Individual-based models have been applied to study a broad spectrum of problems across multiple disciplines, such as the spread of epidemics or the outcome of social dilemma. They are used to investigate the macroscopic effects that arise from the microscopic dynamics of interacting individuals. Fixation describes the taking over of the population by a single type of individual or species. It is a prominent feature in the field of population genetics, which interprets many biological scenarios of evolution. Equilibration describes the process of reaching a heterogeneous steady state. In this thesis we analyse these macroscopic features through techniques derived from statistical physics and the theory of stochastic processes. Birth-death processes are used to describe the interaction of two types of individual in a population, such as competing strains of bacteria. These interactions are often specified using the framework of evolutionary game theory. The environment in which the population evolves can have a crucial impact on selection. In systems where the environment switches between multiple states we develop a general theory to calculate the fixation time statistics of a mutant individual in a population of wild-types, as well as the stationary distributions when mutations are present in the dynamics. In some birth--death processes, and in particular those described by evolutionary game theory, the mean fixation time contains only limited information. By diagonalising the master equation that describes the process, we are able to obtain closed-form expressions for the complete fixation time distributions. Individual-based models can also be used to describe the accumulation of mutations in a cell. This has important consequences for the initiation and progression of cancer. We find that such systems exhibit metastable states in the dynamics, and we can exploit the separation of timescales between relaxing to the quasi-stationary state and reaching fixation to characterise these phenomena. In this scenario we employ the WKB method to describe the population-level dynamics. Although this method has been used to describe numerous stochastic processes, a clear and coherent description is lacking in the literature. Through the use of multiple examples, including the aforementioned cancer initiation model, we carefully explain the multitude of constructs and equations that result from the application of this methodThe analytical characterisation of the evolutionary dynamics that are observed in these stochastic processes has resulted in a greater understanding of fixation and equilibration. This thesis promotes the benefits of analytical, or even semi-analytical methods, and on a more general level contributes toward a more complete understanding of evolutionary processes.

M.Med., Orthopaedic Surgery, Faculty of Health Sciences, University of the Witwatersrand, 2010

The rhizobia-legume symbiosis is the most agriculturally significant source of naturally fixed nitrogen, accounting for almost 25% of all biologically available nitrogen. Rhizobia-legume compatibility restrictions impose limits on symbiotic nitrogen fixation. In many cases, the molecular basis for symbiotic compatibility is not fully understood. The signals required for establishing a symbiotic partnership between nitrogen-fixing bacteria (e.g. Sinorhizobium meliloti) and leguminous plants (e.g. Medicago truncatula) have been partially characterized at the molecular level. The first stage of successful root colonization is competitive occupation of the rhizosphere (which is poorly understood). Here, the bacteria introduce themselves as potential symbiotic partners through the secretion of glycolipid "Nod" factors. In response, the host facilitates a more exclusive mode of colonization by the formation of a root nodule – a new organ capable of hosting dense intracellular populations of symbiotic rhizobia for nitrogen fixation. This dissertation reports the exhaustive identification of S. meliloti genes that permit competitive colonization of the M. truncatula rhizosphere, and includes a mechanistic study of one particular bacterial signaling pathway that is crucial for both rhizosphere colonization and nodulation. I have made use of Tn-seq technology, which relies on deep sequencing of large transposon mutant libraries to monitor S. meliloti genotypes that increase or decrease in relative abundance after competition in the rhizosphere. This work included the collaborative development of a new computational pipeline for performing Tn-seq analysis. Our analysis implicates a large ensemble of bacterial genes and pathways promoting rhizosphere colonization, provides hints about how the host plant shapes this environment, and opens the door for mechanistic studies about how changes in the rhizosphere are sensed and interpreted by the microbial community. Notable among these sensory pathways is a three-protein signaling system, consisting of FeuQ, FeuP, and FeuN, which are important for both rhizosphere colonization and nodule invasion by S. meliloti. The membrane-bound sensor kinase FeuQ can either positively or negatively influence downstream transcription of target genes by modulating the phosphorylation state of the transcriptional activator FeuP. FeuN, a small periplasmic protein, inhibits the positive mode of FeuPQ signaling by its direct interaction with the extracellular region of FeuQ. FeuN is essential for S. meliloti viability, underscoring the vital importance of controlling the activity of downstream genes. In summary, I have employed several powerful genetic, genomic, computational, and biochemical approaches to uncover a network of genes and pathways that coordinate root colonization and nodulation functions.

