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In my doctoral thesis, I present new information about the developmental expression pattern of the potassium chloride cotransporter KCC2 in the rat auditory brain stem and the morphometrical effects caused by KCC2 gene silencing in mice. The thesis is divided into 3 Chapters. Chapter 1 is a general introduction which gives a brief outline of the primary ascending auditory pathway in mammals. Also, it provides information about the presence of a large number of inhibitory inputs in the auditory system and how these inputs develop; the involvement of inhibition in the acoustic processing is mentioned. In addition, the role of the KCC2 cotransporter in the shift of GABA/glycine transmission, and thus, in maintaining the normal level of inhibition in the mature brain, is described. The focus of Chapter 2 was to investigate the KCC2 immunofluorescent signal from postnatal day (P) 0 to P60 in four major nuclei of the rats superior olivary complex (SOC), namely the medial nucleus of the trapezoid body (MNTB), the medial superior olive (MSO), the lateral superior olive (LSO), and the superior paraolivary nucleus (SPN). The lack of a correlation between the continuous presence of KCC2 mRNA/protein in the postnatal rat brain stem on one side, and the shift in GABA/glycinergic polarity (i.e. KCC2 functionality) on the other side, prompted me to search for a specific cellular expression pattern of the KCC2 protein that might correlate with the switch in GABA/glycine signalling. To do so, the KCC2 immunoreactivity was analysed using high-resolution confocal microscopy in three cellular regions of interest: the soma surface, the soma interior, and the neuropil. In the soma surface, I observed an increase of the KCC2 immunofluorescent signal intensity, yet with a moderate magnitude (1.1 to 1.6-fold). Therefore, I conclude that the change in the soma surface signal is only of minor importance and does not explain the change in KCC2 functionality. The KCC2 signal intensity in the soma interior decreased in all nuclei (1.4 to 2-fold) with the exception of the MNTB where no statistically significant change was found. The decrease in the soma interior was probably related to the increase in the soma surface immunoreactivity and the proposed (weak) intracellular trafficking process of the KCC2 protein. The main developmental reorganization (in qualitative as well as in quantitative aspects) of the KCC2 immunofluorescence in the SOC nuclei was observed in the neuropil. The signal changed its pattern from a diffusely stained neuropil early in development (P0-P4) to a crisp and membrane-confined signal later on (P8-P60), with single dendrites becoming apparent. The exception was found in the MNTB, where the neuropil became almost unlabeled. Quantification revealed a statistically significant decrease (2.2 to 3.8-fold) in the neuropil immunoreactivity in all four nuclei, although the remaining KCC2-stained dendrites became thicker and the signal became stronger. I suppose that, at least in part, the neuropil reorganization can be explained by an age-related reduction of dendritic branches via a pruning mechanism and with the absence of an abnormal Cl- load via extrasynaptic GABAA receptors. This is consistent with the proposed additional role of KCC2, namely to maintain the cellular ionic homeostasis and to prevent dendritic swelling (Gulyás et al., 2001). In conclusion, neither the increase in the KCC2 soma surface signal intensity, nor the reorganization in the neuropil can be strictly related to the developmental switch in the GABA/glycine polarity and the onset of KCC2 function, although some correlation (the appearance of a specific membrane-confined dendritic pattern) between structure and function was found. Further implication of different molecular methods, regarding the proposed posttranslational modification of KCC2, will shed light upon the question of what leads to the functional activation of the cotransporter. In Chapter 3, the advantage of loss-of-function KCC2 mice made it possible, via manipulating the duration of the depolarizing phase of GABA/glycine transmission, to analyse the effect of disturbed Cl- regulation and, thus, the effect of disrupted GABA/glycine neurotransmission (lack of inhibition). I asked the following question: how important is the Cl- homeostasis to maintain general aspects (brain weight) and specific aspects (nucleus volume, neuron number, and soma cross-sectional area) of brain development? Brain stem slices from KCC2 knock-out animals (-/-), with a trace amount of transporter (~5%), as well as from wild type animals (+/+) at P3 and P12 were stained for Nissl substance and the analyses were performed with the help of basic morphometrical and stereological methods. In KCC2 (-/-) animals, body growth impairment was observed, in part related to the seizure activity preventing normal feeding (Woo et al., 2002). However, their brains, in terms of brain weight, were less affected. Therefore, I conclude that