Tensor density matrix theory for determining population and alignment of symmetric top molecule using rotationally unresolved fluorescence

General expressions used for transforming raw laser-induced fluorescence (LIF) intensity into the population and alignment parameters of a symmetric top molecule are derived by employing the density matrix approach. The molecular population and alignment are described by molecular state multipoles. The results are presented for a general excitation-detection geometry and then applied to some special geometries. In general cases, the LIF intensity is a complex function of the initial molecular state multipoles, the dynamic factors and the excitation-detection geometrical factors. It contains a population and 14 alignment multipoles. How to extract all initial state multipoles from the rotationally unresolved emission LIF intensity is discussed in detail.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Identification and Development of Enzymes Associated With the Sperm Inner Acrosomal Membrane and Their Function during Fertilization

In order for mammalian fertilization to transpire, spermatozoa must transit through the female reproductive tract and penetrate the outer investments of the oocyte: the cumulus oophorus and the zona pellucida. In order to penetrate the oocyte, spermatozoa must undergo the acrosome reaction. The acrosome reaction results in the exposure of the inner acrosomal membrane (IAM) and proteins that coat it to the extracellular environment. After the acrosome reaction, the IAM becomes the leading edge of spermatozoa undergoing progressive movement. Thus the enzymes which effect lysis of the oocyte investments ought to be located on the IAM. An objective of this study was to identify and characterize enzymatic activity detected on the IAM and provide evidence that they play a role in fertilization. This study also describes procedures for fractionating spermatozoa and isolating the IAM and proteins on its intra- and extra-vesicular surfaces, and describes their development during male gametogenesis. Since the IAM is exposed to the extracellular environment and oviductal milieu after the acrosome reaction, this study also sought to characterize interactions and relationships between factors in the oviductal environment and the enzymes identified on the IAM. The data presented provide evidence that MMP2 and acrosin are co-localized on the IAM, originate from the Golgi apparatus in gametogenesis, and suggest they cooperate in their function. Their localization and results of in vitro fertilization suggests they have a function in zona pellucida penetration. The data also provide evidence that plasminogen, originating from the oviductal epithelium and/or cumulus-oocyte complex, is present in the immediate environment of sperm-egg initial contact and penetration. Additionally, plasminogen interacts with MMP2 and enhances its enzymatic action on the IAM. The data also provide evidence that MMP2 has an important function in penetration of the cumulus oophorus. Holistically, this thesis provides evidence that enzymes on the IAM, originating from the Golgi apparatus in development, have an important function in penetration of the outer investments of the oocyte, and are aided in penetration by plasminogen in the female reproductive tract.

The 67 kDa laminin receptor: structure, function and role in disease

The 67LR (67 kDa laminin receptor) is a cell-surface receptor with high affinity for its primary ligand. Its role as a laminin receptor makes it an important molecule both in cell adhesion to the basement membrane and in signalling transduction following this binding event. The protein also plays critical roles in the metastasis of tumour cells. Isolation of the protein from either normal or cancerous cells results in a product with an approx. molecular mass of 67 kDa. This protein is believed to be derived from a smaller precursor, the 37LRP (37 kDa laminin receptor precursor). However, the precise mechanism by which cytoplasmic 37LRP becomes cell-membrane-embedded 67LR is unclear. The process may involve post-translational fatty acylation of the protein combined with either homo- or hetero-dimerization, possibly with a galectin-3-epitope-containing partner. Furthermore, it has become clear that acting as a receptor for laminin is not the only function of this protein. 67LR also acts as a receptor for viruses, such as Sindbis virus and dengue virus, and is involved with internalization of the prion protein. Interestingly, unmodified 37LRP is a ribosomal component and homologues of this protein are found in all five kingdoms. In addition, it appears to be strongly associated with histones in the eukaryotic cell nucleus, although the precise role of these interactions is not clear. Here we review the current understanding of the structure and function of this molecule, as well as highlighting areas requiring further research.

A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Time-dependent R -matrix theory for ultrafast atomic processes

We describe an ab initio nonperturbative time-dependent R-matrix theory for ultrafast atomic processes. This theory enables investigations of the interaction of few-femtosecond and -attosecond pulse lasers with complex multielectron atoms and atomic ions. A derivation and analysis of the basic equations are given, which propagate the atomic wave function in the presence of the laser field forward in time in the internal and external R-matrix regions. To verify the accuracy of the approach, we investigate two-photon ionization of Ne irradiated by an intense laser pulse and compare current results with those obtained using the R-matrix Floquet method and an alternative time-dependent method. We also verify the capability of the current approach by applying it to the study of two-dimensional momentum distributions of electrons ejected from Ne due to irradiation by a sequence of 2 as light pulses in the presence of a 780 nm laser field.

