Time-resolved photoelectron imaging was used to study non-adiabatic relaxation dynamics in N,N-dimethylisopropylamine, N,N-dimethylpropylamine and N-methylpyrrolidine following excitation at 200 nm. N,N-dimethylisopropylamine, N,N-dimethylpropylamine and N-methylpyrrolidine following excitation at 200 nm. This series of tertiary aliphatic amines are all of similar chemical makeup, but exhibit differences in their structure – being branched, straight-chain and cyclic, respectively. Our experimental investigation, supported by extensive theoretical calculations, provides considerable new insight into the nature of the internal conversion processes that mediate dynamical evolution between electronic states of predominantly Rydberg character in this important class of model photochemical systems. In particular, the angle-resolved data afforded by the imaging approach  offers novel and highly-detailed mechanistic information about the overall relaxation pathway. Strikingly, both the experimental and theoretical findings suggest that a critical factor driving the non-adiabatic dynamics is the evolution of valence character along an N–C stretching coordinate within a member of the 3p manifold. This is in stark contrast to primary and secondary amines, as well as many other small hetero-atom containing organic species, where evolution of valence character within the 3s state is now a well-established phenomenon implicated in mediating ultrafast non-adiabatic photochemistry.Time-resolved photoelectron imaging was used to study non-adiabatic relaxation dynamics in  I.i.e. Δv = 0) transitions to the cation. A lack of spectral congestion then permits subtle details of the dynamical evolution – for example conformational reorganization – to be readily observed. This is a consequence of Rydberg state energies being extremely sensitive to small changes in the geometry of the ion core, with the observation of such effects in photoelectron data sometimes being dubbed “Rydberg fingerprint spectroscopy”.Tertiary aliphatic amines (TAAs) provide useful model systems for studying dynamical interactions between electronically excited states in polyatomic molecules following ultraviolet (UV) excitation. Such systems also provide models for nitrogen chromophore centres in a number of naturally occurring species including peptides and neurotransmitters. The electronically excited states of TAAs are all of predominantly Rydberg character.i.e. sub-picosecond) internal conversion between various low-lying Rydberg states. This raises interesting questions relating to the mechanism via which such interactions are mediated, since molecular states of purely Rydberg character would not be expected to approach a point of electronic degeneracy along any internal vibrational coordinate until extreme distortions of the molecular framework are sampled. However, the ultrafast nature of the internal conversion strongly implicates conical intersections, rather than slower avoided crossings, as the principle drivers of any non-adiabatic dynamics.i.e. methyl-substituted) primary, secondary and tertiary amines, it is now generally believed that excited states exhibiting predominantly s Rydberg character in the vertical Franck–Condon region evolve significant σ* valence character at relatively modest N–H and/or N–CH3 bond extensions.As expanded upon further below, many TAAs display clear evidence of “ultrafast” (i.e. fission of the first carbon–carbon bond from the amine group) on a timescale of a few picoseconds. Motion along the nitrogen inversion coordinate was implicated as playing an important role in mediating the internal conversion via an electronic state with a configuration based upon a 3s ← σ transition.In larger TAA systems the key internal coordinates driving non-adiabatic interactions appear to be less well understood. Zewail and co-workers compared ten different amine species using femtosecond time-resolved mass spectrometry (TR-MS) in conjunction with two-photon excitation at ∼8 eV total pump energy.i.e. 3px, 3py & 3pz), with subsequent internal conversion then populating the lower-lying 3s state. These excited states are all built on electronic configurations based principally on promotion of a non-bonding electron from the nitrogen lone pair orbital. Weber and co-workers investigated internal conversion in N,N-dimethylisopropylamine using a combination of TR-MS and time-resolved photoelectron spectroscopy (TRPES).N-substituents.i.e. the nuclear dynamics only sample a reduced phase space before internal conversion).21Subsequently, more recent studies have focused on excitation in TAAs at energies in the region close to 6 eV (an energy now assumed throughout unless otherwise stated). This initially prepares the 3p Rydberg manifold .x,y to the 3s state was then observed on a slightly more extended timescale. Internal conversion within the 3p manifold has also been observed in the larger triethylamine system, along with additional dynamic processes reflecting conformational reorientation of the flexible carbon chains.In trimethylamine, TRPES measurements have revealed sub-picosecond internal conversion within the initially prepared 3p manifold , N,N-dimethylpropylamine (DMPA) and N-methylpyrrolidine (Mpyr), the structures of which are shown in Here we describe TRPEI studies of three TAA systems following single-photon excitation at 200 nm (6.2 eV). Specifically, these are II.1H-NMR. Prior to commencing photoelectron data collection, preliminary room-temperature UV vapour-phase spectra were obtained for all three molecules using a commercial bench-top spectrophotometer (Camspec M550).Samples of DMIPA and Mpyr were purchased from Sigma-Aldrich (99% purity). DMPA was synthesized “in-house” by dimethylation of isopropylamine in a standard Eschweiler–Clarke reaction.via an Even–Lavie pulsed valve .∅ = 1.0 mm), the molecular beam passed into the main interaction chamber and was intersected at 90° by co-propagating UV pump and probe pulses. These were derived from the 800 nm fundamental output of a 1 kHz regeneratively amplified Ti : Sapphire laser system  seeded by a Ti : Sapphire oscillator . The pump beam  and probe beam  were provided by generating the fourth and third harmonics of this output, respectively, using thin β-barium borate (BBO) crystals. Temporal pump–probe delay was precisely adjusted using a computer-controlled linear translation stage and these beams were then combined on a thin dichroic mirror and focussed into the spectrometer using a 50 cm focal length UV-enhanced concave aluminium mirror.Our TRPEI setup has recently been described in detail elsewhere.Interaction between the UV light pulses and the molecular beam took place between the electrodes of an electrostatic lens set-up optimised for velocity-map imaging.Photoelectron data collection repeatedly scanned the pump–probe delay between –500 fs to +1000 fs in 50 fs increments and 19 exponentially increasing steps beyond this point to +100 ps. At each delay position, time-invariant pump-alone and probe-alone images were recorded for subsequent background subtraction. A pump–probe cross correlation of 180 ± 20 fs was obtained directly inside the spectrometer from non-resonant (1 + 1′) multiphoton ionization of nitric oxide. Energy calibration data was obtained from three-photon, non-resonant ionisation of xenon at 267 nm.III.A.N excitation, and the second band to 3p ← nN . For the 200 nm pump used in the TRPEI measurements, UV vapour-phase spectra obtained for the three amines under study are displayed in B.i.e. photoelectron kinetic energy subtracted from probe photon energy). For completeness, i.e. <1 ps) peak at ∼2.3 eV and a feature at ∼3.0 eV that has a delayed onset from zero pump–probe delay and subsequently decays on an extended (>10 ps) timescale. In DMIPA this longer-time decay is noticeably faster than for DMPA or Mpyr. Based on previous photoelectron studies reported for a number of TAA systems,via internal conversion). Clear evidence of more subtle dynamical evolution is also evident in i.e., Δv ≠ 0) ionization from the 3s state involving a high-frequency vibrational mode (presumably a C–H stretch). No other weak spectral features are observed in any other electron energy region  are described as:g(Δt) denotes the experimentally determined Gaussian cross-correlation function and Ai(E) is the decay associated photoelectron spectrum of the ith data channel with a time dependent population Pi(Δt) defined as follows:To analyse the time-dependence of the photoelectron spectra in more detail, global fits were undertaken using a τ1–3. Two of these (τ1 and τ2) describe sub-picosecond dynamics while the third (τ3) models a much longer-lived (38–160 ps) process. DAS plots are presented in τ1 (160–400 fs) exhibits significant amplitude at Rydberg binding energies close to 2.3 eV (i.e. ionization from the 3p manifold) although there is also evidence of an additional small amplitude feature at ∼3.0 eV – a consequence of some weak excitation directly populating the 3s state. Since τ1 is the only function in the overall fit that originates from zero pump–probe delay, such a process must manifest itself in the τ1 DAS to some extent.This approach yields a series of decay associated spectra (DAS) plotting the relative amplitude of each fit component as a function of Rydberg binding energy that provides a highly instructive way of visualizing the results from the overall global fit. Using eqn (1), data obtained for each TAA system was fitted with three sequentially decaying functions which we label using their respective time constants τ2 (480–640 fs) is striking as the energetic position of the prominent peak produced by the fit is not consistent. In DMPA and DMIPA, this feature appears at slightly higher binding energy than the τ1 feature at ∼2.3 eV (3p ionization) whereas in Mpyr it is located at slightly lower binding energy than the main τ3 feature at ∼3.0 eV (3s ionization).The appearance of the DAS associated with τ3 value) has also been shown to depend exponentially on the pump wavelength,Finally, we note that previously reported TR-MS measurements on DMIPA and DMPA using a 200 nm pump reported exponential decay constants for the parent ion of 619 fs and 739 fs, respectively.C.2 and β4 as a function of excited state electron binding energy E and pump–probe delay time Δt:Pn(cos θ) terms are the nth-order Legendre polynomials, σ is the time-dependent electron energy distribution and θ = 180° is defined by a vertical line running fully through the images shown in via the centre point. TRPEI data obtained using (1 + 1′) ionization with parallel linear polarizations yields photoelectron angular distributions (PADs) described by the anisotropy parameters β2 starts by exhibiting relatively large positive amplitude. This then increases slightly, reaching a maximum at Δt ∼ 200 fs, before falling again. For the corresponding β4 parameter, no initial increase is apparent but some small decay is observed as Δt increases up to 1 ps. At small pump–probe delays (<1 ps), ionization from the 3s state gives rise to a broadly similar trend for the evolution of both β2 and β4 to that seen for the 3p manifold. Following their initial evolution, β2 and β4 then remain constant for ∼10 ps before beginning to slowly rise again. This rise is temporally well-matched to the decay of the associated 3s ionization signal . Initial ground state geometry optimisations were performed using density functional theory (B3LYP)lmax = 1, n = 2–3.5) basis set41x, y and z axes.y) whereas it is the state sitting energetically in the middle of the manifold for DMIPA (3pz) and DMPA (3py). The energy separation between adjacent members of the 3p manifold is relatively small (0.01–0.10 eV) but in some cases this should experimentally resolvable in our TRPEI measurements. Finally, a series of complementary TD-CAM-B3LYP calculations were performed using the aug-cc-pVDZ and aug-cc-pVTZ basis sets. These results are also included in Each TAA system under study was treated to several different theoretical methods to evaluate the energies of the first four singlet excited states  photoionization cross-sections, revealing a highly significant positive linear correlation that has previously proved instructive in the interpretation of TRPEI data.