCO₂ scales with the amount of land flooded in these watersheds. Yet it was only recently that Abril and Borges (19) proposed the importance of flooded land to the “active pipe.” These authors differentiate uplands that unidirectionally drain water downhill (via ground and surface water) from floodplains that bidirectionally exchange water with lakes and rivers (19). They conceptualize how floodplains combine high hydrologic connectivity, high rates of primary production, and high rates of respiration to transfer relatively large amounts of C to tropical freshwaters (19).Methanogenesis inevitably results on floodplains after dissolved oxygen (O₂) and other electron acceptors for anaerobic respiration such as iron and sulfate are consumed (16, 19). Horizontal gradients in dissolved O₂ and reducing conditions have been observed extending from the center of lakes and rivers through their floodplains in the Mekong (20, 21), Congo (22), Pantanal (23), and Amazon watersheds (4). CH₄ production and oxidation occur along such redox gradients (4, 16, 19, 23). CH₄ is produced by acetate fermentation (Eq. 1) and carbonate reduction (Eq. 2) within freshwaters (24, 25). CH₄ production coupled with aerobic oxidation results in CO₂ (Eq. 3 and ref. 25), yet no studies have quantified the relative contribution of coupled CH₄ production and oxidation to CO₂ supersaturation within tropical freshwaters.CH3COOH→CO2+CH4,[1]CO2+8H++8e−→CH4+2H2O,[2]CH4+2O2→CO2+2H2O.[3]The relative contribution of coupled CH₄ production and oxidation to CO₂ supersaturation within tropical freshwaters can be traced with stable C isotopes of CO₂ and CH₄. Methanogenesis results in CH₄ that is depleted in ¹³C (δ¹³C = −65 to −50‰ from acetate fermentation and −110 to −60‰ from carbonate reduction) compared to other potential sources of organic and inorganic C (δ¹³C = −37 to −7.7‰; see Materials and Methods) (24–26). The oxidation of this ¹³C-depleted CH₄ results in ¹³C-depleted CO₂ (24–26). At the same time, CH₄ oxidation enriches the ¹³C/¹²C of residual CH₄ as bacteria and archaea preferentially oxidize ¹²C-CH₄ (25). This means that the ¹³C/¹²C of CO₂ and CH₄ can serve as powerful tools to determine the source of CO₂ supersaturation within freshwaters.Tonle Sap Lake (TSL) is Southeast Asia’s largest lake and an understudied flood pulse ecosystem that supports a regionally important fishery (21, 22, 27). Each May through October, monsoonal rains and Himalayan snowmelt increase discharge in the Mekong River and cause one of its tributaries, the Tonle Sap River, to reverse course from southeast to northwest (21). During this course reversal, the Tonle Sap River floods TSL. The TSL flood pulse increases lake volume from 1.6 to 60 km³ and inundates 12,000 km² of floodplain for 3 to 6 mo per year (21, 27). Holtgrieve et al. (22) have shown that aerobic respiration is consistently greater than primary production in TSL (i.e., net heterotrophy), with the expectation of consistent CO₂ supersaturation. But, the partial pressures, C isotopic compositions, and ultimately the source of dissolved CO₂ in TSL remain unquantified.To quantify CO₂ supersaturation and its origins in TSL, we measured the partial pressures of CO₂ and CH₄ and compared their C isotopic composition to other potential sources of organic and inorganic C. We carried out these measurements in distinct lake environments during the high-water and falling-water stages of the flood pulse, hypothesizing that CH₄ production and oxidation on the TSL floodplain would support CO₂ supersaturation during the high-water stage. We found that coupled CH₄ production and oxidation account for a nontrivial proportion of the total dissolved CO₂ in all TSL environments and during both flood stages, showing that anaerobic degradation of organic C at aquatic–terrestrial transitions can support CO₂ supersaturation within tropical freshwaters.     