Biological nitrogen fixation is accomplished in the bacterium Azotobacter vinelandii by means of three metalloenzymes: The molybdenum, vanadium, and iron-only nitrogenase. The knowledge regarding biological nitrogen fixation has come from studies on the Mo-dependent reaction. However, the V- and Fe-only-dependent reduction of nitrogen remains largely unknown. By using homology modeling techniques, the protein folds that contain the metal cluster active sites for the V- and Fe-only nitrogenases were constructed. The models uncovered similarities and differences existing among the nitrogenases regarding the identity of the amino acid residues lining pivotal structural features for the correct functioning of the proteins. These differences, could account for the differences in catalytic properties depicted by these enzymes. The quaternary structure of the dinitrogenases also differs. Such component in the Mo-nitrogenase is an α2β2 tetramer while for the V- an Fe-only nitrogenase is an α2β2δ2 hexamer. The latter enzymes are unable to reduce N2 in the absence of a functional δ subunit, yet they reduce H+ and the non-physiological substrate C2H2. Therefore, the δ subunit is essential for V- and Fe-only dependent nitrogen fixation by a mechanism that still remains unknown. In attempt to understand why the δ subunit is essential for V-dependent N2 reduction from a structural stand point, this work presents the strategy followed to clone the vnfG gene and purify its expression product, the δ subunit. The purified protein was subjected to crystallization trials and used to stabilize a histidine-tagged VFe protein that would otherwise purify with low Fe2+ content and poor H+ and C2H2 reduction activities. The VFe preparation was used to conduct substrate reduction assays to assess: i) The electron allocation patterns to each of the reduction products of the substrates C2H2, N2, N2H4, and N3−; and ii) Inhibition patterns among substrate and inhibitor of the nitrogenase reaction. This work also reports on the effect N2H4 and N3− has on the electron flux to the products of the C2H2 reduction. The work presented herein provides information with which to compare and contrast biological nitrogen fixation as catalyzed by the Mo- and V-nitrogenases from Azotobacter vinelandii.

The inputs and losses of nitrogen from Great Basin arid soils were studied using the acetylene reduction and 15N techniques. Filamentous blue-green algae were observed to be the predominant algal group in the soil crusts. The bacterial association with this group of algae suggest a phycosphere-like effect, thus allowing heterotrophic nitrogen fixation and denitrification to occur. Up to 17.5 mg N/100 g soil was found to have been fixed in surface soils (0 to 3 em) during a three week incubation period, while 45.9 mg N/100 g soil was fixed in a five week incubation period. Ammonium sulfate and ammonium sulfate plus plant material amendments reduced the gain in nitrogen by 41 to 100 percent. 15 + 15 - Fifty to sixty percent of the applied NH4-N and N0 3-N was denitrified during the first week of incubation while 70 to 80 percent of the NH 4-N was lost in a three- to five-week incubation period. These data suggest that a potential for heterotrophic nitrogen fixation exists, and under optimal conditions, significant gains in soil nitrogen may be achieved. However, in the presence of allelochemic agents, the potential gain in soil nitrogen may be reduced or inhibited. In addition, the denitrification potentials of these soils may also limit the input of nitrogen. The application of protein ( casein) to these soils resulted in an ammonification rate of 50 to 60 percent. 15 Fixed N2 indicated a 21 to 48.8 percent ammonification rate, thus suggesting that the mineraliztion of NH 4 was the rate limiting step for nitrogen loss. Ammonia volatilization accounted for less than a five percent nitrogen loss, regardless of experimental conditions. The inhibitory effects of plant material and litter extracts, and ''N-Serve" on heterotrophic nitrogen fixation has been assessed. The data suggest that the nitrogen fixing population is sensitive to the inhibitory effects of such agents .

The rhizobium – legume symbiosis is a complex process that involves genetic cooperation from both bacteria and plants. Previously, our lab described naturally occurring accessory plasmids in rhizobia that inhibit this cooperation. A transposon mutagenesis was performed on the plasmids to detect the genetic factor that blocked nitrogen fixation. Several of the plasmids were found to possess a replication operon that when disrupted by transposon insertion, restored symbiotic function. This study describes an in-depth investigation into one of those plasmids, pHRC377, and into its replication operon. The operon, which we have called repA2C2, comes from the repABC family of replication and partitioning systems commonly found in alphaproteobacteria. In this study we show that this operon is not necessary for pHRC377 replication in LB culture or free living cells, but is necessary for plasmid amplification in the plant, specifically during rhizobial differentiation into nitrogen fixing bacteroids. We also show how the other repABC type operons on pHRC377 function in relation to plasmid maintenance and copy number during endoreduplication and how they do not have the same phenotypic effect as repA2C2.

