Cortical activity during motor execution,motor imagery,and imagery-based online feedback

Imagery of motor movement plays an important role in learning of complex motor skills, from learning to serve in tennis to perfecting a pirouette in ballet. What and where are the neural substrates that underlie motor imagery-based learning? We measured electrocorticographic cortical surface potentials in eight human subjects during overt action and kinesthetic imagery of the same movement, focusing on power in “high frequency” (76–100 Hz) and “low frequency” (8–32 Hz) ranges. We quantitatively establish that the spatial distribution of local neuronal population activity during motor imagery mimics the spatial distribution of activity during actual motor movement. By comparing responses to electrocortical stimulation with imagery-induced cortical surface activity, we demonstrate the role of primary motor areas in movement imagery. The magnitude of imagery-induced cortical activity change was ∼25% of that associated with actual movement. However, when subjects learned to use this imagery to control a computer cursor in a simple feedback task, the imagery-induced activity change was significantly augmented, even exceeding that of overt movement.     

Overriding native cell coordination enhances external programming of collective cell migration

As collective cell migration is essential in biological processes spanning development, healing, and cancer progression, methods to externally program cell migration are of great value. However, problems can arise if the external commands compete with strong, preexisting collective behaviors in the tissue or system. We investigate this problem by applying a potent external migratory cue—electrical stimulation and electrotaxis—to primary mouse skin monolayers where we can tune cell–cell adhesion strength to modulate endogenous collectivity. Monolayers with high cell–cell adhesion showed strong natural coordination and resisted electrotactic control, with this conflict actively damaging the leading edge of the tissue. However, reducing preexisting coordination in the tissue by specifically inhibiting E-cadherin–dependent cell–cell adhesion, either by disrupting the formation of cell–cell junctions with E-cadherin–specific antibodies or rapidly dismantling E-cadherin junctions with calcium chelators, significantly improved controllability. Finally, we applied this paradigm of weakening existing coordination to improve control and demonstrate accelerated wound closure in vitro. These results are in keeping with those from diverse, noncellular systems and confirm that endogenous collectivity should be considered as a key quantitative design variable when optimizing external control of collective migration.

Collective cell migration enables intricate, coordinated processes that are essential to multicellular life, spanning embryonic development, self-healing upon injury, and cancer invasion modes (1). Control of collective cell migration, therefore, would be a powerful tool for biology and bioengineering as such control would enable fundamentally new ways of regulating these key processes, such as enabling accelerated wound healing. Efficient and precise control over cell motility is becoming increasingly feasible with modern biotechnologies. Tunable chemical gradient generators can redirect chemotaxing cells (2, 3), optogenetics can allow dynamic control of cell contractility (4), micropatterned scaffolds can constrain and direct collective growth (5), and recent work in bioelectric interfaces has even demonstrated truly programmable control over directed cell migration in two dimensions (6, 7). However, despite advances in sophisticated tools, applying them to complex cellular collectives raises a fundamental problem: What happens when we command a tissue to perform a collective behavior that competes with its natural collective behaviors?Paradoxically, those endogenous collective cell behaviors already present in tissues are both a boon and bane for attempts to control and program cell behavior. On the one hand, endogenous collective cell migration means the cells already have established mechanisms for coordinated, directional migration that external cues and control can leverage. For instance, cadherin-mediated cell–cell adhesions in tissues mechanically couple cells together and allow for long-range force transmission and coordinated motion. This coupling allows tissues to migrate collectively and directionally over large distances and maintain cohesion and organization far better than individual cells might (8, 9). On the other hand, imposing a new behavior over an existing collective behavior may generate conflicts. Tight cell coupling can create a “jammed state” or solid-like tissue where cells are so strongly attached and confined that they physically lack the fluidity to migrate as a group (10, 11). Strong coordination established via physical coupling can hinder cells from responding to signals for migration, as shown by the need for zebrafish and other embryos to weaken cell–cell junctions prior to gastrulation to ensure cells collectively migrate to necessary locations (12–14). Hence, how “susceptible” a collective system may be to external control likely depends on a tug-of-war between the resilience and strength of the natural collective processes and the potency of the applied stimulus.Here, we specifically investigate the relationship and interplay between an applied, external command attempting to direct collective cell migration and the strength of the underlying collective behaviors already present in the tissue. We address two key questions. 1) How much does the strength of an endogenous collective migration behavior in a tissue limit our ability to control its collective cell migration? 2) How can we circumvent such limitations? To investigate these questions, we needed both a programmable perturbation capable of controlling collective migration and a physiologically relevant model system allowing for tunable “collectivity.” Here, we use collectivity to describe how strongly cells are coordinated with their neighbors during migration—highly collective cells exhibit strong, coordinated motion and vice versa. As a perturbation, we harnessed a bioelectric phenomenon called “electrotaxis”—directed cell migration in direct current (DC) electric fields—using our SCHEEPDOG bioreactor (6). Briefly, electrotaxis arises when endogenous, ionic fields form during healing or development (∼1 V/cm) and apply gentle electrophoretic or electrokinetic forces to receptors and structures in cell membranes, causing them to aggregate or change conformation to produce a front–rear polarity cue (15, 16). Components spanning phosphatidylinositol phosphates (PIPs), extracellular signal-regulated kinase (ERK), phosphatidylinositol 3-kinase (PI3K), phosphatase and tensin homolog (PTEN), and small guanosine triphosphate (GTP)ases have been implicated in the transduction process, while gap junctions appear to have an inconclusive role (8, 17–19). Crucially, electrotaxis may be one of the broadest and most conserved migratory cues, having been observed in vitro in over 20 cell types across multiple branches of the tree of life (20–22). As electrotaxis in vitro appears to globally stimulate all cells equally and still induce directional motion, it is distinct from more locally dependent cues such as chemotaxis and haptotaxis. However, as no other reported cue has as much versatility and programmability, electrotaxis is an ideal choice for a broadly applicable cellular control cue in this study.To complement electrotaxis, we chose primary mouse skin for our model system as skin injuries were where the endogenous electrochemical fields that cause electrotaxis were first discovered (in vivo, the wound boundary is negative relative to the surrounding epidermis), and we and others have shown layers of keratinocytes to exhibit strong electrotaxis (6, 23–25). Critically, primary mouse keratinocytes have tunable collectivity in culture as the cadherin-mediated cell–cell adhesion strength in this system can be easily tuned by varying calcium levels in the media—with low-calcium media thought to mimic conditions in the basal layers of the epidermis with weak adhesions and high-calcium media akin to conditions in the uppermost layers of skin with strong adhesions (26–28).Together, these experimental approaches allowed us to precisely explore how the ability to externally “steer” collective migration in a living tissue using a powerful bioelectric cue depends on the native collectivity of the underlying tissue. First, we quantify collective strength in cultured skin layers by measuring neighbor coordination of cellular motion [a standard metric for collective motion adapted from collective theory (29)] and then, validate that the collectivity can be tuned in our model system of mouse keratinocyte monolayers by calibrating junctional E-cadherin levels. Next, we demonstrate how applying the same electrical stimulation conditions to tissues with differing native collectivity results in radically different outputs, with weakly collective tissues precisely responding to our attempts to control their motion, while strongly collective tissues exhibited detrimental supracellular responses resulting in tissue collapse. We then prove that E-cadherin is responsible for these differences, ruling out any effects of calcium signaling per se. Finally, we leverage these findings to develop an approach that allows us to effectively control mature, strongly collective tissues, which we utilize to demonstrate that we can accelerate wound repair in vitro.     