Cl- homeostasis is not essential per se to maintain the brain weight. Four auditory nuclei (MNTB, MSO, LSO, and ventral cochlear nucleus (VCN)), were compared with respect to the KCC2 null mutation. The SOC nuclei were not influenced by the lack of KCC2 at P3 considering the morphometric parameters. A difference in the number of neurons occurred in the VCN at P3. I suggest to perform additional immunohistochemical studies of glial presence related to its involvement in the structural and functional support of the neurons and their survival. At P12, the volume of the auditory nuclei in KCC2 (-/-) animals was smaller than in (+/+) animals. However, this is likely to be an epiphenomenon since the brain weight increase was also impaired with the same magnitude. Therefore, I suppose that the Cl- homeostasis is not crucial for the nucleus volume increase in the VCN, the MNTB and the MSO during development. An exception was found for the LSO. Regarding the other morphometric parameters at P12, the four nuclei behaved in a different way: (1) in the VCN, after P3, no parameter underwent a disproportional change due to impaired Cl- homeostasis; (2) the MNTB and the LSO showed less pronounced neuropil in mutants in comparison to age-matched controls and two reasons were proposed: first, the depolarizing GABA/glycine transmission in mutants may contribute to excessive Ca2+ load, excitotoxicity and dendrite damage; second, a decrease of some trophic factors may prevent dendrite development in addition to impaired normal body growth; (3) the MSO neurons in P12 (-/-) animals had smaller soma cross-sectional area than in P12 (+/+) animals. I conclude that the normal Cl- homeostasis is required in the MSO at older ages (P12) to achieve and maintain a proper soma size; (4) the lack of KCC2 did not prevent the process of neuronal differentiation in the VCN and the MNTB during development in both mutant and control animals. In conclusion, the various auditory nuclei have to be discussed independently regarding the influence of Cl- homeostasis on some morphometric parameters. Presumably, this is related to the different time of the shift in the GABA/glycine polarity i.e., the onset of KCC2 function (Srinivasan et al., 2004a). Taken together, my thesis accumulated data about the immunohistological expression pattern of KCC2 in various auditory brain stem nuclei and the influence of impaired Cl- homeostasis on some morphometric features in these nuclei. This information will be helpful for further investigations involved to discover the mechanisms and the events that govern the inhibition and the inhibitory pathway in the central auditory system.
In this thesis we propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field over a given constant field of odd characteristic as well as over its algebraic extensions. Beside theoretical applications, knowing the automorphism group also is useful in cryptography: The Jacobians of hyperelliptic curves have been suggested by Koblitz as groups for cryptographic purposes, because the discrete logarithm is believed to be hard in this kind of groups. In order to obtain "secure" Jacobians, it is necessary to prevent attacks like Pohlig/Hellman's and Duursma/Gaudry/Morain's. The latter is only feasible, if the corresponding function field has an automorphism of large order. According to a theorem by Madan, automorphisms seem to allow the Pohlig/Hellman attack, too. Hence, the function field of a secure Jacobian will most likely have trivial automorphism group. In other words: Computing the automorphism group of a hyperelliptic function field promises to be a quick test for insecure Jacobians. Let us outline our algorithm for computing the automorphism group Aut(F/k) of a hyperelliptic function field F/k. It is well known that Aut(F/k) is finite. For each possible subgroup U of Aut(F/k), Rolf Brandt has given a normal form for F if k is algebraically closed. Hence our problem reduces to deciding, whether a given hyperelliptic function field F=k(x,y), y^2=D_x has a defining equation of the form given by Brandt. This question can be answered using theorem III.18: We have F=k(t,u), u^2=D_t iff x is a fraction of linear polynomials in t and y=pu, where the factor p is a rational function w.r.t. t which can be determined explicitly from the coefficients of x. This condition can be checked efficiently using Gröbner basis techniques. With additional effort, it is also possible to compute Aut(F/k) if k is not algebraically closed. Investigating a huge number of examples one gets the impression that the above motivation of getting a quick test for insecure Jacobians is partially fulfilled: The computation of automorphism groups is quite fast using the suggested algorithm. Furthermore, fields with nontrivial automorphism groups seem to have insecure Jacobians. Only fields of small characteristic seem to have a reasonable chance of having nontrivial automorphisms. Hence, from a cryptographic point of view, computing Aut(F/k) seems to make sense whenever k has small characteristic.