ᾱ for the 3s state is ∼2–4 times larger than that obtained for the members of the 3p manifold. This observation would seem to fit well with the fact that the 3s ionization signals seen in Low-lying singlet and triplet state energies for all three systems obtained at the EOM-CCSD/aug-cc-pVDZ level of theory are shown in All DFT, EOM-CCSD, and CASSCF (see below) calculations were performed with Gaussian09,B.–1 in all cases. Multiple ground state conformers are therefore not expected to be present to any significant extent in the jet-cooled molecular beam conditions of the TRPEI experiment and any conformational dynamics observed may be attributed solely to excited state processes.As well as providing a starting point for evaluation of excited state energies, ground state calculations were also used to reveal a number of low-energy conformers for each amine system. Initial conformer searches were performed using Gaussian09 (B3LYP/aug-cc-pVDZ). Following identification of these structures, the geometries were then optimized using second order Møller–Plesset perturbation theory. Separation between the global minimum and the next lowest energy conformer was found to be >90 cmD0) using unrestricted DFT (UCAM-UB3LYP) in combination with an aug-cc-pVDZ basis set. This approach was utilised as all excited states identified are of predominantly Rydberg character. The cation geometry may therefore be considered a good approximation to that of the excited states. Values returned from these calculations were subsequently corrected to include the additional energy required to access this part of the potential from the true ground state minima. A similar approach has been previously employed by Weber and co-workers.D0 state of the cation increases slightly (0.02–0.15 eV) as conformational relaxation proceeds from the vertical Franck–Condon geometry. In contrast, the gap between the 3p state and D0 in DMIPA and Mpyr undergoes a small (0.06–0.11 eV) decrease. In DMPA the equivalent gap remains almost constant or, for one of the conformers, increases slightly. Overall these finding illustrate that conformational rearrangement effects in all three systems should manifest as small (∼0.1 eV), but potentially experimentally resolvable shifts in the photoelectron peak positions associated with ionization from specific Rydberg states.Calculations were also performed to investigate conformer structures in the previously identified excited states of all three systems under investigation. Excited state conformers were generated on the ground electronic state of the cation (C.iso) bond, the carbon-methyl bond (corresponding to α-cleavage) and the nitrogen inversion co-ordinate. These scans were undertaken for relaxed geometries (i.e. those planar about the N atom), obtained from a UCAM-B3LYP/6-311G constrained series of optimisations on the cation. The output obtained is summarized in x in this instance) develops increased valence character, and crosses the 3s state at relatively modest bond extensions. As discussed in the Introduction, it has been generally established that states of s Rydberg character evolve significant σ* valence character at even relatively modest N–H and/or N–CH3 bond extensions in a wide range of small molecular systems, creating potential pathways for dissociation and/or non-adiabatic decay processes.N-methylisopropylamine (i.e. replacing one of the methyl groups in DMIPA with an H atom) suggest that it is now the 3s state that evolves valence character along the N–H stretching coordinate – as would be predicted on the basis of extensive previous work on dynamics mediated by mixed Rydberg/valence states.To investigate the possibility of dissociative excited state relaxation channels, EOM-CCSD/aug-cc-pVDZ calculations were performed on DMIPA to obtain potential energy curves along the nitrogen-methyl bond, the nitrogen-isopropyl . At 2.0 Å, however, the dominant transition is of predominantly σ* ← nN character (coefficient 0.449), with the next largest components being of mixed Rydberg and valence type.The increase in valence character of the 3pFinally, 13D.x Rydberg states. Branching space vectors  are shown in iso stretch and (to a lesser extent) torsion between the two terminal groups. The nature of the branching space is somewhat reminiscent of the S1/S2 conical intersection in thioanisole.0 states revealed no evidence of any non-adiabatic interaction. We note that this finding also appears to be confirmed by the experimental PAD data, as will be expanded upon further in Section V-B.To investigate the interaction between the 3s and 3p states, complete active space self-consistent field (CASSCF) calculations were undertaken (in the aug-cc-pVDZ basis), once again for DMIPA. An active space was constructed using 8 electrons in 6 orbitals. This was based upon a mapping of configuration interaction singles (CIS) states to those obtained using TD-CAM-B3LYP and then using the corresponding CIS natural orbitals to generate a wavefunction that gave a balanced description of the ground and four excited states required. Using this CASSCF wavefunction a conical intersection was optimised that connects the 3s and 3px and 3s states in DMIPA, we have also considered the diabatic nature of these states across the low-lying potential energy surfaces. The aim here is to understand how much mixing there is in each state between the pure “diabatic” s and p Rydberg components. We quantify this as the ratio of the appropriate diffuse p-type basis functions to s-type basis functions in each state, weighted by the associated orbital transition coefficients in the EOM-CCSD eigenvectors. We have analysed three specific geometries: the S0 minimum, the fully relaxed excited state minimum  and the 3px state the “purest” p-character (as its p/s ratio is largest) relative to the other geometries considered.In addition to the non-adiabatic coupling between the 3pV.Photoelectron spectra presented in A.y ← nN). As such, no significant internal conversion within the 3p manifold is likely to be observed in Mpyr. The initially prepared 3py population therefore rapidly and directly decays to the 3s state (as described by τ1 = 400 ± 30 fs) where conformational reorganization then gives rise to the small observed spectral shift (as described by τ2 = 640 ± 50 fs). The link between the spectral shift and the conformational dynamics may be rationalized in terms of the small changes in the perturbation the outgoing electron “feels” from the  molecular ion core – effectively inducing changes in the quantum defect of the Rydberg state as the nuclear geometry evolves.The shapes and relative amplitudes of both the photoelectron spectra  and assoτ1 = 400 ± 30 fs for Mpyr). Conformational reorganization is also therefore able to take place and contribute to the observed spectral shift before crossing to the 3s state takes place. In DMIPA and DMPA internal conversion within the 3p manifold and conformational reorganization therefore contribute the spectral shift seen in the peak at ∼2.3 eV (as described by τ1) – before decay to the 3s state (described by τ2). Consequently, no evolution of the central peak position is then seen at ∼3.0 eV in DMIPA and DMPA. This interpretation of the data appears fully consistent with similar observations reported in other TAA systems as well as the predictions provided by our own calculations. Additionally, since geometry relaxation occurs before internal conversion in DMIPA and DMPA but afterwards in Mpyr we may infer that planarization about the N atom  is not a significant prerequisite for efficient internal conversion to the 3s state. This observation also appears to be in excellent agreement with the calculated branching space vectors for DMIPA presented in In DMIPA and DMPA the situation is different. Here it is the transition to the state sitting energetically in the middle of the 3p manifold that carries the largest oscillator strength. Following 200 nm excitation internal conversion within the 3p manifold may also now form a significant element of the overall relaxation prior to decay into the 3s state. Given the ∼0.1 eV splitting between the various 3p states see , internal = ±1). The shape of the resulting PAD is not only dependent on the amplitudes of these partial wave components but also their relative phases. PADs associated with ionization from the 3p manifold in our data are directed predominantly along the direction of the laser polarization . This discrepancy may be a consequence of two principal factors: (i) mixed orbital angular momentum electronic character of the “p” state and (ii) the possibility of the outgoing electron wavefunction scattering off the non-spherically symmetric ion core (i.e. a failure of the “atomic” picture assumed as a starting point for discussion) – this must clearly be significant in light of the spectral shifts seen due to conformational rearrangement in the photoelectron spectra in At a purely “atomic” level of interpretation, single-photon ionization from a Rydberg state of exclusively p character should give rise to only s and d photoelectron partial waves on the basis of angular momentum conservation  zero before a subsequent long-time rise (considered later) is then seen. This observation appears consistent with the orbital composition calculation discussed in Section IV, where the character of the 3s state was shown to be “purer” at the relaxed excited state geometry than at the S0 geometry.Once again starting from an “atomic” viewpoint, single-photon ionization from the 3s state should give rise to photoelectron partial waves of predominantly p character, leading to PADs peaking strongly along the laser polarization direction. This is indeed observed, although the βelay see  – althou2 and β4 seen at short (<1 ps) times for ionization of the 3s and 3p states provides a signature of the non-adiabatic coupling process leading to internal conversion from the 3p manifold. A more detailed analysis/discussion of the data is, however, challenging due to the fact that additional dynamical factors also influence/convolute the observed form of the PADs. Primarily these are (i) changes in the relative phases and amplitudes of the outgoing photoelectron partial waves – a consequence of conformational rearrangement modifying the scattering dynamics off the non-spherical ion core potential and (ii) significant changes in excited state Rydberg vs. valance character as a function of nuclear coordinates. Any loss of “Rydbergization”2O.Overall, the rapid dynamical evolution of both βB.via the 3p manifold. In DMIPA, however, the 3s lifetime is noticeably shorter (τ3 = 38 ps) than for DMPA (τ3 = 130 ps) and Mpyr (τ3 = 160 ps). This observation may be rationalized using the energy level data presented in via fluorescence has been suggested as a possible pathway,2 and β4 values at long pump–probe delay times i.e. efficient triplet state ionization should be possible in our experiments but we see no signatures of this process in the experimental data, (ii) since the lowest component of the triplet 3p manifold sits >0.45 eV above the singlet 3s state in all three TAA systems , although we believe this may also be ruled out for several reasons: (i) predicted triplet state energies are only ∼0.05–0.15 eV below the corresponding singlet states see . Given t0 conical intersection proved unsuccessful (see Section IV), a third possibility to consider for the fate of the 3s state is that of direct non-radiative relaxation back to S0. However, such a process appears to be ruled out by the data in 0 character into the 3s state would be extremely unlikely to produce increased β2 values (characteristic of more well-defined angular momentum) at long pump–probe delays .Finally, although our computational attempts to locate a 3s/Svia ultrafast internal conversion from the 3p manifold, population spends an extended time (tens of picoseconds) on the 3s surface. During this period, the initially localized vibrational wavepacket is dispersed and intramolecular vibrational redistribution (IVR) will also occur. Consequently, the system may explore a large volume of phase space, occasionally re-encountering the conical intersection with the 3p state . At this time, re-crossing to the dissociative part of the 3p surface may take place, leading to either rapid direct bond fission along an N–C stretching coordinate or  subsequent non-adiabatic decay to S0via an additional conical intersection at highly extended N–C bond lengths . Overall, the non-adiabatic dynamics appears to be primarily mediated by the evolution of valence character as N–C bonds are extended within a member of the 3p Rydberg manifold. This is somewhat different behaviour to that seen in primary and secondary aliphatic amines (as well as in aromatic systems such as aniline) where evolution of valence character within the 3s state is the key diver of ultrafast population transfer. Our findings offer a clear demonstration of the detailed insight afforded by the energy- and angle-resolved TRPEI methodology. However, the subtle new aspects of the UV relaxation dynamics revealed in TAA systems also highlight the need for additional experimental and theoretical investigations . This is not only required to further understand our initial observations, but also definitively establish the extent to which they apply more generally in other systems. We anticipate that our current work will serve as a stimulus for such undertakings.Time-resolved photoelectron imaging was used to investigate non-adiabatic relaxation dynamics operating in a series of three tertiary aliphatic amines following excitation at 200 nm. This was supported by