Structure-based analysis of the molecular interactions between acyltransferase and acyl carrier protein in vicenistatin biosynthesis

Acyltransferases (ATs) are key determinants of building block specificity in polyketide biosynthesis. Despite the importance of protein–protein interactions between AT and acyl carrier protein (ACP) during the acyltransfer reaction, the mechanism of ACP recognition by AT is not understood in detail. Herein, we report the crystal structure of AT VinK, which transfers a dipeptide group between two ACPs, VinL and VinP1LdACP, in vicenistatin biosynthesis. The isolated VinK structure showed a unique substrate-binding pocket for the dipeptide group linked to ACP. To gain greater insight into the mechanism of ACP recognition, we attempted to crystallize the VinK–ACP complexes. Because transient enzyme–ACP complexes are difficult to crystallize, we developed a covalent cross-linking strategy using a bifunctional maleimide reagent to trap the VinK–ACP complexes, allowing the determination of the crystal structure of the VinK–VinL complex. In the complex structure, Arg-153, Met-206, and Arg-299 of VinK interact with the negatively charged helix II region of VinL. The VinK–VinL complex structure allows, to our knowledge, the first visualization of the interaction between AT and ACP and provides detailed mechanistic insights into ACP recognition by AT.Polyketide synthases (PKSs) are multifunctional enzymes responsible for the biosynthesis of various polyketide natural products (1). Bacterial modular PKSs comprise several catalytic modules that are each responsible for a single round of the polyketide chain elongation reaction. Each module minimally consists of a ketosynthase (KS) domain, an acyltransferase (AT) domain, and an acyl carrier protein (ACP) domain. The AT domain recognizes a specific acyl building block and catalyzes its transfer reaction onto the 4′-phosphopantetheine arm of the ACP. KS extends the polyketide chain by condensing the resulting ACP-bound building blocks with the elongated acyl–ACPs. Although standard modular PKSs contain AT domains in their modules, some modular PKSs lack AT domains in each module and instead receive their acyl building blocks by standalone trans-acting ATs (2).The selection of the starter unit is generally governed by the substrate specificity of the AT domain in the loading module (1). In some modular PKS systems, a didomain-type loading module comprising a loading AT domain and an ACP domain selects an acyl starter building block such as an acetate unit to generate an acyl–ACP intermediate, which is transferred to the downstream extension module for polyketide chain elongation. Alternatively, in a KS_Q-type loading module consisting of three domains, the AT domain selects an α-carboxyacyl substrate such as a malonyl group, and the KS_Q domain subsequently catalyzes its decarboxylation to construct an acyl–ACP thioester. For polyketide chain elongation, the AT domain of the extension module generally recognizes a specific α-carboxyacyl–CoA as an extender building block (3). Malonyl– and methylmalonyl–CoA are commonly used as extender building blocks in biosynthetic pathways. Some ATs were reported to recognize ACP-bound substrates such as methoxymalonyl–, hydroxymalonyl–, and aminomalonyl–ACP (3, 4). Thus, ATs are key determinants of building block specificity in polyketide biosynthesis and attractive targets to change the substrate specificity to obtain biologically active unnatural polyketide products (5). However, the substitution of an AT domain by a homologous AT domain possessing different substrate specificity resulted in reduced or abolished production of polyketide analogs in many cases, probably because of disruption of proper protein–protein interactions or the inability of downstream modules to process polyketide analogs (5, 6).The importance of protein–protein interaction between AT and ACP during the acyltransfer reaction was proposed in previous studies (7, 8). Wong et al. described that AT recognizes its cognate ACP from other ACPs through protein–protein interactions (7). Proper AT–ACP interactions are believed to be essential for kinetically efficient polyketide chain elongation. However, the mechanism of ACP recognition is not well understood because isolated AT structures provide no detailed information on the AT–ACP interactions (9). Structural determination of the AT–ACP complex is necessary for the complete understanding of the basis of ACP recognition for the acyltransfer reaction.Macrolactam antibiotics are an important class of macrocyclic polyketides, and most contain a unique β-amino acid starter unit in their polyketide skeletons (10). Vicenistatin, produced by Streptomyces halstedii HC34, possesses a 3-aminoisobutyrate unit at the starter position of the polyketide backbone (11). This starter unit is biosynthesized from l-glutamate via (2S,3S)-3-methylaspartate, which is initially transferred onto the standalone ACP VinL by the adenylation enzyme VinN (12, 13). After decarboxylation, the resulting 3-aminoisobutyrate unit is aminoacylated with l-alanine to give dipeptidyl–VinL by another adenylation enzyme VinM. Then, the dipeptidyl moiety is transferred from VinL to the ACP domain (VinP1LdACP) of the VinP1PKS loading module by the trans-acting AT VinK (Fig. 1). These β-amino acid carrying enzymes are conserved in various macrolactam polyketide biosynthetic gene clusters, suggesting that β-amino acid starter units are loaded to PKS through the same mechanism in their biosynthesis (10).Open in a separate windowFig. 1.Biosynthetic pathway of vicenistatin, including the VinK reaction. The 3-aminoisobutyrate unit is shown in red.During the dipeptide transfer reaction from VinL to VinP1LdACP, VinK is supposed to recognize the VinL region as well as the dipeptidyl moiety to overcome the kinetic disadvantage of the diffusion-controlled limit. Additionally, VinK should distinguish VinP1LdACP as an acyl acceptor from other ACPs. Thus, we assume that the specific protein–protein interaction between VinK and two ACPs is important for the reaction. However, the origins of ACP selectivity cannot be predicted from the amino acid sequence of VinK. In this study, we carried out mutational and structural studies on VinK to clarify how VinK recognizes ACPs. The covalent VinK–VinL complex structure allows, to our knowledge, the first visualization of the interactions between AT and ACP and provides detailed mechanistic insights into ACP recognition by AT.     

