Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Reassessing spatial and temporal dynamics of kangaroo populations

Long-running datasets from aerial surveys of kangaroos (Macropus giganteus, Macropus [uliginosus, Macropus robustus and Macropus rufus) across Queensland, New South Wales and South Australia have been analysed, seeking better predictors of rates of increase which would allow aerial surveys to be undertaken less frequently than annually. Early models of changes in kangaroo numbers in response to rainfall had shown great promise, but much variability. We used normalised difference vegetation index (NDVI) instead, reasoning that changes in pasture condition would provide a better predictor than rainfall. However, except at a fine scale, NDVI proved no better; although two linked periods of rainfall proved useful predictors of rates of increase, this was only in some areas for some species. The good correlations reported in earlier studies were a consequence of data dominated by large droughtinduced adult mortality, whereas over a longer time frame and where changes between years are less dramatic, juvenile survival has the strongest influence on dynamics. Further, harvesting, density dependence and competition with domestic stock are additional and important influences and it is now clear that kangaroo movement has a greater influence on population dynamics than had been assumed. Accordingly, previous conclusions about kangaroo populations as simple systems driven by rainfall need to be reassessed. Examination of this large dataset has permitted descriptions of shifts in distribution of three species across eastern Australia, changes in dispersion in response to rainfall, and an evaluation of using harvest statistics as an index of density and harvest rate. These results have been combined into a risk assessment and decision theory framework to identify optimal monitoring strategies.

Impacts of grazing management options on pasture and animal productivity in a Heteropogon contortus (black speargrass) pasture in central Queensland. 2. Population dynamics of Heteropogon contortus and Stylosanthes scabra cv. Seca.

The dynamics of Heteropogon contortus and Stylosanthes scabra cv. Seca populations were studied in a subset of treatments in an extensive grazing study conducted in central Queensland between 1988 and 2001. These treatments were 4 stocking rates in native pasture and 2 of these stocking rates in legume oversown and supplement/spring burning treatments. For the 1999-2000 summer, population data for H. contortus in 5 of these native pasture and supplement/burning treatments were compared with those for an additional burnt treatment. Seasonal rainfall throughout this study was below the long-term mean and mean annual pasture utilisation ranged from 24 to 61%. Increasing stocking rate from 5 to 2 ha/steer in native pasture reduced H. contortus plant density. Increasing stocking rate reduced seedling recruitment as a result of its effect on soil seedbanks. Seedling recruitment was the major determinant of change in plant density, although some individual H. contortus plants did survive throughout the study. Burning in spring 1999, particularly at light stocking rate, promoted seedling recruitment above that in both unburnt native and legume oversown pasture and resulted in increased H. contortus plant density. In the legume oversown treatments, S. scabra cv. Seca density increased rapidly from 15 plants/m2 in 1988 to 140 plants/m2 in 2001 following a lag phase between 1988 and 1993. This increased S. scabra density was associated with an eventual decline in H. contortus plant density through reduced seedling recruitment. It was concluded that H. contortus population density is sustainable at stocking rates of 4 and 5 ha/steer (30% pasture utilisation) and that spring burning at light stocking rate can promote H. contortus populations. Increasing densities of S. scabra need to be managed to prevent its dominance.

Net radiation dynamics: performance of 20 daily net radiation models as related to model structure and intricacy in two climates.