Tumor-induced bone disease is common among patients with advanced solid cancers, especially those with breast, prostate, and lung malignancies. The tendency of these cancers to metastasize to bone and induce bone destruction is, in part, due to alterations in integrin expression and signaling. Substantial evidence from preclinical studies shows that increased expression of integrin αvβ3 in tumor cells promotes the metastatic and bone-invasive phenotype. Integrin αvβ3 mediates cell adhesion to several extracellular matrix proteins in the bone microenvironment which is necessary for tumor cell colonization as well as the transmission of mechanical signals for tumor progression. This review will discuss the αvβ3 integrin receptor in the context of tumor-induced bone disease. Specifically, the focus will be the role of αvβ3 in modulating cancer metastasis to bone and tumor cell response to the bone microenvironment, including downstream signaling pathways that contribute to tumor-induced osteolysis. A better understanding of integrin dysregulation in cancer is critical to developing new therapeutics for the prevention and treatment of bone metastases. Advanced solid tumors frequently metastasize to bone, occurring in approximately 70–80% of patients with breast or prostate cancer, and in 30–40% of lung cancer patients . MetastaIntegrin αvβ3 is a heterodimeric transmembrane glycoprotein that mediates cell adhesion to the extracellular matrix (ECM) through recognition of conserved arginine–glycine–aspartic acid (RGD) motifs in various ligands including osteopontin, vitronectin, and fibronectin . Like otMetastasis is a multi-step process whereby cancer cells detach from the primary tumor, locally invade the surrounding tissue, transit through the vasculature or lymphatics, and colonize distant sites. Each stage of the metastatic cascade requires the activity of many different cell adhesion molecules, including integrins. Although several integrin heterodimers have been implicated in tumor cell interactions with the bone microenvironment  , αvβ3 haAnother study illustrated that bone-metastatic subclones of a parental cancer cell line constitutively overexpressed integrin αvβ3 . SpecifiIn a more recent report, de novo expression of integrin αvβ3 in tumor cells that typically metastasize to the lungs was sufficient to promote homing to bone . First, It is well-established that metastatic cancers induce osteoclastogenesis to initiate bone resorption, which facilitates tumor expansion in this metastatic niche ,3,35. EvThe molecular mechanisms by which tumor-specific αvβ3 promotes osteolysis are still being explored, but prior studies have shown that αvβ3 signaling resulted in the nuclear localization of transcription factors such as Runx2, which upregulated matrix metalloproteinases  and soluble receptor activator of NF-κB ligand (RANKL) to aid in bone matrix dissolution as well as osteoclast recruitment, differentiation, and function ,38. More10 Pa, which is orders of magnitude more rigid than soft tissues (102–106 Pa) [Over the past few decades, the ECM has been increasingly recognized as an important regulator of cell behavior and gene expression. For instance, matrix stiffness is increased in fibrotic soft tissues and has been linked to the malignant transformation of epithelial cells ,41. Matr–106 Pa) ,43. One –106 Pa) . MDA-MB-The mechanism by which matrix rigidity mediates osteolytic gene expression in metastatic tumors was further elucidated in a more recent study . SpecifiCurrently, the standard of care for patients with TIBD are drugs that interfere with osteoclast-mediated bone resorption such as bisphosphonates  and RANKSeveral αvβ3-targeting drug candidates have advanced to clinical trials for the treatment of osteoporosis and cancer. The RGD-mimetic cyclic peptide cilengitide was first developed for treatment of glioblastoma multiforme ,51 but hPatients with advanced solid cancers frequently develop TIBD which involves growth of metastatic tumors in bone as well as osteoclast-mediated bone destruction. Despite palliative treatments, TIBD remains a highly debilitating disease for many cancer patients. Current therapies focus on inhibiting osteoclast-mediated bone resorption to reduce the risk of SREs, but there is a compelling need for therapies directly targeting metastatic tumor cells in bone. Despite the failure of existing drugs against advanced soft tissue tumors in clinical trials, integrin αvβ3 may be a promising therapeutic target for patients with TIBD as it is highly expressed in several bone-metastatic tumors including breast, prostate, and lung cancer. Preclinical studies have also demonstrated that the aberrant expression of tumor-specific αvβ3 promotes metastasis to bone, thereby increasing skeletal tumor burden and osteolysis. Mechanistically, integrin αvβ3 has been shown to mediate tumor cell response to the rigid bone microenvironment, which results in the upregulation of genes associated with bone destruction . Still,


We present a directed -in vitro- evolution platform that extracts the enzyme from its biological context to provide a new avenue for Rubisco engineering. Precambrian and extant form II Rubiscos were subjected to an ensemble of directed evolution strategies aimed at improving thermostability. The most recent ancestor of proteobacteria -dating back 2.4 billion years- was uniquely tolerant to mutagenic loading. Adaptive evolution, focused evolution and genetic drift revealed a panel of thermostable mutants, some deviating from the characteristic trade-offs in CO2-fixing speed and specificity. Our findings provide a novel approach for identifying Rubisco variants with improved catalytic evolution potential.Rubisco is an ancient, catalytically conserved yet slow enzyme, which plays a central role in the biosphere’s carbon cycle. The design of Rubiscos to increase agricultural productivity has hitherto relied on the use of  In photosynthesis, the physiological role of this ancient enzyme  is the fixation of atmospheric CO2 into biomass through the Calvin cycle2. Specifically, Rubisco carboxylates the pentose sugar ribulose-1,5-bisphosphate (RuBP) and cleaves it into two molecules of 3-phosphoglycerate (3PGA), the central precursor for carbohydrate synthesis in plants3. Despite this important role in natural energy production, Rubisco is a slow biocatalyst with turnover rates as low as 1 to 10 s−1. The Rubisco carboxylation reaction is competitively inhibited by O2. The inability by Rubisco to fully discriminate between CO2 and O2 is due to their close electrostatic nature4 and the inability of Rubisco to directly bind either gas substrate in an enzyme Michaelis complex. The oxygenation reaction of RuBP produces 3PGA and 2-phosphoglycolate (2PG), the latter a compound that is inhibitory to other Calvin cycle enzymes5 necessitating its recycling back to 3PGA through energy demanding photorespiration7.Ribulose-1,5-bisphosphate carboxylase/oxygenase, Rubisco (EC 4.1.1.39), is the most abundant enzyme on earth, due to its necessity in plants, algae and wide distribution in bacteria9. This challenge arises from the realisation that to meet the food demands of a growing global population we will have to produce more food in the next 50 years than has been consumed in the history of human kind10. The most promising results in Rubisco bioengineering have arrived through directed evolution, a biotechnological approach that emulates the process of natural evolution to tailor enzymes and metabolic pathways for industrial and environmental purposes12. To date, all the directed evolution studies reported on Rubisco have been assisted by in vivo -genetic- screening based on photosynthetic selection (e.g. Rhodobacter capsulatus and Chlamydomonas reinhardtii) and Rubisco dependent Escherichia coli (RDE) selection15. Using these strategies form I Rubisco (that comprise 8 large (RbcL) and 8 small (RbcS) subunits) and Rubisco forms II and III (each comprising between 2 and 10 RbcL-subunits) have been evolved to generate an array of variants, mostly with improved solubility23 and only more recently meaningful kinetic improvements24. These evolution campaigns have involved engineering cellular metabolism to be dependent on Rubisco activity for survival. In most instances this metabolic remodeling has reduced cell viability, lowered selection fidelity, constrained screening throughput and limited mutagenic screening to 25 °C24. Such factors have limited the suitability of these Rubisco evolution studies to improving thermal stability, a biophysical trait that is intrinsically connected to protein evolvability in terms of mutational tolerance, fitness and biological function25.Given Rubisco’s catalytic inefficiency, the last decade has witnessed many attempts in laboratories worldwide to engineer more efficient Rubiscos in a drive towards more productive agriculturein vitro- evolution platform that allows Rubisco to be evolved independently of its host’s physiology. We reconstructed and resurrected several Rubisco nodes from the Precambrian era, dating from 3.2 to 1.9 billion years ago. The most recent common ancestor of proteobacteria was evolved, together with the modern form II Rubisco from Rhodospirillum rubrum, using a variety of evolution strategies aimed at improving thermostability that included adaptive evolution, focused evolution and neutral genetic drift. Rubisco mutant libraries were explored in vitro with a dual high-throughput screening (HTS) system that rapidly identified highly thermostable and functional variants. Comprehensive biochemical characterization of both the evolved extant and ancestral Rubisco mutants was undertaken to provide evidence for the first successful directed evolution of an ancestral -Precambrian- protein.In this study, we report a robust directed -Rhodospirillum rubrum (RubRr) was chosen as the template for directed -in vitro- evolution and ancestral resurrection. RubRr comprises two 50 kDa RbcL subunits arranged into a functional RbcL2 dimer that does not require a Rubisco activase for metabolic repair. Accordingly, the folding and assembly of functional form II Rubisco are readily met in E. coli26, unlike the form I Rubisco isoforms of plants or algae. As RubRr production in E. coli can be toxic to growth11 the culture and induction conditions were