Electron Density Map Research Articles

A general model for rapid simulation of hot dense plasmas under non-local thermal equilibrium conditions

Aiming at the requirement of the on-line detailed atomic model in radiation hydrodynamic simulations, we propose a general model, multi-average ion collisional-radiative model (MAICRM), to rapidly simulate the ionization and charge state distribution of hot dense plasma under non-local thermal equilibrium (NLTE) conditions. In this model, an average ion is used to characterize the features of all the atomic states at one single charge state, including the average orbital occupation and the total population of the atomic states. The rate equations for the orbital occupations and the population are derived from the rate equations of the detailed configurations and separated into two sets under the two assumptions: one is the single orbital rate coefficients (including no occupation nor hole number of the relative orbital) that are only dependent on the charge state, and the other is the coupling of the excitation/de-excitation process and ionization/recombination process, which are weak. Namely, the orbital occupation of an average ion is mainly determined by the excitation/de-excitation process under a certain density and temperature; the population of the average ions is determined by the ionization/recombination process with the fixed orbital occupation. The two sets of rate equations are solved sequentially and iteratively until a set of converged orbital occupation and population values is obtained. The interplay between the occupation and the population is implicit in the excitation/de-excitation rate coefficient and ionization/recombination rate coefficient, each of which is a function of electron density and temperature as well as occupation. In this work, using the newly developed method and codes, the mean ionizations and charge state distributions of Fe, Xe and Au plasmas under different plasma conditions are calculated and in good agreement with the experimental results and DCA/SCA calculations. Meanwhile, compared with the DCA/SCA calculations, in which hundreds or thousands of detailed atomic states at each charge state are considered to obtain a converged ionization balance, MAICRM only considers one kind of ion at one single charge state, thus the computational cost of MAICRM is much reduced and lower than that of DCA/SCA. Due to its good degree of accuracy for ionization balance and its low computational cost, MAICRM is expected to be incorporated into the radiation hydrodynamic program to realize the online calculation of detailed nonequilibrium atomic models in the future.

Structural modeling of a novel membrane-bound globin-coupled sensor in Geobacter sulfurreducens

Globin-coupled sensors (GCS) usually consist of three domains: a sensor/globin, a linker, and a transmitter domain. The globin domain (GD), activated by ligand binding and/or redox change, induces an intramolecular signal transduction resulting in a response of the transmitter domain. Depending on the nature of the transmitter domain, GCSs can have different activities and functions, including adenylate and di-guanylate cyclase, histidine kinase activity, aerotaxis and/or oxygen sensing function.The gram-negative delta-proteobacterium Geobacter sulfurreducens expresses a protein with a GD covalently linked to a four transmembrane domain, classified, by sequence similarity, as GCS (GsGCS). While its GD is fully characterized, not so its transmembrane domain, which is rarely found in the globin superfamily.In the present work, GsGCS was characterized spectroscopically and by native ion mobility-mass spectrometry in combination with cryo-electron microscopy. Although lacking high resolution, the oligomeric state and the electron density map were valuable for further rational modeling of the full-length GsGCS structure. This model demonstrates that GsGCS forms a transmembrane domain-driven tetramer with minimal contact between the GDs and with the heme groups oriented outward. This organization makes an intramolecular signal transduction less likely.Our results, including the auto-oxidation rate and redox potential, suggest a potential role for GsGCS as redox sensor or in a membrane-bound e−/H+ transfer. As such, GsGCS might act as a player in connecting energy production to the oxidation of organic compounds and metal reduction.Database searches indicate that GDs linked to a four or seven helices transmembrane domain occur more frequently than expected.

Synthesis of TiO2 Tubes Via Dissolution of TiOSO4 Rod Using H2O2

We demonstrate here for the first time an original and facile approach to preparing titanium oxide (TiO2) tubes using hydrogen peroxide (H2O2) and titanyl (IV) oxysulfate (TiOSO4) as sacrificial templates. The method involves dissolving TiOSO4 powder in H2O2 solution and subsequently applying thermal treatment on the resulting amorphous precipitate. Prepared samples were characterized by X-ray diffraction, scanning electron microscopy (SEM) images, thermogravimetric (TG) analysis, and UV-vis analysis. Experimental results indicated that the samples exhibit tube-like structures with lengths of approximately 1.9 mm in diameter and 11.5 mm in length. Anatase and rutile phases were formed after annealing at different temperatures in air. The crystallite size estimated by Rietveld refinement showed an increase from 34.69 to 354.28 nm with an increase in the annealing temperature from 600 to 1000 °C. At the same time, the band gap values decreased from 3.14 to 2.97 eV. The electron density maps were calculated, and the electronic density was observed to increase from 497.56 e- Å-2 (600 °C) to 533.10e- Å-2 (740 °C) and decrease with the annealing temperature of samples. A possible mechanism for the formation of TiO2 tubes was proposed.

