Energy-dependent point interactions in one dimension

We consider a new type of point interaction in one-dimensional quantum mechanics. It is characterized by a boundary condition at the origin that involves the second and/or higher order derivatives of the wavefunction. The interaction is effectively energy dependent. It leads to a unitary S-matrix for the transmission-reflection problem. The energy dependence of the interaction can be chosen such that any given unitary S-matrix (or the transmission and reflection coefficients) can be reproduced at all energies. Generalization of the results to coupled-channel cases is discussed.

Fermi pseudo-potential and energy-dependent point interactions in one dimension

There are point interactions in one dimension that can be interpreted as self-adjoint extensions (SAEs) of the kinetic energy [KE] operator. Here, we report the results obtained in two recent papers cited in [1]. In the first, we consider point interactions in one dimension in the form of the Fermi pseudo-potential, in one and two-channel cases. In the second, we consider a new type of point interactions that are self-adjoint and effectively energy-dependent. © 2005 American Institute of Physics.

Cell-cell signal-dependent dynamic interactions between HD-GYP and GGDEF domain proteins mediate virulence in Xanthomonas campestris

RpfG is a paradigm for a class of widespread bacterial two-component regulators with a CheY-like receiver domain attached to a histidine-aspartic acid-glycine-tyrosine-proline (HD-GYP) cyclic di-GMP phosphodiesterase domain. In the plant pathogen Xanthomonas campestris pv. campestris (Xcc), a two-component system comprising RpfG and the complex sensor kinase RpfC is implicated in sensing and responding to the diffusible signaling factor (DSF), which is essential for cell-cell signaling. RpfF is involved in synthesizing DSF, and mutations of rpfF, rpfG, or rpfC lead to a coordinate reduction in the synthesis of virulence factors such as extracellular enzymes, biofilm structure, and motility. Using yeast two-hybrid analysis and fluorescence resonance energy transfer experiments in Xcc, we show that the physical interaction of RpfG with two proteins with diguanylate cyclase (GGDEF) domains controls a subset of RpfG-regulated virulence functions. RpfG interactions were abolished by alanine substitutions of the three residues of the conserved GYP motif in the HD-GYP domain. Changing the GYP motif or deletion of the two GGDEF-domain proteins reduced Xcc motility but not the synthesis of extracellular enzymes or biofilm formation. RpfG-GGDEF interactions are dynamic and depend on DSF signaling, being reduced in the rpfF mutant but restored by DSF addition. The results are consistent with a model in which DSF signal transduction controlling motility depends on a highly regulated, dynamic interaction of proteins that influence the localized expression of cyclic di-GMP.

Energy-dependent point interaction: Self-adjointness

Recently, we constructed an energy-dependent point interaction (EDPI) in its most general form in one-dimensional quantum mechanics. In this paper, we show that stationary solutions of the Schrodinger equation with the EDPI form a complete set. Then any nonstationary solution of the time-dependent Schrodinger equation can be expressed as a linear combination of stationary solutions. This, however, does not necessarily mean that the EDPI is self-adjoint and the time-development of the nonstationary state is unitary. The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another. We illustrate situations in which this orthogonality condition is not satisfied.

Many-body system with a four-parameter family of point interactions in one dimension

We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual delta-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the delta-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is nor satisfied except when the four-parameter family is essentially reduced to the delta-function potential.

PT-invariant point interactions in one dimension

By using Wu and Yu's pseudo-potential, we construct point interactions in one dimension that are complex but conform to space-time reflection (PT) invariance. The resulting point interactions are equivalent to those obtained by Albeverio, Fei and Kurasov as self-adjoint extensions of the kinetic energy operator.

Time-reversal aspect of the point interactions in one-dimensional quantum mechanics

It is known that there is a four-parameter family of point interactions in one-dimensional quantum mechanics. We point out that, as far as physics is concerned, it is sufficient to use three of the four parameters. The fourth parameter is redundant. The apparent violation of time-reversal invariance in the presence of the fourth parameter is an artifact.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Hyperhoneycomb Iridate β-li_{2}iro_{3} As A Platform For Kitaev Magnetism.

