Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Immunoglobulin classes in aquatic mammals. Characterization by serologic cross-reactivity, molecular size and binding of human free secretory component.

On the basis of serologic cross-reactivity, three immunoglobulin classes homologous to human IgG, IgM and IgA were identified in two species of acquatic mammal representing the orders Cetacea (dolphin) and Pinnipedea (sea lion). Molecular size was estimated by sucrose density gradient ultracentrifugation and Sephadex G-200 chromatography, indicating a 7S IgG, 19S IgM and heterogeneous serum IgA. Human secretory component was readily bound to the IgM of both species and to an apparently lesser extent to the larger molecular size populations of IgA. No binding was observed with IgG. Several antisera specific for human γ-chains gave a single precipitin line with the sea lion IgG but when made to react with dolphin serum produced two lines, suggesting the presence of two different subclasses of IgG in this species.

IL-2- and CD25-dependent immunoregulatory mechanisms in the homeostasis of T-cell subsets.

IL-2 plays a pivotal role in regulating the adaptive immune system by controlling the survival and proliferation of regulatory T (Treg) cells, which are required for the maintenance of immune tolerance. Moreover, IL-2 is implicated in the differentiation and homeostasis of effector T-cell subsets, including T(H)1, T(H)2, T(H)17, and memory CD8+ T cells. The IL-2 receptor is composed of 3 distinct subunits, namely the alpha (CD25), beta (CD122), and gamma (gammac) chains. Of crucial importance for the delivery of IL-2 signals to Treg cells is the expression of CD25, which, along with CD122 and gammac, confers high affinity binding to IL-2. Notably, recent findings suggest a novel role for CD25, whereby CD25 molecules on Treg cells and possibly other cells are capable of influencing T-cell homeostasis by means of IL-2 deprivation. This review explores these findings and integrates them into our current understanding of T-cell homeostasis.

Biased V beta usage in immature thymocytes is independent of DJ beta proximity and pT alpha pairing.

During thymus development, the TCR beta locus rearranges before the TCR alpha locus. Pairing of productively rearranged TCR beta-chains with an invariant pT alpha chain leads to the formation of a pre-TCR and subsequent expansion of immature pre-T cells. Essentially nothing is known about the TCR V beta repertoire in pre-T cells before or after the expression of a pre-TCR. Using intracellular staining, we show here that the TCR V beta repertoire is significantly biased at the earliest developmental stage in which VDJ beta rearrangement has occurred. Moreover (and in contrast to the V(H) repertoire in immature B cells), V beta repertoire biases in immature T cells do not reflect proximity of V beta gene segments to the DJ beta cluster, nor do they depend upon preferential V beta pairing with the pT alpha chain. We conclude that V gene repertoires in developing T and B cells are controlled by partially distinct mechanisms.

trEST, trGEN and Hits: access to databases of predicted protein sequences.

High throughput genome (HTG) and expressed sequence tag (EST) sequences are currently the most abundant nucleotide sequence classes in the public database. The large volume, high degree of fragmentation and lack of gene structure annotations prevent efficient and effective searches of HTG and EST data for protein sequence homologies by standard search methods. Here, we briefly describe three newly developed resources that should make discovery of interesting genes in these sequence classes easier in the future, especially to biologists not having access to a powerful local bioinformatics environment. trEST and trGEN are regularly regenerated databases of hypothetical protein sequences predicted from EST and HTG sequences, respectively. Hits is a web-based data retrieval and analysis system providing access to precomputed matches between protein sequences (including sequences from trEST and trGEN) and patterns and profiles from Prosite and Pfam. The three resources can be accessed via the Hits home page (http://hits. isb-sib.ch).

Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

The beta-catenin--TCF-1 pathway ensures CD4(+)CD8(+) thymocyte survival.

The association of trans-acting T cell factors (TCFs) or lymphoid enhancer factor 1 (LEF-1) with their coactivator beta-catenin mediates transient transcriptional responses to extracellular Wnt signals. We show here that T cell maturation depends on the presence of the beta-catenin--binding domain in TCF-1. This domain is necessary to mediate the survival of immature CD4(+)CD8(+) double-positive (DP) thymocytes. Accelerated spontaneous thymocyte death in the absence of TCF-1 correlates with aberrantly low expression of the anti-apoptotic protein Bcl-x(L). Increasing anti-apoptotic effectors in thymocytes by the use of a Bcl-2 transgene rescued TCF-1-deficient DP thymocytes from apoptosis. Thus, TCF-1, upon association with beta-catenin, transiently ensures the survival of immature T cells, which enables them to generate and edit T cell receptor (TCR) alpha chains and attempt TCR-mediated positive selection.

Characterization of human fibroleukin, a fibrinogen-like protein secreted by T lymphocytes.