A measure for the identification of preferred particle orientations in cryo-electron microscopy data: A simulation study.

Cryo-electron microscopy (cryo-EM) is an important experimental technique for the structural analysis of biomolecules that are difficult or impossible to crystallize. The three-dimensional structure of a biomolecule can be reconstructed using two-dimensional electron-density maps, which are experimentally sampled via the electron beam irradiation of vitreous ice in which the target biomolecules are embedded. One assumption required for this reconstruction is that the orientation of the biomolecules in the vitreous ice is isotropic. However, this is not always the case and two-dimensional electron-density maps are often sampled using preferred biomolecular orientations, which can make reconstruction difficult or impossible. Compensation for under-represented views is computationally feasible for the reconstruction of three-dimensional electron density maps, but one must know whether or not there is any missing information in the sampled two-dimensional electron density maps. Thus, a measure to identify whether a cryo-EM data is obtained from the bio­molecules adopting preferred orientations is required. In the present study, we propose a measure for which the geometry of manifold projected onto a low-dimensional space is used. To show the usefulness of the measure, we perform simulations for cryo-EM experiment of a protein. It is found that the geometry of manifold projected onto a two-dimensional space for a protein adopting a preferred biomolecular orientation is significantly different from that for a protein adopting a uniform orientation. This result suggests that the geometry of manifold projected onto a low-dimensional space can be used for the measure for the identification that the biomolecules adopt preferred orientations.

Studying RNA-Protein Complexes Using X-Ray Crystallography.

A wide range of biological processes rely on complexes between ribonucleic acids (RNAs) and proteins. Determining the three-dimensional structures of RNA-protein complexes is crucial to elucidate the relationship between structure and biological function. X-ray crystallography represents the most widely used technique to characterize RNA-protein complexes at atomic resolution; however, determining their three-dimensional structures remains challenging. RNase contamination can ruin crystallization experiments by degrading RNA in complex with protein, leading to sample heterogeneity, and the conformational flexibility inherent in both protein and RNA can limit crystallizability. Furthermore, the three-dimensional structure can be difficult to accurately model at the typical diffraction limit of 2.5Å resolution or lower for RNA-protein complex crystals. At this resolution, phosphates, which are electron dense, and bases, which are large, rigid, and planar, tend to be well resolved and easy to position in the electron density map, whereas other features, e.g., sugar atoms, can be difficult to accurately position. This chapter focuses on methods that can be used to overcome the unique problems faced when crystallizing RNA-protein complexes and determining their three-dimensional structures using X-ray crystallography.

Crystal Structure, Experimental and DFT of (Z)-4-((4-Fluorophenyl)amino)pent-3-en-2-one

Single crystals of a organic compound, (Z)-4-((4-fluorophenyl)amino)pent-3-en-2-one (4FPA) were grown by the slow evaporation technique and characterized by X-ray diffraction and FT-IR spectra. The normal mode frequencies, intensities and the corresponding vibrational assignments were calculated using the GAUSSIAN 09W set of quantum chemistry codes at the DFT/B3LYP levels of theory using the 6-31+G(d,p) basis set. The Fourier transform infrared spectrum was obtained for the title molecule at room temperature. Reactivity features were determined based on global descriptors, electron density mapping and Fukui analysis to reveal the electrophilic and nucleophilic coordination of them. The thermodynamic and intramolecular interactions were also investigated. The non-covalent interaction mapped by reduced density gradient method reveals possible methyl (CH3) influence on the ring and NH groups with their reactivity and non-linear optical properties of 4FPA were found by first-order hyperpolarizability.