Effect of Application of a Bio-Adhesive on the Removal Torque Value and Rotational Misfit at the Implant–Abutment Junction: An In Vitro Study

The aim of this study was to assess the effect of application of a recently developed bio-adhesive (Impladhesive) to abutment screw threads on the removal torque value and rotational misfit at the implant–abutment junction. This in vitro study evaluated 20 implant fixtures and 20 straight abutments. Specimens were randomly divided into two groups (n = 10) with/without adhesive application. In the adhesive group, the abutment was dipped in Impladhesive before torquing. In the control group, the abutment was torqued conventionally without adhesive application. The removal torque value was recorded after completion of the cyclic loading of 500,000 cycles with 2 Hz frequency and 75 N load. Rotational misfit was recorded using a video measuring machine. After applying the torque, the change in the bisector angle on the abutment hex was recorded for each implant. The biocompatibility of Impladhesive was evaluated using a MTT cell vitality assay. Normal distribution of data was assessed using the Kolmogorov–Smirnov test. Data were analyzed using a t-test and Pearson’s correlation coefficient The application of Impladhesive at the implant–abutment interface resulted in significantly greater mean removal torque value compared to the control group (p = 0.008). In addition, the mean rotational misfit at the implant–abutment interface was significantly lower in the use of Impladhesive compared to the control group (p = 0.001). In addition, the cell vitality was found to be greater than 80% at all evaluated time points. It can be concluded that the application of Impladhesive on the abutment screw significantly decreased rotational misfit and increased the removal torque value. Future studies are needed to evaluate the efficacy of this bio-adhesive an in vivo setting.     

Viscosity of deeply supercooled water and its coupling to molecular diffusion

The viscosity of a liquid measures its resistance to flow, with consequences for hydraulic machinery, locomotion of microorganisms, and flow of blood in vessels and sap in trees. Viscosity increases dramatically upon cooling, until dynamical arrest when a glassy state is reached. Water is a notoriously poor glassformer, and the supercooled liquid crystallizes easily, making the measurement of its viscosity a challenging task. Here we report viscosity of water supercooled close to the limit of homogeneous crystallization. Our values contradict earlier data. A single power law reproduces the 50-fold variation of viscosity up to the boiling point. Our results allow us to test the Stokes–Einstein and Stokes–Einstein–Debye relations that link viscosity, a macroscopic property, to the molecular translational and rotational diffusion, respectively. In molecular glassformers or liquid metals, the violation of the Stokes–Einstein relation signals the onset of spatially heterogeneous dynamics and collective motions. Although the viscosity of water strongly decouples from translational motion, a scaling with rotational motion remains, similar to canonical glassformers.Water, considered as a potential glassformer, has been a long-lasting topic of intense activity. Its possible liquid–glass transition was reported 50 years ago to be in the vicinity of 140?K (1, 2). However, ice nucleation hinders the access to this transition from the liquid side. Bypassing crystallization requires hyperquenching the liquid at tremendous cooling rates, ca. 10⁷?K ? s^?1 (3). As a consequence, many questions about supercooled and glassy water and its glass–liquid transition remain open (4–7).As an example, crystallization of water is accompanied by one of the largest known relative changes in sound velocity, which has been attributed to the relaxation effects of the hydrogen bond network (8, 9). Indeed, whereas the sound velocity is around 1,400 m⋅s−1 in liquid water at 273?K, it reaches around 3,300 m⋅s−1 in ice at 273?K and a similar value in the known amorphous phases of ice at 80?K (10). Such a large jump is usually the signature of a strong glass, i.e., one in which relaxation times or viscosity follow an Arrhenius law upon cooling. However, pioneering measurements on bulk supercooled water by NMR (11) and quasi-elastic neutron scattering (12), as well as recent ones by optical Kerr effect (8, 9), reveal a large super-Arrhenius behavior between 340 and 240?K, similar to what is observed in fragile glassformers (13, 14). The temperature dependence of the relaxation time is well described by a power law (8, 9), as expected from mode-coupling theory (15, 16), which usually applies well to liquids with a small change of sound velocity upon vitrification. Based on these and other observations, it has been hypothesized that supercooled water experiences a fragile-to-strong transition (17). This idea has motivated experimental efforts to measure dynamic properties of supercooled water and has received some indirect support from experiments on nanoconfined water (18–20) and from simulations (21, 22).In usual glassformers, many studies have focused on the coupling or decoupling between the following dynamic quantities: viscosity (η) and self or tracer diffusion coefficients for translation (D_t) and rotation (D_r). If objects as small as molecules were to follow macroscopic hydrodynamics, one would expect that the preceding quantities would be related through the Stokes–Einstein (SE), D_t ∝ T/η, and Stokes–Einstein–Debye (SED), D_r ∝ T/η, relations, where T is the temperature. These relations are indeed obeyed by many liquids at sufficiently high temperature. However, they might break down at low temperature. Pioneering experiments were performed by the groups of Sillescu (23–25) and Ediger (26–28) where a series of molecular glassformers were investigated. SE relation is obeyed at sufficiently high temperature but violated around 1.3T_g, where T_g is the glass transition temperature, thus indicating decoupling between translational diffusion and viscosity. In contrast, it was observed for ortho-terphenyl (23, 24, 26) that rotational diffusion and viscosity remain strongly coupled (i.e., obey the SED relation) even very close to T_g. A corollary is that translational and rotational diffusion decouple from each other at low temperature. These observations imply that deeply supercooled liquids exhibit spatially heterogeneous dynamics (29–31). Dynamic heterogeneities have been confirmed by direct observations of several single fluorescent molecules immersed in ortho-terphenyl (32) or nanorods immersed in glycerol (33). Physically different systems also show analogous behavior. Colloids near the colloidal glass transition violate SE but obey SED (34). In the metallic alloy Zr₆₄Ni₃₆, SE relation is even violated without supercooling, more than 35% above the liquidus temperature (35). This has also been related to the emergence of dynamic heterogeneities (36).For water, SE already breaks down at ambient temperature, which corresponds to around 2.1?T_g (T_g ? 136?K). Molecular dynamics simulations (37–39) have proposed that this occurs concurrently to dynamic heterogeneities caused by a putative liquid–liquid critical point. However, SE and SED also fail by application of high pressure at 400?K (40) where no liquid–liquid transition is expected. To gain more insight, the test of SE and SED in supercooled water deserves further investigation. Translational self-diffusion coefficient D_t (41) and rotational correlation time τ_r (assumed to scale as 1/D_r) (42) have thus been measured down to the homogeneous crystallization temperature (238?K) at ambient pressure. Their comparison reveals a decoupling between rotation and translation that increases with supercooling (42), similar to glassformers. However, viscosity data are needed for a direct test of SE and SED relations. Quite surprisingly, there are only two sets of data for the viscosity η at significant supercooling. Using Poiseuille flow in capillaries, Hallett (43) reached 249.35?K, and Osipov et al. (44) reached 238.15?K. However, the two sets disagree below 251?K, with an 8% difference at 249?K, beyond the reported uncertainties. The measurements in ref. 44 are suspected of errors (45) because of the small capillary diameter used. Here we report η at ambient pressure down to 239.27?K. Our study completes the knowledge of the main dynamic parameters of water down to the homogeneous crystallization limit and allows us to check the coupling of viscosity to molecular translation or rotation, as has been done for usual glassformers.     

