Case study using Python in the teaching of numerical analysis

In this case study we describe the rationale, methodology and results of teaching Python as part of a third year optional Numerical Analysis module taken by undergraduate BSc Mathematics students at the University of the West of England, Bristol. In particular we focus on how we have used programming mini-tasks to engage and prepare students for using Python to complete a more significant piece of coursework, taken later in the course. These mini-tasks are marked electronically using the Dewis e-assessment system which provides the students with immediate and tailored feedback on their Python code

Chauffeur braking

An experienced driver will `feather' the brakes so as to unwind the suspension compliance and stop the vehicle with only just enough torque in the brakes to hold the vehicle stationary on any gradient, or against the residual torque from an automatic transmission’s torque converter. An optimal stopping problem that minimises the total jerk was formulated and solved. This model was extended by including a linear relationship between the brake pressure and the acceleration of the car where the coefficients are estimated by linear regression. Finally, a Kalman filter estimates the state of the car using the tone wheel

An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations

We present an algebraic multigrid algorithm for fully coupled implicit Runge-Kutta and Boundary Value Method time-discretizations of the div-grad and curl-curl equations. The algorithm uses a blocksmoother and a multigrid hierarchy derived from the hierarchy built by any algebraic multigrid algorithm for the stationary version of the problem. By a theoretical analysis and numerical experiments, we show that the convergence is similar to or better than the convergence of the scalar algebraic multigrid algorithm on which it is based. The algorithm benefits from several possibilities for implementation optimization. This results in a computational complexity which, for a modest number of stages, scales almost linearly as a function of the number of variables. © 2008 IMACS

The baculovirus Ac108 protein is a per os infectivity factor and a component of the ODV entry complex

Wild-type ODVs (Wt) have an intact ODV entry complex in their envelope and are orally infectious towards insect larvae (left panel). In the absence of Ac108 (mut ac108), the stable core is still present but nevertheless fails to form an entry complex, affecting the ODV oral infectivity (right panel). The components of the core complex are depicted in yellow and the loosely associated components are depicted in red. PIF7 is depicted in green as its affinity with the complex is currently not known.Baculoviruses orally infect insect larvae when they consume viral occlusion bodies (OBs). OBs consist of a crystalline protein matrix in which the infectious virus particles, the occlusion-derived viruses (ODVs), are embedded. The protein matrix dissolves in the alkaline environment of the insect's midgut lumen. The liberated ODVs can then infect midgut endothelial cells through the action of at least nine different ODV-envelope proteins, called per os infectivity factors (PIFs). These PIF proteins mediate ODV oral infectivity, but are not involved in the systemic spread of the infection by budded viruses (BVs). Eight of the known PIFs form a multimeric complex, named the ODV entry complex. In this study, we show for Autographa californica multiple nucleopolyhedrovirus that mutation of the ac108ORF abolishes the ODV oral infectivity, while production and infectivity of the BVs remains unaffected. Furthermore, repair of the ac108 mutant completely recovered oral infectivity. With an HA-tagged repair mutant, we were able to demonstrate by Western analysis that the Ac108 protein is a constituent of the ODV entry complex, where the formation was abolished in the absence of this protein. Based on these results, we conclude that ac108 encodes a per os infectivity factor (PIF9) that is also an essential constituent of the ODV entry complex.</p

FcgammaR expression on macrophages is related to severity and chronicity of synovial inflammation and cartilage destruction during experimental immune-complex-mediated arthritis (ICA)