In this thesis, the enhanced Galerkin (eG) finite element method in time is presented. The eG method leads to higher order accurate energy and momentum conserving time integrators for the underlying finite-dimensional Hamiltonian systems. This thesis is concerned with particle dynamics and semi-discrete nonlinear elastodynamics. The conservation is generally related to the collocation property of the eG method. The momentum conservation renders the Gaussian quadrature and the energy conservation is obtained by using a new projection technique. An objective time discretisation of the used strain measures avoids artificial strains for large superimposed rigid body motions. The numerical examples show the well long term performance in the presence of stiffness as well as for calculating large-strain motions.
In this thesis we show that the theory of algebraic correspondences introduced by Deuring in the 1930s can be applied to construct non-trivial homomorphisms between the Jacobi groups of hyperelliptic function fields. Concretely, we deduce algorithms to add and multiply correspondences which perform in a reasonable time if the degrees of the associated divisors of the double field are small. Moreover, we show how to compute the differential matrices associated to prime divisors of the double field for arbitrary genus. These matrices give a representation for the homomorphisms or endomorphisms in the additive group (ring) of matrices which is even faithful if the ground field has characteristic zero. As first examples for non-trivial correspondences we investigate multiplication by m endomorphisms. Afterwards we use factorisations of certain bivariate polynomials to construct prime divisors of the double field that are not equivalent to 0 in a coarser sense. Applying the theory of Deuring, these divisors yield homomorphisms between the Jacobi groups of special classes of hyperelliptic function fields. Finally, we generalise the Richelot isogeny to higher genus and by this way derive a class of hyperelliptic function fields given in terms of their defining polynomials which admit non-trivial homomorphisms. These include homomorphisms between the Jacobi groups of hyperelliptic curves of different as well as of equal genus. In addition we provide an explicit method to construct genus 2 function fields the endomorphism ring of which contains a sqrt(2) multiplication with the help of the Cholesky decomposition of a certain matrix.
Compared to our current knowledge of neuronal excitation, little is known about the development and maturation of inhibitory circuits. Recent studies show that inhibitory circuits develop and mature in a similar way like excitatory circuit. One such similarity is the development through excitation, irrespective of its inhibitory nature. Here in this current study, I used the inhibitory projection between the medial nucleus of the trapezoid body (MNTB) and the lateral superior olive (LSO) as a model system to unravel some aspects of the development of inhibitory synapses. In LSO neurons of the rat auditory brainstem, glycine receptor-mediated responses change from depolarizing to hyperpolarizing during the first two postnatal weeks (Kandler and Friauf 1995, J. Neurosci. 15:6890-6904). The depolarizing effect of glycine is due to a high intracellular chloride concentration ([Cl-]i), which induces a reversal potential of glycine (EGly) more positive than the resting membrane potential (Vrest). In older LSO neurons, the hyperpolarizing effect is due to a low [Cl-]i (Ehrlich et al., 1999, J. Physiol. 520:121-137). Aim of the present study was to elucidate the molecular mechanism behind Clhomeostasis in LSO neurons which determines polarity of glycine response. To do so, the role and developmental expression of Cl-cotransporters, such as NKCC1 and KCC2 were investigated. Molecular biological and gramicidin perforated patchclamp experiments revealed, the role of KCC2 as an outward Cl-cotransporter in mature LSO neurons (Balakrishnan et al., 2003, J Neurosci. 23:4134-4145). But, NKCC1 does not appear to be involved in accumulating chloride in immature LSO neurons. Further experiments, indicated the role of GABA and glycine transporters (GAT1 and GLYT2) in accumulating Cl- in immature LSO neurons. Finally, the experiments with hypothyroid animals suggest the possible role of thyroid hormone in the maturation of inhibitory synapse. Altogether, this thesis addressed the molecular mechanism underlying the Cl- regulation in LSO neurons and deciphered it to some extent.