We have recently cloned the human homologue of the murine pT49 cDNA (hpT49h), a transcript encoding a protein homologous to the beta- and gamma-chains of fibrinogen. Here, we report the identification of the hpT49h gene product using mAbs generated against a peptide corresponding to the carboxyl-terminal end of the deduced protein and a recombinant protein fragment expressed in Escherichia coli. mAbs 23A6, 7B12, and 3F4 specifically recognized a protein of 70 kDa in reducing SDS-PAGE in the culture supernatant of 293T cells transiently transfected with the full length hpT49h cDNA and freshly isolated PBMC. Under nonreducing conditions, the material migrated with a molecular mass of 250 to 300 kDa, indicating that the 70-kDa protein forms a disulfide bonded complex. Because of its homology with fibrinogen, we have termed this protein fibroleukin. Fibroleukin is spontaneously secreted in vitro by freshly isolated CD4+ and CD8+ T lymphocytes. RT-PCR analysis revealed preferential expression of fibroleukin mRNA in memory T lymphocytes (CD3+/CD45R0+) compared with naive T lymphocytes (CD3+/CD45RA+). Fibroleukin production by PBMC was rapidly lost in culture. Production could be partially maintained in the presence of IFN-gamma, while T lymphocyte activation had no effect. To demonstrate fibroleukin production in vivo, we analyzed colon mucosa by immunohistology. Fibroleukin staining was detected in the extracellular matrix of the T lymphocyte-rich upper portion of the lamina propria mucosa. While the exact function of fibroleukin remains to be defined, these data suggest that fibroleukin may play a role in physiologic lymphocyte functions at mucosal sites.

Protein-binding site at the immunoglobulin mu membrane polyadenylylation signal: possible role in transcription termination.

mRNAs specifying immunoglobulin mu and delta heavy chains are encoded by a single large, complex transcription unit (mu + delta gene). The transcriptional activity of delta gene segments in terminally differentiated, IgM-secreting B lymphocytes is 10-20 times lower than in earlier B-lineage cells expressing delta mRNA. We find that transcription of the mu + delta gene in IgM-secreting murine myeloma cells terminates within a region of 500-1000 nucleotides immediately following the mu membrane (mu m) polyadenylylation site. Transcription decreases only minimally through this region in murine cell lines representative of earlier stages in B-cell development. A DNA fragment containing the mu m polyadenylylation signal gives protein-DNA complexes with different mobilities in gel retardation assays with nuclear extracts from myeloma cells than with nuclear extracts from earlier B-lineage cells. However, using a recently developed "footprinting" procedure in which protein-DNA complexes resolved in gel retardation assays are subjected to nucleolytic cleavage while still in the polyacrylamide gel, we find that the DNA sequences protected by factors from the two cell types are indistinguishable. The factor-binding site on the DNA is located 5' of the mu m polyadenylylation signal AATAAA and includes the 15-nucleotide-long A + T-rich palindrome CTGTAAACAAATGTC. This type of palindromic binding site exhibits orientation-dependent activity consistent with the reported properties of polymerase II termination signals. This binding site is followed by two sets of directly repeated DNA sequences with different helical conformation as revealed by their reactivity with the chemical nuclease 1,10-phenanthroline-copper. The close proximity of these features to the signals for mu m mRNA processing may reflect a linkage of the processes of developmentally regulated mu m polyadenylylation and transcription termination.

Comparison between computational alanine scanning and per-residue binding free energy decomposition for protein-protein association using MM-GBSA: application to the TCR-p-MHC complex.

Recognition by the T-cell receptor (TCR) of immunogenic peptides (p) presented by Class I major histocompatibility complexes (MHC) is the key event in the immune response against virus-infected cells or tumor cells. A study of the 2C TCR/SIYR/H-2K(b) system using a computational alanine scanning and a much faster binding free energy decomposition based on the Molecular Mechanics-Generalized Born Surface Area (MM-GBSA) method is presented. The results show that the TCR-p-MHC binding free energy decomposition using this approach and including entropic terms provides a detailed and reliable description of the interactions between the molecules at an atomistic level. Comparison of the decomposition results with experimentally determined activity differences for alanine mutants yields a correlation of 0.67 when the entropy is neglected and 0.72 when the entropy is taken into account. Similarly, comparison of experimental activities with variations in binding free energies determined by computational alanine scanning yields correlations of 0.72 and 0.74 when the entropy is neglected or taken into account, respectively. Some key interactions for the TCR-p-MHC binding are analyzed and some possible side chains replacements are proposed in the context of TCR protein engineering. In addition, a comparison of the two theoretical approaches for estimating the role of each side chain in the complexation is given, and a new ad hoc approach to decompose the vibrational entropy term into atomic contributions, the linear decomposition of the vibrational entropy (LDVE), is introduced. The latter allows the rapid calculation of the entropic contribution of interesting side chains to the binding. This new method is based on the idea that the most important contributions to the vibrational entropy of a molecule originate from residues that contribute most to the vibrational amplitude of the normal modes. The LDVE approach is shown to provide results very similar to those of the exact but highly computationally demanding method.

Catalytic core of a membrane-associated eukaryotic polyphosphate polymerase.

