Spatial dynamics of a population with stage-dependent diffusion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Pattern formation for a reaction-diffusion system: Catalytic-dependent diffusion coefficients

[ES]Se considera un modelo de reacción-difusión para dos reactantes en presencia de un tercero, que actúa de catalizador. La escala temporal para el catalizador se compara con la de los reactantes y los coeficientes de difusión dependen solamente de la concentración en el estado de equilibrio del catalizador. Se realizan experimentos para diferentes cinéticas

Detecting and resolving position-dependent temperature effects in real-time quantitative polymerase chain reaction

Real-time quantitative polymerase chain reaction (qPCR) depends on precise temperature control of the sample during cycling. In the current study, we investigated how temperature variation in plate-based qPCR instruments influences qPCR results. Temperature variation was measured by amplicon melting analysis as a convenient means to assess well-to-well differences. Multiple technical replicates of several SYBR Green I-based qPCR assays allowed correlation of relative well temperature to quantification cycle. We found that inadequate template denaturation results in an inverse correlation and requires increasing the denaturation temperature, adding a DNA destabilizing agent, or pretreating with a restriction enzyme. In contrast, inadequate primer annealing results in a direct correlation and requires lowering the annealing temperature. Significant correlations were found in 18 of 25 assays. The critical nature of temperature-dependent effects was shown in a blinded study of 29 patients for the diagnosis of Prader-Willy and Angelman syndromes, where eight diagnoses were incorrect unless temperature-dependent effects were controlled. A method to detect temperature-dependent effects by pairwise comparisons of replicates in routine experiments is presented and applied. Systematic temperature errors in qPCR instruments can be recognized and their effects eliminated when high precision is required in quantitative genetic diagnostics and critical complementary DNA analyses.

Position-dependent effects on stability in tricyclo-DNA modified oligonucleotide duplexes

A series of oligodeoxyribonucleotides and oligoribonucleotides containing single and multiple tricyclo(tc)-nucleosides in various arrangements were prepared and the thermal and thermodynamic transition profiles of duplexes with complementary DNA and RNA evaluated. Tc-residues aligned in a non-continuous fashion in an RNA strand significantly decrease affinity to complementary RNA and DNA, mostly as a consequence of a loss of pairing enthalpy DeltaH. Arranging the tc-residues in a continuous fashion rescues T(m) and leads to higher DNA and RNA affinity. Substitution of oligodeoxyribonucleotides in the same way causes much less differences in T(m) when paired to complementary DNA and leads to substantial increases in T(m) when paired to complementary RNA. CD-spectroscopic investigations in combination with molecular dynamics simulations of duplexes with single modifications show that tc-residues in the RNA backbone distinctly influence the conformation of the neighboring nucleotides forcing them into higher energy conformations, while tc-residues in the DNA backbone seem to have negligible influence on the nearest neighbor conformations. These results rationalize the observed affinity differences and are of relevance for the design of tc-DNA containing oligonucleotides for applications in antisense or RNAi therapy.

Position-dependent activity of α-fetoprotein enhancer element III in the adult liver is due to negative regulation

α-Fetoprotein (AFP) transcription is activated early in hepatogenesis, but is dramatically repressed within several weeks after birth. AFP regulation is governed by multiple elements including three enhancers termed EI, EII, and EIII. All three AFP enhancers continue to be active in the adult liver, where EI and EII exhibit high levels of activity in pericentral hepatocytes with a gradual reduction in activity in a pericentral-periportal direction. In contrast to these two enhancers, EIII activity is highly restricted to a layer of cells surrounding the central veins. To test models that could account for position-dependent EIII activity in the adult liver, we have analyzed transgenes in which AFP enhancers EII and EIII were linked together. Our results indicate that the activity of EIII is dominant over that of EII, indicating that EIII is a potent negative regulatory element in all hepatocytes except those encircling the central veins. We have localized this negative activity to a 340-bp fragment. This suggests that enhancer III may be involved in postnatal AFP repression.

