On the link Floer homology of L-space links

We will prove that, for a 2 or 3 component L-space link, HFL^- is completely determined by the multi-variable Alexander polynomial of all the sub-links of L, as well as the pairwise linking numbers of all the components of L. We will also give some restrictions on the multi-variable Alexander polynomial of an L-space link. Finally, we use the methods in this paper to prove a conjecture of Yajing Liu classifying all 2-bridge L-space links.

Topological strings, double affine Hecke algebras, and exceptional knot homology

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

Distinct intron DNA structures in simian virus 40 T-antigen and adenovirus 2 E1A genes

Distinct structures delineating the introns of Simian Virus 40 T-antigen and Adenovirus 2 E1A genes have been discovered. The structures, which are centered around the branch points of the genes inserted in supercoiled double-stranded plasmids, are specifically targeted through photoactivated strand cleavage by the metal complex tris(4,7-diphenyl-1,10-phenanthroline)rhodium(III). The DNA sites that are recognized lack sequence homology but are similar in demarcating functionally important sites on the RNA level. The single-stranded DNA fragments corresponding to the coding strands of the genes were also found to fold into a structure apparently identical to that in the supercoiled genes based on the recognition by the metal complex. Further investigation of different single-stranded DNA fragments with other structural probes, such as another metal complex bis(1,10-phenanthroline)(phenanthrenequinone diimine)rhodium(III), AMT (4'aminomethyl-4,5',8 trimethylpsoralen), restriction enzyme Mse I, and mung bean nuclease, showed that the structures require the sequ ences at both ends of the intron plus the flanking sequences but not the middle of the intron. The two ends form independent helices which interact with each other to form the global tertiary structures. Both of the intron structures share similarities to the structure of the Holliday junction, which is also known to be specifically targeted by the former metal complex. These structures may have arisen from early RNA intron structures and may have been used to facilitate the evolution of genes through exon shuffling by acting as target sites for recombinase enzymes.

Regulation of mitochondrial division by the Drp1 receptors

Mitochondria can remodel their membranes by fusing or dividing. These processes are required for the proper development and viability of multicellular organisms. At the cellular level, fusion is important for mitochondrial Ca2+ homeostasis, mitochondrial DNA maintenance, mitochondrial membrane potential, and respiration. Mitochondrial division, which is better known as fission, is important for apoptosis, mitophagy, and for the proper allocation of mitochondria to daughter cells during cellular division.

The functions of proteins involved in fission have been best characterized in the yeast model organism Sarccharomyces cerevisiae. Mitochondrial fission in mammals has some similarities. In both systems, a cytosolic dynamin-like protein, called Dnm1 in yeast and Drp1 in mammals, must be recruited to the mitochondrial surface and polymerized to promote membrane division. Recruitment of yeast Dnm1 requires only one mitochondrial outer membrane protein, named Fis1. Fis1 is conserved in mammals, but its importance for Drp1 recruitment is minor. In mammals, three other receptor proteins—Mff, MiD49, and MiD51—play a major role in recruiting Drp1 to mitochondria. Why mammals require three additional receptors, and whether they function together or separately, are fundamental questions for understanding the mechanism of mitochondrial fission in mammals.

We have determined that Mff, MiD49, or MiD51 can function independently of one another to recruit Drp1 to mitochondria. Fis1 plays a minor role in Drp1 recruitment, suggesting that the emergence of these additional receptors has replaced the system used by yeast. Additionally, we found that Fis1/Mff and the MiDs regulate Drp1 activity differentially. Fis1 and Mff promote constitutive mitochondrial fission, whereas the MiDs activate recruited Drp1 only during loss of respiration.

To better understand the function of the MiDs, we have determined the atomic structure of the cytoplasmic domain of MiD51, and performed a structure-function analysis of MiD49 based on its homology to MiD51. MiD51 adopts a nucleotidyl transferase fold, and binds ADP as a co-factor that is essential for its function. Both MiDs contain a loop segment that is not present in other nucleotidyl transferase proteins, and this loop is used to interact with Drp1 and to recruit it to mitochondria.