We compared daily net radiation (Rn) estimates from 19 methods with the ASCE-EWRI Rn estimates in two climates: Clay Center, Nebraska (sub-humid) and Davis, California (semi-arid) for the calendar year. The performances of all 20 methods, including the ASCE-EWRI Rn method, were then evaluated against Rn data measured over a non-stressed maize canopy during two growing seasons in 2005 and 2006 at Clay Center. Methods differ in terms of inputs, structure, and equation intricacy. Most methods differ in estimating the cloudiness factor, emissivity (e), and calculating net longwave radiation (Rnl). All methods use albedo (a) of 0.23 for a reference grass/alfalfa surface. When comparing the performance of all 20 Rn methods with measured Rn, we hypothesized that the a values for grass/alfalfa and non-stressed maize canopy were similar enough to only cause minor differences in Rn and grass- and alfalfa-reference evapotranspiration (ETo and ETr) estimates. The measured seasonal average a for the maize canopy was 0.19 in both years. Using a = 0.19 instead of a = 0.23 resulted in 6% overestimation of Rn. Using a = 0.19 instead of a = 0.23 for ETo and ETr estimations, the 6% difference in Rn translated to only 4% and 3% differences in ETo and ETr, respectively, supporting the validity of our hypothesis. Most methods had good correlations with the ASCE-EWRI Rn (r2 > 0.95). The root mean square difference (RMSD) was less than 2 MJ m-2 d-1 between 12 methods and the ASCE-EWRI Rn at Clay Center and between 14 methods and the ASCE-EWRI Rn at Davis. The performance of some methods showed variations between the two climates. In general, r2 values were higher for the semi-arid climate than for the sub-humid climate. Methods that use dynamic e as a function of mean air temperature performed better in both climates than those that calculate e using actual vapor pressure. The ASCE-EWRI-estimated Rn values had one of the best agreements with the measured Rn (r2 = 0.93, RMSD = 1.44 MJ m-2 d-1), and estimates were within 7% of the measured Rn. The Rn estimates from six methods, including the ASCE-EWRI, were not significantly different from measured Rn. Most methods underestimated measured Rn by 6% to 23%. Some of the differences between measured and estimated Rn were attributed to the poor estimation of Rnl. We conducted sensitivity analyses to evaluate the effect of Rnl on Rn, ETo, and ETr. The Rnl effect on Rn was linear and strong, but its effect on ETo and ETr was subsidiary. Results suggest that the Rn data measured over green vegetation (e.g., irrigated maize canopy) can be an alternative Rn data source for ET estimations when measured Rn data over the reference surface are not available. In the absence of measured Rn, another alternative would be using one of the Rn models that we analyzed when all the input variables are not available to solve the ASCE-EWRI Rn equation. Our results can be used to provide practical information on which method to select based on data availability for reliable estimates of daily Rn in climates similar to Clay Center and Davis.

Characterization of the mitochondrial active-site serine protein LACTB: filaments in the mitochondrial intermembrane space

Mitochondria have evolved from endosymbiotic alpha-proteobacteria. During the endosymbiotic process early eukaryotes dumped the major component of the bacterial cell wall, the peptidoglycan layer. Peptidoglycan is synthesized and maintained by active-site serine enzymes belonging to the penicillin-binding protein and the β-lactamase superfamily. Mammals harbor a protein named LACTB that shares sequence similarity with bacterial penicillin-binding proteins and β-lactamases. Since eukaryotes lack the synthesis machinery for peptidoglycan, the physiological role of LACTB is intriguing. Recently, LACTB has been validated in vivo to be causative for obesity, suggesting that LACTB is implicated in metabolic processes. The aim of this study was to investigate the phylogeny, structure, biochemistry and cell biology of LACTB in order to elucidate its physiological function. Phylogenetic analysis revealed that LACTB has evolved from penicillin binding-proteins present in the bacterial periplasmic space. A structural model of LACTB indicates that LACTB shares characteristic features common to all penicillin-binding proteins and β-lactamases. Recombinat LACTB protein expressed in E. coli was recovered in significant quantities. Biochemical and cell biology studies showed that LACTB is a soluble protein localized in the mitochondrial intermembrane space. Further analysis showed that LACTB preprotein underwent proteolytic processing disclosing an N-terminal tetrapeptide motif also found in a set of cell death-inducing proteins. Electron microscopy structural studies revealed that LACTB can polymerize to form stable filaments with lengths ranging from twenty to several hundred nanometers. These data suggest that LACTB filaments define a distinct microdomain in the intermembrane space. A possible role of LACTB filaments is proposed in the intramitochondrial membrane organization and microcompartmentation. The implications of these findings offer novel insight into the evolution of mitochondria. Further studies of the LACTB function might provide a tool to treat mitochondria-related metabolic diseases.