Polyphosphate (polyP) occurs ubiquitously in cells, but its functions are poorly understood and its synthesis has only been characterized in bacteria. Using x-ray crystallography, we identified a eukaryotic polyphosphate polymerase within the membrane-integral vacuolar transporter chaperone (VTC) complex. A 2.6 angstrom crystal structure of the catalytic domain grown in the presence of adenosine triphosphate (ATP) reveals polyP winding through a tunnel-shaped pocket. Nucleotide- and phosphate-bound structures suggest that the enzyme functions by metal-assisted cleavage of the ATP gamma-phosphate, which is then in-line transferred to an acceptor phosphate to form polyP chains. Mutational analysis of the transmembrane domain indicates that VTC may integrate cytoplasmic polymer synthesis with polyP membrane translocation. Identification of the polyP-synthesizing enzyme opens the way to determine the functions of polyP in lower eukaryotes.

Characterization of glycoinositol phospholipids in the amastigote stage of the protozoan parasite Leishmania major.

The major macromolecules on the surface of the parasitic protozoan Leishmania major appear to be down-regulated during transformation of the parasite from an insect-dwelling promastigote stage to an intracellular amastigote stage that invades mammalian macrophages. In contrast, the major parasite glycolipids, the glycoinositol phospholipids (GIPLs), are shown here to be expressed at near-constant levels in both developmental stages. The structures of the GIPLs from tissue-derived amastigotes have been determined by h.p.l.c. analysis of the deaminated and reduced glycan head groups, and by chemical and enzymic sequencing. The deduced structures appear to form a complete biosynthetic series, ranging from Man alpha 1-4GlcN-phosphatidylinositol (PI) to Gal alpha 1-3Galf beta 1-3Man alpha 1-3Man alpha 1-4GlcN-PI (GIPL-2). A small proportion of GIPL-2 was further extended by addition of a Gal residue in either alpha 1-6 or beta 1-3 linkage. From g.c.-m.s. analysis and mild base treatment, all the GIPLs were shown to contain either alkylacylglycerol or lyso-alkylglycerol lipid moieties, where the alkyl chains were predominantly C18:0, with lower levels of C20:0, C22:0 and C24:0. L. major amastigotes also contained at least two PI-specific phospholipase C-resistant glycolipids which are absent from promastigotes. These neutral glycolipids were resistant to both mild acid and mild base hydrolysis, contained terminal beta-Gal residues and were not lost during extensive purification of amastigotes from host cell membranes. It is likely that these glycolipids are glycosphingolipids acquired from the mammalian host. The GIPL profile of L. major amastigotes is compared with the profiles found in L. major promastigotes and L. donovani amastigotes.

Scaling behavior and equilibrium lengths of knotted polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease. on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.

Selective absence of CD8+ TCRalpha beta+ intestinal epithelial cells in transgenic mice expressing beta2-microglobulin-associated ligands exclusively on thymic cortical epithelium.

Whereas interactions between the TCRalpha beta and self MHC:peptide complexes are clearly required for positive selection of mature CD4(+) and CD8(+) T cells during intrathymic development, the role of self or foreign ligands in maintaining the peripheral T cell repertoire is still controversial. In this report we have utilized keratin 14-beta2-microglobulin (K14-beta2m)-transgenic mice expressing beta2m-associated ligands exclusively on thymic cortical epithelial cells to address the possible influence of TCR:ligand interactions in peripheral CD8(+) T cell homeostasis. Our data indicate that CD8(+) T cells in peripheral lymphoid tissues are present in normal numbers in the absence of self MHC class I:peptide ligands. Surprisingly, however, steady state homeostasis of CD8(+) T cells in the intestinal epithelium is severely affected by the absence of beta2m-associated ligands. Indeed TCRalpha beta(+) IEL subsets expressing CD8alpha beta or CD8alpha alpha are both dramatically reduced in K14-beta2m mice, suggesting that the development, survival or expansion of CD8(+) IEL depends upon interaction of the TCR with MHC class I:peptide or other beta2m-associated ligands elsewhere than on thymic cortical epithelium. Collectively, our data reveal an unexpected difference in the regulation of CD8(+) T cell homeostasis by beta2m-associated ligands in the intestine as compared to peripheral lymphoid organs.

MAMOT: hidden Markov modeling tool.

Hidden Markov models (HMMs) are probabilistic models that are well adapted to many tasks in bioinformatics, for example, for predicting the occurrence of specific motifs in biological sequences. MAMOT is a command-line program for Unix-like operating systems, including MacOS X, that we developed to allow scientists to apply HMMs more easily in their research. One can define the architecture and initial parameters of the model in a text file and then use MAMOT for parameter optimization on example data, decoding (like predicting motif occurrence in sequences) and the production of stochastic sequences generated according to the probabilistic model. Two examples for which models are provided are coiled-coil domains in protein sequences and protein binding sites in DNA. A wealth of useful features include the use of pseudocounts, state tying and fixing of selected parameters in learning, and the inclusion of prior probabilities in decoding. AVAILABILITY: MAMOT is implemented in C++, and is distributed under the GNU General Public Licence (GPL). The software, documentation, and example model files can be found at http://bcf.isb-sib.ch/mamot