Abstract The ubiquity of the Calvin-Benson-Bassham cycle (CBB) amongst autotrophic organisms suggests that it provides an advantage over a wide range of environmental conditions. However, in some habitats, such as hydrothermal vents, the reductive citric acid cycle (rCAC) is an equally predominant carbon fixation pathway. It has been suggested that the CBB cycle poses a disadvantage under certain circumstances due to being more energetically demanding compared to other carbon fixation pathways. The purpose of this study was to compare the relative metabolic cost of cell biosynthesis by an autotrophic cell using either the CBB cycle or the rCAC. For both pathways, the energy, in ATP, required to synthesize the macromolecules (DNA, RNA, protein, and cell envelope) for one gram of biomass was calculated, beginning with CO2. Two sulfur-oxidizing chemolithoautotrophic proteobacteria, Thiomicrospira crunogena XCL-2, and Sulfurimonas autotrophica were used to model the CBB cycle and rCAC, respectively while Escherichia coli was used to model both pathways because it has had its cell composition extremely well-characterized. Since these organisms have had their genomes sequenced, it was possible to reconstruct the biochemical pathways necessary for intermediate and macromolecule synthesis. Prior estimates, based solely on the ATP cost of pyruvate biosynthesis, suggested that the cellular energetic expense for biosynthesis from the CBB cycle was more than that from the rCAC. The results of this study support this conclusion; however the difference in expense between the two pathways may not be as extreme as suggested by pyruvate synthesis. Other factors, such as oxygen sensitivity, may act in concert with energetic expense in contributing to the selective advantages between different autotrophic carbon fixation pathways.

No description available.

Abstract not available

Bacteroids of B. japonicum from nodules of soybean roots were isolated using differential centrifugation (the standard bench method) and density gradient centrifugation methods (either sucrose- or Percoll-) under anaerobic conditions in which N2 fixation was preserved. The relationships between N2 fixation and respiration, O2 supply, O2 demand, substrate (mainly malate) transport and metabolism in bacteroids were investigated using the flow chamber system. In related experiments, the primary products of N2 fixation which leave the bacteroids were investigated using a 15N-labelling technique in a closed shaken system and other biochemical methods.¶ In the flow chamber experiments, the rates at which O2 was supplied to bacteroids in the chamber were varied by (a) changing the flow rate of reaction medium through the chamber; (b) by changing the [O2 free] in the inflowing reaction medium by using either 3-5% (v/v) or 100% air in the gas mixture above the stirred reaction medium in two reservoir flasks; (c) by successively withdrawing bacteroids from the chamber, thus increasing the supply of O2 per bacteroid to those remaining in the chamber. The results showed that the rate of O2 supply regulates respiratory demand for O2 by bacteroids rather than the O2 concentration present in the reaction system. Respiration is always coupled to N2 fixation. ¶ Uptake of malate by bacteroids withdrawn from the flow chamber was measured under microaerobic conditions. Malate uptake by these N2-fixing bacteroids was lower than that by bacteroids isolated under aerobic conditions, which eliminate N2 fixation of bacteroids, but is closely correlated with bacteroid respiration rates. When respiration was increased by an increase in O2 supply, malate uptake by bacteroids was also increased. This suggested that transport of malate through the bacteroid membrane is also regulated by O2 supply, but indirectly. Higher uptake by bacteroids under aerobic conditions was observed because respiration was enhanced by the high availability of O2, but the fast uptake of malate by bacteroids driven by the abnormal respiration rates may not reflect the reality of malate demand in vivo by bacteroids when N2 fixation by bacteroids is fully coupled. ¶ The results of 15N labelling experiments and other biochemical assays once again demonstrated that ammonia is the principal significant 15N labelled product of N2 fixation accumulated during 30 min in shaken assays with 0.008-0.01 atm O2. Alanine although sometimes found in low concentrations in the flow chamber reactions, was not labelled with 15N in shaken closed system experiments. No evidence could be obtained from the other biochemical assays, either. Therefore, it is concluded that these and earlier results were not due to contamination with host cytosolic enzymes as suggested by Waters et al. (Proc. Natl. Aca. Sci. 95, 1998, pp 12038-12042). ¶ Malate transported into bacteroids is oxidized in a modified TCA cycle present in bacteroids. The results of flow chamber experiments with a sucA mutant (lacking a-ketoglutarate dehydrogenase) showed that respiratory demand for O2 by the mutant bacteroids is regulated by O2 supply in the same way as the wild-type. Despite differences in other symbiotic properties, rates of nitrogen fixation by the mutant bacteroids, based on the bacteroid dry weight, appeared to be the same as in the wild-type. Also N2 fixation was closely coupled with respiration in the same manner in both mutant bacteroids and wild type bacteroids. These results and other supporting data, strongly support the conclusion that there is an alternative pathway of the TCA cycle in bacteroids, which enables the missing step in the mutant to be by-passed with sufficient activity to support metabolism of transported malate.