Cytochrome cbb3 of Thioalkalivibrio is a Na+-pumping cytochrome oxidase

Cytochrome c oxidases (Coxs) are the basic energy transducers in the respiratory chain of the majority of aerobic organisms. Coxs studied to date are redox-driven proton-pumping enzymes belonging to one of three subfamilies: A-, B-, and C-type oxidases. The C-type oxidases (cbb₃ cytochromes), which are widespread among pathogenic bacteria, are the least understood. In particular, the proton-pumping machinery of these Coxs has not yet been elucidated despite the availability of X-ray structure information. Here, we report the discovery of the first (to our knowledge) sodium-pumping Cox (Scox), a cbb₃ cytochrome from the extremely alkaliphilic bacterium Thioalkalivibrio versutus. This finding offers clues to the previously unknown structure of the ion-pumping channel in the C-type Coxs and provides insight into the functional properties of this enzyme.The known terminal oxidases according to the structure of their active centers and their phylogenetic relations are subdivided into two superfamilies (1). One is composed of numerous representatives containing a heme-copper binuclear active center (BNC). Oxidases belonging to the other superfamily have no copper. This superfamily includes bacterial oxidases of the bd type. The superfamily of representatives with heme-copper BNC is subdivided in turn into two groups, cytochrome c oxidases (Coxs) and quinol oxidases, depending upon the electron donor, which can be either cytochrome c or quinol. Quinol oxidases with a heme-copper BNC are found only in prokaryotes, whereas Coxs are widespread among living organisms of all domains: Eukarya (where they are found in mitochondria and chloroplasts), Bacteria, and Archaea. Although terminal oxidases with heme-copper BNC constitute a diverse group of multisubunit enzymes having from 2 to 13 subunits, conservatism and similar architecture are obviously inherent in their main (catalytic) subunit. The catalytic center of the main subunit always contains two hemes and copper as redox active prosthetic groups and a redox active tyrosine covalently bound to histidine in the polypeptide chain (2–5). Iron of one of the hemes and copper constitute the BNC. Coxs are the best-studied group of terminal oxidases. The basic mechanism of energy transduction by Coxs during respiration consists of the oxidation of cytochrome c by molecular oxygen (O₂) coupled to transmembrane pumping of protons (H⁺). This process results in reduction of O₂ to water by the BNC, where O₂ is bound. In Coxs, it requires four protons (“chemical” H⁺ for water production) taken from the inner side of the membrane and can be coupled to the translocation of another four protons (“pumped” H⁺) from the inner to the outer side of the membrane into the intermembrane or the periplasmic space of mitochondria or prokaryotic cells, respectively, according to the following equation (6–8):4cytc2++4Hin,chem++4Hin,chem++4Hin,pump++O2→4cytc3++4Hout,pump++2H2O.In A-type Coxs, two H⁺ pathways in the main subunit were identified, the so-called D channel, conducting all pumped and part of chemical H⁺, and the K channel, conducting most of chemical H⁺ (9). In C-type Coxs, only a K-channel analog was found (10). The described catalytic events are accomplished through generation of a transmembrane difference in H⁺ potentials (Δμ¯H+), which is used as a convertible membrane-linked biological currency. Microorganisms living in an alkaline environment maintain a nearly neutral cytoplasmic pH (11). This presents a problem for alkaliphiles because it gives rise to an inverted pH gradient that decreases the Δμ¯H+ (12, 13). Some alkaliphilic microorganisms solve this problem by using an Na⁺-pumping NADH-CoQ reductase (NQR) (14), and perhaps a Na⁺-pumping terminal oxidase, as was assumed (15). At present, NQR is the only respiratory chain enzyme for which Na⁺ pumping has been directly and undoubtedly established (16). However, NQR is absent in the extremely alkaliphilic bacterium Thioalkalivibrio versutus AL2, which inhabits an alkaline (∼pH 10) Siberian soda lake at saturating salt concentrations (17). T. versutus is a chemolithotroph that oxidizes sulfur compounds and employs Cox as a terminal component of its aerobic electron transport chain. Here we report that T. versutus uses a novel C-type Cox that (i) specifically requires Na⁺ for its activity and (ii) electrogenically exports Na⁺ from cells or right-side-out subcellular membrane vesicles, the process being coupled to oxidation of ascorbate by O₂.     

