Fourier-transform rheology on anionically synthesised polymer melts and solutions of various topology

Aim of this thesis was to further extend the applicability of the Fourier-transform (FT) rheology technique especially for non-linear mechanical characterisation of polymeric materials on the one hand and to investigated the influence of the degree of branching on the linear and non-linear relaxation behaviour of polymeric materials on the other hand. The latter was achieved by employing in particular FT-rheology and other rheological techniques to variously branched polymer melts and solutions. For these purposes, narrowly distributed linear and star-shaped polystyrene and polybutadiene homo-polymers with varying molecular weights were anionically synthesised using both high-vacuum and inert atmosphere techniques. Furthermore, differently entangled solutions of linear and star-shaped polystyrenes in di-sec-octyl phthalate (DOP) were prepared. The several linear polystyrene solutions were measured under large amplitude oscillatory shear (LAOS) conditions and the non-linear torque response was analysed in the Fourier space. Experimental results were compared with numerical predictions performed by Dr. B. Debbaut using a multi-mode differential viscoelastic fluid model obeying the Giesekus constitutive equation. Apart from the analysis of the relative intensities of the harmonics, a detailed examination of the phase information content was developed. Further on, FT-rheology allowed to distinguish polystyrene melts and solutions due to their different topologies where other rheological measurements failed. Significant differences occurred under LAOS conditions as particularly reflected in the phase difference of the third harmonic, Ħ3, which could be related to shear thinning and shear thickening behaviour.

Mapping the elastic response of epithelial apical cell membranes suspended across porous array

As the elastic response of cell membranes to mechanical stimuli plays a key role in various cellular processes, novel biophysical strategies to quantify the elasticity of native membranes under physiological conditions at a nanometer scale are gaining interest. In order to investigate the elastic response of apical membranes, elasticity maps of native membrane sheets, isolated from MDCK II (Madine Darby Canine kidney strain II) epithelial cells, were recorded by local indentation with an Atomic Force Microscope (AFM). To exclude the underlying substrate effect on membrane indentation, a highly ordered gold coated porous array with a pore diameter of 1.2 μm was used to support apical membranes. Overlays of fluorescence and AFM images show that intact apical membrane sheets are attached to poly-D-lysine coated porous substrate. Force indentation measurements reveal an extremely soft elastic membrane response if it is indented at the center of the pore in comparison to a hard repulsion on the adjacent rim used to define the exact contact point. A linear dependency of force versus indentation (-dF/dh) up to 100 nm penetration depth enabled us to define an apparent membrane spring constant (kapp) as the slope of a linear fit with a stiffness value of for native apical membrane in PBS. A correlation between fluorescence intensity and kapp is also reported. Time dependent hysteresis observed with native membranes is explained by a viscoelastic solid model of a spring connected to a Kelvin-Voight solid with a time constant of 0.04 s. No hysteresis was reported with chemically fixated membranes. A combined linear and non linear elastic response is suggested to relate the experimental data of force indentation curves to the elastic modulus and the membrane thickness. Membrane bending is the dominant contributor to linear elastic indentation at low loads, whereas stretching is the dominant contributor for non linear elastic response at higher loads. The membrane elastic response was controlled either by stiffening with chemical fixatives or by softening with F-actin disrupters. Overall, the presented setup is ideally suitable to study the interactions of the apical membrane with the underlying cytoskeleton by means of force indentation elasticity maps combined with fluorescence imaging.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Differential cell type-specific transcriptional regulation of the CYP1A1 gene

