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At the ferroelectric surface, the broken translational symmetry induced bound charge should significantly alter the local atomic configurations. Experimentally revealing the atomic structure of ferroelectric surface, however, is very challenging due to the strong spatial variety between nano-sized domains, and strong interactions between the polarization and other structural parameters. Here, we study surface structures of Pb(Zr0.2Ti0.8)O3 thin film by using the annular bright-field imaging. We find that six atomic layers with suppressed polarization and a charged 180 domain wall are at negatively poled surfaces, no reconstruction exists at positively poled surfaces, and seven atomic layers with suppressed polarization and a charged 90 domain wall exist at nominally neutral surfaces in ferroelastic domains. Our results provide critical insights into engineering ferroelectric thin films, fine grain ceramics and surface chemistry devices. The state-of-the-art methodology demonstrated here can greatly advance our understanding of surface science for oxides.

Atomic Reconstruction download for windows 7

These distinct surface structures in different domains can be explained by the subsurface polarization-induced bound charge at the surface, which requires to be screened by either structural distortion, electronic reconstruction or re-distribution of free carriers. On the negatively poled surface, the holes must move to the p states of surface oxygen, or alternatively, oxygen vacancies should form on the surface acting as positively charged defects that contribute to screen the depolarization field. For the perovskite oxide, on the surface the formation energy of oxygen vacancy is usually lower because of the asymmetric bonding. With high-density oxygen vacancies at the surface, the bound charge can be effectively screened but meanwhile the structure prefers to expand the lattice because of the increased Coulomb repulsion between cations31. The measured reconstruction thickness of six atomic layers is basically in agreement with previous calculations8 of PbTiO3 for which four atomic layers reconstruction may exist on the negatively poled surface. However, the experimental observations indicate the surface reconstruction is even thicker and much more complicated containing charged domain walls.

The thicknesses of the surface reconstruction ranging from zero to seven atomic layers is much smaller than that predicted from the mesoscopic measurements18. The polarization prefers to point towards the free surface irrespective to the electric dipoles at the subsurface, suggesting the non-stoichometric surface of our sample can locally stabilize the upward polar vectors. The c-lattice parameter at the negatively poled surface expands, whereas in the ferroelastic domain it contracts. In both of the cases, the tetragonality increases while ferroelectricity decreases. Overall, the surface structure is very distinct from the bulk-like subsurface and largely governed by the subsurface polarization via strong interactions between the structural parameters. Furthermore, the conclusion of polarization-dependent surface reconstruction is unlikely affected by the thin-surface amorphous layer or tiny specimen alignment (more details in the Supplementary Fig. 10 and Supplementary Discussion).

Citation: Amyot R, Marchesi A, Franz CM, Casuso I, Flechsig H (2022) Simulation atomic force microscopy for atomic reconstruction of biomolecular structures from resolution-limited experimental images. PLoS Comput Biol 18(3): e1009970.

Since reconstruction of both SthK lattices relied on the atomic structure of the inactive channel conformation (active state data is unfortunately lacking), our model cannot directly resolve changes of peripheral VSDs related to channel activation. However, the arrangement obtained for the SthK active state lattice leads us to hypothesize that such motions may indeed be involved in the activation process as a result from cAMP ligands binding at the remote intracellular NBDs. The existence of this allosteric communication provides a possible structural rationale for the relationship between ligand binding, transmembrane voltage modulation, and channel activation observed in functional assays of SthK [30] and other eukaryotic homologue channels [31, 32].

Applications ranging from single molecular machines, protein filaments, to large-scale assemblies of protein lattices, demonstrate how the obtained full atomistic information advances the molecular understanding beyond the original AFM topography image. We have shown that the molecular arrangement of functional domains in multimeric proteins and even their nucleotide-state can be disambiguated from AFM surface scans. In particular, applications to AFM images of 2D lattices for the cyclic nucleotide-gated SthK channel stand out to exemplify the explanatory power of atomic reconstruction. Structural characterization of the transmembrane domains, which are not accessible to the scanning tip during imaging, allows to identify possible interactions sites between neighboring channels within the membrane and elucidate the pattern distinguishing the resting state from the activated state.

