Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

The periplasmic domain of the barrel assembly machinery protein A (BamA) from Escherichia coli assists folding of outer membrane protein A

The assembly of outer membranes of the cell wall of Gram-negative bacteria and of various organelles of eukaryotic cells requires the evolutionarily conserved β-barrel-assembly machinery (BAM) complex. This thesis describes the biochemical and biophysical properties of the periplasmic domain of the β-barrel assembly machinery protein A (PD-BamA) of the E. coli BAM complex, its effect on insertion and folding of the Outer membrane protein A (OmpA) into lipid bilayers and the identification of regions of PD-BamA that may be involved in protein-protein interactions. The secondary structure of PD-BamA in mixed lipid bilayers, analyzed by Circular dichroism (CD) spectroscopy, contained less β-sheet at an increased content of phosphatidylglycerol (PG) in the lipid membrane. This result showed membrane binding, albeit only in the presence of negatively charged lipids. Fluorescence spectroscopy demonstrated that PD-BamA only binds to lipid bilayers containing the negatively charged DOPG, confirming the results of CD spectroscopy. PD-BamA did not bind to zwitterionic but overall neutral lipid bilayers. PD-BamA bound to OmpA at a stoichiometry of 1:1. PD-BamA strongly facilitated insertion and folding of OmpA into lipid membranes. Kinetics of PD-BamA mediated folding of OmpA was well described by two parallel folding processes, a fast folding process and a slow folding process, differing by 2-3 orders of magnitude in their rate constants. The folding yields of OmpA depended on the concentration of lipid membranes and also on the lipid head groups. The presence of PD-BamA resulted in increased folding yields of OmpA in negatively charged DOPG, but PD-BamA did not affect the folding kinetics of OmpA into bilayers of zwitterionic but overall neutral lipids. The efficiency of folding and insertion of OmpA into lipid bilayers strongly depended on the ratio PD-BamA/OmpA and was optimal at equimolar concentrations of PD-BamA and OmpA. To examine complexes of unfolded OmpA with PD-BamA in more detail, site-directed spectroscopy was used to explore contact regions in both, PD-BamA and OmpA. Similarly, contact regions were also investigated for another protein complex formed by PD-BamA and the lipoprotein BamD. The obtained data suggest, that the site of interaction on PD-BamA for OmpA might be oriented towards the exterior environment away from the preceding POTRA domains, but that PD-BamA is oriented with its short α-helix α1 of POTRA domain 5 towards the C-terminal end of BamD.

Field measurements of the CO2 evolution rate under different crops during an irrigation cycle in a mountain oasis of Oman

For millennia oasis agriculture has been the backbone of rural livelihood in the desertic Sultanate of Oman. However, little is known about the functioning of these oasis systems, in particular with respect to the C turnover. The objective was to determine the effects of crop, i.e. alfalfa, wheat and bare fallow on the CO2 evolution rate during an irrigation cycle in relation to changes in soil water content and soil temperature. The gravimetric soil water content decreased from initially 24% to approximately 16% within 7 days after irrigation. The mean CO2 evolution rates increased significantly in the order fallow (27.4 mg C m^−2 h^−1) < wheat (45.5 mg C m^−2 h^−1) < alfalfa (97.5 mg C m^−2 h^−1). It can be calculated from these data that the CO2 evolution rate of the alfalfa root system was nearly four times higher than the corresponding rate in the wheat root system. The decline in CO2 evolution rate, especially during the first 4 days after irrigation, was significantly related to the decline in the gravimetric water content, with r = 0.70. CO2 evolution rate and soil temperature at 5 cm depth were negatively correlated (r = -0.56,n = 261) due to increasing soil temperature with decreasing gravimetric water content.

Effects of fertilizer type and rate on partitioning of soil organic matter into pools of different stability