Integral finite surgeries on knots in S^3

Using the correction terms in Heegaard Floer homology, we prove that if a knot in S³ admits a positive integral T-, O-, or I-type surgery, it must have the same knot Floer homology as one of the knots given in our complete list, and the resulting manifold is orientation-preservingly homeomorphic to the p-surgery on the corresponding knot.

A Detailed Analysis of Transcriptional Regulators Affecting the Saccharomyces cerevisiae Heat-shock Gene SSA1

The yeast Saccharomyces cerevisiae contains a family of hsp70 related genes. One member of this family, SSA1, encodes a 70kD heat-shock protein which in addition to its heat inducible expression has a significant basal level of expression. The first 500 bp upstream of the SSA1 start point of transcription was examined by DNAse I protection analysis. The results reveal the presence of at least 14 factor binding sites throughout the upstream promoter region. The function of these binding sites has been examined using a series of 5' promoter deletions fused to the recorder gene lacZ in a centromere-containing yeast shuttle vector. The following sites have been identified in the promoter and their activity in yeast determined individually with a centromere-based recorder plasmid containing a truncated CYC1 /lacZ fusion: a heat-shock element or HSE which is sufficient to convey heat-shock response on the recorder plasmid; a homology to the SV40 'core' sequence which can repress the GCN4 recognition element (GCRE) and the yAP1 recognition element (ARE), and has been designated a upstream repression element or URE; a 'G'-rich region named G-box which can also convey heatshock response on the recorder plasmid; and a purine-pyrimidine alternating sequence name GT-box which is an activator of transcription. A series of fusion constructs were made to identify a putative silencer-like element upstream of SSA1. This element is position dependent and has been localized to a region containing both an ABF1 binding site and a RAP1 binding site. Five site-specific DNA-binding factors are identified and their purification is presented: the heat-shock transcription factor or HSTF, which recognizes the HSE; the G-box binding factor or GBF; the URE recognition factor or URF; the GT-box binding factor; and the GC-box binding factor or yeast Sp1.

Structure Prediction of G-Protein Coupled Receptors

G-protein coupled receptors (GPCRs) form a large family of proteins and are very important drug targets. They are membrane proteins, which makes computational prediction of their structure challenging. Homology modeling is further complicated by low sequence similarly of the GPCR superfamily.

In this dissertation, we analyze the conserved inter-helical contacts of recently solved crystal structures, and we develop a unified sequence-structural alignment of the GPCR superfamily. We use this method to align 817 human GPCRs, 399 of which are nonolfactory. This alignment can be used to generate high quality homology models for the 817 GPCRs.

To refine the provided GPCR homology models we developed the Trihelix sampling method. We use a multi-scale approach to simplify the problem by treating the transmembrane helices as rigid bodies. In contrast to Monte Carlo structure prediction methods, the Trihelix method does a complete local sampling using discretized coordinates for the transmembrane helices. We validate the method on existing structures and apply it to predict the structure of the lactate receptor, HCAR1. For this receptor, we also build extracellular loops by taking into account constraints from three disulfide bonds. Docking of lactate and 3,5-dihydroxybenzoic acid shows likely involvement of three Arg residues on different transmembrane helices in binding a single ligand molecule.

Protein structure prediction relies on accurate force fields. We next present an effort to improve the quality of charge assignment for large atomic models. In particular, we introduce the formalism of the polarizable charge equilibration scheme (PQEQ) and we describe its implementation in the molecular simulation package Lammps. PQEQ allows fast on the fly charge assignment even for reactive force fields.

Computational Predictions of G Protein-Coupled Receptor Structures and Binding Sites