A complex iridium oxide β-Li_{2}IrO_{3} crystallizes in a hyperhoneycomb structure, a three-dimensional analogue of honeycomb lattice, and is found to be a spin-orbital Mott insulator with J_{eff}=1/2 moment. Ir ions are connected to the three neighboring Ir ions via Ir-O_{2}-Ir bonding planes, which very likely gives rise to bond-dependent ferromagnetic interactions between the J_{eff}=1/2 moments, an essential ingredient of Kitaev model with a spin liquid ground state. Dominant ferromagnetic interaction between J_{eff}=1/2 moments is indeed confirmed by the temperature dependence of magnetic susceptibility χ(T) which shows a positive Curie-Weiss temperature θ_{CW}∼+40  K. A magnetic ordering with a very small entropy change, likely associated with a noncollinear arrangement of J_{eff}=1/2 moments, is observed at T_{c}=38  K. With the application of magnetic field to the ordered state, a large moment of more than 0.35  μ_{B}/Ir is induced above 3 T, a substantially polarized J_{eff}=1/2 state. We argue that the close proximity to ferromagnetism and the presence of large fluctuations evidence that the ground state of hyperhoneycomb β-Li_{2}IrO_{3} is located in close proximity of a Kitaev spin liquid.

Differential expression of E-cadherin gene in human neuroepithelial tumors

Cadherins are cell-to-cell adhesion molecules that play an important role in the establishment of adherent-type junctions by mediating calcium-dependent cellular interactions. The CDH1 gene encodes the transmembrane glycoprotein E-cadherin which is important in maintaining homophilic cell-cell adhesion in epithelial tissues. E-cadherin interacts with catenin proteins to maintain tissue architecture. Structural defects or loss of expression of E-cadherin have been reported as a common feature in several human cancer types. This study aimed to evaluate the expression of E-cadherin and their correlation with clinical features in microdissected brain tumor samples from 81 patients, divided into 62 astrocytic tumors grades I to IV and 19 medulloblastomas, and from 5 white matter non-neoplasic brain tissue samples. E-cadherin (CDH1) gene expression was analyzed by quantitative real-time polymerase chain reaction. Mann-Whitney, Kruskal-Wallis, Kaplan-Meir, and log-rank tests were performed for statistical analyses. We observed a decrease in expression among pathological grades of neuroepithelial tumors. Non-neoplasic brain tissue showed a higher expression level of CDH1 gene than did neuroepithelial tumors. Expression of E-cadherin gene was higher in astrocytic than embryonal tumors (P = 0.0168). Low-grade malignancy astrocytomas (grades I-II) showed higher CDH1 expression than did high-grade malignancy astrocytomas (grades III-IV) and medulloblastomas (P < 0.0001). Non-neoplasic brain tissue showed a higher expression level of CDH1 gene than grade I malignancy astrocytomas, considered as benign tumors (P = 0.0473). These results suggest that a decrease in E-cadherin gene expression level in high-grade neuroepithelial tumors may be a hallmark of malignancy in dedifferentiated tumors and that it may be possibly correlated with their progression and dissemination.

Crystallization and preliminary X-ray diffraction studies of FHA domains of Dun1 and Rad53 protein kinases

Forkhead-associated (FHA) domains are modular protein–protein interaction domains of ~130 amino acids present in numerous signalling proteins. FHA-domain-dependent protein interactions are regulated by phosphorylation of target proteins and FHA domains may be multifunctional phosphopeptide-recognition modules. FHA domains of the budding yeast cell-cycle checkpoint protein kinases Dun1p and Rad53p have been crystallized. Crystals of the Dun1-FHA domain exhibit the symmetry of the space group P6122 or P6522, with unit-cell parameters a = b = 127.3, c = 386.3 Å; diffraction data have been collected to 3.1 Å resolution on a synchrotron source. Crystals of the N-terminal FHA domain (FHA1) of Rad53p diffract to 4.0 Å resolution on a laboratory X-ray source and have Laue-group symmetry 4/mmm, with unit-cell parameters a = b = 61.7, c = 104.3 Å.

CD28/CTLA4-B7 interaction is dispensable for T cell stimulation by mouse mammary tumor virus superantigen but not for B cell differentiation and virus dissemination.