Superatomic Rydberg State Excitation

Superatomic molecular orbitals (SAMOs) have symmetries (angular quantum numbers) similar to those of atoms and thus it is possible to realize Rydberg state excitations (RSEs) in superatomic molecules. In this letter, the feasibility of superatomic Rydberg state excitation (SRSE) is explored using gold superatoms based on first-principles calculations. The results show that the SRSE exists in both the high and low excited states of the gold superatoms and their SAMOs make a major contribution to electronic transitions. The radial distribution function (RDF) of electronic density shows that the main distribution of electrons in the lowest unoccupied molecular orbitals and other unoccupied superatomic molecular orbitals is extremely far from the geometric center and thus they can be unambiguously identified as Rydberg orbitals. We found that due to two-dimensional ductility of planar superatoms’ transition orbitals, superatoms have the superiority in RSE regulation. Our findings provide a new source of superatom-based RSE and will contribute to the regulation and efficient preparation of Rydberg states.

The distribution of the electron density and spin density in the interplanar areas CuFeS2by NMR63,65Cu in a local field

Chalcopyrite CuFeS2is a known semiconductor mineral with a wide range of unique physical and chemical properties. These materials can be used as elements of solar batteries, coherent and incoherent sources of polarized radiation, in photovoltaic, thermoelectric and spintronic devices. Despite the relatively large number of studies on CuFeS2, many questions about its magnetic and electronic properties, are still outstanding. In this paper we were carried out studies of the distribution of the electron density and spin density in the nuclei of iron and copper in the semiconductor mineral CuFeS2. Special attention was devoted to interrelation of electronic and spin subsystems of the compound. The results of studies of the compound obtained in NMR63,65Cu local field at low temperatures were used to perform the corresponding analysis. The cluster approach was used. The biggest cluster had Cu9Fe10S28-4formula. Calculations were carried out in the framework of restricted self-consistent Hartree - Fock with open shells (SCF-LCAO-ROHF), MINI basis. The calculations were made with the “foundation” on the quadrupole parameters (quadrupole νQ frequency and the asymmetry parameter of the electric field gradient tensor η), obtained from the experiment. Study of electron density maps were performed for the regions containing chains of Fe-S-Cu and S-Fe-S for the different layers of metals and sulfur atoms. It is shown that the nature of the connection of iron atoms belonging to neighboring layers with sulfur atoms of the intermediate layer is different, which is reflected on the electron density distribution.

The 1.3-Å resolution structure of bovine cytochrome c oxidase suggests a dimerization mechanism

Cytochrome c oxidase (CcO) in the respiratory chain catalyzes oxygen reduction by coupling electron and proton transfer through the enzyme and proton pumping across the membrane. Although the functional unit of CcO is monomeric, mitochondrial CcO forms a monomer and a dimer, as well as a supercomplex with respiratory complexes I and III. A recent study showed that dimeric CcO has lower activity than monomeric CcO and proposed that dimeric CcO is a standby form for enzymatic activation in the mitochondrial membrane. Other studies have suggested that the dimerization is dependent on specifically arranged lipid molecules, peptide segments, and post-translationally modified amino acid residues. To re-examine the structural basis of dimerization, we improved the resolution of the crystallographic structure to 1.3 Å by optimizing the method for cryoprotectant soaking. The observed electron density map revealed many weakly bound detergent and lipid molecules at the interface of the dimer. The dimer interface also contained hydrogen bonds with tightly bound cholate molecules, hydrophobic interactions between the transmembrane helices, and a Met–Met interaction between the extramembrane regions. These results imply that binding of physiological ligands structurally similar to cholate could trigger dimerization in the mitochondrial membrane and that non-specifically bound lipid molecules at the transmembrane surface between monomers support the stabilization of the dimer. The weak interactions involving the transmembrane helices and extramembrane regions may play a role in positioning each monomer at the correct orientation in the dimer.