Cytochrome P450 1A1 (CYP1A1) monooxygenase plays an important role in the metabolism of environmental pollutants such as polycyclic aromatic hydrocarbons (PAHs) and halogenated polycyclic aromatic hydrocarbons (HAHs). Oxidation of these compounds converts them to the metabolites that subsequently can be conjugated to hydrophilic endogenous entities e.g. glutathione. Derivates generated in this way are water soluble and can be excreted in bile or urine, which is a defense mechanism. Besides detoxification, metabolism by CYP1A1 may lead to deleterious effects since the highly reactive intermediate metabolites are able to react with DNA and thus cause mutagenic effects, as it is in the case of benzo(a) pyrene (B[a]P). CYP1A1 is normally not expressed or expressed at a very low level in the cells but it is inducible by many PAHs and HAHs e.g. by B[a]P or 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Transcriptional activation of the CYP1A1 gene is mediated by aryl hydrocarbon receptor (AHR), a basic-helix-loop-helix (bHLH) transcription factor. In the absence of a ligand AHR stays predominantly in the cytoplasm. Ligand binding causes translocation of AHR to the nuclear compartment, its heterodimerization with another bHLH protein, the aryl hydrocarbon nuclear translocator (ARNT) and binding of the AHR/ARNT heterodimer to a DNA motif designated dioxin responsive element (DRE). This process leads to the transcriptional activation of the responsive genes containing DREs in their regulatory regions, e.g. that coding for CYP1A1. TCDD is the most potent known agonist of AHR. Since it is not metabolized by the activated enzymes, exposure to this compound leads to a persisting activation of AHR resulting in diverse toxic effects in the organism. To enlighten the molecular mechanisms that mediate the toxicity of xenobiotics like TCDD and related compounds, the AHR-dependent regulation of the CYP1A1 gene was investigated in two cell lines: human cervix carcinoma (HeLa) and mouse hepatoma (Hepa). Study of AHR activation and its consequence concerning expression of the CYP1A1 enzyme confirmed the TCDD-dependent formation of the AHR/ARNT complex on DRE leading to an increase of the CYP1A1 transcription in Hepa cells. In contrast, in HeLa cells formation of the AHR/ARNT heterodimer and binding of a protein complex containing AHR and ARNT to DRE occurred naturally in the absence of TCDD. Moreover, treatment with TCDD did not affect the AHR/ARNT dimer formation and binding of these proteins to DRE in these cells. Even though the constitutive complex on DRE exists in HeLa, transcription of the CYP1A1 gene was not increased. Furthermore, the CYP1A1 level in HeLa cells remained unchanged in the presence of TCDD suggesting repressional mechanism of the AHR complex function which may hinder the TCDD-dependent mechanisms in these cells. Similar to the native, the mouse CYP1A1-driven reporter constructs containing different regulatory elements were not inducible by TCDD in HeLa cells, which supported a presence of cell type specific trans-acting factor in HeLa cells able to repress both the native CYP1A1 and CYP1A1-driven reporter genes rather than species specific differences between CYP1A1 genes of human and rodent origin. The different regulation of the AHR-mediated transcription of CYP1A1 gene in Hepa and HeLa cells was further explored in order to elucidate two aspects of the AHR function: (I) mechanism involved in the activation of AHR in the absence of exogenous ligand and (II) factor that repress function of the exogenous ligand-independent AHR/ARNT complex. Since preliminary studies revealed that the activation of PKA causes an activation of AHR in Hepa cells in the absence of TCDD, the PKA-dependent signalling pathway was the proposed endogenous mechanism leading to the TCDD-independent activation of AHR in HeLa cells. Activation of PKA by forskolin or db-cAMP as well as inhibition of the kinase by H89 in both HeLa and Hepa cells did not lead to alterations in the AHR interaction with ARNT in the absence of TCDD and had no effect on binding of these proteins to DRE. Moreover, the modulators of PKA did not influence the CYP1A1 activity in these cells in the presence and in the absence of TCDD. Thus, an involvement of PKA in the regulation of the CYP1A1 Gen in HeLa cells was not evaluated in the course of this study. Repression of genes by transcription factors bound to their responsive elements in the absence of ligands has been described for nuclear receptors. These receptors interact with protein complex containing histone deacetylase (HDAC), enzyme responsible for the repressional effect. Thus, a participation of histone deacetylase in the transcriptional modulation of CYP1A1 gene by the constitutively DNA-bound AHR/ARNT complex was supposed. Inhibition of the HDAC activity by trichostatin A (TSA) or sodium butyrate (NaBu) led to an increase of the CYP1A1 transcription in the presence but not in the absence of TCDD in Hepa and HeLa cells. Since amount of the AHR and ARNT proteins remained unchanged upon treatment of the cells with TSA or NaBu, the transcriptional upregulation of CYP1A1 gene was not due to an increased expression of the regulatory proteins. These findings strongly suggest an involvement of HDAC in the repression of the CYP1A1 gene. Similar to the native human CYP1A1 also the mouse CYP1A1-driven reporter gene transfected into HeLa cells was repressed by histone deacetylase since the presence of TSA or NaBu led to an increase in the reporter activity. Induction of reporter gene did not require a presence of the promoter or negative regulatory regions of the CYP1A1 gene. A promoter-distal fragment containing three DREs together with surrounding sequences was sufficient to mediate the effects of the HDAC inhibitors suggesting that the AHR/ARNT binding to its specific DNA recognition site may be important for the CYP1A1 repression. Histone deacetylase is recruited to the specific genes by corepressors, proteins that bind to the transcription factors and interact with other members of the HDAC complex. Western blot analyses revealed a presence of HDAC1 and the corepressors mSin3A (mammalian homolog of yeast Sin3) and SMRT (silencing mediator for retinoid and thyroid hormone receptor) in both cell types, while the corepressor NCoR (nuclear receptor corepressor) was expressed exclusively in HeLa cells. Thus the high inducibility of CYP1A1 in Hepa cells may be due to the absence of NCoR in these cells in contrast to the non-responsive HeLa cells, where the presence of NCoR would support repression of the gene by histone deacetylase. This hypothesis was verified in reporter gene experiments where expression constructs coding for the particular members of the HDAC complex were cotransfected in Hepa cells together with the TCDD-inducible reporter constructs containing the CYP1A1 regulatory sequences. An overexpression of NCoR however did not decrease but instead led to a slight increase of the reporter gene activity in the cells. The expected inhibition was observed solely in the case of SMRT that slightly reduced constitutive and TCDD-induced reporter gene activity. A simultaneous expression of NCoR and SMRT shown no further effects and coexpression of HDAC1 with the two corepressors did not alter this situation. Thus, additional factors that are likely involved in the repression of CYP1A1 gene by HDAC complex remained to be identified. Taking together, characterisation of an exogenous ligand independent AHR/ARNT complex on DRE in HeLa cells that repress transcription of the CYP1A1 gene creates a model system enabling investigation of endogenous processes involved in the regulation of AHR function. This study implicates HDAC-mediated repression of CYP1A1 gene that contributes to the xenobiotic-induced expression in a tissue specific manner. Elucidation of these processes gains an insight into mechanisms leading to deleterious effects of TCDD and related compounds.