The polydispersive nature of the turbulent droplet swarm in agitated liquid-liquid contacting equipment makes its mathematical modelling and the solution methodologies a rather sophisticated process. This polydispersion could be modelled as a population of droplets randomly distributed with respect to some internal properties at a specific location in space using the population balance equation as a mathematical tool. However, the analytical solution of such a mathematical model is hardly to obtain except for particular idealized cases, and hence numerical solutions are resorted to in general. This is due to the inherent nonlinearities in the convective and diffusive terms as well as the appearance of many integrals in the source term. In this work two conservative discretization methodologies for both internal (droplet state) and external (spatial) coordinates are extended and efficiently implemented to solve the population balance equation (PBE) describing the hydrodynamics of liquid-liquid contacting equipment. The internal coordinate conservative discretization techniques of Kumar and Ramkrishna (1996a, b) originally developed for the solution of PBE in simple batch systems are extended to continuous flow systems and validated against analytical solutions as well as published experimental droplet interaction functions and hydrodynamic data. In addition to these methodologies, we presented a conservative discretization approach for droplet breakage in batch and continuous flow systems, where it is found to have identical convergence characteristics when compared to the method of Kumar and Ramkrishna (1996a). Apart from the specific discretization schemes, the numerical solution of droplet population balance equations by discretization is known to suffer from inherent finite domain errors (FDE). Two approaches that minimize the total FDE during the solution of the discrete PBEs using an approximate optimal moving (for batch) and fixed (for continuous systems) grids are introduced (Attarakih, Bart & Faqir, 2003a). As a result, significant improvements are achieved in predicting the number densities, zero and first moments of the population. For spatially distributed populations (such as extraction columns) the resulting system of partial differential equations is spatially discretized in conservative form using a simplified first order upwind scheme as well as first and second order nonoscillatory central differencing schemes (Kurganov & Tadmor, 2000). This spatial discretization avoids the characteristic decomposition of the convective flux based on the approximate Riemann Solvers and the operator splitting technique required by classical upwind schemes (Karlsen et al., 2001). The time variable is discretized using an implicit strongly stable approach that is formulated by careful lagging of the nonlinear parts of the convective and source terms. The present algorithms are tested against analytical solutions of the simplified PBE through many case studies. In all these case studies the discrete models converges successfully to the available analytical solutions and to solutions on relatively fine grids when the analytical solution is not available. This is accomplished by deriving five analytical solutions of the PBE in continuous stirred tank and liquid-liquid extraction column for especial cases of breakage and coalescence functions. As an especial case, these algorithms are implemented via a windows computer code called LLECMOD (Liquid-Liquid Extraction Column Module) to simulate the hydrodynamics of general liquid-liquid extraction columns (LLEC). The user input dialog makes the LLECMOD a user-friendly program that enables the user to select grids, column dimensions, flow rates, velocity models, simulation parameters, dispersed and continuous phases chemical components, and droplet phase space-time solvers. The graphical output within the windows environment adds to the program a distinctive feature and makes it very easy to examine and interpret the results very quickly. Moreover, the dynamic model of the dispersed phase is carefully treated to correctly predict the oscillatory behavior of the LLEC hold up. In this context, a continuous velocity model corresponding to the manipulation of the inlet continuous flow rate through the control of the dispersed phase level is derived to get rid of this behavior.