A Common Position-Dependent Mechanism Controls Cell-Type Patterning and GLABRA2 Regulation in the Root and Hypocotyl Epidermis of Arabidopsis1

A position-dependent pattern of epidermal cell types is produced during root development in Arabidopsis thaliana. This pattern is reflected in the expression pattern of GLABRA2 (GL2), a homeobox gene that regulates cell differentiation in the root epidermis. GL2 promoter::GUS fusions were used to show that the TTG gene, a regulator of root epidermis development, is necessary for maximal GL2 activity but is not required for the pattern of GL2 expression. Furthermore, GL2-promoter activity is influenced by expression of the myc-like maize R gene (35S::R) in Arabidopsis but is not affected by gl2 mutations. A position-dependent pattern of cell differentiation and GL2-promoter activity was also discovered in the hypocotyl epidermis that was analogous to the pattern in the root. Non-GL2-expressing cell files in the hypocotyl epidermis located outside anticlinal cortical cell walls exhibit reduced cell length and form stomata. Like the root, the hypocotyl GL2 activity was shown to be influenced by ttg and 35S::R but not by gl2. The parallel pattern of cell differentiation in the root and hypocotyl indicates that TTG and GL2 participate in a common position-dependent mechanism to control cell-type patterning throughout the apical-basal axis of the Arabidopsis seedling.

Template-nucleated alanine-lysine helices are stabilized by position-dependent interactions between the lysine side chain and the helix barrel.

The helicity in water has been determined for several series of alanine-rich peptides that contain single lysine residues and that are N-terminally linked to a helix-inducing and reporting template termed Ac-Hel1. The helix-propagating constant for alanine (sAla value) that best fits the properties of these peptides lies in the range of 1.01-1.02, close to the value reported by Scheraga and coworkers [Wojcik, J., Altmann, K.-H. & Scheraga, H.A. (1990) Biopolymers 30, 121-134], but significantly lower than the value assigned by Baldwin and coworkers [Chakrabartty, A., Kortemme, T. & Baldwin, R.L. (1994) Protein Sci. 3,843-852]. From a study of conjugates Ac-Hel1-Ala(n)-Lys-Ala(m)-NH2 and analogs in which the methylene portion of the lysine side chain is truncated, we find that the unusual helical stability of Ala(n)Lys peptides is controlled primarily by interactions of the lysine side chain with the helix barrel, and only passively by the alanine matrix. Using 1H NMR spectroscopy, we observe nuclear Overhauser effect crosspeaks consistent with proton-proton contacts expected for these interactions.

Position-dependent variegation of globin transgene expression in mice.

Expression of genes in eukaryotes has commonly been analyzed in a whole tissue, and levels of expression have been interpreted as the result of equivalent rates of transcription in every cell. We have produced transgenic mouse lines that express beta-galactosidase under the control of globin promoters linked to the major tissue-specific regulatory element of the alpha-globin locus, which permits the analysis of transgene expression in individual red blood cells. We find that expression of the transgene within all mouse lines is heterocellular. Individual cells either do not express the transgene at all or express it at a level characteristic of that line. The number of beta-galactosidase-expressing cells varies greatly between different lines of transgenic mice at any defined stage of development, but within a transgenic line, individual mice have strikingly similar numbers of expressing cells. This suggests that the degree of heterocellular expression is determined by the site of integration, as is seen in position-effect variegation.

Novel strategies in feedforward adaptation to a position-dependent perturbation

To investigate the control mechanisms used in adapting to position-dependent forces, subjects performed 150 horizontal reaching movements over 25 cm in the presence of a position-dependent parabolic force field (PF). The PF acted only over the first 10 cm of the movement. On every fifth trial, a virtual mechanical guide (double wall) constrained subjects to move along a straight-line path between the start and target positions. Its purpose was to register lateral force to track formation of an internal model of the force field, and to look for evidence of possible alternative adaptive strategies. The force field produced a force to the right, which initially caused subjects to deviate in that direction. They reacted by producing deviations to the left, into the force field, as early as the second trial. Further adaptation resulted in rapid exponential reduction of kinematic error in the latter portion of the movement, where the greatest perturbation to the handpath was initially observed, whereas there was little modification of the handpath in the region where the PF was active. Significant force directed to counteract the PF was measured on the first guided trial, and was modified during the first half of the learning set. The total force impulse in the region of the PF increased throughout the learning trials, but it always remained less than that produced by the PF. The force profile did not resemble a mirror image of the PF in that it tended to be more trapezoidal than parabolic in shape. As in previous studies of force-field adaptation, we found that changes in muscle activation involved a general increase in the activity of all muscles, which increased arm stiffness, and selectively-greater increases in the activation of muscles which counteracted the PF. With training, activation was exponentially reduced, albeit more slowly than kinematic error. Progressive changes in kinematics and EMG occurred predominantly in the region of the workspace beyond the force field. We suggest that constraints on muscle mechanics limit the ability of the central nervous system to employ an inverse dynamics model to nullify impulse-like forces by generating mirror-image forces. Consequently, subjects adopted a strategy of slightly overcompensating for the first half of the force field, then allowing the force field to push them in the opposite direction. Muscle activity patterns in the region beyond the boundary of the force field were subsequently adjusted because of the relatively-slow response of the second-order mechanics of muscle impedance to the force impulse.