Mitochondrial Malfunction in Tumor Formation and Neuromuscular Diseases : Consequences of defects in fumarate hydratase and in the respiratory chain

The mitochondrion is an organelle of outmost importance, and the mitochondrial network performs an array of functions that go well beyond ATP synthesis. Defects in mitochondrial performance lead to diseases, often affecting nervous system and muscle. Although many of these mitochondrial diseases have been linked to defects in specific genes, the molecular mechanisms underlying the pathologies remain unclear. The work in this thesis aims to determine how defects in mitochondria are communicated within - and interpreted by - the cells, and how this contributes to disease phenotypes. Fumarate hydratase (FH) is an enzyme of the citrate cycle. Recessive defects in FH lead to infantile mitochondrial encephalopathies, while dominant mutations predispose to tumor formation. Defects in succinate dehydrogenase (SDH), the enzyme that precedes FH in the citrate cycle, have also been described. Mutations in SDH subunits SDHB, SDHC and SDHD are associated with tumor predisposition, while mutations in SDHA lead to a characteristic mitochondrial encephalopathy of childhood. Thus, the citrate cycle, via FH and SDH, seems to have essential roles in mitochondrial function, as well as in the regulation of processes such as cell proliferation, differentiation or death. Tumor predisposition is not a typical feature of mitochondrial energy deficiency diseases. However, defects in citrate cycle enzymes also affect mitochondrial energy metabolism. It is therefore necessary to distinguish what is specific for defects in citrate cycle, and thus possibly associated with the tumor phenotype, from the generic consequences of defects in mitochondrial aerobic metabolism. We used primary fibroblasts from patients with recessive FH defects to study the cellular consequences of FH-deficiency (FH-). Similarly to the tumors observed in FH- patients, these fibroblasts have very low FH activity. The use of primary cells has the advantage that they are diploid, in contrast with the aneuploid tumor cells, thereby enabling the study of the early consequences of FH- in diploid background, before tumorigenesis and aneuploidy. To distinguish the specific consequences of FH- from typical consequences of defects in mitochondrial aerobic metabolism, we used primary fibroblasts from patients with MELAS (mitochondrial encephalopathy with lactic acidosis and stroke-like episodes) and from patients with NARP (neuropathy, ataxia and retinitis pigmentosa). These diseases also affect mitochondrial aerobic metabolism but are not known to predispose to tumor formation. To study in vivo the systemic consequences of defects in mitochondrial aerobic metabolism, we used a transgenic mouse model of late-onset mitochondrial myopathy. The mouse contains a transgene with an in-frame duplication of a segment of Twinkle, the mitochondrial replicative helicase, whose defects underlie the human disease progressive external ophthalmoplegia. This mouse model replicates the phenotype in the patients, particularly neuronal degeneration, mitochondrial myopathy, and subtle decrease of respiratory chain activity associated with mtDNA deletions. Due to the accumulation of mtDNA deletions, the mouse was named deletor. We first studied the consequences of FH- and of respiratory chain defects for energy metabolism in primary fibroblasts. To further characterize the effects of FH- and respiratory chain malfunction in primary fibroblasts at transcriptional level, we used expression microarrays. In order to understand the in vivo consequences of respiratory chain defects in vivo, we also studied the transcriptional consequences of Twinkle defects in deletor mice skeletal muscle, cerebellum and hippocampus. Fumarate accumulated in the FH- homozygous cells, but not in the compound heterozygous lines. However, virtually all FH- lines lacked cytoplasmic FH. Induction of glycolysis was common to FH-, MELAS and NARP fibroblasts. In deletor muscle glycolysis seemed to be upregulated. This was in contrast with deletor cerebellum and hippocampus, where mitochondrial biogenesis was in progress. Despite sharing a glycolytic pattern in energy metabolism, FH- and respiratory chain defects led to opposite consequences in redox environment. FH- was associated with reduced redox environment, while MELAS and NARP displayed evidences of oxidative stress. The deletor cerebellum had transcriptional induction of antioxidant defenses, suggesting increased production of reactive oxygen species. Since the fibroblasts do not represent the tissues where the tumors appear in FH- patients, we compared the fibroblast array data with the data from FH- leiomyomas and normal myometrium. This allowed the determination of the pathways and networks affected by FH-deficiency in primary cells that are also relevant for myoma formation. A key pathway regulating smooth muscle differentiation, SRF (serum response factor)-FOS-JUNB, was found to be downregulated in FH- cells and in myomas. While in the deletor mouse many pathways were affected in a tissue-specific basis, like FGF21 induction in the deletor muscle, others were systemic, such as the downregulation of ALAS2-linked heme synthesis in all deletor tissues analyzed. However, interestingly, even a tissue-specific response of FGF21 excretion could elicit a global starvation response. The work presented in this thesis has contributed to a better understanding of mitochondrial stress signalling and of pathways interpreting and transducing it to human pathology.