Herbivory is discussed as a key agent in maintaining dynamics and stability of tropical forested ecosystems. Accordingly increasing attention has been paid to the factors that structure tropical herbivore communities. The aim of this study was (1) to describe diversity, density, distribution and host range of the phasmid community (Phasmatodea) of a moist neotropical forest in Panamá, and (2) to experimentally assess bottom-up and top-down factors that may regulate populations of the phasmid Metriophasma diocles. The phasmid community of Barro Colorado Island was poor in species and low in density. Phasmids mainly occurred along forest edges and restricted host ranges of phasmid species reflected the successional status of their host plants. Only M. diocles that fed on early and late successional plants occurred regularly in the forest understory. A long generation time with a comparably low fecundity converted into a low biotic potential of M. diocles. However, modeled potential population density increased exponentially and exceeded the realized densities of this species already after one generation indicating that control factors continuously affect M. diocles natural populations. Egg hatching failure decreased potential population growth by 10 % but was of no marked effect at larger temporal scale. Interspecific differences in defensive physical and chemical leaf traits of M. diocles host plants, amongst them leaf toughness the supposedly most effective anti-herbivore defense, seemed not to affect adult female preference and nymph performance. Alternatively to these defenses, I suggest that the pattern of differential preference and performance may be based on interspecific differences in qualitative toxic compounds or in nutritive quality of leaves. The significant rejection of leaf tissue with a low artificial increase of natural phenol contents by nymphs indicated a qualitative defensive pathway in Piper evolution. In M. diocles, oviposition may not be linked to nymph performance, because the evolutionary prediction of a relation between female adult preference and nymph performance was missing. Consequently, the recruitment of nymphs into the reproductive adult phase may be crucially affected by differential performance of nymphs. Neonate M. diocles nymphs suffered strong predation pressure when exposed to natural levels of predation. Concluding from significantly increased predation-related mortality at night, I argue that arthropods may be the main predators of this nocturnal herbivore. Migratory behavior of nymphs seemed not to reflect predation avoidance. Instead, I provided first evidence that host plant quality may trigger off-plant migration. In conclusion, I suggest that predation pressure with its direct effects on nymph survival may be a stronger factor regulating M. diocles populations, compared to direct and indirect effects of host plant quality, particularly because slow growth and off-host migration both may feed back into an increase of predation related mortality.
In this dissertation we consider complex, projective hypersurfaces with many isolated singularities. The leading questions concern the maximal number of prescribed singularities of such hypersurfaces in a given linear system, and geometric properties of the equisingular stratum. In the first part a systematic introduction to the theory of equianalytic families of hypersurfaces is given. Furthermore, the patchworking method for constructing hypersurfaces with singularities of prescribed types is described. In the second part we present new existence results for hypersurfaces with many singularities. Using the patchworking method, we show asymptotically proper results for hypersurfaces in P^n with singularities of corank less than two. In the case of simple singularities, the results are even asymptotically optimal. These statements improve all previous general existence results for hypersurfaces with these singularities. Moreover, the results are also transferred to hypersurfaces defined over the real numbers. The last part of the dissertation deals with the Castelnuovo function for studying the cohomology of ideal sheaves of zero-dimensional schemes. Parts of the theory of this function for schemes in P^2 are generalized to the case of schemes on general surfaces in P^3. As an application we show an H^1-vanishing theorem for such schemes.
In the present work, various aspects of the mixed continuum-atomistic modelling of materials are studied, most of which are related to the problems arising due to a development of microstructures during the transition from an elastic to plastic description within the framework of continuum-atomistics. By virtue of the so-called Cauchy-Born hypothesis, which is an essential part of the continuum-atomistics, a localization criterion has been derived in terms of the loss of infinitesimal rank-one convexity of the strain energy density. According to this criterion, a numerical yield condition has been computed for two different interatomic energy functions. Therewith, the range of the Cauchy-Born rule validity has been defined, since the strain energy density remains quasiconvex only within the computed yield surface. To provide a possibility to continue the simulation of material response after the loss of quasiconvexity, a relaxation procedure proposed by Tadmor et al. leading necessarily to the development of microstructures has been used. Thereby, various notions of convexity have been overviewed in details. Alternatively to the above mentioned criterion, a stability criterion has been applied to detect the critical deformation. For the study in the postcritical region, the path-change procedure proposed by Wagner and Wriggers has been adapted for the continuum-atomistic and modified. To capture the deformation inhomogeneity arising due to the relaxation, the Cauchy-Born hypothesis has been extended by assumption that it represents only the 1st term in the Taylor's series expansion of the deformation map. The introduction of the 2nd, quadratic term results in the higher-order materials theory. Based on a simple computational example, the relevance of this theory in the postcritical region has been shown. For all simulations including the finite element examples, the development tool MATLAB 6.5 has been used.