optimized in a microtiter plate format for sufficient Rubisco expression without compromising host viability . To evolve Rubisco in vitro, a dual HTS assay was established that couples both spectrophotometric and chromatographic detection under saturating CO2 conditions. The spectrophotometric method is a NADH-linked enzymatic depletion assay27 adapted to measure RuBP carboxylation activity in RubRr mutant libraries,  was estimated to be 64 °C in the fresh lysates and this was the main selecting force used during screening , the most recent common ancestor of all the proteobacteria (MRPro), and the most recent common ancestor of proteobacteria and the cyanobacteria firmicutes (MRProFir), which date back between 1.9 to 3.2 billion years  were found to depart substantially from accepted phylogenies, in particular with respect to that reported in the TimeTree of Life38. Therefore, we used the TimeTree of Life to date the nodes in our phylogenetic tree. We hypothesized that the two groups most distant from the query sequence were the result of early horizontal transfer events and/or that they include other Rubisco isoforms. Consequently, we only retained the sequences belonging to the group closest to the query for sequence reconstruction. The three ancestral nodes were successfully resurrected  and the stronger activity of MRPro (2.4 billion years old) in preliminary biochemical measures of Rubisco activity in the cellular protein, made it the most promising candidate for directed evolution  were applied to these libraries, as confirmed by DNA sequencing of a random sample of clones. The resulting evolution landscapes were quite different, producing 76% of inactive clones from RubRr and only 26% of unfolded variants for the ancestral MRPro enzyme  the core catalytic pocket, a sequence block spanning 55 residues  that contains several amino acids directly involved in catalysis ; and ii) loop 6, a 12 amino acid segment (G323-D336) that shows different conformational states upon RuBP binding42  to 56% (in clone B9) of the total soluble protein (tsp) as opposed to ∼30% for the modern RubRr enzyme  in ; Supplementary Table in vitro evolution experiments. For example, the melting temperature (Tm) of clone 25 derived by adaptive evolution outperformed that of RubRr by ∼7 °C  while the Tm of clones 11 and 27 showed improvements of ~4 °C , more than 3-fold reductions in CO2-fixation rate (kcatC) and carboxylation efficiency  is the apparent Km for CO2 in an O2–free atmosphere). This finding is in good agreement with the higher CO2 to O2 atmospheric ratio Precambrian Rubisco experienced prior to biogeochemical elevation of O2 in the atmosphere (estimated to occur 2.5 Gyr ago)43. Consistent with its focused evolution of catalytically critical domains, the MORPHING mutant Clone B2 showed >2-fold impediments in kcatC, KC and affinity for substrate RuBP (KmRuBP) relative to MRPro  agrees well with the recent work reporting ancestral form I Rubiscos from the Mesoproterozoic (>1 Gyr ago)2 and O2. These features often impair the rate of photosynthesis in plants making Rubisco a key target for engineered improvement as a means to increase agricultural productivity and carbon sequestration. The natural trade-off between the carboxylation activity and CO2/O2 specificity (SC/O) of Rubisco has hampered the selection of Rubisco mutants with the desired improvements in kcatC, KC and SC/O. Paradoxically, despite its low carboxylation rates, modern Rubisco has a catalytic efficiency similar to the mean of all known enzymes45 but atypically necessitates large amounts of the enzyme (~25 to 50% of leaf protein) to sustain adequate rates of photosynthesis3. This provides evidence that the evolution of Rubisco kinetics may be naturally constrained thereby offering an explanation as to why attempts to evolve superior Rubiscos in the laboratory have met with limited success24 with most selecting for mutants with increased solubility11.Although Rubisco constitutes the primary bridge between the inorganic and organic phases of the biosphere’s carbon cycle, its carboxylation activity is inherently slow and flawed in its capacity to discriminate between CO46. Moreover there is extensive catalytic diversity naturally found among, and within, the different Rubisco lineages despite all sharing a highly conserved catalytic site and reaction mechanism – suggesting kinetic improvement is not immutable. Certainly, we take hope from directed evolution studies using Rubisco-dependent E. coli (RDE) selection that have discovered unchartered domains in cyanobacterial RbcL8RbcS8 Rubisco and mutations in RbcL10 archaeal Rubisco that significantly improve their carboxylation properties24. However, the dependence on low temperature to slow cell growth of both RDE and photosynthetic screens used in directed evolution applications make them unsuitable to evolve the thermostability of Rubisco, a biophysical trait which may expand the sequence space available for improving catalytic function. Towards addressing this hypothesis, here we uniquely employed novel in vitro HTS assays to screen over 10,000 modern RubRr and resurrected Precambrian form II MRPro Rubisco clones in several campaigns of adaptive evolution, focused evolution and neutral genetic drift to identify a panel of thermostable variants. MRPro and its derivatives exhibited the properties consistent with an ancestral high CO2/low O2 environment (i.e. high solubility and impaired carboxylation properties) in addition to a higher mutational tolerance than RubRr. This suggests resurrected ancestral Rubiscos may serve as better substrates for evolutionary catalytic adaptation, possibly including variants harboring mutations in highly conserved catalytic regions as found here for the MORPHING mutant Clone B2. Notably this enhanced mutational robustness may arise independent of an improved stability as conformational flexibility may be a common feature of ancient proteins that are hypothesized to be more generalist in function47. Conversely, our study provides proof of concept into the versatility of using predicted Precambrian enzymes to address the promiscuity and evolvability for ancestral proteins using modern directed evolution techniques. While we postulate the approach of selecting form II Rubisco mutants suitable for evolving properties that improve catalytic function, the feasibility of translating these properties to other Rubiscos, in particular the form IB Rubisco in crops, remains uncertain. A promising feature of RubRr is that its catalytic mechanism and catalytic pocket amino acid composition is conserved in all Rubiscos. The minimal assembly requirements of RubRr that allow abundant expression in heterologous hosts, including in leaf chloroplasts, have also favored its use as a model for Rubisco structure-function studies and translational testing in plants. By contrast the assembly requirements of form IB plant Rubisco are not met by E. coli. This has necessitated the use of laborious plant genome transformation methods that restrict mutagenic study of plant Rubisco and preclude their suitability with high throughput directed evolution approaches12 Circumventing this obstacle now appears feasible with the demonstration that plant Rubisco assembly in E. coli requires the co-expression of multiple components from the assembly machinery from chloroplasts48, and possibly also its metabolic repair protein Rubisco activase if Rubisco activity is desired. As recently highlighted49, this breakthrough provides new opportunities for mutagenic study of plant Rubisco, including application of the directed in vitro evolution platform technology described in this study.Yet there are reasons to be optimistic if we consider the favored catalytic behavior of Rubisco from some red algae that have the potential to improve plant photosynthesis and growthwww.ncbi.nlm.nih.gov/genome). This search produced 295 protein sequences. We discarded sequences that were too long or too sort, resulting in a set of 201 sequences. The sequences were aligned using MUSCLE (available at https://www.ebi.ac.uk/Tools/msa/muscle/) and a distance matrix was then generated using one minus the sequence similarity as the parameter to assess the evolutionary distance between two sequences. The distribution for the calculated distances revealed three different groups and we found that several taxa were represented in the three groups of sequences, specifically: cyanobacteria; firmicutes; and α, β and γ proteobacteria. The sequences belonging to the group closest to the query were retained for sequence reconstruction resulting in 136 sequences. Since Mr. Bayes efficiency depends strongly on sequence set size, we selected 46 sequences for phylogenetic analysis. We made sure, however, that this subset provided a uniform coverage of the cyanobacteria, firmicutes, α-, β-, δ- and γ-proteobacteria taxa. A literature search confirmed that all the selected sequences belong to Rubisco type II. An Archean sequence was used as outgroup to generate a rooted tree making a total of 47 sequences . This analysis used the Jones substitution model and two independent Markov-chain Monte Carlo runs, each with four chains, and it was performed for 3,603,600 generations to ensure adequate convergence (0.037). The nodes obtained in the tree had posterior probabilities higher than 0.8. However, we targeted the three oldest nodes of the tree for sequence reconstruction, which had a probability of essential unity  and with the WAG evolutionary model (available at https://www.ebi.ac.uk/goldman-srv/WAG/). Subsequently, the proteins encoded by the most probable sequences at each of the three nodes targeted were prepared in the laboratory  and characterized experimentally . Each plate contained an internal standard with Rubisco parental type  and a negative control .PCRs products were cleaned and concentrated. They were cloned behind the trc (trp-lac) promoter of the expression vector pTrcHis2 B using the Gibson Assembly Master Mix. g, the medium was discarded and the cell pellets were frozen at −80 °C. After 12 h the frozen cell pellets were re-suspended in a lysis mixture of Tricine-KOH buffer  containing lysozyme (0.25 mg/mL), DNase I (1.5 U/mL) and 10 mM MgCl2. After 60 min at 37 °C and 250 rpm the lysates were centrifuged at 3000 g and the supernatant was used for the dual HTS assay as well as for the thermostability screening protocol.The plates (master plates) were incubated at 37 °C with shaking at 250 rpm and 80% relative humidity in a humidity shaker . After 16 h, clones from this pre-culture were inoculated  into deep well plates with fresh LB-Amp (lysate plates). After 5 hours of incubation at 37 °C, 250 rpm and 80% relative humidity, LB-Amp with IPTG was added . The plates were incubated at 25 °C with shaking at 250 rpm and 80% relative humidity for 16 h. The plates were centrifuged at 3000 2 and 40 mM NaHCO3 in 100 mM Tris-KOH buffer pH 8.0) was added to each well of the reaction plate. Reaction plates were briefly stirred and after 15 min at room temperature 70 µL of the Rubisco reaction buffer was added. The reaction buffer contained 20 mM MgCl2, 40 mM NaHCO3, 0.5 mM RuBP (for spectrophotometric assay) or 3 mM RuBP (for HPLC-ELSD assay) in 100 mM Tris-KOH buffer, pH 8.0.60 µL of the supernatant from lysate plates were transferred with the help of a liquid handler station  to the reaction plates. 