Exact ground states for the four-electron problem in a two-dimensional finite Hubbard square system

We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works for arbitrary even particle number and lattice sites, is based on explicitly given symmetry adapted base vectors constructed in r-space. The Hamiltonian acting on these states generates a closed system of 85 linear equations providing by its minimum eigenvalue the exact ground state of the system. The presented results, described with the aim to generate further creative developments, not only show how the ground state can be exactly obtained and what kind of contributions enter in its construction, but emphasize further characteristics of the spectrum. On this line i) possible explications are found regarding why weak coupling expansions often provide a good approximation for the Hubbard model at intermediate couplings, or ii) explicitly given low lying energy states of the kinetic energy, avoiding double occupancy, suggest new roots for pairing mechanism attracting decrease in the kinetic energy, as emphasized by kinetic energy driven superconductivity theories.Comment: 37 pages, 18 figure

Contribution of Distinct Homeodomain DNA Binding Specificities to Drosophila Embryonic Mesodermal Cell-Specific Gene Expression Programs

Homeodomain (HD) proteins are a large family of evolutionarily conserved transcription factors (TFs) having diverse developmental functions, often acting within the same cell types, yet many members of this family paradoxically recognize similar DNA sequences. Thus, with multiple family members having the potential to recognize the same DNA sequences in cis-regulatory elements, it is difficult to ascertain the role of an individual HD or a subclass of HDs in mediating a particular developmental function. To investigate this problem, we focused our studies on the Drosophila embryonic mesoderm where HD TFs are required to establish not only segmental identities (such as the Hox TFs), but also tissue and cell fate specification and differentiation (such as the NK-2 HDs, Six HDs and identity HDs (I-HDs)). Here we utilized the complete spectrum of DNA binding specificities determined by protein binding microarrays (PBMs) for a diverse collection of HDs to modify the nucleotide sequences of numerous mesodermal enhancers to be recognized by either no or a single subclass of HDs, and subsequently assayed the consequences of these changes on enhancer function in transgenic reporter assays. These studies show that individual mesodermal enhancers receive separate transcriptional input from both I–HD and Hox subclasses of HDs. In addition, we demonstrate that enhancers regulating upstream components of the mesodermal regulatory network are targeted by the Six class of HDs. Finally, we establish the necessity of NK-2 HD binding sequences to activate gene expression in multiple mesodermal tissues, supporting a potential role for the NK-2 HD TF Tinman (Tin) as a pioneer factor that cooperates with other factors to regulate cell-specific gene expression programs. Collectively, these results underscore the critical role played by HDs of multiple subclasses in inducing the unique genetic programs of individual mesodermal cells, and in coordinating the gene regulatory networks directing mesoderm development.National Institutes of Health (U.S.) (Grant R01 HG005287

A Machine Learning Approach for Identifying Novel Cell Type–Specific Transcriptional Regulators of Myogenesis

Transcriptional enhancers integrate the contributions of multiple classes of transcription factors (TFs) to orchestrate the myriad spatio-temporal gene expression programs that occur during development. A molecular understanding of enhancers with similar activities requires the identification of both their unique and their shared sequence features. To address this problem, we combined phylogenetic profiling with a DNA–based enhancer sequence classifier that analyzes the TF binding sites (TFBSs) governing the transcription of a co-expressed gene set. We first assembled a small number of enhancers that are active in Drosophila melanogaster muscle founder cells (FCs) and other mesodermal cell types. Using phylogenetic profiling, we increased the number of enhancers by incorporating orthologous but divergent sequences from other Drosophila species. Functional assays revealed that the diverged enhancer orthologs were active in largely similar patterns as their D. melanogaster counterparts, although there was extensive evolutionary shuffling of known TFBSs. We then built and trained a classifier using this enhancer set and identified additional related enhancers based on the presence or absence of known and putative TFBSs. Predicted FC enhancers were over-represented in proximity to known FC genes; and many of the TFBSs learned by the classifier were found to be critical for enhancer activity, including POU homeodomain, Myb, Ets, Forkhead, and T-box motifs. Empirical testing also revealed that the T-box TF encoded by org-1 is a previously uncharacterized regulator of muscle cell identity. Finally, we found extensive diversity in the composition of TFBSs within known FC enhancers, suggesting that motif combinatorics plays an essential role in the cellular specificity exhibited by such enhancers. In summary, machine learning combined with evolutionary sequence analysis is useful for recognizing novel TFBSs and for facilitating the identification of cognate TFs that coordinate cell type–specific developmental gene expression patterns