Characterization of neuronal activity in the auditory brainstem of rats: An optical imaging approach
(2004)
In this doctoral thesis, several aspects of neuronal activity in the rat superior olivary complex (SOC), an auditory brainstem structure, were analyzed using optical imaging with voltage-sensitive dyes (VSD). The thesis is divided into 5 Chapters. Chapter 1 is a general introduction, which gives an overview of the auditory brainstem and VSD imaging. In Chapter 2, an optical imaging method for the SOC was standardized, using the VSD RH795. To do so, the following factors were optimized: (1) An extracellular potassium concentration of 5 mM is necessary during the incubation and recording to observe synaptically evoked responses in the SOC. (2) Employing different power supplies reduced the noise. (3) Averaging of 10 subsequent trials yielded a better signal-to-noise ratio. (4) RH795 of 100 µM with 50 min prewash was optimal to image SOC slices for more than one hour. (5) Stimulus-evoked optical signals were TTX sensitive, revealing action potential-driven input. (6) Synaptically evoked optical signals were characterized to be composed of pre- and postsynaptic components. (7) Optical signals were well correlated with anatomical structures. Overall, this method allows the comparative measurement of electrical activity of cell ensembles with high spatio-temporal resolution. In Chapter 3, the nature of functional inputs to the lateral superior olive (LSO), the medial superior olive (MSO), and the superior paraolivary nucleus (SPN) were analyzed using the glycine receptor blocker strychnine and the AMPA/kainate receptor blocker CNQX. In the LSO, the known glutamatergic inputs from the ipsilateral, and the glycinergic inputs from the ipsilateral and contralateral sides, were confirmed. Furthermore, a CNQX-sensitive input from the contralateral was identified. In the MSO, the glutamatergic and glycinergic inputs from the ipsilateral and contralateral sides were corroborated. In the SPN, besides the known glycinergic input from the contralateral, I found a glycinergic input from the ipsilateral and I also identified CNQX-sensitive inputs from the contralateral and ipsilateral sides. Together, my results thus corroborate findings obtained with different preparations and methods, and provide additional information on the pharmacological nature of the inputs. In Chapter 4, the development of glycinergic inhibition for the LSO, the MSO, the SPN, and the medial nucleus of the trapezoid body (MNTB) was studied by characterizing the polarity of strychnine-sensitive responses. In the LSO, the high frequency region displayed a shift in the polarity at P4, whereas the low frequency region displayed at P6. In the MSO, both the regions displayed the shift at P5. The SPN displayed a shift in the polarity at E18-20 without any regional differences. The MNTB lacked a shift between P3-10. Together, these results demonstrate a differential timing in the development of glycinergic inhibition in these nuclei. In Chapter 5, the role of the MSO in processing bilateral time differences (t) was investigated. This was done by stimulating ipsilateral and contralateral inputs to the MSO with different t values. In preliminary experiments, the postsynaptic responses showed a differential pattern in the spread of activity upon different t values. This data demonstrates a possible presence of delay lines as proposed by Jeffress in the interaural time difference model of sound localization. In conclusion, this study demonstrates the usage of VSD imaging to analyze the neuronal activity in auditory brainstem slices. Moreover, this study expands the knowledge of the inputs to the SOC, and has identified one glycinergic and three AMPA/kainate glutamatergic novel inputs to the SOC nuclei.