50 µL of activation buffer . The depletion assay was followed in kinetic mode (340 nm) using a plate reader  .Spectrophotometric assay: The reaction plate was stirred briefly and after 4 min at room temperature 40 µL of each well were transferred to a new plate containing 40 µL of 80% (v/v) ethanol to quench the reaction. The plates were stirred and after 5 minutes 120 µL of the NADH depletion buffer was added. Spectrophotometric-depletion buffer composition: 1.5 mM MgClHPLC-ELSD assay: Selected clones of the spectrophotometric assay were transferred from the lysate plate to a new reaction plate and analysed by the HPLC-ELSD (high-performance liquid chromatography with evaporative light scattering detector) assay. The reaction plate was stirred briefly and after 30 min at room temperature 400 mM acetic acid was added to stop the reaction. The HPLC conditions were 50% Buffer A , 40% Buffer B  and 10% C (acetonitrile). The final concentration of n-amylamine was 80 mM. The HPLC analysis was performed with a pump  coupled to a Nucleosil C18  kept at 30 °C. Autosampler  was set to 10 °C to prevent evaporation of the samples. The ELSD conditions were 118 °C and 3.2 L/min of nitrogen flow. Quantification was made with the aid of calibration curves of RuBP and 3PG. Chromatograms were analyzed with Varian Star v.6.41 software.First re-screening: aliquots of 10 µL of the best clones were removed from master plates to inoculate in 90 µL of LB-Amp in new 96 deep well plates. Columns 1 and 12 (rows A and H) were not used. After 16 h of incubation at 37 °C and 250 rpm and 80% relative humidity, 10 µL were transferred to the adjacent wells, containing 90 µL of fresh LB-Amp and further incubated for 5 hours in the same conditions. Then 300 µL of LB-Amp with IPTG were added. The plates were incubated at 25 °C with shaking at 250 rpm and 80% relative humidity for 16 h. Accordingly, every single mutant was grown in 4 wells. Parent types were subjected to the same procedure . Plates were assessed using the same protocol of the screening described above.E.coli. After 16 h at 37 °C, five colonies of every single mutant were picked, inoculated in 100 µL of LB-Amp and re-screened as described above.Second re-screening: An aliquot from the best clones of the first re-screening was inoculated in 10 mL of LB-Amp and incubated at 37 °C and 250 rpm for 16 h. Plasmids from these cultures were extracted with NucleoSpin Plasmid kit and they were transformed together with the parental type into 2 and 40 mM NaHCO3 in 100 mM Tris-KOH buffer pH 8.0) Plates were briefly stirred and after 15 min at room temperature 70 µL of the Rubisco reaction buffer was added and the plates subjected to the spectrophotometric assay as described above. Relative activities were calculated from the difference between the absorption after incubation and that of the initial measurements normalized against the parental type in the corresponding plate. Thermostability values came from the ratio between residual activities (RA) and initial activities (IA) values. Selected clones were subjected to HPLC-ELSD analysis and to two consecutive re-screenings as described above.RubRr and MRPro mutant libraries from adaptive evolution, focused evolution and a random sample of the outcome from the genetic drift campaign were subjected to a thermostability screening protocol. Lysate plates were duplicated with the help of the liquid handler station by transferring 85 µL of lysates to a thermocycler plate  and 60 µL to the initial activity plate. Thermocycler plates were sealed with thermo resistant film  and incubated at 64 °C in the thermocycler . Incubation took place for 10 min . Then, thermocycler plates were placed on ice for 10 min and further incubated for 5 min at room temperature. 60 µL of lysates were transferred from thermocycler plate to a new plate  with the help of the robot. Each well of both residual and initial activity plates was filled with 50 µL of activation buffer (20 mM MgCl2 kinetics, RuBP kinetics, CO2/O2 specificity, DNA sequencing and protein modeling.A full description of the biochemical characterization used in this study is provided in Supporting Information, including: Production and purification of variants, thermostability measurements, expression analysis, COSupporting Information


Conductance quantization is the quintessential feature of electronic transport in non-interacting mesoscopic systems. This phenomenon is observed in quasi one-dimensional conductors at zero magnetic field B, and the formation of edge states at finite magnetic fields results in wider conductance plateaus within the quantum Hall regime. Electrostatic interactions can change this picture qualitatively. At finite B, screening mechanisms in narrow, gated ballistic conductors are predicted to give rise to an increase in conductance and a suppression of quantization due to the appearance of additional conduction channels. Despite being a universal effect, this regime has proven experimentally elusive because of difficulties in realizing one-dimensional systems with sufficiently hard-walled, disorder-free confinement. Here, we experimentally demonstrate the suppression of conductance quantization within the quantum Hall regime for graphene nanoconstrictions with low edge roughness. Our findings may have profound impact on fundamental studies of quantum transport in finite-size, two-dimensional crystals with low disorder. Conductance quantization is the hallmark of non-interacting confined systems. The authors show that the quantization in graphene nanoconstrictions with low edge disorder is suppressed in the quantum Hall regime. This is explained by the addition of new conductance channels due to electrostatic screening. B, conductance quantization arises due to the formation of transverse subbands in confined, quasi one-dimensional (1D) systems such as quantum point contacts (QPC) or quantum wires2. As B increases, the system gradually enters the quantum Hall (QH) regime, where propagating modes evolve from magnetoelectric subbands interacting with both edges, to chiral edge states surrounding an incompressible, gapped bulk2. Within a one-electron picture, both propagation states lead to a quantized two-terminal conductance given by G = Ne2/h 2. The situation changes when taking into account Coulomb interactions13 between injected carriers and/or their coupling to an external gate. For example, the conductance of a 1D channel with repulsive electron–electron interactions vanishes in the presence of any scattering potential at |B| = 0 T ref3. Furthermore, the observation of the so-called 0.7 anomaly12 or the 0.25 feature13 in the conductance quantization of QPCs at |B| = 0 T are also signatures of electron–electron interactions. In a perpendicular B, the interplay between screening mechanisms and the Hall potential causes a reconstruction of the edge states into alternating conductive (compressible) and insulating (incompressible) regions no longer strictly linked to the topology of the conductor8. Compressible zones are characterized by partially filled Landau levels (LLs) pinned at the Fermi energy with a variable electron concentration. Conversely, incompressible regions (strips) consist of fully occupied LLs and display the typical insulating behavior of a QH state8.At zero magnetic field 9. This universal transport regime should occur in narrow, ballistic systems confined by hard-wall potentials11, where a large accumulation of charge carriers near sharp edges and a pronounced inner depletion inhibits the formation of stable incompressible strips9. Although both interactions between carriers and their coupling to the external gate can affect conductance9, it is the electrostatic screening of the gate potential which is the main contributing mechanism10 to the CQS effect.We focus on the ballistic conductance of gated quasi-1D systems, where screening theories predict conductance quantization suppression (CQS) in the QH regime24. Commonly studied QPCs in two-dimensional (2D) electron gases have soft-confining potentials because the gates and dopant layers are far away from the actual carrier layer2. Graphene, on the other hand, provides extraordinary opportunities to examine the physics of the QH effect16. First, it exhibits a natural hard-wall confinement at its borders. Furthermore, the distance to the gate can be arbitrarily selected since electrons in strict 2D materials reside right at the surface. Both features enable the possibility of designing specific device geometries which are (heavily) dominated by screening effects. An example of such a geometry is a narrow graphene strip with a width comparable or smaller than the thickness of the dielectric spacer10. Indeed, CQS in a perpendicular magnetic field has been predicted to occur in gated graphene nanoribbons11. In these systems, the suppression of conductance quantization is related solely to the simultaneous existence of compressible strips in the center of the ribbon and the appearance of additional counter-propagating states11. Nevertheless, experiments conducted with different types of narrow, high-quality graphene devices have so far not confirmed these predictions24.To date, the experimental realization of such narrow, disorder-free, sharp-edged devices has been inherently difficultB18, similar to gate-defined, soft-potential, narrow ballistic graphene channels19. These discrepancies between experiments and theoretical predictions motivate us to investigate devices which have been designed to meet the required theoretically predicted conditions for CQS;11 specifically, a device geometry able to produce a large charge density gradient across the nanostructure, a narrow ballistic channel, and low edge disorder.In more detail, the magnetoconductance of ballistic graphene constrictions remains quantized when increasing By addressing these factors, we experimentally demonstrate the suppression of conductance quantization within the QH regime for graphene nanoconstrictions with low edge roughness. Our findings are a strong experimental confirmation that the single-electron picture is inadequate for describing the transport behavior of finite-size, two-dimensional crystals with low disorder.8, incompressible strips must be wider than the magnetic length lB to be stable. For a given LL with level index k, the minimum charge carrier density gradient across a graphene nanostructure, which prevents the formation of a stable incompressible strip, is (Methods)ε is the permittivity of the dielectric and vF ~ 106 ms−1 the Fermi velocity in graphene.According to QH theoriesB| and k, normalized by the average density navg = 1016 m−22 as dielectric material. Values of |B| of 0–10 T, k of 0, 1, 2, and navg are experimentally accessible in our study. For |B| ≤ 10 T and k ≤ 2, an estimated threshold of 7 m−1 prevents incompressible strips from forming in graphene devices. Figure Figure W and dielectric thicknesses b to examine the stability condition  used for the theoretical prediction of the CQS9 (green curve) shows x > 0.13W across the device. This length is comparable to lB = 0.16W at |B| = 10 T, preventing the appearance of stable incompressible strips. A similar situation occurs (blue curve) in slightly wider constrictions (W = 100 nm) on a dielectric with b = 100 nm. Notably, wider geometries have the added advantage of reducing the significance of edge disorder in experimental devices. Much wider constrictions with sizes close to samples reported in literature18  show lB at |B| = 10 T. This condition remains satisfied for smaller |B| and k, and so this geometry enables the formation of incompressible strips8 and results in a quantized magnetoconductance18.Here, we consider two distinct geometries (ribbons and constrictions) with different widths ion (Eq. ). The riL = W ~ 100 nm on b = 100 nm SiO2 substrates (Methods). Our graphene flakes were exfoliated on hydrophobic SiO225, resulting in mean free paths larger than L,W  of the two types of studied sample. Their geometry and fabrication steps are similar with the exception of the last etching step, which defines the edge disorder of the nanoconstriction26. While all our devices have a certain degree of edge disorder, Sample type 1 , a clear indication of size quantization18. These modulations are significant in Sample type 1, with step heights ΔG up to ~ 2e2/h. Further analysis at |B| = 0 T can be found in the Supplementary Information , dramatically differing from the single-electron picture. Particularly, when increasing the gate voltage Vg, G shows a peak whose value is larger than the expected quantization plateau and cannot be explained by accounting for geometrical corrections in spatially uniform and homogeneous conductors28 , in agreement with the well-known, geometrical