Type and rate of fertilizers influence the level of soil organic carbon (Corg) and total nitrogen (Nt) markedly, but the effect on C and N partitioning into different pools is open to question. The objectives of the present work were to: (i) quantify the impact of fertilizer type and rate on labile, intermediate and passive C and N pools by using a combination of biological, chemical and mathematical methods; (ii) explain previously reported differences in the soil organic matter (SOM) levels between soils receiving farmyard manure with or without biodynamic preparations by using Corg time series and information on SOM partitioning; and (iii) quantify the long-term and short-term dynamics of SOM in density fractions and microbial biomass as affected by fertilizer type and rate and determine the incorporation of crop residues into labile SOM fractions. Samples were taken from a sandy Cambisol from the long-term fertilization trial in Darmstadt, Germany, founded in 1980. The nine treatments (four field replicates) were: straw incorporation plus application of mineral fertilizer (MSI) and application of rotted farmyard manure with (DYN) or without (FYM) addition of biodynamic preparations, each at high (140 – 150 kg N ha-1 year-1; MSIH, DYNH, FYMH), medium (100 kg N ha-1 year-1; MSIM, DYNM, FYMM) and low (50 – 60 kg N ha-1 year-1; MSIL, DYNL, FYML) rates. The main findings were: (i) The stocks of Corg (t ha-1) were affected by fertilizer type and rate and increased in the order MSIL (23.6), MSIM (23.7), MSIH (24.2) < FYML (25.3) < FYMM (28.1), FYMH (28.1). Stocks of Nt were affected in the same way (C/N ratio: 11). Storage of C and N in the modelled labile pools (turnover times: 462 and 153 days for C and N, respectively) were not influenced by the type of fertilizer (FYM and MSI) but depended significantly (p ≤ 0.05) on the application rate and ranged from 1.8 to 3.2 t C ha 1 (7 – 13% of Corg) and from 90 to 140 kg N ha-1 (4-5% of Nt). In the calculated intermediate pool (C/N ratio 7), stocks of C were markedly higher in FYM treatments (15-18 t ha-1) compared to MSI treatments (12-14 t ha-1). This showed that differences in SOM stocks in the sandy Cambisol induced by fertilizer rate may be short-lived in case of changing management, but differences induced by fertilizer type may persist for decades. (ii) Crop yields, estimated C inputs (1.5 t ha-1 year-1) with crop residue, microbial bio¬mass C (Cmic, 118 – 150 mg kg-1), microbial biomass N (17 – 20 mg kg-1) and labile C and N pools did not differ significantly between FYM and DYN treatments. However, labile C increased linearly with application rate (R2 = 0.53) from 7 to 11% of Corg. This also applied for labile N (3.5 to 4.9% of Nt). The higher contents of Corg in DYN treatments existed since 1982, when the first sampling was conducted for all individual treatments. Contents of Corg between DYN and FYM treatments con-verged slightly since then. Furthermore, at least 30% of the difference in Corg was located in the passive pool where a treatment effect could be excluded. Therefore, the reported differences in Corg contents existed most likely since the beginning of the experiment and, as a single factor of biodynamic agriculture, application of bio-dynamic preparations had no effect on SOM stocks. (iii) Stocks of SOM, light fraction organic C (LFOC, ρ ≤ 2.0 g cm-3), light fraction organic N and Cmic decreased in the order FYMH > FYML > MSIH, MSIL for all sampling dates in 2008 (March, May, September, December). However, statistical significance of treatment effects differed between the dates, probably due to dif-ferences in the spatial variation throughout the year. The high proportion of LFOC on total Corg stocks (45 – 55%) highlighted the importance of selective preservation of OM as a stabilization mechanism in this sandy Cambisol. The apparent turnover time of LFOC was between 21 and 32 years, which agreed very well with studies with substantially longer vegetation change compared to our study. Overall, both approaches; (I) the combination of incubation, chemical fractionation and simple modelling and (II) the density fractionation; provided complementary information on the partitioning of SOM into pools of different stability. The density fractionation showed that differences in Corg stocks between FYM and MSI treatments were mainly located in the light fraction, i.e. induced by higher recalcitrance of the organic input in the FYM treatments. Moreover, the use of the combination of biological, chemical and mathematical methods indicated that effects of fertilizer rate on total Corg and Nt stocks may be short-lived, but that the effect of fertilizer type may persist for longer time spans in the sandy Cambisol.

Large-Size AlGaN/GaN HEMT Large-Signal Electrothermal Characterization and Modeling for Wireless Digital Communications

The rapid growth in high data rate communication systems has introduced new high spectral efficient modulation techniques and standards such as LTE-A (long term evolution-advanced) for 4G (4th generation) systems. These techniques have provided a broader bandwidth but introduced high peak-to-average power ratio (PAR) problem at the high power amplifier (HPA) level of the communication system base transceiver station (BTS). To avoid spectral spreading due to high PAR, stringent requirement on linearity is needed which brings the HPA to operate at large back-off power at the expense of power efficiency. Consequently, high power devices are fundamental in HPAs for high linearity and efficiency. Recent development in wide bandgap power devices, in particular AlGaN/GaN HEMT, has offered higher power level with superior linearity-efficiency trade-off in microwaves communication. For cost-effective HPA design to production cycle, rigorous computer aided design (CAD) AlGaN/GaN HEMT models are essential to reflect real response with increasing power level and channel temperature. Therefore, large-size AlGaN/GaN HEMT large-signal electrothermal modeling procedure is proposed. The HEMT structure analysis, characterization, data processing, model extraction and model implementation phases have been covered in this thesis including trapping and self-heating dispersion accounting for nonlinear drain current collapse. The small-signal model is extracted using the 22-element modeling procedure developed in our department. The intrinsic large-signal model is deeply investigated in conjunction with linearity prediction. The accuracy of the nonlinear drain current has been enhanced through several issues such as trapping and self-heating characterization. Also, the HEMT structure thermal profile has been investigated and corresponding thermal resistance has been extracted through thermal simulation and chuck-controlled temperature pulsed I(V) and static DC measurements. Higher-order equivalent thermal model is extracted and implemented in the HEMT large-signal model to accurately estimate instantaneous channel temperature. Moreover, trapping and self-heating transients has been characterized through transient measurements. The obtained time constants are represented by equivalent sub-circuits and integrated in the nonlinear drain current implementation to account for complex communication signals dynamic prediction. The obtained verification of this table-based large-size large-signal electrothermal model implementation has illustrated high accuracy in terms of output power, gain, efficiency and nonlinearity prediction with respect to standard large-signal test signals.