Estimation of concentration-dependent diffusion coefficient in drying process from the space-averaged concentration versus time with experimental data

The estimation of a concentration-dependent diffusion coefficient in a drying process is known as an inverse coefficient problem. The solution is sought wherein the space-average concentration is known as function of time (mass loss monitoring). The problem is stated as the minimization of a functional and gradient-based algorithms are used to solve it. Many numerical and experimental examples that demonstrate the effectiveness of the proposed approach are presented. Thin slab drying was carried out in an isothermal drying chamber built in our laboratory. The diffusion coefficients of fructose obtained with the present method are compared with existing literature results.

Position-dependent spin-orbit coupling for ultracold atoms

We theoretically explore atomic Bose-Einstein condensates (BECs) subject to position-dependent spin-orbit coupling (SOC). This SOC can be produced by cyclically laser coupling four internal atomic ground (or metastable) states in an environment where the detuning from resonance depends on position. The resulting spin-orbit coupled BEC (SOBEC) phase separates into domains, each of which contain density modulations-stripes-aligned either along the x or y direction. In each domain, the stripe orientation is determined by the sign of the local detuning. When these stripes have mismatched spatial periods along domain boundaries, non-trivial topological spin textures form at the interface, including skyrmions-like spin vortices and anti-vortices. In contrast to vortices present in conventional rotating BECs, these spin-vortices are stable topological defects that are not present in the corresponding homogenous stripe-phase SOBECs.

Two-dimensional drift-diffusion simulation of organic solar cells

The aim of this master's thesis is to develop a two-dimensional drift-di usion model, which describes charge transport in organic solar cells. The main bene t of a two-dimensional model compared to a one-dimensional one is the inclusion of the nanoscale morphology of the active layer of a bulk heterojunction solar cell. The developed model was used to study recombination dynamics at the donor-acceptor interface. In some cases, it was possible to determine e ective parameters, which reproduce the results of the two-dimensional model in the one-dimensional case. A summary of the theory of charge transport in semiconductors was presented and discussed in the context of organic materials. Additionally, the normalization and discretization procedures required to nd a numerical solution to the charge transport problem were outlined. The charge transport problem was solved by implementing an iterative scheme called successive over-relaxation. The obtained solution is given as position-dependent electric potential, free charge carrier concentrations and current densities in the active layer. An interfacial layer, separating the pure phases, was introduced in order to describe charge dynamics occurring at the interface between the donor and acceptor. For simplicity, an e ective generation of free charge carriers in the interfacial layer was implemented. The pure phases simply act as transport layers for the photogenerated charges. Langevin recombination was assumed in the two-dimensional model and an analysis of the apparent recombination rate in the one-dimensional case is presented. The recombination rate in a two-dimensional model is seen to e ectively look like reduced Langevin recombination at open circuit. Replicating the J-U curves obtained in the two-dimensional model is, however, not possible by introducing a constant reduction factor in the Langevin recombination rate. The impact of an acceptor domain in the pure donor phase was investigated. Two cases were considered, one where the acceptor domain is isolated and another where it is connected to the bulk of the acceptor. A comparison to the case where no isolated domains exist was done in order to quantify the observed reduction in the photocurrent. The results show that all charges generated at the isolated domain are lost to recombination, but the domain does not have a major impact on charge transport. Trap-assisted recombination at interfacial trap states was investigated, as well as the surface dipole caused by the trapped charges. A theoretical expression for the ideality factor n_id as a function of generation was derived and shown to agree with simulation data. When the theoretical expression was fitted to simulation data, no interface dipole was observed.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.