effects for homogeneous devices with L > W [k = 1, 2 in Sample type 2 showing G values lower than the expected quantization values. These trends are confirmed in further devices and analysis , which exhibits a quantized = 0 Fig. . Furtherth L > W  (Supplemmentclasspt{minima10 (Methods). This potential corresponds closely to those generated by more complex models, such as self-consistent solutions within the Hartree approximation29. Although such approaches can account for both Coulomb interactions between injected carriers and their coupling to the external gate, the electrostatic screening of the gate potential is the primary factor determining the charge density distribution in these systems30. The interpretation given above is supported by tight-binding calculations, where the inhomogeneous electrostatic potential across the device is introduced using the analytical model proposed by Silvestrov and EfetovFigure 9. These new dispersive states support propagation in both directions and unlike QH states, are susceptible to backscattering due to the overlap between forward and backward propagating states9 and disorder11. Therefore the channels lose their exact quantization as edge disorder is increased, forming peak-like conductance features at low edge disorder levels, before being completely suppressed by stronger scattering  is the electron density across the device at |B| = 0 T, ε is the dielectric constant of the insulating material, kth incompressible strip, and Ek is the Landau spectrum. In the case of spin-degenerate graphene, we get 16. Thus, for the graphene nanodevice to be free of incompressible strips, the charge carrier density gradient The competition between the Hall and screened potentials determines the stability of incompressible strips in a perpendicular magnetic fieldmentclass2pt{minimnel(x) can be calculated33 using the expression Ez(x) is the perpendicular electric field component in the corresponding gated devices at y = 0 at a distance z = 0.5 nm above the flake and ε = 3.9ε0 is the permittivity of the SiO2. Ez(x) can be obtained for any geometry by solving the Poisson equation in the device using a finite-element method33 solver , achieved by the mechanical exfoliation of graphene on hydrophobic25 Si/SiO2 substrates (SiO2 thickness b = 100 nm) and contact resistance Rc below 600 Ω. To test these initial device parameters , we first shape, contact and measure the magnetotransport properties of rectangular two-terminal devices with a width of ~1 µm  and Au (30 nm) at low pressure (<5 × 10−7 mbar). The subsequent definition of the nanoconstrictions is done via electron beam lithography using polymethyl-methacrylate developed at −5 °C in a 1:3 IPA:H2O solution.We fabricate devices with field-effect mobility 26. Devices with a higher amount of edge disorder (Sample type 2) are defined by plasma ashing, which, despite being known to introduce instabilities and localized states in graphene nanodevices, is widely used to shape graphene nanostructures24. In contrast, devices with a much lower amount of edge disorder (Sample type 1) were produced by RIE26 . We achieve an edge roughness ≤1 nm with the RIE etching procedure, as demonstrated in the transmission electron micrograph shown in the Supplementary Fig. The edge quality in our constrictions is defined with two complementary etching processes: oxygen plasma ashing and RIE34. After these 18 h, the devices are dipped for 5 s in acetone, 5 s in IPA, and then dried with nitrogen.Prior to measuring their electrical properties, we dip our devices for 18 h in a pure hexamethyldisilazane solution to reduce the effect of environmental contaminants that may have been adsorbed on the basal plane of graphene or at the edges during the processing stepsOur measurements were done in an Oxford Instrument Teslatron PT cryostat. Measurements of differential conductance were performed using a Stanford SR830 lock-in amplifier with an excitation voltage of 80 μV at a frequency of 17.77 Hz.L = W = 100 nm) and different degrees of edge disorder (Supplementary Note In our simulations, we consider zigzag nanoribbons with similar dimensions to the experimentally measured constrictions (i. The hopping parameters tij take the values t1 = −2.7 eV, t2 = −0.2 eV, and t3 = −0.18 eV, respectively35.The electronic structure is described by a single π-orbital third-nearest-neighbor tight-binding HamiltonianThe effect of a magnetic field is included using the Peierls’ phase approach. This involves introducing a field-dependent phase factor in the tight-binding hopping parametersy-direction.We choose the Landau gauge GR and GA are the retarded and advanced Green’s functions respectively.The conductance through the ribbon is evaluated in terms of the transmissionThe effect of a gate voltage is introduced by fixing the Fermi energy and instead changing the onsite energy potentials according to25n010A uniform carrier density can be included using an infinite plane capacitor26, which gives rise to the stronger CQS observed for LL0 in our experiments (Supplementary Fig. Furthermore, in Fig. The data that support the findings of this study are available from the corresponding authors on request.Supplementary InformationPeer Review File


Symbiodinium). Here, we report that Stylophora pistillata from a highly diverse reef in the Gulf of Aqaba showed no signs of bleaching despite spending 1.5 months at 1–2°C above their long-term summer maximum (amounting to 11 degree heating weeks) and a seawater pH of 7.8. Instead, their symbiotic dinoflagellates exhibited improved photochemistry, higher pigmentation and a doubling in net oxygen production, leading to a 51% increase in primary productivity. Nanoscale secondary ion mass spectrometry imaging revealed subtle cellular-level shifts in carbon and nitrogen metabolism under elevated temperatures, but overall host and symbiont biomass proxies were not significantly affected. Now living well below their thermal threshold in the Gulf of Aqaba, these corals have been evolutionarily selected for heat tolerance during their migration through the warm Southern Red Sea after the last ice age. This may allow them to withstand future warming for a longer period of time, provided that successful environmental conservation measures are enacted across national boundaries in the region.Coral reefs are currently experiencing substantial ecological impoverishment as a result of anthropogenic stressors, and the majority of reefs are facing immediate risk. Increasing ocean surface temperatures induce frequent coral mass bleaching events—the breakdown of the nutritional photo-symbiosis with intracellular algae (genus:  These symbionts are essential because they transfer assimilated inorganic nutrients to the coral host, complementing an otherwise heterotrophic lifestyle, and provide the coral with a substantial ecological advantage in generally nutrient-poor tropical oceans -bicarbonate and [15N]-nitrate) experiment, with subsequent nanoscale secondary ion mass spectrometry (NanoSIMS) and electron microscopy (EM) imaging, was performed on 8 June 2014.All physiological proxies were assessed after 47 days of exposure to combined temperature and pH stress. Cumulative heat stress, expressed as degree heating week , amount2.4.−2 s−1 PAR, 20 s intervals), using an Imaging-PAM fluorometer . All pulse amplitude modulation (PAM) measurements were conducted between 8.00 and 10.00. Characteristic parameters of RLC  were derived from computational curve-fitting using SigmaPlot12.3, following previously published methods , followed by one hour in the dark under their respective treatment conditions. Oxygen saturation was monitored with an optode connected to an OXY-4 mini  and used to calculate the linear slopes of change in relative oxygen saturation after blank correction and accounting for the effects of temperature and salinity on oxygen saturation . Note that only the steepest linear part of the curve was used, i.e. dark respiration values represent dark-acclimated dark respiration based on the last approximately 40 min of the incubation . Gross photosynthetic rates were derived from the equation: net photosynthesis (light) = gross photosynthesis (light) − respiration (dark), assuming a negligible difference between coral respiration in the light and dark. Productivity was expressed as daily productivity (Pgross : R ratio with 14 h : 24 h) and host O2 demand in the light was calculated as the direct R : Pgross ratio. Calcification rate was determined from the change in total alkalinity in water samples taken at the beginning and end of all respirometry measurements. Samples were titrated by a titrosampler  and calcification rates determined accordingly  osmium tetroxide in water for 1 h. Post-fixed samples were dehydrated, embedded in Spur resin blocks and microtomed following published protocols  on TEM grids and corresponding semi-thin (500 nm) sections on glass coverslips were gold-coated and bombarded with a 16 keV primary Cs+ ion beam. Raster scans of the area of interest (6 layers) were performed with a primary beam spot size of around 150 nm. Image resolution was set to 256 × 256 pixels with a beam dwell time of 5 ms per pixel. Image size was set to 40 × 40 µm, which provided a complete cross section of the epidermis and oral gastrodermis with sufficient resolution for subcellular features to be clearly resolved. Approximately 10–15 images were obtained per sample in order to cover enough area to image 50–60 symbiont cells and their surrounding host tissue. In case multiple sections from the same sample block were required to obtain enough cells, they were taken at least 20 µm apart to avoid cutting and imaging another layer of the same symbiont cells. The secondary ions 12C2−, 13C12C−, 12C14N− and 12C15N− were simultaneously counted at a mass resolution of about 10 000  in electron multipliers.Based on TEM imaging, areas of interest were analysed for 13C/12C and 15N/14N enrichment were derived from drift-corrected image ratios of 13C12C− and 12C2−, and 12C15N− and 12C14N−, respectively. Quantification of isotopic abundance in different compartments was achieved by drawing regions of interest (ROIs) on ratio images. The following ROIs were defined and manually drawn based on contour outlines visible on the 12C14N− image and/or both ratio images: Symbiont, host gastrodermis (excluding symbionts), host epidermis and host lipid droplets. Isotopic enrichments were converted to atom percent excess (APE) [NanoSIMS data were processed using the L'IMAGE software . Maps of ss (APE) , which r2.9.post hoc test where appropriate. All statistical analyses were performed using the software JMP v. 11.2.1 .The effects of temperature and pH on the physiological parameters were tested as part of a factorial design with two levels for each factor. All treatments were replicated in three separate tanks with three different coral colonies per tank. Data were analysed with a linear mixed model with a restricted maximum-likelihood approach (REML), using temperature, pH and replicate group as fixed factors, and replicate as a random factor. While the factors temperature and pH were crossed to assess their combined effect, replicate tank  was only used as a main factor in the model in order to test whether there was a difference due to the replicate tank that was consistent across all treatments. Replicate (nested within replicate tank) was included as a random factor to assess how much of the variance in the experiment was attributed to the randomly selected colony replicates . When high interaction terms were not significant, the full factorial model was reduced to a minimal adequate model. All dependent variables were tested for normal distribution using the Shapiro–Wilk test and when necessary were transformed to achieve normality. Tukey's HSD test was applied as a t-tests for each class of ROI. Data were checked for normality and homoscedasticity using the Shapiro–Wilk test and Levene's test, respectively, and transformed if necessary.Effects of temperature on carbon and nitrogen assimilation (NanoSIMS