Sequential extracellular matrix-focused and baited-global cluster analysis of serial transcriptomic profiles identifies candidate modulators of renal tubulointerstitial fibrosis in murine adriamycin-induced nephropathy

Transcriptome analysis using microarray technology represents a powerful unbiased approach for delineating pathogenic mechanisms in disease. Here molecular mechanisms of renal tubulointerstitial fibrosis (TIF) were probed by monitoring changes in the renal transcriptome in a glomerular disease-dependent model of TIF ( adriamycin nephropathy) using Affymetrix (mu74av2) microarray coupled with sequential primary biological function-focused and secondary

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Time-dependent R-matrix theory applied to two-photon double ionization of He

We introduce a time-dependent R-matrix theory generalized to describe double-ionization processes. The method is used to investigate two-photon double ionization of He by intense XUV laser radiation. We combine a detailed B-spline-based wave-function description in an extended inner region with a single-electron outer region containing channels representing both single ionization and double ionization. A comparison of wave-function densities for different box sizes demonstrates that the flow between the two regions is described with excellent accuracy. The obtained two-photon double-ionization cross sections are in excellent agreement with other cross sections available. Compared to calculations fully contained within a finite inner region, the present calculations can be propagated over the time it takes the slowest electron to reach the boundary.

Rare and common variants in extracellular matrix gene Fibrillin 2 (FBN2) are associated with macular degeneration

Neurodegenerative diseases affecting the macula constitute a major cause of incurable vision loss and exhibit considerable clinical and genetic heterogeneity, from early-onset monogenic disease to multifactorial late-onset age-related macular degeneration (AMD). As part of our continued efforts to define genetic causes of macular degeneration, we performed whole exome sequencing in four individuals of a two-generation family with autosomal dominant maculopathy and identified a rare variant p.Glu1144Lys in Fibrillin 2 (FBN2), a glycoprotein of the elastin-rich extracellular matrix (ECM). Sanger sequencing validated the segregation of this variant in the complete pedigree, including two additional affected and one unaffected individual. Sequencing of 192 maculopathy patients revealed additional rare variants, predicted to disrupt FBN2 function. We then undertook additional studies to explore the relationship of FBN2 to macular disease. We show that FBN2 localizes to Bruch's membrane and its expression appears to be reduced in aging and AMD eyes, prompting us to examine its relationship with AMD. We detect suggestive association of a common FBN2 non-synonymous variant, rs154001 (p.Val965Ile) with AMD in 10,337 cases and 11,174 controls (OR=1.10; p-value=3.79×10(-5)). Thus, it appears that rare and common variants in a single gene - FBN2 - can contribute to Mendelian and complex forms of macular degeneration. Our studies provide genetic evidence for a key role of elastin microfibers and Bruch's membrane in maintaining blood-retina homeostasis and establish the importance of studying orphan diseases for understanding more common clinical phenotypes.

Attenuation of urokinase activity during experimental ischaemia protects the cerebral barrier from damage through regulation of matrix metalloproteinase-2 and NAD(P)H oxidase

Ischaemic injury impairs the integrity of the blood-brain barrier (BBB). In this study, we investigated the molecular causes of this defect with regard to the putative correlations among NAD(P)H oxidase, plasminogen-plasmin system components, and matrix metalloproteinases. Hence, the activities of NAD(P)H oxidase, matrix metalloproteinase-2, urokinase-type plasminogen activator (uPA), and tissue-type plasminogen activator (tPA), and superoxide anion levels, were assessed in human brain microvascular endothelial cells (HBMECs) exposed to oxygen-glucose deprivation (OGD) alone or OGD followed by reperfusion (OGD + R). The integrity of an in vitro model of BBB comprising HBMECs and astrocytes was studied by measuring transendothelial electrical resistance and the paracellular flux of albumin. OGD with or without reperfusion (OGD ± R) radically perturbed barrier function while concurrently enhancing uPA, tPA and NAD(P)H oxidase activities and superoxide anion release in HBMECs. Pharmacological inactivation of NAD(P)H oxidase attenuated OGD ± R-mediated BBB damage through modulation of matrix metalloproteinase-2 and tPA, but not uPA activity. Overactivation of NAD(P)H oxidase in HBMECs via cDNA electroporation of its p22-phox subunit confirmed the involvement of tPA in oxidase-mediated BBB disruption. Interestingly, blockade of uPA or uPA receptor preserved normal BBB function by neutralizing both NAD(P)H oxidase and matrix metalloproteinase-2 activities. Hence, selective targeting of uPA after ischaemic strokes may protect cerebral barrier integrity and function by concomitantly attenuating basement membrane degradation and oxidative stress.

Classification of incomplete feature vectors by radial basis function networks

The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method uses the fact that any marginal distribution of a Gaussian distribution can be determined from the mean vector and covariance matrix of the joint distribution.

Evolution of the extracellular matrix in deuterostomes and the influence of calcitropic hormones

Tese de dout., Biologia (Biologia Molecular), Faculdade de Ciências e Tecnologia, Univ. do Algarve, 2010

Higher order derivatives and norms of certain matrix functions

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), Universidade de Lisboa, Faculdade de Ciências, 2014