Collaborative learning approach to introduce computational fluid dynamics

This paper presents the design, implementation and evaluation of a collaborative learning activity designed to replace traditional face-to-face lectures in a large classroom. This activity aims to better engage the students with their learning and improve the students’ experience and outcomes. This project is implemented in the Fluid Mechanics unit of the Mechanical Engineering degree at the Queensland University of Technology to introduce students with the concept, terminology and process of Computational Fluid Dynamics (CFD). The approach integrates a constructive collaborative assignment which is a key element in the overall quality of teaching and learning, and an integral component of the students’ experience. A detailed survey, given to the students, showed an overall high level of satisfaction. However, the results also highlighted the gap between students’ expectations both for contents and assignment and teacher expectations. Discussions to address this issue are presented in the paper based on a critical reflection.

A molecular dynamics investigation of the structure of PbO---PbF2 glasses*1

The structure of PbO---PbF2 glasses has been studied using molecular dynamics (MD). The existence of [OPb4] structural units is observed over the entire glass-forming range, in conformity with a model proposed earlier based on various structural investigations of this system. Various other features of the structural model are also supported by the MD calculations.

A conformational approach to the study of the dynamics of enzyme inhibition: studies on thermolysin

The preferred conformations of β-phenylpropionyl-Image -phenylalanine (β-PPP) and N-carbobenzoxy-L-phenylalanine (Cbz-Phe), two inhibitors of thermolysin, have been determined by computing potential energy using empirial potential energy functions. Of the 15 to 20 conformations that are favoured for each of these inhibitors only a few have the right conformation to reach the active site of the enzyme. The conformer of β-PPP that initiates binding with the enzyme is different from the bound one, while for Cbz-Phe the bound and initiating conformers are quite similar. Thus, β-PPP favours the ‘induced fit’ model while Cbz-Phe follows the ‘lock and key’ model of binding. The inhibitors differ in their alignment at the active site.

Evidence for extensive population structure in the white-spotted eagle ray within the Indo-Pacific inferred from mitochondrial gene sequences

The white-spotted eagle ray Aetobatus narinari is a species complex that occurs circumglobally throughout warm-temperate waters. Aetobatus narinari is semi-pelagic and large (up to 300 cm disc width), suggesting high dispersal capabilities and gene flow on a wide spatial scale. Sequence data from two mitochondrial genes, cytochrome b (cytb) and NADH dehydrogenase subunit 4 (ND4), were used to determine the genetic variability within and among 18 sampling locations in the central Indo-Pacific biogeographical region. Populations in the Indo-Pacific were highly genetically structured with c. 70% of the total genetic variation found among three geographical regions (East China Sea, Southeast Asia and Australia). FST was 0.64 for cytb and 0.53 for ND4, with φST values being even larger, that is, 0.78 for cytb and 0.65 for ND4. This high-level genetic partitioning provides strong evidence against extensive gene flow in A. narinari. The degree of genetic population structuring in the Indo-Pacific was similar to that found on a global scale. Global FST was 0.63 for cytb and 0.57 for ND4, and global φST values were 0.94 for cytb and 0.82 for ND4. This suggests that the A. narinari complex may be more speciose than the two or three species proposed to date. Further sampling and genetic analyses are likely to uncover the ‘evolutionarily significant’ and ‘management’ units that are critical to determine the susceptibilities of individual populations to regional fishing pressures and to provide advice on management options. Network analyses showed a close genetic relationship between haplotypes from the central Indo-Pacific and South Africa, providing support for a proposed dispersal pathway from the possible centre of origin of the A. narinari species complex in the Indo-Pacific into the Atlantic Ocean.

