A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Alu distribution and mutation types of cancer genes

Background: Alu elements are the most abundant retrotransposable elements comprising ~11% of the human genome. Many studies have highlighted the role that Alu elements have in genetic instability and how their contribution to the assortment of mutagenic events can lead to cancer. As of yet, little has been done to quantitatively assess the association between Alu distribution and genes that are causally implicated in oncogenesis.Results: We have investigated the effect of various Alu densities on the mutation type based classifications of cancer genes. In order to establish the direct relationship between Alus and the cancer genes of interest, genome wide Alu-related densities were measured using genes rather than the sliding windows of fixed length as the units. Several novel genomic features, such as the density of the adjacent Alu pairs and the number of Alu-Exon-Alu triplets, were developed in order to extend the investigation via the multivariate statistical analysis toward more advanced biological insight. In addition, we characterized the genome-wide intron Alu distribution with a mixture model that distinguished genes containing Alu elements from those with no Alus, and evaluated the gene-level effect of the 5\u27-TTAAAA motif associated with Alu insertion sites using a two-step regression analysis method.Conclusions: The study resulted in several novel findings worthy of further investigation. They include: (1) Recessive cancer genes (tumor suppressor genes) are enriched with Alu elements (p \u3c 0.01) compared to dominant cancer genes (oncogenes) and the entire set of genes in the human genome; (2) Alu-related genomic features can be used to cluster cancer genes into biological meaningful groups; (3) The retention of exon Alus has been restricted in the human genome development, and an upper limit to the chromosome-level exon Alu densities is suggested by the distribution profile; (4) For the genes with at least one intron Alu repeat in individual chromosomes, the intron Alu densities can be well fitted by a Gamma distribution; (5) The effect of the 5\u27-TTAAAA motif on Alu densities varies across different chromosomes

RAD59 and RAD1 cooperate in translocation formation by single-strand annealing in Saccharomyces cerevisiae

Studies in the budding yeast, Saccharomyces cerevisiae, have demonstrated that a substantial fraction of double-strand break repair following acute radiation exposure involves homologous recombination between repetitive genomic elements. We have previously described an assay in S. cerevisiae that allows us to model how repair of multiple breaks leads to the formation of chromosomal translocations by single-strand annealing (SSA) and found that Rad59, a paralog of the single-stranded DNA annealing protein Rad52, is critically important in this process. We have constructed several rad59 missense alleles to study its function more closely. Characterization of these mutants revealed proportional defects in both translocation formation and spontaneous direct-repeat recombination, which is also thought to occur by SSA. Combining the rad59 missense alleles with a null allele of RAD1, which encodes a subunit of a nuclease required for the removal of non-homologous tails from annealed intermediates, substantially suppressed the low frequency of translocations observed in rad1-null single mutants. These data suggest that at least one role of Rad59 in translocation formation by SSA is supporting the machinery required for cleavage of non-homologous tails

Estimating genomic instability mediated by Alu retroelements in breast cancer

Alu-PCR is a relatively simple technique that can be used to investigate genomic instability in cancer. This technique allows identification of the loss, gain or amplification of gene sequences based on the analysis of segments between two Alu elements coupled with quantitative and qualitative analyses of the profiles obtained from tumor samples, surgical margins and blood. In this work, we used Alu-PCR to identify gene alterations in ten patients with invasive ductal breast cancer. Several deletions and insertions were identified, indicating genomic instability in the tumor and adjacent normal tissue. Although not associated with specific genes, the alterations, which involved chromosomal bands 1p36.23, 1q41, 11q14.3, 13q14.2, occurred in areas of well-known genomic instability in breast and other types of cancer. These results indicate the potential usefulness of Alu-PCR in identifying altered gene sequences in breast cancer. However, caution is required in its application since the Alu primer can produce non-specific amplification

MLL leukemia-associated rearrangements in peripheral blood lymphocytes from healthy individuals