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Numerical simulation of some viscoelastic fluids

Numerical simulation of the Oldroyd-B type viscoelastic fluids is a very challenging problem. rnThe well-known High Weissenberg Number Problem" has haunted the mathematicians, computer scientists, and rnengineers for more than 40 years. rnWhen the Weissenberg number, which represents the ratio of elasticity to viscosity, rnexceeds some limits, simulations done by standard methods break down exponentially fast in time. rnHowever, some approaches, such as the logarithm transformation technique can significantly improve rnthe limits of the Weissenberg number until which the simulations stay stable. rnrnWe should point out that the global existence of weak solutions for the Oldroyd-B model is still open. rnLet us note that in the evolution equation of the elastic stress tensor the terms describing diffusive rneffects are typically neglected in the modelling due to their smallness. However, when keeping rnthese diffusive terms in the constitutive law the global existence of weak solutions in two-space dimension rncan been shown. rnrnThis main part of the thesis is devoted to the stability study of the Oldroyd-B viscoelastic model. rnFirstly, we show that the free energy of the diffusive Oldroyd-B model as well as its rnlogarithm transformation are dissipative in time. rnFurther, we have developed free energy dissipative schemes based on the characteristic finite element and finite difference framework. rnIn addition, the global linear stability analysis of the diffusive Oldroyd-B model has also be discussed. rnThe next part of the thesis deals with the error estimates of the combined finite element rnand finite volume discretization of a special Oldroyd-B model which covers the limiting rncase of Weissenberg number going to infinity. Theoretical results are confirmed by a series of numerical rnexperiments, which are presented in the thesis, too.