data) were tested in paired 3.a; electronic supplementary material, table S1) and symbiont total chlorophyll concentration significantly increased by 44% in the combined stress scenario, predominantly driven by temperature (+45%), compared to pH (−9%) . Variables related to electron flow in photosystem II showed a synergistic effect of pH and elevated temperature: rapid light curves indicated significantly higher maximum quantum yields of photosystem II  with increased maximal relative electron transport rates  (figure 3a). These changes in pigmentation and photochemistry corresponded to an increased light demand to saturate photosynthesis  and decreased chl a/chl 2c ratio (−10%) at elevated temperatures .After six weeks of exposure to elevated temperature and a pH of 7.8, none of the colonies showed visual signs of bleaching. Indeed, symbiont densities were not significantly affected by any of the treatments (figure 3gross) and net oxygen production (Pnet) per surface area were improved substantially by exposure to elevated temperatures (+83%) and effectively doubled (+129%) in the combined treatment (b). Holobiont respiration showed minor, non-significant changes (+7%) under these conditions . Notably, reduced pH had an additive positive effect on net oxygen production only at elevated temperature and not under ambient conditions. Reduced pH also significantly enhanced the efficiency of gross oxygen generation per unit of chlorophyll, independent of temperature (b). As a result of this profound shift in symbiont photosynthesis with temperature and minor changes in holobiont respiration, the amount of respired O2 relative to the total production  significantly declined by almost a third . Scaling the metabolic oxygen data to a daily budget  indicates a daily productivity for the coral holobiont of 1.14 ± 0.22  under ambient conditions. This ratio significantly increased to 1.72 ± 0.33 under the combined pH/temp treatment (figure 3b). Again, this was driven by a strong positive effect of temperature (+39%), although reduced pH also enhanced this ratio (+12%).As a consequence of the increase in the light reaction of photosynthesis, gross . Protein and carbohydrate content in symbionts and host tissue showed no significant changes in any treatments after two months of exposure . Of the antioxidant markers, only catalase activity in the host tissue was elevated in response to higher temperatures , but this was not accompanied by higher host superoxide dismutase (SOD). Activity of these two antioxidant enzymes did not significantly change in the symbiont population in any treatment (figure 3c).The increase in holobiont productivity did not translate to significant changes in coral calcification or energetic proxies such as carbohydrate and protein content of host and symbiont. While coral calcification tended to decline slightly under elevated temperatures, neither light nor dark calcification was significantly affected across treatments  to investigate rates and allocation of photosynthetically fixed nutrients. Combined with transmission electron microscopy (data not shown) and NanoSIMS isotopic imaging [a–c). Symbionts primarily store photosynthetically fixed C as starch and lipids, which showed the highest 13C-enrichments (b). Assuming steady-state conditions, 5.5 ± 0.4% of the total symbiont structural C was replaced over the 6-hour incubation period under ambient temperatures, whereas 8.0 ± 0.2% of C in host lipids was replaced in the same time period (d). Almost all translocated C (97–100%) and N (91–95%) was detected in the oral gastrodermis, rather than the epidermis .Temperature was observed to be the main driver for changes in photosynthesis and productivity of the coral holobiont. Therefore, after two months of exposure, we performed a 6 h incubation with [ imaging , this prichments b. Assumie period d. Almostd,e; electronic supplementary material, tables S2 and S3), although strong variability was observed at this cellular level between three replicates . In the following we therefore indicate in parenthesis the full range of observed responses. At elevated temperatures, coral symbionts displayed an average change in the amount of fixed C and N of −17% (+1 to −31%) and −6% (+26 to −30%), respectively . Likewise, both the host gastrodermis (−35%) and epidermis (−36%) assimilated less translocated N , whereas reduced C assimilation (−31%) was only detected for the gastrodermis (−1 to −65%).NanoSIMS imaging of the polyp-connecting coenosarc tissue showed reduced symbiont C and N fixation and subsequent host assimilation under elevated temperatures (figure 4N = 282). Allocation of photosynthetic C to these reservoirs tended to decline at higher temperature, but this was not statistically significant . While translocated N was not found in specific hotspots in the host tissue, it tended to be more concentrated in the vicinity of the symbiosomes containing the symbionts (c). Interestingly, the fraction of replaced N in host LBs was comparable to that in the gastrodermis as a whole  and while elevated temperature significantly reduced the N turnover in these structures by 21% (−5 to −41%), its impact was smaller than in the overall gastrodermis (figure 4e).The major stores for translocated C were lipid bodies (LBs) in the host gastrodermis with an average size of 2.6 ± 1.3 µm  with up to 2°C above its long-term summer maximum of 27.67 ± 0.75°C . A greater oxygen efflux from the colony surface might improve local water oxygenation during the day and therefore locally attenuate the negative effects of decreased oxygen solubility in warmer water (a drop of −9% between 23°C and 28°C), benefiting aerobic biological processes that are accelerated under elevated temperature, such as microbial activity and fish respiration [pO2 tends to promote the generation of reactive oxygen species [± 0.75°C . In natu Red Sea ,40. Whil Red Sea . Our stused here . The pigpiration ,43. From species , especia species , but we Stylophora pistillata, based on oxygen metabolism, indicated a balanced metabolic budget, similar to the estimated total productivity of a coral reef community of around one [gross : R ratios under elevated temperature and reduced pH was, however, not reflected in changes in symbiont or host protein biomass or carbohydrate content that one would expect to accompany improved photosynthesis. An increase in skeletal extension rate could have partly masked an increase in colony tissue growth, since it is normalized to surface, but no significant change in overall calcification was detected. It thus seems conceivable that the coral host experienced a shift in the relative activity of catabolic versus anabolic processes with productivity increases primarily invested into energy metabolism rather than tissue/skeletal growth.Under ambient conditions, the daily productivity of ound one . The cona–c), we interpret the NanoSIMS results as changes in the utilization efficiency of CO2 by Rubisco and a decoupling between the light and dark reactions of photosynthesis at elevated temperatures. The specific constellation of increased O2 production and decreased C-fixation points towards photorespiratory mechanisms, which might also be stimulated by the low ability of the dinoflagellate type-II Rubisco to discriminate between O2 and CO2 [d), confirming that these structures are the major transient C stores in the host tissue [13CO2 from the system.The NanoSIMS data provided evidence that elevated temperature causes subtle declines in C and N acquisition in the coral tissue that were, however, not reflected in the biomass proxies within the experimental observation period. Considering the increased oxygen productivity and the absence of photoinhibition or elevated SOD activity a–c, we i and CO2 . In this and CO2 . This me and CO2 –51. The  and CO2 . Given tt tissue . While ct tissue . In gene4.1.Stylophora pistillata from the GoA is resistant to summer conditions to be expected for the second half of the century. The positive effect of elevated temperature on key physiological parameters suggests that these corals are currently living at suboptimal temperatures in the Northern Red Sea in comparison to specimens in the Central and Southern Red Sea, where the annual and summer mean SST are much higher. Thus, under continuous warming, it is likely that S. pistillata in the GoA will actually continue to show improved performance until its thermal threshold is approached. Our findings strongly underpin previous suggestions on the temperature resistance of corals in the GoA as a result of their evolutionary history [Our experiment showed that  history ,54,55. C history ,40.Diploastrea heliopora in the Central Red Sea [S. pistillata calcification appears robust against the combination of elevated temperature and reduced pH in our experiment and other work on a Red Sea specimen has demonstrated that it can maintain calcification rates and skeletal integrity at a pH of 7.8 under ambient temperature for even longer exposure periods (more than 1 year) [Despite these positive physiological data, further work on the effects of elevated temperature and reduced pH is required to understand the ecological implications with regard to recruitment success, growth rates and competitive performance. Long-term sublethal effects are equally important to consider. For example, reduced calcification in the absence of obvious bleaching is still a major problem for overall reef growth, as shown for  Red Sea . Red Sea 1 year) .S. pistillata is an r-strategist coral, given its rapid growth rate, early reproductive age and tendency to colonize unpredictable habitats. Another support of the species being a typical r-strategist stems from a massive die-off of S. pistillata following local environmental disturbances such as an anomalously low tide. The present study demonstrates physiological resistance of this species to global environmental change in the marine environment (ocean warming and acidification). While the latter gives hope of survival under ‘business-as-usual’ climate change scenarios, it has to be considered that local disturbances, including pollution, eutrophication and physical damage may lower the capacity of S. pistillata to withstand global future environmental conditions.Loya  suggesteConsidering the rapid decline of coral reefs worldwide, our study emphasizes the urgent need to reduce local stressors in the GoA region. Physical damage, pollution and eutrophication amplify the impact of global stressors. The semi-enclosed GoA currently harbours extensive fringing reefs and sea grass meadows, but it is also subject to increasing pressure from industrial and urban developments. Previous case studies have demonstrated the devastating impact that pollution and wastewater discharge can have on the local coral population in the GoA ,59. It i