G protein-coupled receptors (GPCRs) are the largest family of proteins within the human genome. They consist of seven transmembrane (TM) helices, with a N-terminal region of varying length and structure on the extracellular side, and a C-terminus on the intracellular side. GPCRs are involved in transmitting extracellular signals to cells, and as such are crucial drug targets. Designing pharmaceuticals to target GPCRs is greatly aided by full-atom structural information of the proteins. In particular, the TM region of GPCRs is where small molecule ligands (much more bioavailable than peptide ligands) typically bind to the receptors. In recent years nearly thirty distinct GPCR TM regions have been crystallized. However, there are more than 1,000 GPCRs, leaving the vast majority of GPCRs with limited structural information. Additionally, GPCRs are known to exist in a myriad of conformational states in the body, rendering the static x-ray crystal structures an incomplete reflection of GPCR structures. In order to obtain an ensemble of GPCR structures, we have developed the GEnSeMBLE procedure to rapidly sample a large number of variations of GPCR helix rotations and tilts. The lowest energy GEnSeMBLE structures are then docked to small molecule ligands and optimized. The GPCR family consists of five subfamilies with little to no sequence homology between them: class A, B1, B2, C, and Frizzled/Taste2. Almost all of the GPCR crystal structures have been of class A GPCRs, and much is known about their conserved interactions and binding sites. In this work we particularly focus on class B1 GPCRs, and aim to understand that family’s interactions and binding sites both to small molecules and their native peptide ligands. Specifically, we predict the full atom structure and peptide binding site of the glucagon-like peptide receptor and the TM region and small molecule binding sites for eight other class B1 GPCRs: CALRL, CRFR1, GIPR, GLR, PACR, PTH1R, VIPR1, and VIPR2. Our class B1 work reveals multiple conserved interactions across the B1 subfamily as well as a consistent small molecule binding site centrally located in the TM bundle. Both the interactions and the binding sites are distinct from those seen in the more well-characterized class A GPCRs, and as such our work provides a strong starting point for drug design targeting class B1 proteins. We also predict the full structure of CXCR4 bound to a small molecule, a class A GPCR that was not closely related to any of the class A GPCRs at the time of the work.

Organization and function of the phage Lambda chromosome

The process of prophage integration by phage λ and the function and structure of the chromosomal elements required for λ integration have been studied with the use of λ deletion mutants. Since att^φ, the substrate of the integration enzymes, is not essential for λ growth, and since att^φ resides in a portion of the λ chromosome which is not necessary for vegetative growth, viable λ deletion mutants were isolated and examined to dissect the structure of att^φ.

Deletion mutants were selected from wild type populations by treating the phage under conditions where phage are inactivated at a rate dependent on the DNA content of the particles. A number of deletion mutants were obtained in this way, and many of these mutants proved to have defects in integration. These defects were defined by analyzing the properties of Int-promoted recombination in these att mutants.

The types of mutants found and their properties indicated that att^φ has three components: a cross-over point which is bordered on either side by recognition elements whose sequence is specifically required for normal integration. The interactions of the recognition elements in Int-promoted recombination between att mutants was examined and proved to be quite complex. In general, however, it appears that the λ integration system can function with a diverse array of mutant att sites.

The structure of att^φ was examined by comparing the genetic properties of various att mutants with their location in the λ chromosome. To map these mutants, the techniques of heteroduplex DNA formation and electron microscopy were employed. It was found that integration cross-overs occur at only one point in att^φ and that the recognition sequences that direct the integration enzymes to their site of action are quite small, less than 2000 nucleotides each. Furthermore, no base pair homology was detected between att^φ and its bacterial analog, att^B. This result clearly demonstrates that λ integration can occur between chromosomes which have little, if any, homology. In this respect, λ integration is unique as a system of recombination since most forms of generalized recombination require extensive base pair homology.

An additional study on the genetic and physical distances in the left arm of the λ genome was described. Here, a large number of conditional lethal nonsense mutants were isolated and mapped, and a genetic map of the entire left arm, comprising a total of 18 genes, was constructed. Four of these genes were discovered in this study. A series of λdg transducing phages was mapped by heteroduplex electron microscopy and the relationship between physical and genetic distances in the left arm was determined. The results indicate that recombination frequency in the left arm is an accurate reflection of physical distances, and moreover, there do not appear to be any undiscovered genes in this segment of the genome.