Differential curvature sensing and generating activities of dynamin isoforms provide opportunities for tissue-specific regulation

Dynamin 1 (Dyn1) and Dyn2 are neuronal and ubiquitously expressed isoforms, respectively, of the multidomain GTPase required for clathrin-mediated endocytosis (CME). Although they are 79% identical, Dyn1 and Dyn2 are not fully functionally redundant. Through direct measurements of basal and assembly-stimulated GTPase activities, membrane binding, self-assembly, and membrane fission on planar and curved templates, we have shown that Dyn1 is an efficient curvature generator, whereas Dyn2 is primarily a curvature sensor. Using Dyn1/Dyn2 chimeras, we identified the lipid-binding pleckstrin homology domain as being responsible for the differential in vitro properties of these two isoforms. Remarkably, their in vitro activities were reversed by a single amino acid change in the membrane-binding variable loop 3. Reconstitution of KO mouse embryo fibroblasts showed that both the pleckstrin homology and the Pro/Arg-rich domains determine the differential abilities of these two isoforms to support CME. These domains are specific to classical dynamins and are involved in regulating their activity. Our findings reveal opportunities for fundamental differences in the regulation of Dyn1, which mediates rapid endocytosis at the synapse, vs. Dyn2, which regulates early and late events in CME in nonneuronal cells.     

Rate and mechanism of the photoreduction of birnessite (MnO2) nanosheets

The photoreductive dissolution of Mn(IV) oxide minerals in sunlit aquatic environments couples the Mn cycle to the oxidation of organic matter and fate of trace elements associated with Mn oxides, but the intrinsic rate and mechanism of mineral dissolution in the absence of organic electron donors is unknown. We investigated the photoreduction of δ-MnO₂ nanosheets at pH 6.5 with Na or Ca as the interlayer cation under 400-nm light irradiation and quantified the yield and timescales of Mn(III) production. Our study of transient intermediate states using time-resolved optical and X-ray absorption spectroscopy showed key roles for chemically distinct Mn(III) species. The reaction pathway involves (i) formation of Jahn–Teller distorted Mn(III) sites in the octahedral sheet within 0.6 ps of photoexcitation; (ii) Mn(III) migration into the interlayer within 600 ps; and (iii) increased nanosheet stacking. We propose that irreversible Mn reduction is coupled to hole-scavenging by surface water molecules or hydroxyl groups, with associated radical formation. This work demonstrates the importance of direct MnO₂ photoreduction in environmental processes and provides a framework to test new hypotheses regarding the role of organic molecules and metal species in photochemical reactions with Mn oxide phases. The timescales for the production and evolution of Mn(III) species and a catalytic role for interlayer Ca²⁺ identified here from spectroscopic measurements can also guide the design of efficient Mn-based catalysts for water oxidation.Manganese is a key element in environmental processes, catalytic materials, and biological systems due to its rich redox chemistry and ability to form species with a high oxidizing potential. Photochemical processes can enhance significantly the cycling of Mn between the +4, +3, and +2 valence states (1–3). Photoreduction of Mn(IV) is the first step in the reductive dissolution of birnessite minerals in the euphotic zone of marine and lacustrine environments (4–6). This process couples the biogeochemical cycle of Mn to the redox cycling of carbon and trace metals associated with Mn oxide phases. In addition, the greater role of Mn(IV) photoreduction relative to microbial Mn(II) oxidation leads to the predominance of dissolved over particulate Mn in the photic zone of natural waters (1). Thermodynamic calculations predict that direct photoexcitation of Mn oxides in water by visible light will lead to net metal reduction over a wide range of environmentally relevant pH values (7). However, experimental evidence of direct photoexcitation of MnO₂ and subsequent photoreduction of Mn(IV) in the absence of organic electron donors is currently lacking. Experimental studies on the photochemical cycling of Mn have incorporated natural organic ligands that can enhance metal reduction via multiple pathways (5, 8, 9). These studies have identified aqueous Mn(II) as a reaction end product but have not investigated the fate of Mn(III) in the dissolution process, even though Mn(III) is a necessary intermediate in the reduction of Mn(IV) to Mn(II) (10) and an important component of environmental systems (11).The photochemistry of Mn also enables solar energy harvesting (12) and water oxidation catalysis in synthetic and biological systems (3, 13, 14). Mn-based cluster compounds (15, 16) and disordered birnessite nanoparticles (2) can exhibit analogous reactivity to the water-oxidizing center of photosystem II. Metal reduction is a key step in water oxidation using Mn oxide catalysts (2, 15, 17, 18) with evidence that Mn(III) plays an important role in O₂ generation (19). However, no information on the intrinsic kinetics or efficiency of Mn(IV) reduction has been reported to date. The structural and chemical constraints on the mechanism of Mn photoreduction are not known for any Mn phase (17, 18), although a recent study of MnO₂-based water oxidation showed that the substitution of Na with Ca in the interlayer of MnO₂ greatly enhances reactivity (15). The mineralogy literature suggests that the interlayer cations, which balance the excess charge in the MnO₂ sheet, may influence its photoreactivity because the interlayer cations are known to bind water molecules to the neighboring MnO₂ octahedral sheets via hydrogen bonding, with the strength of the interactions dependent on the cation valence (20–22). However, the specific role of Ca in the photoreduction process is unknown (15).The current work combines laboratory-based experiments and ultrafast pump–probe spectroscopy to investigate the photoreduction of δ-MnO₂, a fully oxidized synthetic analog of natural birnessites, which is comprised of randomly stacked MnO₂ nanosheets that extend only a few nanometers in the ab plane. The first objective was to measure the photoreduction efficiency of δ-MnO₂ in flow-through experiments by 400-nm illumination of aqueous suspensions of δ-MnO₂, with Na (Na-MnO₂) or Ca (Ca-MnO₂) as the interlayer cation. The second objective was to elucidate the mechanism of photoreduction by following the coupled changes in Mn valence and coordination that follow photon absorption over picosecond-to-microsecond timescales using time-resolved optical (23) and X-ray (24) absorption spectroscopy. Pyrophosphate was used in the flow-through experiments to quantitate Mn(III) but was not added during spectroscopic experiments because the timescale for Mn(III) production could be determined directly from the transient X-ray absorption data.     