The present strain gradient, resulting from the disclinations in the BiFeO3 nanostructures array grown on LaAlO3 substrates via a high deposition flux, induces a polarization of several microcoulomb per square centimetre. It leads to a large built-in electric field of several megavoltage per metre, and gives rise to a large enhancement of solar absorption. Our results indicate that it is possible to build up large-scale strain-dominated nanostructures with exotic properties, which in turn could be useful in the development of novel devices for electromechanical and photoelectric applications.Although elastic strains, particularly inhomogeneous strains, are able to tune, enhance or create novel properties of some nanoscale functional materials, potential devices dominated by inhomogeneous strains have not been achieved so far. Here we report a fabrication of inhomogeneous strains with a linear gradient as giant as 10 et al. report a fabrication of inhomogeneous strains with a linear gradient as giant as 106 per meter in a BiFeO3 nanostructure array grown on a LaAlO3 substrate.Inherent elastic strains are useful to tune the physical properties of functional materials but it is difficult to build. Here, Tang  These should involve at least the lead-free piezoelectric elements containing no piezoelectric materials working through flexoelectric couplings2223242526272830Nevertheless, the above proposals are based on either the theoretical simulations16242517181930323 as a perovskite prototype3637a<100> and a<110> type interfacial dislocations is identified to account for the lattice mismatch of the heteroepitaxial system. Such a relaxation mechanism results in a long-range and giant linear strain gradient across the rhombohedral (R phase) BiFeO3 nanostructures displaying remarkable disclination characters. We find that the giant strain gradient enables to transfer when the BiFeO3/LaAlO3 films are repeatedly grown, suggesting a controllability of such inhomogeneous strains in abundant lead-free perovskites without the need of taking dimension constrain into account. Our results deviate from the general understanding that giant strain gradients and the resultant flexoelectricity only matter at a nanoscale, and provide an example to quantitatively measure the inhomogeneous strains through directly atomic imaging.In this work, we report a fabrication of giant linear strain gradients in the lead-free perovskite nanostructures and their real-space measurements at the atomic scale. We choose single-phase room temperature multiferroic BiFeO3/BiFeO3 (LAO/BFO) are epitaxially grown on a LAO(001) substrate by pulsed laser deposition with a high deposition flux mode. High frequency 5 Hz is chosen and a fresh surface of the ceramic target  is used to insure a high growth rate of the first BFO layer. In the further growth of upper LAO and BFO layers, the laser was first focused on the ceramic targets for 30 min pre-sputtering to stabilize the target surfaces. The stabilized targets allow a lower deposition flux  and LAO  away from the interface is actually derived from a synergetic effect of the special array of interfacial dislocations.High-angle annular dark-field (HAADF) scanning transmission electron microscopic (STEM) imaging is applied to investigate the atomic details. ω) and in-plane strain (εxx) maps of the LAO/BFO/LAO nanostructure. Giant lattice rotation resulting from the interfacial dislocations array is obviously visible. The lattice rotation map exhibits systematical inhomogeneity, which increases gradually from left to right of the image. Three line-profiles of the lattice rotations are shown in εxx) map was extracted, as shown in εxx) and out-of-plane .GPA and directly atomic position mappings are effective and accurate tools which show great potential to extract complex and inhomogeneous strain distributions81039404344ane εyy, strain ma[011] dislocations are separated by three a[010] dislocations; in the middle, a[010] and a[011] dislocations appear one by one; and at the right side, only a[011] dislocations emerge. The a[011] dislocation contains out-of-plane component (a[001]) and consequently rotates the BFO lattice. However, at the left side, the a[011] dislocations are well separated by the a[010] dislocations which contain no out-of-plane component, so their rotation effect is restrained. Nonetheless, at the right side, the three well aligned a[011] dislocations result in giant lattice rotation in the BFO and LAO lattice, which spreads for a long distance across the entire BFO and LAO films. Finally, the right BFO lattice is severely rotated, while the left BFO lattice still holds the same orientation as the LAO substrate. This synergetic effect of the a[001] components resembles the low-angle boundaries (or tilt boundaries) formed by a[001] dislocation array in perovskite bicrystalIt is worthwhile to mention that the array of these dislocations is in an aperiodic fashion . At the εxx strain in the LAO/BFO/LAO lattice show obvious and systematic inhomogeneity, as shown in εxx decreases from the bottom to top, which is consistent with the character of bending deformation of materialsεxx is shown in εxx can be seen directly as the slopes of strains in the BFO and above LAO lattice. Note the strains in the LAO substrate reference lattice are constant 0 which confirms the validity of strain gradients in above BFO and LAO lattice. The strain gradients of εxx in BFO are estimated by the slopes of the curves, which are well above 106 m−1 order. Such a giant linear strain gradient is not occasionally observed in the present lead-free perovskite and more examples are displayed in As above mentioned, continuous lattice rotation is relevant to a bending deformation, thus the lateral deformation must be accompanieda[010] type dislocation arrays, consequently the bending of all above perovskite lattice is preserved, since there is no a[001] component to accommodate the lattice rotation (εyy) and shear (εxy) strain mappings are given in The giant linear strain gradient identified in the present study can be preserved and transferred into multilayers. For example, when BFO nanostructure is further grown on top of the LAO/BFO/LAO(001) nanostructures with lower growth rate , the benrotation . The outl × t × h, where l and t are the in-plane dimensions vertical to or along the imaging direction . The elastic energy of the fully strained BFO island displays highly increasing linear distribution with increasing of thickness, which is calculated through the elastic properties of 2D strained filmsThe formation of linear strain gradient at nanoscale can be understood through an elastic energy consideration, and we find that the elastic energy consumption for producing such a giant strain gradient is unexpectedly low, as shown in irection , h is thh) and the location of neutral plane (y) of the BFO nanostructure under linear strain gradient, as shown in 6 m−1) and maximum elastic limit of nanomaterials ≈160 nm, when the neutral plane y is in the middle of hm). Note that the minimum elastic energy consumption occurs when h=2y, that is, pure bending (more details can be found in h) and mismatch of the same size BFO nanostructure under fully 2D strained state is shown in h=50 nm BFO nanostructure under linear strain gradient, its elastic energy is probably <1 × 10−14 J. However, when the same BFO nanostructure is fully 2D strained on a LAO substrate, its elastic energy is ∼13 × 10−14 J, which is more than 10 times bigger than the former ones. The elastic energy consumption for linear strain state tends to more negligible when the thickness h decreases.The present study features general implications for other perovskite oxides. We further formulate the elastic energy consumption distribution versus thickness  of perovskite materials other than the generally accepted elastic energy considerations of epitaxial films50It is known that the 2D compressive strain strongly determines the domain structures, phase constitutions and piezoelectricity. And many unique properties of BiFeOO3 refs. , 52, 53,6 m−1 (defined as ΔS) corresponds to a radius of curvature (r) much <1,000 nm, which is probably the biggest gradient attainable in long-range linear strains expect for the local strain gradients observed at ferroelectric domain walls and other interfaces30f ) for perovskite are on the order of 10−9–10−8 Cm−1  as estimated according to Pf=f × ΔS. Although this value is not so large compared with the spontaneous polarization (Ps) of BFO, an important signification is that the flexoelectric behaviour under the form of giant linear strain gradient is applicable for all dielectric materials when integrated into an electronic devices.The giant linear strain gradient over 10m−1 refs , 20, 30.Ef), which can be estimated according to the following formulaIn addition, the flexoelectric coupling also leads to a large flexoelectricity-driven electric field (e is the electronic charge (1.602 × 10−19 C), −12 Fm−1), a is the lattice parameter. An Ef well exceeding 1MVm−1 is estimated. This value is comparable to the internal field in the conventional p–n junctions and Schottky diodes293 and other perovskite materials nanostructures as flexible electronics, electromechanical or photoelectric devices could thus be stimulated. It is worthwhile to mention that, although flexoelectricity is generally discussed in terms of dielectric insulators, a very recent study by a three-point bending reveals that the flexoelectric-like coupling is much larger in doped oxide semiconductors than in dielectric insulatorswhere 2 photocatalyst316To further verify how the strain gradient affects the macroscopic property of the present perovskite nanostructures, we have performed ultraviolet–visible absorption measurements on the multilayered LAO/BFO nanostructures . For com3/LaAlO3 multilayer nanostructures by a controlled pulsed laser deposition via a high deposition flux mode. Aberration-corrected STEM observation shows that the as-received giant strain gradients are dominated by synergetic interfacial dislocation arrays with a<100> and a<110> Burger vectors. The well aligned a[001] Burger vector components severely rotate the BiFeO3 lattice, result in a long-range giant strain gradient and lead to many exotic properties. The interfacial dislocations herein are very useful modulations other than deleterious ingredients as generally cognized. Our calculations indicate the elastic energy consumption for producing such a giant strain gradient is extremely lower than previously regarded, and our experiments show that the giant strain gradient enables to transfer across a multilayer structure possibly reaching a practical scale. The present results may also stimulate the relevant studies on other epitaxial systems with large lattice mismatch, which are not favoured in the past. Our study provides an opportunity to quantitatively measure the contribution of inhomogeneous strains and assemble them in a nanostructure for the development of novel device concepts, which should involve lead-free electromechanical actuators, high-efficient energy harvesting devices and photocatalysts.In summary, we have artificially produced a giant linear strain gradient in the BiFeO3 nanostructures were deposited by pulsed laser deposition, using a Lambda Physik LPX 305i KrF (λ=248 nm) excimer laser. A sintered BiFeO3 ceramic target (3 mol% Bi-enriched) and a stoichiometric LaAlO3 ceramic target were used. The target-substrate distance was 40 mm. The background pressure was 10−5 Pa. Before deposition, all substrates were pre-heated at 750 °C for 5 min to clean the substrate surface and then cooled down to the growth temperature (10 °C min−1). After deposition, the samples were annealed at their growth temperature in an oxygen pressure of 5 × 104 Pa for 10 min, and then cooled down to room temperature at a cooling rate of ∼5 °C min−1. Commercial, one-side polishing LaAlO3(001) single-crystal substrates with 10 mm × 10 mm × 0.5 mm dimension were used for film deposition.BiFeOThe samples for the HAADF–STEM experiments were prepared by slicing, gluing, grinding, dimpling and finally ion milling. A Gatan PIPS was used for the final ion milling. Before ion milling, the samples were dimpled down to <20 μm. The final ion milling voltage was <1 kV to reduce ion beam damage. HAADF–STEM images were recorded using aberration-corrected scanning transmission electron microscopes (Titan Cubed 60–300 kV microscope (FEI) fitted with a high-brightness field-emission gun (X-FEG) and double Cs corrector from CEOS, and a monochromator operating at 300 kV). The beam convergence angle is 25 mrad, and thus yields a probe size of <0.10 nm. The diffraction contrast image was recorded using a conventional TEM (Tecnai G2 F30 (FEI) working at 300 kV). Large-scale strain fields were deduced by using custom plugins of GPA under the framework of Gatan DigitalMicrograph software. The visualization of the strains and lattice rotations was carried out using Gatan DigitalMicrograph software.ω) are derived from the HAADF–STEM images via GPA, during which LaAlO3 substrate is chosen as the reference lattice. The observed linear strain gradient resulting from the lattice rotation can be persevered in lead-free perovskiteLattice rotations .Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.