Cellular and gene expression patterns associated with root bifurcation in Selaginella.

The roots of lycophytes branch through dichotomy or bifurcation, during which the root apex splits into two daughter roots. This is morphologically distinct from lateral root (LR) branching in the extant euphyllophytes, with LRs developing along the root axis at different distances from the apex. Although the process of root bifurcation is poorly understood, such knowledge can be important, because it may represent an evolutionarily ancient strategy that roots recruited to form new stem cells or meristems. In this study, we examined root bifurcation in the lycophyte Selaginella moellendorffii. We characterized an in vitro developmental time frame based on repetitive apex bifurcations, allowing us to sample different stages of dichotomous root branching and analyze the root meristem and root branching in S. moellendorffii at the microscopic and transcriptomic level. Our results showed that, in contrast to previous assumptions, initial cells (ICs) in the root meristem are mostly not tetrahedral but rather show an irregular shape. Tracking down the early stages of root branching argues for the occurrence of a symmetric division of the single IC, resulting in two apical stem cells that initiate root meristem bifurcation. Moreover, we generated a S. moellendorffii root branching transcriptome that resulted in the delineation of a subset of core meristem genes. The occurrence of multiple putative orthologs of meristem genes in this dataset suggests the presence of conserved pathways in the control of meristem and root stem cell establishment or maintenance.

Direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions: The influence of three-index N-representability conditions.

This work proposes the variational determination of two-electron reduced density matrices corresponding to the ground state of N-electron systems within the doubly occupied-configuration-interaction methodology. The P, Q, and G two-index N-representability conditions have been extended to the T1 and T2 (T2') three-index ones and the resulting optimization problem has been addressed using a standard semidefinite program. We report results obtained from the doubly occupied-configuration-interaction method, from the two-index constraint variational procedure and from the two- and three-index constraint variational treatment. The discussion of these results along with a study of the computational cost demanded shows the usefulness of our proposal.

Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions.

A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.

Structural and biochemical characterization of SmoPG1, an exo-polygalacturonase from Selaginella moellendorffii.

Polygalacturonases (PGs) can modulate chemistry and mechanical properties of the plant cell wall through the degradation of pectins, one of its major constituents. PGs are largely used in food, beverage, textile, and paper industries to increase processes' performances. To improve the use of PGs, knowledge of their biochemical, structural and functional features is of prime importance. Our study aims at characterizing SmoPG1, a polygalacturonase from Selaginella moellendorffii, that belongs to the lycophytes. Transcription data showed that SmoPG1 was mainly expressed in S. moellendorffii shoots while phylogenetic analyses suggested that SmoPG1 is an exo-PG, which was confirmed by the biochemical characterization following its expression in heterologous system. Indeed, LC-MS/MS oligoprofiling using various pectic substrates identified galacturonic acid (GalA) as the main hydrolysis product. We found that SmoPG1 was most active on polygalacturonic acid (PGA) at pH 5, and that its activity could be modulated by different cations (Ca2+, Cu2+, Fe2+, Mg2+, Mn2+, Na2+, Zn2+). In addition, SmoPG1 was inhibited by green tea catechins, including (-)-epigallocatechin-3-gallate (EGCG). Docking analyses and MD simulations showed in detail amino acids responsible for the SmoPG1-EGCG interaction. Considering its expression yield and activity, SmoPG1 appears as a prime candidate for the industrial production of GalA.

Spatial transcriptomics of a lycophyte root sheds light on root evolution.

Plant roots originated independently in lycophytes and euphyllophytes, whereas early vascular plants were rootless. The organization of the root apical meristem in euphyllophytes is well documented, especially in the model plant Arabidopsis. However, little is known about lycophyte roots and their molecular innovations during evolution. In this study, spatial transcriptomics was used to detect 97 root-related genes in the roots of the lycophyte Selaginella moellendorffii. A high number of genes showed expression patterns similar to what has been reported for seed plants, supporting the idea of a highly convergent evolution of mechanisms to control root development. Interaction and complementation data of SHORTROOT (SHR) and SCARECROW (SCR) homologs, furthermore, support a comparable regulation of the ground tissue (GT) between euphyllophytes and lycophytes. Root cap formation, in contrast, appears to be differently regulated. Several experiments indicated an important role of the WUSCHEL-RELATED HOMEOBOX13 gene SmWOX13a in Selaginella root cap formation. In contrast to multiple Arabidopsis WOX paralogs, SmWOX13a is able to induce root cap cells in Arabidopsis and has functionally conserved homologs in the fern Ceratopteris richardii. Lycophytes and a part of the euphyllophytes, therefore, may share a common mechanism regulating root cap formation, which was diversified or lost during seed plant evolution. In summary, we here provide a new spatial data resource for the Selaginella root, which in general advocates for conserved mechanisms to regulate root development but shows a clear divergence in the control of root cap formation, with a novel putative role of WOX genes in root cap formation in non-seed plants.

Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions.

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and three-index conditions on the density matrix [J. R. Hammond et al., Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi et al., Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter, we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J. R. Hammond et al., Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time, we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.

Reproducibility in density functional theory calculations of solids.

The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

Critical analysis of the accuracy of models predicting or extracting liquid structure information.

This work aims at a critical assessment of properties predicting or extracting information on the density and structure of liquids. State-of-the-art NVT and NpT molecular dynamics (MD) simulations have been performed on five liquids: methanol, chloroform, acetonitrile, tetrahydrofuran, and ethanol. These simulations allow the computation of properties based on first principles, including the equilibrium density and radial distribution functions (RDFs), characterizing the liquid structure. Refinements have been incorporated in the MD simulations by taking into account basis set superposition errors (BSSE). An extended BSSE model for an instantaneous evaluation of the BSSE corrections has been proposed, and their impact on the liquid properties has been assessed. If available, the theoretical RDFs have been compared with the experimentally derived RDFs. For some liquids, significant discrepancies have been observed, and a profound but critical investigation is presented to unravel the origin of these deficiencies. This discussion is focused on tetrahydrofuran where the experiment reveals some prominent peaks completely missing in any MD simulation. Experiments providing information on liquid structure consist mainly of neutron diffraction measurements offering total structure factors as the primary observables. The splitting of these factors in reciprocal space into intra- and intermolecular contributions is extensively discussed, together with their sensitivity in reproducing correct RDFs in coordinate space.