Crystal structure and mutational analysis of the human TRIM7 B30.2 domain provide insights into the molecular basis of its binding to glycogenin-1

Tripartite motif (TRIM)7 is an E3 ubiquitin ligase that was first identified through its interaction with glycogenin-1 (GN1), the autoglucosyltransferase that initiates glycogen biosynthesis. A growing body of evidence indicates that TRIM7 plays an important role in cancer development, viral pathogenesis, and atherosclerosis and, thus, represents a potential therapeutic target. TRIM family proteins share a multidomain architecture with a conserved N-terminal TRIM and a variable C-terminal domain. Human TRIM7 contains the canonical TRIM motif and a B30.2 domain at the C terminus. To contribute to the understanding of the mechanism of action of TRIM7, we solved the X-ray crystal structure of its B30.2 domain (TRIM7B30.2) in two crystal forms at resolutions of 1.6 Å and 1.8 Å. TRIM7B30.2 exhibits the typical B30.2 domain fold, consisting of two antiparallel β-sheets of seven and six strands, arranged as a distorted β-sandwich. Furthermore, two long loops partially cover the concave face of the β-sandwich defined by the β-sheet of six strands, thus forming a positively charged cavity. We used sequence conservation and mutational analyses to provide evidence of a putative binding interface for GN1. These studies showed that Leu423, Ser499, and Cys501 of TRIM7B30.2 and the C-terminal 33 amino acids of GN1 are critical for this binding interaction. Molecular dynamics simulations also revealed that hydrogen bond and hydrophobic interactions play a major role in the stability of a modeled TRIM7B30.2-GN1 C-terminal peptide complex. These data provide useful information that could be used to target this interaction for the development of potential therapeutic agents.

Charge-storage mechanism of highly defective NiO nanostructures on carbon nanofibers in electrochemical supercapacitors.

An electrode composed of highly defective nickel oxide (NiO) nanostructures supported on carbon nanofibers (CNFs) and immersed in an Li+-based aqueous electrolyte is studied using Raman spectroscopy under dynamic polarization conditions to address the charge-storage phenomenon. By this operando technique, the formation of Li2SO4·H2O during the discharge process is verified. At the same time, we observed the phase transformation of NiO to NiOOH. The Ni(OH)2/NiOOH redox couple is responsible for the pseudocapacitive behavior with intercalation of cationic species in the different Ni structures. A 'substitutive solid-state redox reaction' is proposed to represent the amphoteric nature of the oxide, resulting in proton intercalation, while the insertion of Li+ occurs to a less extent. The electrode material exhibits outstanding stability with 98% coulombic efficiency after 10 000 charge-discharge cycles. The excellent electrode properties can be ascribed to a synergism between CNFs and NiO, where the carbon nanostructures ensured rapid electron transport from the hydrated nickel nanoparticles. The NiO@CNF composite material is a promising candidate for future applications in aqueous-based supercapacitors. DFT simulation elucidates that compressive stress and Ni-site displacement lead to a decrease up-to 3.5-fold on the electron density map located onto the Ni-atom, which promotes NiO/Ni(OH)2/NiOOH transition.

Development of Finnis-Sinclair potential of metal Nb and the influence of potential function form on the properties of material

<sec>Researchers’ work on computational materials is often hampered by the lack of suitable intera tomic potentials. In this paper, under the framework of Finnis-Sinclair (FS) potentials, the process of fitting, testing and correction of interatomic potential is given in detail by developing the FS potential for metal Nb. First, the relationship between the interatomic potential and the macroscopic properties of the material is established. Then, the Finnis-Sinclair potential of metal Nb is fitted by reproducing the experimental data, such as the cohesive energy, bulk modulus, surface energy, vacancy formation energy and equilibrium lattice constant, and the fitting mean square error is less than 10<sup>–7</sup>. In order to test the interatomic potential, the elastic constant, shear modulus and Cauchy pressure of metal Nb are calculated by the constructed interatomic potential. In addition, how the form of the interatomic potential function affects the interstitial performance is discussed, and the constructed interatomic potential is modified according to the results of density functional theory (DFT) of the interstitial formation energy. The treatment of cutoff distance is also discussed. In the paper, the results are as follows. 1) The original form of FS potential is not suitable for extending the atomic interaction to the third nearest neighbor. Through analysis and test, it is found that when the modified electron density function is in the form of the fourth power and the form of the pair potential function is in the form of the sixth power polynomial, the interatomic potential can better describe the interatomic interaction; 2) The result of interstitial formation energy is taken as the target value to modify the behavior of the pair potential function in the near distance, and the modified interatomic potential gives the interstitial formation energy close to the result of DFT. When the interstitial energy calculated by the interatomic potential is larger than the target value, the pair potential curve of near distance will be softened by the superposition of a polynomial term, otherwise, the pair potential curve will be stiffened; 3) When the physical quantity under equilibrium state is used as the fitting data, the fitted potential parameters and the elastic constant results will not be affected, while adjusting the curve form of the potential function, as long as none of the function value, the slope and the curvature of the function curve is changed at each neighbor position. The magnitude of interstitial energy will be affected by changing the shape of the curve that is less than the first neighbor range; 4) Under the cutoff strategy in this paper, changing the cutoff distance has almost no influence on the calculated results of potential parameters or crystal properties, but has a slight influence on the mean square error of the fitting results. </sec><sec>The results of this paper provide some information for the construction of interatomic potentials database, and lay a foundation for constructing the Nb-related interatomic potential of alloy. And it also provides a method and basis for developing and improving the quality of interatomic potential.</sec>