B cells are the primary targets of infection for mouse mammary tumor virus (MMTV). However, for productive retroviral infection, T cell stimulation through the virally-encoded superantigen (SAG) is necessary. It activates B cells and leads to cell division and differentiation. To characterize the role of B cell differentiation for the MMTV life cycle, we studied the course of infection in transgenic mice deficient for CD28/CTLA4-B7 interactions (mCTLA4-H gamma 1 transgenic mice). B cell infection occurred in CTLA4-H gamma 1 transgenic mice as integrated proviral DNA could be detected in draining lymph node cells early after infection by polymerase chain reaction analysis. In mice expressing I-E, B cells were able to present the viral SAG efficiently to V beta 6+ T cells. These cells expanded specifically and were triggered to express the activation marker CD69. Further stages of progression of infection appeared to be defective. Kinetics experiments indicated that T and B cell stimulation stopped more rapidly than in control mice. B cells acquired an activated CD69+ phenotype, were induced to produce IgM but only partially switched to IgG secretion. Finally, the dissemination of infected cells to other lymph nodes and spleen was reduced and the peripheral deletion of V beta 6+ T cells was minimal. In contrast, in mice lacking I-E, T cell stimulation was also impaired and B cell activation undetectable. These data implicate B7-dependent cellular interactions for superantigenic T cell stimulation by low-affinity TCR ligands and suggest a role of B cell differentiation in viral dissemination and peripheral T cell deletion.

TCR-MHC class II interaction is required for peripheral expansion of CD4 cells in a T cell-deficient host.

It is well established that T cell-deficient nude and SCID mice can be reconstituted by i.v. injection of small numbers of purified peripheral CD4+ T cells; however, the requirements for expansion of the transferred T cells in such systems are not clear. We show here that blood and lymphoid organs of MHC class II-deficient mice (which selectively lack mature CD4+ T cells) cannot be reconstituted by transfer of purified splenic CD4+ T cells, whereas TCRalpha-deficient mice (which lack both CD4+ and CD8+ mature T cells) are readily reconstituted. The failure of CD4+ T cell reconstitution in MHC class II-deficient mice was not due to the presence of CD8+ T cells, since similar results were obtained in TCRalpha-MHC class II double-deficient mice. Consistent with most previous studies CD4+ T cells in reconstituted TCRalpha-deficient mice had a diverse TCR Vbeta repertoire and were predominantly of an activated/memory (CD44high) phenotype. Collectively our data demonstrate that the expansion of peripheral CD4+ T cells in a T cell-deficient host is dependent upon interactions of the TCR with MHC class II.

Dimensions and dynamics in integrin function

Integrins play crucial roles in cell adhesion, migration, and signaling by providing transmembrane links between the extracellular matrix and the cytoskeleton. Integrins cluster in macromolecular complexes to generate cell-matrix adhesions such as focal adhesions. In this mini-review, we compare certain integrin-based biological responses and signaling during cell interactions with standard 2D cell culture versus 3D matrices. Besides responding to the composition of the matrix, cells sense and react to physical properties that include three-dimensionality and rigidity. In routine cell culture, fibroblasts and mesenchymal cells appear to use focal adhesions as anchors. They then use intracellular actomyosin contractility and dynamic, directional integrin movements to stretch cell-surface fibronectin and to generate characteristic long fibrils of fibronectin in "fibrillar adhesions". Some cells in culture proceed to produce dense, three-dimensional matrices similar to in vivo matrix, as opposed to the flat, rigid, two-dimensional surfaces habitually used for cell culture. Cells within such more natural 3D matrices form a distinctive class of adhesion termed "3D-matrix adhesions". These 3D adhesions show distinctive morphology and molecular composition. Their formation is heavily dependent on interactions between integrin alpha5ß1 and fibronectin. Cells adhere much more rapidly to 3D matrices. They also show more rapid morphological changes, migration, and proliferation compared to most 2D matrices or 3D collagen gels. Particularly notable are low levels of tyrosine phosphorylation of focal adhesion kinase and moderate increases in activated mitogen-activated protein kinase. These findings underscore the importance of the dimensionality and dynamics of matrix substrates in cellular responses to the extracellular matrix.