Substrate binding site flexibility of the small heat shock protein molecular chaperones

Small heat shock proteins (sHSPs) serve as a first line of defense against stress-induced cell damage by binding and maintaining denaturing proteins in a folding-competent state. In contrast to the well-defined substrate binding regions of ATP-dependent chaperones, interactions between sHSPs and substrates are poorly understood. Defining substrate-binding sites of sHSPs is key to understanding their cellular functions and to harnessing their aggregation-prevention properties for controlling damage due to stress and disease. We incorporated a photoactivatable cross-linker at 32 positions throughout a well-characterized sHSP, dodecameric PsHsp18.1 from pea, and identified direct interaction sites between sHSPs and substrates. Model substrates firefly luciferase and malate dehydrogenase form strong contacts with multiple residues in the sHSP N-terminal arm, demonstrating the importance of this flexible and evolutionary variable region in substrate binding. Within the conserved α-crystallin domain both substrates also bind the β-strand (β7) where mutations in human homologs result in inherited disease. Notably, these binding sites are poorly accessible in the sHSP atomic structure, consistent with major structural rearrangements being required for substrate binding. Detectable differences in the pattern of cross-linking intensity of the two substrates and the fact that substrates make contacts throughout the sHSP indicate that there is not a discrete substrate binding surface. Our results support a model in which the intrinsically-disordered N-terminal arm can present diverse geometries of interaction sites, which is likely critical for the ability of sHSPs to protect efficiently many different substrates.     

Conformational selection and induced fit mechanism underlie specificity in noncovalent interactions with ubiquitin

Noncovalent binding interactions between proteins are the central physicochemical phenomenon underlying biological signaling and functional control on the molecular level. Here, we perform an extensive structural analysis of a large set of bound and unbound ubiquitin conformers and study the level of residual induced fit after conformational selection in the binding process. We show that the region surrounding the binding site in ubiquitin undergoes conformational changes that are significantly more pronounced compared with the whole molecule on average. We demonstrate that these induced-fit structural adjustments are comparable in magnitude to conformational selection. Our final model of ubiquitin binding blends conformational selection with the subsequent induced fit and provides a quantitative measure of their respective contributions.     

Elastically driven Kelvin–Helmholtz-like instability in straight channel flow

Originally, Kelvin–Helmholtz instability (KHI) describes the growth of perturbations at the interface separating counterpropagating streams of Newtonian fluids of different densities with heavier fluid at the bottom. Generalized KHI is also used to describe instability of free shear layers with continuous variations of velocity and density. KHI is one of the most studied shear flow instabilities. It is widespread in nature in laminar as well as turbulent flows and acts on different spatial scales from galactic down to Saturn’s bands, oceanographic and meteorological flows, and down to laboratory and industrial scales. Here, we report the observation of elastically driven KH-like instability in straight viscoelastic channel flow, observed in elastic turbulence (ET). The present findings contradict the established opinion that interface perturbations are stable at negligible inertia. The flow reveals weakly unstable coherent structures (CSs) of velocity fluctuations, namely, streaks self-organized into a self-sustained cycling process of CSs, which is synchronized by accompanied elastic waves. During each cycle in ET, counter propagating streaks are destroyed by the elastic KH-like instability. Its dynamics remarkably recall Newtonian KHI, but despite the similarity, the instability mechanism is distinctly different. Velocity difference across the perturbed streak interface destabilizes the flow, and curvature at interface perturbation generates stabilizing hoop stress. The latter is the main stabilizing factor overcoming the destabilization by velocity difference. The suggested destabilizing mechanism is the interaction of elastic waves with wall-normal vorticity leading to interface perturbation amplification. Elastic wave energy is drawn from the main flow and pumped into wall-normal vorticity growth, which destroys the streaks.