Inversion Symmetry Breaking in Order-Disorder Transitions of Globular Ligands Coordinating to Cobalt(II) and Nickel(II) Bisacetylacetonato Complexes During Heating.

Unexpected inversion-symmetry breaking was observed in the order-disorder phase transitions of [M(acac)2 (abco)2 ] (1; M=Co2+ , 2; Ni2+ , acac- =2,4-pentanedionato, abco=1-azabicyclo-[2.2.2]-octane=quinuclidine) during heating. The isostructural, transition-free complexes [M(acac)2 (cabco)2 ] (3; M=Co2+ , 4; Ni2+ , cabco=3-chloro-1-azabicyclo-[2.2.2]-octane=3-chloroquinuclidine) were also studied for comparison. Complexes 1 and 2 crystallized in ordered phases in the centrosymmetric I2/m space group at 100 K, whereas they crystallized in disordered phases in the non-symmetric I2 space group at 300 K. The 60° step rotation disordering of the abco ligands was observed in the electron density maps of 1 and 2, which was consistent with the transition enthalpies estimated by differential scanning calorimetry (DSC). Gradual phase transitions were observed for 1 and 2 by DSC and powder X-ray diffraction (PXRD) at approximately 225 K. The inversion-symmetry disordering was likely induced by the local pseudo-symmetry of the abco ligands, increasing from trigonal to hexagonal and the increased steric repulsion pathways among them.

Phase separated bi-metallic PtNi nanoparticles formed by pulsed laser dewetting

We present morphological and compositional analysis of phase-separated Pt–Ni alloy nanoparticles (NPs) formed by ns pulsed laser dewetting. The PtNi NPs obtained by the pulsed laser dewetting consist of phase-separated multiple domains including Pt3Ni, PtNi and PtNi3 phases with various crystal orientations as revealed by transmission electron microscopy, which is in contrast to thermal dewetting resulting NPs of a uniform composition. A three-dimensional (3D) electron density map of a dewetted PtNi NP obtained using the coherent x-ray diffraction microscopy elucidates the 3D morphology of Pt- and Ni-rich regions together with a nano-cavity formed during the pulsed laser irradiation.

The A component (SmhA) of a tripartite pore-forming toxin from Serratia marcescens: expression, purification and crystallographic analysis.

Tripartite α-pore-forming toxins are constructed of three proteins (A, B and C) and are found in many bacterial pathogens. While structures of the B and C components from Gram-negative bacteria have been described, the structure of the A component of a Gram-negative α-pore-forming toxin has so far proved elusive. SmhA, the A component from the opportunistic human pathogen Serratia marcescens, has been cloned, overexpressed and purified. Crystals were grown of selenomethionine-derivatized protein and anomalous data were collected. Phases were calculated and an initial electron-density map was produced.

Dose distribution correction for the influence of magnetic field using a deep convolutional neural network for online MR-guided adaptive radiotherapy.

This study aimed to develop a deep convolutional neural network (CNN)-based dose distribution conversion approach for the correction of the influence of a magnetic field for online MR-guided adaptive radiotherapy. Our model is based on DenseNet and consists of two 2D input channels and one 2D output channel. These three types of data comprise dose distributions without a magnetic field (uncorrected), electron density (ED) maps, and dose distributions with a magnetic field. These data were generated as follows: both types of dose distributions were created using 15-field IMRT in the same conditions except for the presence or absence of a magnetic field with the GPU Monte Carlo dose in Monaco version 5.4; ED maps were acquired with planning CT images using a clinical CT-to-ED table at our institution. Data for 50 prostate cancer patients were used; 30 patients were allocated for training, 10 for validation, and 10 for testing using 4-fold cross-validation based on rectum gas volume. The accuracy of the model was evaluated by comparing 2D gamma-indexes against the dose distributions in each irradiation field with a magnetic field (true). The gamma indexes in the body for CNN-corrected uncorrected dose against the true dose were 94.95%±4.69% and 63.19%±3.63%, respectively. The gamma indexes with 2%/2-mm criteria were improved by 10% in most test cases (99.36%). Our results suggest that the CNN-based approach can be used to correct the dose-distribution influences with a magnetic field in prostate cancer treatment.