Investigations of nonhistone chromosomal proteins

The major nonhistone chromosomal proteins (NHC proteins) are a group of 14-20 acidic proteins associated with DNA in eukaryotic chromatin. In comparisons by SDS gel electrophoresis (molecular weight sieving) one observes a high degree of homology among the NHC protein fractions of different tissues from a given species. Tissue-specific protein bands are also observed. The appearance of a new NHC protein, A, in the NHC proteins of rat liver stimulated to divide by partial hepatectomy and of rat ascites cells suggests that this protein may play a role in preparing the cell for division. The NHC proteins of the same tissue from different species are also very similar. Quantitative but not qualitative changes in the NHC proteins of rat uterus are observed on stimulation (in vivo) with estrogen. These observations suggest that the major NHC proteins play a general role in chromatin structure and the regulation of genome expression; several may be enzymes of nucleic acid and histone metabolism and/or structural proteins analogous to histones. One such enzyme, a protease which readily and preferentially degrades histones, can be extracted from chromatin with 0.7 N NaCl.

Although the NHC proteins readily aggregate, they can be separated from histone and fractionated by ion exchange chromatography on Sephadex SE C-25 resin in 10 M urea-25% formic acid (pH 2.5). Following further purification, four fractions of NHC protein are obtained; two of these are single purified proteins, and the other two contain 4-6 and 4-7 different proteins. These NHC proteins show a ratio of acidic to basic amino acids from 2.7 to 1.2 and isoelectric points from apparently less than 3.7 to 8.0. These isolated fractions appear more soluble and easier to work with than any whole NHC protein preparation.

Studies on T-even bacteriophage DNA

Part I. The regions of sequence homology and non-homology between the DNA molecules of T2, T4, and T6 have been mapped by the electron microscopic heteroduplex method. The heteroduplex maps have been oriented with respect to the T4 genetic map. They show characteristic, reproducible patterns of substitution and deletion loops. All heteroduplex molecules show more than 85% homology. Some of the loop patterns in T2/T4 heteroduplexes are similar to those in T4/T6.

We find that the rII, the lysozyme and ac genes, the D region, and gene 52 are homologous in T2, T4, and T6. Genes 43 and 47 are probably homologous between T2 and T4. The region of greatest homology is that bearing the late genes. The host range region, which comprises a part of gene 37 and all of gene 38, is heterologous in T2, T4, and T6. The remainder of gene 37 is partially homologous in the T2/T4 heteroduplex (Beckendorf, Kim and Lielausis, 1972) but it is heterologous in T4/T6 and in T2/T6. Some of the tRNA genes are homologous and some are not. The internal protein genes in general seem to be non-homologous.

The molecular lengths of the T-even DNAs are the same within the limit of experimental error; their calculated molecular weights are correspondingly different due to unequal glucosylation. The size of the T2 genome is smaller than that of T4 or T6, but the terminally repetitious region in T2 is larger. There is a length distribution of the terminal repetition for any one phage DNA, indicating a variability in length of the DNA molecules packaged within the phage.

Part II. E. coli cells infected with phage strains carrying extensive deletions encompassing the gene for the phage ser-tRNA are missing the phage tRNAs normally present in wild type infected cells. By DNA-RNA hybridization we have demonstrated that the DNA complementary to the missing tRNAs is also absent in such deletion mutants. Thus the genes for these tRNAs must be clustered in the same region of the genome as the ser-tRNA gene. Physical mapping of several deletions of the ser-tRNA and lysozyme genes, by examination of heteroduplex DNA in the electron microscope, has enabled us to locate the cluster, to define its maximum size, and to order a few of the tRNA genes within it. That such deletions can be isolated indicates that the phage-specific tRNAs from this cluster are dispensable.

Part III. Genes 37 and 38 between closely related phages T2 and T4 have been compared by genetic, biochemical, and hetero-duplex studies. Homologous, partially homologous and non-homologous regions of the gene 37 have been mapped. The host range determinant which interacts with the gene 38 product is identified.

Part IV. A population of double-stranded ØX-RF DNA molecules carrying a deletion of about 9% of the wild-type DNA has been discovered in a sample cultivated under conditions where the phage lysozyme gene is nonessential. The structures of deleted monomers, dimers, and trimers have been studied by the electron microscope heteroduplex method. The dimers and trimers are shown to be head-to-tail repeats of the deleted monomers. Some interesting examples of the dynamical phenomenon of branch migration in vitro have been observed in heteroduplexes of deleted dimer and trimer strands with undeleted wild-type monomer viral strands.