The original Kelvin–Helmholtz instability (KHI) results from perturbations of interface between two parallel counterpropagating streams of different velocities and densities of Newtonian fluids with the heavier fluid at the bottom (1, 2). Over time, KHI has come into use to describe a more general and realistic class of instabilities of a free shear (or mixing) layer with continuous variations of velocity and density (1, 2). It is one of the most studied shear flow instabilities, which are widespread in nature from the galactic scales explaining an expanding ring of young stars (3, 4), Saturn''s bands, and oceanographic and meteorological flows (1, 2) down to the technological and laboratory scales. For about the last 40 y, various theoretical, numerical, and experimental attempts to understand the role of elasticity in KHI of mixing layer flow of viscoelastic fluid at the various Reynolds (Re) and Weissenberg (Wi) numbers from moderate to large were undertaken leading to the conclusion that elastic stress stabilizes the flow (5, 6). Here, Wi is the second control parameter in the problem defining the degree of polymer stretching (5). This conclusion, probably, discouraged the study of elastically driven KHI at low Re and high Wi (5, 6). Here, both Re = ρUL/η and Wi = λU/L are defined via the mean fluid velocity U, the vessel size L, and ρ, η, λ, that are the density, dynamic viscosity, and longest polymer relaxation time of the fluid, respectively. The first detailed stability analysis of KHI in a mixing layer of a viscoelastic fluid at Re >> 1, Wi >> 1, and the elasticity El = Wi/Re∼1, formed by two counter propagating fluid streams, showed that the elastic stress has a stabilizing effect at large wave numbers (k) and with increasing El the range of k increases (7–9). They have been numerically studied for both two-dimensional (2D) and three-dimensional (3D) roll up of vortices and used to explain the vortex suppression in turbulent drag reduction (DR). It yielded predictions consistent with the observations of delay of roll up and pairing, the typical structures in plane free shear layers, resulting in almost complete suppression of small-scale structures by polymer additives at Re >> 1 reported in ref. 10. However, recent theoretical investigation (11) demonstrates that the destabilizing effect of the elastic stress at large elasticity El = Wi/Re may appear at sufficiently small wave numbers, while at moderate El∼1 the flow is indeed stabilized, in accord with ref. 7.In the present study, we deal with a dilute polymer solution in a quasi-2D channel flow. A tiny addition of long, flexible polymer molecules strongly affects laminar flows at Re << 1 and Wi > 1 with curvilinear streamlines resulting in elastic instability and further at Wi >> 1 in a chaotic flow, called elastic turbulence (ET) (6, 12–14). However, both the elastic instability and ET disappear in the limit of zero curvature (6, 15). ET is a chaotic, inertialess flow driven solely by nonlinear elastic stress generated by stretching of polymers due to the main flow, which is strongly modified by a feedback reaction of the elastic stress. A back reaction of the elastic stress field on the flow leads to a stationary stochastic state of ET (16).Recently, our group studied the elastic instability and transition to ET in a mixing layer of viscoelastic fluid flow between two widely spaced cylinders hindering a channel flow at Re << 1 and Wi >> 1 (17). The flow instability occurs due to prior appearance of a pair of small vortices, which initiate the secondary Hopf bifurcation at Wi_c. The latter is the normal mode oscillatory instability, whose frequency grows linearly with Wi–Wi_c. Due to the primary instability, two vortices grow and finally fill the space between the obstacles completely, and the flow shows a transition to ET with simultaneous generation of elastic waves. In the ET regime, two large-scale counterrotating vortices form two mixing layers with nonuniform velocity profiles containing two inflection points. The presence of inflection point in the velocity profile of a mixing layer flow of Newtonian inviscid fluid is the necessary (but not sufficient) condition for KHI and leads to a generation of vortices at the interface (1, 2). As suggested in ref. 17, the intermittent appearance of small vortices near the inflection points in ET at increasing Wi may be associated with a possibility of the elastically driven KH-like instability. Thus, two indications, numerical (11) and experimental (17), of a possible observation of the elastically driven KHI in the mixing layer of viscoelastic fluid at Re << 1 and Wi >> 1 hint that more convincing and quantitative confirmation of the elastically driven KH-like instability may be found in parallel shear viscoelastic flows.In elastically driven parallel shear flows at Re << 1 and Wi >> 1, linear stability analysis predicts stability at all Wi (6), similar to Newtonian parallel shear flows (1, 2). Despite this proof, recent experiments in straight pipe (18) and square microchannel (19–21) shear flows of viscoelastic fluid with strong prearranged perturbations at the inlet reveal large velocity fluctuations (18, 19) at Wi > 1 and Re << 1. Large velocity fluctuations are also accompanied by an increased flow resistance and a power-law decay in velocity spectra (20, 21). Motivated by this development (18–21), we conducted experiments in quasi-2D straight, long channel flow of viscoelastic fluid, where the elastically driven instability and further ET and DR regimes are observed with increasing Wi >> 1 for Re << 1 (22). Furthermore, we discover weakly unstable coherent structures (CSs) of stream-wise rolls and streaks self-organized into cycling process, synchronized by elastic waves and leading to stochastically steady state as reported in ref. 22.Here, we report a strong quantitative evidence of the elastically driven KH-like instability in quasi-2D straight channel flow of viscoelastic fluid in ET at Re << 1 and Wi >> 1. We show that the stream-wise streaks, which are the CS of the stream-wise counterpropagating velocity fluctuations u′ in a frame moving with the mean velocity u_m(z), are destroyed in each cycle by the elastically driven KH-like instability. Its temporal interface dynamics strongly recall the Newtonian KHI, though the elastically driven instability mechanism is distinctly different.     

Effects of Elastic Couplings in a Compressed Plate Element with Cut-Out

Analytical calculations were performed on carbon fiber-reinforced polymer (CFRP) laminates in an asymmetrical configuration. The asymmetric configuration of composites was investigated, where extension–twisting and extension–bending couplings were used to obtain the elastic element. Analysis of the presence of elastic couplings was conducted according to Classical Laminate Theory (CLT). Components of matrices A, B, and D, as well as the parameters D_c and B_t, were obtained using the MATLAB software environment. The results show that couplings between the extension and bending, as well as between the extension and twisting, were strongly dependent on specimen plies’ orientation. Moreover, additional analysis was performed on the influence of layer angle on the terms which are components of the B_t and D_c coefficients. The results indicate that the angle of laying fibers around 45–50° significantly amplifies the effects of elastic couplings.     

Membrane insertion mechanism of the caveola coat protein Cavin1

Caveolae are small plasma membrane invaginations, important for control of membrane tension, signaling cascades, and lipid sorting. The caveola coat protein Cavin1 is essential for shaping such high curvature membrane structures. Yet, a mechanistic understanding of how Cavin1 assembles at the membrane interface is lacking. Here, we used model membranes combined with biophysical dissection and computational modeling to show that Cavin1 inserts into membranes. We establish that initial phosphatidylinositol (4, 5) bisphosphate [PI(4,5)P₂]–dependent membrane adsorption of the trimeric helical region 1 (HR1) of Cavin1 mediates the subsequent partial separation and membrane insertion of the individual helices. Insertion kinetics of HR1 is further enhanced by the presence of flanking negatively charged disordered regions, which was found important for the coassembly of Cavin1 with Caveolin1 in living cells. We propose that this intricate mechanism potentiates membrane curvature generation and facilitates dynamic rounds of assembly and disassembly of Cavin1 at the membrane.