Vanishing nematic order beyond the pseudogap phase in overdoped cuprate superconductors

During the last decade, translational and rotational symmetry-breaking phases—density wave order and electronic nematicity—have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant X-ray scattering in a cuprate high-temperature superconductor La1.6−xNd0.4SrxCuO4 (Nd-LSCO) to navigate the cuprate phase diagram, probing the relationship between electronic nematicity of the Cu 3d orbitals, charge order, and the pseudogap phase as a function of doping. We find evidence for a considerable decrease in electronic nematicity beyond the pseudogap phase, either by raising the temperature through the pseudogap onset temperature T* or increasing doping through the pseudogap critical point, p*. These results establish a clear link between electronic nematicity, the pseudogap, and its associated quantum criticality in overdoped cuprates. Our findings anticipate that electronic nematicity may play a larger role in understanding the cuprate phase diagram than previously recognized, possibly having a crucial role in the phenomenology of the pseudogap phase.

There is a growing realization that the essential physics of the cuprate high-temperature superconductors, and perhaps other strongly correlated materials, involves a rich interplay between different electronic symmetry-breaking phases (1–3) like superconductivity, spin or charge density wave (SDW or CDW) order (4–7), antiferromagnetism, electronic nematicity (8–14), and possibly other orders such as pair density wave order (15) or orbital current order (16).One or more of these orders may also be linked with the existence of a zero-temperature quantum critical point (QCP) in the superconducting state of the cuprates, similar to heavy-fermion, organic, pnictide, and iron-based superconductors (17–19). The significance of the QCP in describing the properties of the cuprates, as a generic organizing principle where quantum fluctuations in the vicinity of the QCP impact a wide swath of the cuprate phase diagram, remains an open question. Evidence for such a QCP and its influence include a linear in temperature resistivity extending to low temperature, strong mass enhancement via quantum oscillation studies (20), and an enhancement in the specific heat (21) in the field induced normal state, with some of the more-direct evidence for a QCP in the cuprates coming from measurements in the material La1.6−xNd0.4SrxCuO4 (Nd-LSCO). Moreover, the QCP also appears to be the endpoint of the pseudogap phase (21) that is marked, among other features, by transition of the electronic structure from small Fermi surface that is folded or truncated by the antiferromagnetic zone boundary in the pseudogap phase to a large Fermi surface at higher doping (22, 23) that is consistent with band structure calculations (24). However, in the cuprates, neither the QCP nor the change in the electronic structure have been definitively associated with a particular symmetry-breaking phase.In this article, we interrogate the possibility that the cuprates exhibit a connection between electronic nematic order, the pseudogap, and its associated QCP. In the pnictide superconductors, which are similar in many respects to the cuprates, electronic nematic order is more clearly established experimentally, and there have been reports of nematic fluctuations (25), non-Fermi liquid transport (26), and a change in the topology of the Fermi surface associated with a nematic QCP (27). Electronic nematicity refers to a breaking of rotational symmetry of the electronic structure in a manner that is not a straightforward result of crystalline symmetry, such that an additional electronic nematic order parameter beyond the structure would be required to describe the resulting phase. The manifestation of nematic order may therefore depend on the details of the crystal structure of the materials, such as whether the structure is tetragonal or orthorhombic. However, such a state can be difficult to identify in materials that have orthorhombic structures, which would naturally couple to any electronic nematic order and vice versa. Despite these challenges, experimental evidence for electronic nematic order that is distinct from the crystal structure include reports of electronic nematicity from bulk transport (8–10) and magnetometry measurements (11) in YBa2Cu3Oy (YBCO), scanning tunneling microscopy (STM) (13, 14, 28) in Bi2Sr2CaCu2O8+δ (Bi2212), inelastic neutron scattering (12) in YBCO, and resonant X-ray scattering (29) in (La,Nd,Ba,Sr,Eu)₂CuO₄. Moreover, STM