Chromosomal translocations are characteristic of hematopoietic neoplasias and can lead to unregulated oncogene expression or the fusion of genes to yield novel functions. In recent years, different lymphoma/leukemia-associated rearrangements have been detected in healthy individuals. In this study, we used inverse PCR to screen peripheral lymphocytes from 100 healthy individuals for the presence of MLL (Mixed Lineage Leukemia) translocations. Forty-nine percent of the probands showed MLL rearrangements. Sequence analysis showed that these rearrangements were specific for MLL translocations that corresponded to t(4;11)(q21;q23) (66%) and t(9;11) (20%). However, RT-PCR failed to detect any expression of t(4;11)(q21;q23) in our population. We suggest that 11q23 rearrangements in peripheral lymphocytes from normal individuals may result from exposure to endogenous or exogenous DNA-damaging agents. In practical terms, the high susceptibility of the MLL gene to chemically-induced damage suggests that monitoring the aberrations associated with this gene in peripheral lymphocytes may be a sensitive assay for assessing genomic instability in individuals exposed to genotoxic stress

The c-kit ligand potentiates the allogeneic mixed lymphocyte reaction

The allogeneic mixed lymphocyte reaction (MLR) is a complex in vitro assay of T-cell recognition and responsiveness in which interleukin-2 (IL-2) plays a central role. We have previously demonstrated that c-kit ligand (KL) can enhance IL-2-induced proliferation in a subset of human natural killer cells expressing the c-kit tyrosine kinase receptor. In the present study, we asked whether KL could enhance IL-2-mediated T-cell proliferation in the allogeneic MLR. We demonstrate that the vast majority of activated human T-cell clones express the c-kit mRNA transcript. Binding studies performed on activated T cells with radioiodinated KL were consistent with the expression of a single class of c-kit receptors. The addition of exogenous KL to the MLR led to an increase in tritiated thymidine (3[H]-TdR) incorporation in the absence of other exogenous cytokines, and did so in a dose-dependent fashion. A reproducible increase in 3[H]-TdR incorporation was noted at concentrations of KL, which approximate those normally found in vivo. Antibody blocking of KL binding to c-kit, T-cell depletion and sorting experiments suggest that the action of KL is mediated at least in part by a direct effect on both CD4+ and CD8+ T-cells. KL's enhancement of the MLR also requires the binding of IL-2 to its high-affinity IL-2 receptor. Given the abundance of KL normally found in human serum, these data suggest that this cytokine may have a role during T-cell activation in vivo.</jats:p

Persistence of the AML1/ETO fusion transcript in patients treated with allogeneic bone marrow transplantation for t(8;21) leukemia

The AML1/ETO fusion transcript is expressed in virtually all patients with t(8;21) (q22;q22) acute myeloid leukemia (AML). The fusion transcript can be detected by reverse transcription-polymerase chain reaction (RT-PCR) in most of these patients in long-term complete remission (CR) following conventional chemotherapy or autologous bone marrow transplantation (BMT). However, AML1/ETO expression has not been analyzed in a series of patients following allogeneic BMT. We examined CR bone marrow (BM) samples and, in some cases, blood samples from 10 patients with t(8;21) leukemia who underwent allogeneic BMT in either first or second remission or first or second relapse. A variety of myeloablative regimens were used. Eight patients received non-T-cell depleted BM from matched sibling donors, one patient received a T-cell depleted haploidentical BM, and one patient received a non-T-cell depleted BM from a matched unrelated donor (MUD). Five patients developed acute and/ or chronic graft versus host disease (GVHD). The furthest time points analyzed for the AML1/ETO transcript in the 10 patients in CR following allogeneic BMT ranged from 7.5 to 83.0 months. Sufficient RNA was extracted from the most recent BM or BM and blood samples from nine patients to assay for presence or absence of the AML1/ETO fusion transcript by RT-PCR. The fusion transcript was detected by RT-PCR in all nine of these patient samples; eight were positive in BM and one was negative in BM, but positive in blood. The fusion transcript could not be detected in a BM sample from the tenth patient obtained 7.5 months after BMT, but the amount of RNA available was suboptimal. Hematopoietic chimerism could be demonstrated in sorted CD34+ BM cells from two of four patient CR BM samples with RT-PCR evidence of the fusion transcript. Additionally, in one of the two cases with chimerism, we demonstrated an abnormal clonal population of recipient cells in the CR BM sample by fluorescence in situ hybridization. One patient died of complications from GVHD, while the other nine patients remain alive without evidence of relapse, with a median follow-up time of 27 (range, 7.5 to 87) months post-BMT. These data suggest that allogeneic BMT, like conventional chemotherapy and autologous BMT, is not sufficient to eradicate cells expressing AML1/ETO, and that a positive RT-PCR for the fusion transcript post allogeneic BMT is compatible with continued CR.</jats:p