The typical small bulb-shaped invaginations of the plasma membrane termed “caveolae” are found in most vertebrate cells. They are highly abundant in adipocytes, muscle, and endothelial cells and are important for various physiological processes like regulation of membrane tension, lipid metabolism, and cellular signaling (1, 2). Lack or dysfunction of caveolae is connected to severe human diseases such as muscular dystrophy, cardiomyopathy, and lipodystrophy. Caveolae formation is dependent on membrane lipid composition and the coat components Caveolin1 (CAV1) and Cavin1 (3). Caveolae are enriched in cholesterol and sphingolipids (1, 2), which not only accumulate in caveolae but are actively sequestered (4). The negatively charged lipids phosphatidylserine (PS) and phosphatidylinositol (4, 5) bisphosphate [PI(4,5)P₂] are also enriched in caveolae (5). Lipid mapping in cells showed that both CAV1 and Cavin1 recruit specific lipid species to caveolae, hereby acting synergistically to generate the unique lipid nanoenvironment of caveolae (6, 7). CAV1 and Cavin1 are universal structural elements, and knockout of either of these proteins leads to loss of caveolae (1, 2). Electron microscopy studies on caveolae have revealed a striated protein coat lining, which is believed to comprise CAV1 and the cavin proteins (8, 9). CAV1 belongs to a family of integral membrane proteins (CAV1 to 3), where both the N and C termini protrude into the cytoplasm. CAV1 has been shown to form high-order 8S oligomers in membranes following cholesterol binding (10). Cavin1 belongs to a family composed of four different proteins (Cavin1 to 4), which exhibit tissue-specific expression patterns (3). The cavin proteins are thought to assemble with CAV1 8S complexes to form 60S and 80S complexes building up the caveola coat (11). Importantly, Cavin1 is required for membrane invagination of caveolae (12). Cryoelectron microscopy studies of such complexes proposed an architecture composed of an inner cage of polygonal units of caveolins and an outer cavin coat (13, 14). The models propose that cavin arranges into a web-like architecture composed of an interbranched trimeric complex (13) or alternatively that the cavins are stacked in rod-like trimers (14). However, it is still not understood how the unique striped or spiral pattern of the caveola coat is assembled and what intermolecular forces join the molecular components together.The cavin proteins share a common pattern in their domain structure, containing negatively charged disordered regions (DRs) interspersed with positively charged helical regions (HRs) (Fig. 1A). The crystal structures of HR1 (Protein Data Bank [PDB] ID codes 4QKV and 4QKW) revealed an extended α-helical trimeric coiled-coil structure (15). The HR1 domain has been shown to mediate trimeric homooligomerization of Cavin1 and formation of heterocomplexes with either Cavin2 or Cavin3 in solution (15, 16). HR2 is also thought to build up a trimeric coiled coil, but this structural arrangement is dependent on HR1. In vitro studies have shown that Cavin1 binds both PI(4,5)P₂ and PS (15, 17). The positively charged amino acids (Lys115, Arg117, Lys118, Lys124, Arg127) in the HR1 domain mediate specific binding to PI(4,5)P₂ (15), whereas a repeated sequence of 11 amino acids of the HR2 domain, identified as an undecad repeat (UC1), was shown to bind PS (17). Furthermore, Cavin1 has been shown to generate membrane curvature in vitro (15). Both HRs and DRs were required for this, and it was proposed that Cavin1 drives membrane curvature by molecular crowding via weak electrostatic interactions between the DRs and HRs (18). Interestingly, the assembly of both CAV1 and Cavin1 was found to be dependent on the acyl chain composition of PS, suggesting that Cavin1 might also interact with the hydrophobic region of the membrane (6). Membrane insertion of Cavin1 could contribute to membrane curvature generation and the formation of caveolae. Yet, based on the current structural understanding, it is not clear how Cavin1 orients and assembles at the membrane interface.Open in a separate windowFig. 1.Cavin1 binding and insertion into model lipid membranes. (A) Scheme of the domain structure of Cavin1 with DRs and HRs. White stripes mark undecad repeats. The crystal structure of HR1 (PDB ID code 4QKV) is displayed (Top). Regions involved in binding to PI(4,5)P₂, PS, and CAV1 are indicated. (B) Liposome cosedimentation of Cavin1. Cavin1 was incubated with or without DOPC:DOPE:PI(4,5)P₂ liposomes and centrifuged, and supernatant (S) and pellet (P) fractions were analyzed by SDS-PAGE. Band intensities were quantified and data are shown as mean ± SEM (n = 3). (C, Top) Scheme of SLB formation. (C, Bottom) QCM-D measurement showing a shift in frequency (ΔF) (black line) and dissipation (ΔD) (red line) upon SLB formation. (D, Top) Illustration of QCM-D setup. (D, Bottom) QCM-D monitoring of Cavin1 adsorption to an SLB. The responses in ΔF and ΔD correspond to Cavin1 injection and buffer rinses as indicated. The gray dotted line shows extrapolation of protein desorption from the first rinse (150 mM NaCl). (E, Top) Scheme of monolayer protein adsorption experiments. (E, Bottom) Cavin1 adsorption to DOPC:DOPE:PI(4,5)P₂ monolayers. Cavin1 was injected underneath the film at π₀ = 20 mN⋅m⁻¹ and Δπ was recorded over time. (F) Cavin1 adsorption to lipid monolayers was measured at different π₀. The MIP value was determined by extrapolation of the Δπ/π₀ plot to the x axis.In this work, we address the detailed mechanism by which Cavin1 binds and assembles at the lipid interface using model membranes in combination with a variety of biophysical techniques. We found that Cavin1 inserted into the membrane via the HR1 domain in a PI(4,5)P₂-mediated process. Membrane insertion involved partial separation of the helices in the HR1 domains in a process aided by the DR domains.     

Learning the molecular grammar of protein condensates from sequence determinants and embeddings

Intracellular phase separation of proteins into biomolecular condensates is increasingly recognized as a process with a key role in cellular compartmentalization and regulation. Different hypotheses about the parameters that determine the tendency of proteins to form condensates have been proposed, with some of them probed experimentally through the use of constructs generated by sequence alterations. To broaden the scope of these observations, we established an in silico strategy for understanding on a global level the associations between protein sequence and phase behavior and further constructed machine-learning models for predicting protein liquid–liquid phase separation (LLPS). Our analysis highlighted that LLPS-prone proteins are more disordered, less hydrophobic, and of lower Shannon entropy than sequences in the Protein Data Bank or the Swiss-Prot database and that they show a fine balance in their relative content of polar and hydrophobic residues. To further learn in a hypothesis-free manner the sequence features underpinning LLPS, we trained a neural network-based language model and found that a classifier constructed on such embeddings learned the underlying principles of phase behavior at a comparable accuracy to a classifier that used knowledge-based features. By combining knowledge-based features with unsupervised embeddings, we generated an integrated model that distinguished LLPS-prone sequences both from structured proteins and from unstructured proteins with a lower LLPS propensity and further identified such sequences from the human proteome at a high accuracy. These results provide a platform rooted in molecular principles for understanding protein phase behavior. The predictor, termed DeePhase, is accessible from https://deephase.ch.cam.ac.uk/.