A genome-scale metabolic reconstruction is a structured knowledge-base that abstracts pertinent information on the biochemical transformations taking place within an organism [6]. Such reconstructions form the basis for the development of condition-specific metabolic models whose functions are simulated and validated by comparison with experimental results. These models are then used in a wide range of biological, biotechnological and biomedical research scenarios. Manual curation reconstructions involves extensive literature review [7] and sometimes sufficient experimental literature is not in existence. This situation has driven the development of a range of software tools that seek to automate parts of the process to generate reconstruction content, e.g., [8]. Recon 3D is the latest human metabolic reconstruction [9], that adds three dimensional metabolite and protein structures to a genome-scale reconstruction for the first time. It is envisaged that this reconstruction and the models derived from it will drive deeper understanding how biochemical processes relate to mechanisms at the atomic scale.

Recon 3D is a genome-scale metabolic reconstruction of human metabolism accounting for 12,000 metabolic reactions involving 8000 metabolites [9]. It is not cell-type specific, rather it is an amalgamation of the known metabolic capabilities ocurring in at least one human cell, regardless of type. Recon 3D is the most complete global human network model to date and the first to account for mechanisms at the atomic scale.

In the rest of this chapter, X-ray fluorescence holography and reconstruction of atomic images are explained in Sect. 2. Parallelization of atomic image reconstruction is explained in Sect. 3 and its performance results are shown in Sect. 4. Finally, concluding remarks are given in Sect. 5

As pointed out in Sect. 2, it is an issue that it takes long time to analyze the crystal structure because reconstruction of two-dimensional atomic images and observation of the images are repeated several times. We therefore try to improve the reconstruction of three-dimensional atomic images by parallelizing DFT with parallel programming language XcalableMP and parallel API OpenMP on multi-node PC clusters.

Presently, according to the Eq. (1), in the loop of reconstruction of two-dimensional atomic images at certain z on x-y plane, five loops of x, y, θ, ϕ, and λ are nested from outer to inner loop. In this chapter, θ loop denotes the loop which accesses contiguous elements in a dimension of array θ for short.

In reconstruction of two-dimensional atomic images, some calls of trigonometric functions such as sin and cos in nested loops are replaced with references of arrays. The values of the trigonometric functions are stored in the arrays before entering the nested loops.

In reconstruction of three-dimensional atomic images, according to the Eq. (1), by extending the optimized and parallelized nested loop of reconstruction of two-dimensional atomic images as described in Sect. 3.1, the six loops of λ, z, x, y, θ, and ϕ are nested from outer to inner loop. Similar to the two-dimensional loop, the values of some trigonometric functions are calculated in advance before entering the six nested loop.

Among the six nested loops, the outer z loop and the inner x loop are parallelized by XcalableMP and OpenMP. In other words, the nested loops are parallelized among inter-nodes by the z loop level and also parallelized within each node by the x loop level. The parallelized kernel loop of three-dimensional atomic image reconstruction is shown in Fig. 5. Other combinations of parallelizing x, y, and z loops are also performed and discussed in Sect 4.

In this section, we show the performance results of parallel runs of reconstruction of two-dimensional atomic images parallelized by OpenMP executed on a single node and reconstruction of three-dimensional atomic images parallelized by XcalableMP and OpenMP on a multi-node PC cluster. Comparison of XcalableMP and MPI for multi-node parallelization with respect to the performance and productivity of programming are also demonstrated.

In order to compare the productivity of parallel programming, we also implemented the reconstruction of three-dimensional atomic images with MPI. The number of lines of the program in C already parallelized by OpenMP is 350 and the number of modified or inserted lines for multi-node parallelization by XcalableMP is 32, while that by MPI is 53. This program can be parallelized with less effort in XcalableMP than in MPI.

This chapter describes parallelization of reconstruction of three-dimensional atomic images in X-ray fluorescence holography, which is an analysis method of material science. In order to execute it on large-scale PC clusters and supercomputer, we adopt hybrid parallelization, or inter- and intra-node parallelization by XcalableMP and OpenMP.

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