studies in Bi2212 have reported intraunit cell nematicity disappearing around the pseudogap endpoint (30), which also seems to be a region of enhanced electronic nematic fluctuations (31, 32). In YBCO, there have also been reports of association between nematicity and the pseudogap onset temperature (9, 11).Here, we use resonant X-ray scattering to measure electronic nematic order in the cuprate Nd-LSCO as a function of doping and temperature to explore the relationship of electronic nematicity with the pseudogap phase. While evidence that a quantum critical point governs a wide swath of the phase diagram in hole-doped cuprates and is generic to many material systems remains unclear, investigation of Nd-LSCO provides the opportunity to probe the evolution of electronic nematicity over a wide range of doping in the same material system where some of the most compelling signatures of quantum criticality and electronic structure evolution have been observed. These include a divergence in the heat capacity (21), a change in the electronic structure from angle-dependent magnetoresistance (ADMR) measurements (24) in the vicinity of the QCP at x = 0.23, and the onset of the pseudogap (23). Our main result is that we observe a vanishing of the electronic nematic order in Nd-LSCO as hole doping is either increased above x = 0.23, which has been identified as the QCP doping for this system (21), or when temperature is increased above the pseudogap onset temperature T* (23). These observations indicate that electronic nematicity in Nd-LSCO is intimately linked to the pseudogap phase.     

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Lyotropic chromonic liquid crystals (LCLCs) are aqueous dispersions of organic disk-like molecules that self-assemble into cylindrical aggregates, which form nematic or columnar liquid crystal phases under appropriate conditions of concentration and temperature (1–6). These materials have gained increasing attention in both fundamental and applied research over the past decade, due to their distinct structural properties and biocompatibility (4, 7–14). Used as a replacement for isotropic fluids in microfluidic devices, nematic LCLCs have been employed to control the behavior of bacteria and colloids (13, 15–20).Nematic liquid crystals form topological defects under flow, which gives rise to complex dynamical structures that have been extensively studied in thermotropic liquid crystals (TLCs) and liquid crystal polymers (LCPs) (21–29). In contrast to lyotropic liquid crystals that are dispersed in a solvent and whose phase can be tuned by either concentration or temperature, TLCs do not need a solvent to possess a liquid-crystalline state and their phase depends only on temperature (30). Most TLCs are shear-aligned nematics, in which the director evolves toward an equilibrium out-of-plane polar angle. Defects nucleate beyond a critical Ericksen number due to the irreconcilable alignment of the directors from surface anchoring and shear alignment in the bulk flow (24, 31–33). With an increase in shear rate, the defect type can transition from π-walls (domain walls that separate regions whose director orientation differs by an angle of π) to ordered disclinations and to a disordered chaotic regime (34). Recent efforts have aimed to tune and control the defect structures by understanding the relation between the selection of topological defect types and the flow field in flowing TLCs. Strategies to do so include tuning the geometry of microfluidic channels, inducing defect nucleation through the introduction of isotropic phases or designing inhomogeneities in the surface anchoring (35–39). LCPs are typically tumbling nematics for which α2α3 < 0, where α2 and α3 are the Leslie viscosities. This leads to a nonzero viscous torque for any orientation of the director, which allows the director to rotate in the shear plane (22, 29, 30, 40). The tumbling character of LCPs facilitates the nucleation of singular topological defects (22, 40). Moreover, the molecular rotational relaxation times of LCPs are longer than those of TLCs, and they can exceed the timescales imposed by the shear rate. As a result, the rheological behavior of LCPs is governed not only by spatial gradients of the director field from the Frank elasticity, but also by changes in the molecular order parameter (25, 41–43). With increasing shear rate, topological defects in LCPs have been shown to transition from disclinations to rolling cells and to worm-like patterns (25, 26, 43).Topological defects occurring in the flow of nematic LCLCs have so far received