Liquid–liquid phase separation (LLPS) is a widely occurring biomolecular process that underpins the formation of membraneless organelles within living cells (1–4). This phenomenon and the resulting condensate bodies are increasingly recognized to play important roles in a wide range of biological processes, including the onset and development of metabolic diseases and cancer (5–11). Understanding the factors that drive the formation of protein-rich biomolecular condensates has thus become an important objective and been the focus of a large number of studies, which have collectively yielded valuable information about the factors that govern protein phase behavior (3, 4, 12, 13).While changes in extrinsic conditions, such as temperature, ionic strength, or the level of molecular crowding, can strongly modulate LLPS (14–17), of fundamental importance to condensate formation is the linear amino acid sequence of a protein, its primary structure. A range of sequence-specific factors governing the formation of protein condensates have been postulated with electrostatic interactions, π–π and cation–π contacts, and hydrophobic interactions and the valency and patterning of the low-complexity regions (LCRs) in particular brought forward as central features (12, 13, 18–22). The predictive power of some of these hypotheses has been recently reviewed (23). In parallel, studies examining the relationship between protein phase behavior and its sequence alterations through deletion, truncation, and site-specific mutation events have determined various sequence-specific features to be important in modulating the protein phase separation of specific proteins, such as the high abundance of arginine and tyrosine residues in the context of the fused in sarcoma (FUS)-family proteins (22), the positioning of tryptophan and other aromatic amino acid residues in TAR DNA-binding protein 43 (TDP-43) (24), arginine- and glycine-rich disordered domains in LAF-1 protein (25), and multivalent interactions for the UBQLN2 protein (26).To broaden the scope of these observations and understand on a global level the associations between the primary structure of a protein and its tendency to form condensates, here, we developed an in silico strategy for analyzing the associations between LLPS propensity of a protein and its amino acid sequence and used this information to construct machine-learning classifiers for predicting LLPS propensity from the amino acid sequence (Fig. 1). Specifically, by starting with a previously published LLPSDB database collating information on protein phase behavior under different environmental conditions (27) and by analyzing the concentration under which LLPS had been observed to take place in these experiments, we constructed two datasets including sequences of different LLPS propensity and compared them to fully ordered structures from the Protein Data Bank (PDB) (29) as well as the Swiss-Prot (30) database. We observed phase-separating proteins to be more hydrophobic, more disordered, and of lower Shannon entropy and have their low-complexity regions enriched in polar residues. Moreover, high LLPS propensity correlated with high abundance of polar residues yet the lowest saturation concentrations were reached when their abundance was balanced with a sufficiently high hydrophobic content.Open in a separate windowFig. 1.(A) DeePhase predicts the propensity of proteins to undergo phase separation by combining engineered features computed directly from protein sequences with protein sequence embedding vectors generated using a pretrained language model. The DeePhase model was trained using three datasets, namely two classes of intrinsically disordered proteins with a different LLPS propensity (LLPS+ and LLPS−) and a set of structured sequences (PDB*). (B) To generate the LLPS+ and LLPS− datasets, the entries in the LLPSDB database (27) were filtered for single-protein systems. The constructs that phase separated at an average concentration below c = 100 μM were classified as having a high LLPS propensity (LLPS+; 137 constructs from 77 UniProt IDs) with the remaining 25 constructs together with constructs that had not been observed to phase separate homotypically classified as low-propensity dataset (LLPS−; 84 constructs from 52 UniProt IDs). (C) The 221 sequences clustered into 123 different clusters [Left, CD-hit clustering algorithm (28) with the lowest threshold of 0.4]. (Right) The 110 parent sequences showed high diversity by forming 94 distinct clusters. (D) The PDB* dataset (1,563 constructs) was constructed by filtering the entries in the PDB (29) to fully structured full-protein single chains and clustering for sequence similarity with a single entry selected from each cluster.Moreover, we used the outlined sequence-specific features as well as implicit protein sequence embeddings generated using a neural network-derived word2vec model and trained classifiers for predicting the propensity of unseen proteins to phase separate. We showed that even though the latter strategy required no specific feature engineering, it allowed constructing classifiers that were comparably effective at identifying LLPS-prone sequences as the model that used knowledge-based features, demonstrating that language models can learn the molecular grammar of phase separation. Our final model, combining knowledge-based features with unsupervised embeddings, showed a high performance both when distinguishing LLPS-prone proteins from structured ones and when identifying them within the human proteome. Overall, our results shed light onto the physicochemical factors modulating protein condensate formation and provide a platform rooted in molecular principles for the prediction of protein phase behavior.     

Calculation of strong and weak interactions in TDA1 and RangDP52 by the kernel energy method

Using the Kernel Energy Method we apply ab initio quantum mechanics to study the relative importance of weak and strong interactions (including hydrogen bonds) in the crystal structures of the title compounds TDA1 and RangDP52. Perhaps contrary to widespread belief, in these compounds the weak interaction energies, because of their large number and cooperativity, can be significant to the binding energetics of the crystal, and thus also to its other properties.     

Tracking the progressive spread of the SARS-CoV-2 Omicron variant in Italy,December 2021 to January 2022

BackgroundThe SARS-CoV-2 variant of concern Omicron was first detected in Italy in November 2021.AimTo comprehensively describe Omicron spread in Italy in the 2 subsequent months and its impact on the overall SARS-CoV-2 circulation at population level.MethodsWe analyse data from four genomic surveys conducted across the country between December 2021 and January 2022. Combining genomic sequencing results with epidemiological records collated by the National Integrated Surveillance System, the Omicron reproductive number and exponential growth rate are estimated, as well as SARS-CoV-2 transmissibility.ResultsOmicron became dominant in Italy less than 1 month after its first detection, representing on 3 January 76.9–80.2% of notified SARS-CoV-2 infections, with a doubling time of 2.7–3.3 days. As of 17 January 2022, Delta variant represented < 6% of cases. During the Omicron expansion in December 2021, the estimated mean net reproduction numbers respectively rose from 1.15 to a maximum of 1.83 for symptomatic cases and from 1.14 to 1.36 for hospitalised cases, while remaining relatively stable, between 0.93 and 1.21, for cases needing intensive care. Despite a reduction in relative proportion, Delta infections increased in absolute terms throughout December contributing to an increase in hospitalisations. A significant reproduction numbers’ decline was found after mid-January, with average estimates dropping below 1 between 10 and 16 January 2022.ConclusionEstimates suggest a marked growth advantage of Omicron compared with Delta variant, but lower disease severity at population level possibly due to residual immunity against severe outcomes acquired from vaccination and prior infection.     

Unraveling the Phase Stability and Physical Property of Modulated Martensite in Ni2Mn1.5In0.5 Alloys by First-Principles Calculations

Large magnetic field-induced strains can be achieved in modulated martensite for Ni-Mn-In alloys; however, the metastability of the modulated martensite imposes serious constraints on the ability of these alloys to serve as promising sensor and actuator materials. The phase stability, magnetic properties, and electronic structure of the modulated martensite in the Ni₂Mn_1.5In_0.5 alloy are systematically investigated. Results show that the 6M and 5M martensites are metastable and will eventually transform to the NM martensite with the lowest total energy in the Ni₂Mn_1.5In_0.5 alloy. The physical properties of the incommensurate 7M modulated martensite (7M–IC) and nanotwinned 7M martensite (7M−(52¯)2) are also calculated. The austenite (A) and 7M−(52¯)2 phases are ferromagnetic (FM), whereas the 5M, 6M, and NM martensites are ferrimagnetic (FIM), and the FM coexists with the FIM state in the 7M–IC martensite. The calculated electronic structure demonstrates that the splitting of Jahn–Teller effect and the strong Ni–Mn bonding interaction lead to the enhancement of structural stability.