Isomerization Dynamics In Solution In The Absence Of An Activation Barrier - Evaluation Of The Potential Parameters

We analyze recent experimental results of Sundström and Gillbro by using the theory of Bagchi, Fleming and Oxtoby. The experimental results are in good agreement with this theory, but not with the earlier theory of Förster and Hoffmann. By fitting the new experimental results to the theory, we obtain approximate estimates of the frequency of the excited surface (assumed harmonic) and the width of the sink function.

The spatiotemporal dynamics of Tribolium castaneum (Herbst): adult flight and gene flow.

Tribolium castaneum (Herbst) has been used as a model organism to develop and test important ecological and evolutionary concepts and is also a major pest of grain and grain products globally. This beetle species is assumed to be a good colonizer of grain storages through anthropogenic movement of grain, and active dispersal by flight is considered unlikely. Studies using T. castaneum have therefore used confined or walking insects. We combine an ecological study of dispersal with an analysis of gene flow using microsatellites to investigate the spatiotemporal dynamics and adult flight of T. castaneum in an ecological landscape in eastern Australia. Flying beetles were caught in traps at grain storages and in fields at least 1 km from the nearest stored grain at regular intervals for an entire year. Significantly more beetles were trapped at storages than in fields, and almost no beetles were caught in native vegetation reserves many kilometres from the nearest stored grain. Genetic differentiation between beetles caught at storages and in fields was low, indicating that although T. castaneum is predominantly aggregated around grain storages, active dispersal takes place to the extent that significant gene flow occurs between them, mitigating founder effects and genetic drift. By combining ecological and molecular techniques, we reveal much higher levels of active dispersal through adult flight in T. castaneum than previously thought. We conclude that the implications of adult flight to previous and future studies on this model organism warrant consideration.

Impact of control strategies on bellyache bush (Jatropha gossypiifolia L.) mortality, seedling recruitment, population dynamics, pasture yield and cost analysis

Bellyache bush (Jatropha gossypiifolia L.) is an invasive weed that has the potential to greatly reduce biodiversity and pasture productivity in northern Australia’s rangelands. This paper reports an approach to develop best practice options for controlling medium to dense infestations of bellyache bush using combinations of control methods. The efficacy of five single treatments including foliar spraying, slashing, stick raking, burning and do nothing (control) were compared against 15 combinations of these treatments over 4 successive years. Treatments were evaluated using several attributes, including plant mortality, changes in population demographics, seedling recruitment, pasture yield and cost of treatment. Foliar spraying once each year for 4 years proved the most cost-effective control strategy, with no bellyache bush plants recorded at the end of the study. Single applications of slashing, stick raking and to a lesser extent burning, when followed up with foliar spraying also led to significantly reduced densities of bellyache bush and changed the population from a growing one to a declining one. Total experimental cost estimates over 4 successive years for treatments where burning, stick raking, foliar spraying, and slashing were followed with foliar spraying were AU$408, AU$584, AU$802 and AU$789 ha–1, respectively. Maximum pasture yield of 5.4 t ha–1 occurred with repeated foliar spraying. This study recommends that treatment combinations using either foliar spraying alone or as a follow up with slashing, stick raking or burning are best practice options following consideration of the level of control, changes in pasture yield and cost effectiveness.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.