The electronic states and vibronic absorption spectrum of berberine in aqueous solution

AbstractThe time‐dependent density functional theory was used to calculate the vibronic absorption spectrum of berberine (BER) in an aqueous solution. The best agreement with the experimental spectrum gives the O3LYP functional. Functionals with long‐range correction showed poor agreement with experiment. The molecular orbitals of BER involved in the electronic transition during light absorption in the visible spectral region have been obtained. The dipole moments and atomic charges of the ground and excited states of the BER molecule have been calculated. Maps of BER electron density and electrostatic potential have been drawn. A significant photoinduced electron transfer from the outer di‐oxygen five‐membered heterocycle to the center of the BER chromophore has been found. According to our calculations, vibronic coupling and Boltzmann distribution play a significant role in the absorption spectrum of BER.

A Creative “Spark” for High-Entropy Alloys

In this issue of Matter, Feng et al. make a breakthrough understanding of an aerosol system for manufacturing unprecedented alloys with excellent catalytic properties. This work will inspire improved 3D nanoprinting techniques for creating new matter forms for broad applications, including additive manufacturing, catalysts, and metallurgy.

Pauli energy and information-theoretic approach for evaluating dynamic and nondynamic electron correlation

Even though the quantification of different correlation regimes among electrons is controversial and a robust and generally applicable approach in this context is still lacking, accurately accounting for the electron correlation is a must. As the prominent and most well-known terms used to classify correlation effects, dynamic and nondynamic electron correlation is of concern herein. In this work, we consider a different tack to qualitative and quantitative description of the dynamic and nondynamic correlations, where Pauli energy and information-theoretic approach are considered for the purpose. To do so, several versions of the Pauli energy based on approximate kinetic energy density (KED) functionals and information-theoretic (IT) quantities like Fisher information, Shannon entropy, Onicescu information energy, and Ghosh–Berkowitz–Parr entropy with the two representations of electron density and shape function have been utilized. It is shown that although some KEDs may not reproduce the accurate Pauli energy results, their prediction for dynamic and nondynamic electron correlation can be desirable. There are also KEDs providing much better Pauli energy results than others, while their shortcomings can still be unveiled when they are used to describe electron correlation regimes. On the other hand, to more balanced treatment of electron correlation effects we propose to use the IT quantities with significantly different views from the perspectives of electron density distribution, scaling properties, and physiochemical meanings in the framework of Pauli energy. The efficiency and usefulness of the developed models have been demonstrated for both the dynamic and nondynamic electron correlation in molecular systems.

The detailed electronic structure, spectroscopic features, and reactivity of dimethylanisoles

The spectroscopic features, reactive natures, molecular docking, and electronic properties of anisole and six dimethylanisoles (DMAs) are investigated thoroughly to have insight into the effect of methyl substitution in anisole derivatives. The spectroscopic properties of studied molecules, including FT-IR, FT-Raman, and 1H and 13C NMR spectra were have been obtained by using DFT calculations at B3LYP/6–311++G(d,p) level of theory, and compared with the ones measured experimentally. Reactivity features were determined based on global descriptors, electron density mapping, and Fukui analysis to reveal the electrophilic and nucleophilic nature of them. The methyl position mainly affects the reactivity of the methoxy group and the aromatic nature of the ring. The methyl position dependency of aromaticity and π-stacking ability in DMAs have been explored through the nuclear independent chemical shielding (NICS) calculations, aromaticity indexes, and π orbital overlapping analysis. The static and dynamic polarizability and first and second hyperpolarizability have been carried out to explore the potential of the molecules in optical applications and the effect of methyl position on these characteristics. Bioactive potency and toxicity characteristics have been tested through molecular docking of the molecules to the odorant-binding protein.