much more limited attention (44, 45). At rest, LCLCs exhibit unique properties distinct from those of TLCs and LCPs (1, 2, 4–6, 44). In particular, LCLCs have significant elastic anisotropy compared to TLCs; the twist Frank elastic constant, K2, is much smaller than the splay and bend Frank elastic constants, K1 and K3. The resulting relative ease with which twist deformations can occur can lead to a spontaneous symmetry breaking and the emergence of chiral structures in static LCLCs under spatial confinement, despite the achiral nature of the molecules (4, 46–51). When driven out of equilibrium by an imposed flow, the average director field of LCLCs has been reported to align predominantly along the shear direction under strong shear but to reorient to an alignment perpendicular to the shear direction below a critical shear rate (52–54). A recent study has revealed a variety of complex textures that emerge in simple shear flow in the nematic LCLC disodium cromoglycate (DSCG) (44). The tumbling nature of this liquid crystal leads to enhanced sensitivity to shear rate. At shear rates γ˙<1 s−1, the director realigns perpendicular to the flow direction adapting a so-called log-rolling state characteristic of tumbling nematics. For 1 s−1<γ˙<10 s−1, polydomain textures form due to the nucleation of pure-twist disclination loops, for which the rotation vector is parallel to the loop normal, and mixed wedge-twist disclination loops, for which the rotation vector is perpendicular to the loop normal (44, 55). Above γ˙>10 s−1, the disclination loops gradually transform into periodic stripes in which the director aligns predominantly along the flow direction (44).Here, we report on the structure and dynamics of topological defects occurring in the pressure-driven flow of nematic DSCG. A quantitative evaluation of such dynamics has so far remained challenging, in particular for fast flow velocities, due to the slow image acquisition rate of current quantitative polarization-resolved imaging techniques. Quantitative polarization imaging traditionally relies on three commonly used techniques: fluorescence confocal polarization microscopy, polarizing optical microscopy, and LC-Polscope imaging. Fluorescence confocal polarization microscopy can provide accurate maps of birefringence and orientation angle, but the fluorescent labeling may perturb the flow properties (56). Polarizing optical microscopy requires a mechanical rotation of the polarizers and multiple measurements, which severely limits the imaging speed. LC-Polscope, an extension of conventional polarization optical microscopy, utilizes liquid crystal universal compensators to replace the compensator used in conventional polarization microscopes (57). This leads to an enhanced imaging speed and better compensation for polarization artifacts of the optical system. The need for multiple measurements to quantify retardance, however, still limits the acquisition rate of LC-Polscopes.We overcome these challenges by using a single-shot quantitative polarization microscopy technique, termed polarized shearing interference microscopy (PSIM). PSIM combines circular polarization light excitation with off-axis shearing interferometry detection. Using a custom polarization retrieval algorithm, we achieve single-shot mapping of the retardance, which allows us to reach imaging speeds that are limited only by the camera frame rate while preserving a large field-of-view and micrometer spatial resolution. We provide a brief discussion of the optical design of PSIM in Materials and Methods; further details of the measurement accuracy and imaging performance of PSIM are reported in ref. 58.Using a combination of experiments, numerical simulations and scaling analysis, we show that in the pressure-driven flow of nematic DSCG solutions in a microfluidic channel, pure-twist disclination loops emerge for a certain range of shear rates. These loops are elongated in the flow with a fixed aspect ratio. We demonstrate that the disclination loops nucleate at the boundary between regions where the director aligns predominantly along the flow direction close to the channel walls and regions where the director aligns predominantly perpendicular to the flow direction in the center of the channel. The large elastic stresses of the director gradient at the boundary are then released by the formation of disclination loops. We show that both the characteristic size and the fluctuations of the pure-twist disclination loops can be tuned by controlling the flow rate.     

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).