INTRODUCTION: Fcγ receptors (FcγRs) present on cells of the haematopoietic lineage communicate with IgG-containing immune complexes that are abundant in the synovial tissue of patients with rheumatoid arthritis (RA). In mice, three classes of FcγR (RI, RII, and RIII) have been described. Binding of these receptors leads to either activation (FcγRI and RIII) or deactivation (FcγRII) of intracellular transduction pathways. Together, the expression of activating and inhibitory receptors is thought to drive immune-complex-mediated diseases. Earlier studies in our laboratory showed that macrophages of the synovial lining are of utmost importance in the onset and propagation of immune-complex-driven arthritic diseases. Selective depletion of macrophages in the joint downregulated both inflammation and cartilage destruction. As all three classes of FcγR are expressed on synovial macrophages, these cells are among the first that come in contact with immune complexes deposited in the joint. Recently, we observed that when immune complexes were injected into the knee joints of mice, strains susceptible to collagen-type-II arthritis (DBA/1, B10.RIII) developed more severe arthritis than nonsusceptible strains did, or even developed chronic arthritis. One reason why these strains are more susceptible might be their higher levels of FcγRs on macrophage membranes. To test this hypothesis, we investigated the role of FcγRs in inflammation and cartilage damage during immune-complex-mediated arthritis (ICA). First, we studied arthritis and subsequent cartilage damage in mice lacking functional FcγRI and RIII (FcR γ-chain(-/-) mice). Next, DBA/1 mice, which are prone to develop collagen-type-II arthritis (`collagen-induced arthritis'; CIA) and are hypersensitive to immune complexes, were compared with control C57BL/6 mice as regards cartilage damage and the expression and function of FcγRs on their macrophages. AIMS: To examine whether FcγR expression on macrophages is related to severity of synovial inflammation and cartilage destruction during immune-complex-mediated joint inflammation. METHODS: ICA was induced in three strains of mice (FcR γ-chain(-/-), C57BL/6, and DBA/1, which have, respectively, no functional FcγRI and RIII, intermediate basal expression of FcγRs, and high basal expression of FcγRs) by passive immunisation using rabbit anti-lysozyme antibodies, followed by poly-L-lysine lysozyme injection into the right knee joint 1 day later. In other experiments, streptococcal-cell-wall (SCW)- or zymosan-induced arthritis was induced by injecting SCW (25 μg) or zymosan (180 μg) directly into the knee joint. At several time points after arthritis induction, knee joints were dissected and studied either histologically (using haematoxylin/eosin or safranin O staining) or immuno-histochemically. The arthritis severity and the cartilage damage were scored separately on an arbitrary scale of 0-3. FcγRs were immunohistochemically detected using the monoclonal antibody 2.4G2, which detects both FcγRII and RIII. Deposition of IgG and C3c in the arthritic joint tissue was also detected immunohistochemically. Expression of FcγRs by murine peritoneal macrophages was measured using a fluorescence-activated cell sorter (FACS). Peritoneal macrophages were stimulated using heat-aggregated gamma globulins (HAGGs), and production of IL-1 was measured using a bioassay. To assess the levels of IL-1 and its receptor antagonist (IL-1Ra) during arthritis, tissue was dissected and washed in RPMI medium. Washouts were tested for levels of IL-1 and IL-1Ra using radioimmunoassay and enzyme-linked immunosorbent assay. mRNA was isolated from the tissue, and levels of macrophage inflammatory protein (MIP)-2, monocyte chemoattractant protein (MCP)-1, IL-1, and IL-1Ra were determined using semiquantitative reverse-transcription polymerase chain reaction (RT-PCR). RESULTS: ICA induced in knee joints of C57BL/6 mice caused a florid inflammation at day 3 after induction. To investigate whether this arthritis was FcγR-mediated, ICA was induced in FcR γ-chain(-/-) mice, which lack functional FcγRI and RIII. At day3, virtually no inflammatory cells were found in their knee joints. Levels of mRNA of IL-1, IL-1Ra, MCP-1, and MIP-2, which are involved in the onset of this arthritis, were significantly lower in FcR γ-chain(-/-) mice than in control C57BL/6 mice. Levels of IL-1 protein were also measured. At 6 h after ICA induction, FcR γ-chain(-/-) mice and control C57BL/6 mice showed similar IL-1 production as measured by protein level. By 24 h after induction, however, IL-1 production in the FcR γ-chain(-/-) mice was below the detection limit, whereas the controls were still producing a significant amount. To investigate whether the difference in reaction to immune complexes between the DBA/1 and C57BL/6 mice might be due to variable expression of FcγRs in the knee joint, expression in situ of FcγRs in naïve knee joints of these mice was determined. The monoclonal antibody 2.4G2, which detects both FcγRII and RIII, stained macrophages from the synovial lining of DBA/1 mice more intensely than those from C57BL/6 mice. This finding suggests a higher constitutive expression of FcγRs by macrophages of the autoimmune-prone DBA/1 mice. To quantify the difference in FcγR expression on macrophages of the two strains, we determined the occurrence of FcγRs on peritoneal macrophages by FACS analysis. The levels of FcγR expressed by macrophages were twice as high in the DBA/1 mice as in the C57BL/6 mice (mean fluorescence, respectively, 440 ± 50 and 240 ± 30 intensity per cell). When peritoneal macrophages of both strains were stimulated with immune complexes (HAGGs), we found that the difference in basal FcγR expression was functional. The stimulated macrophages from DBA/1 mice had significantly higher IL-1α levels (120 and 135 pg/ml at 24 and 48 h, respectively) than cells from C57BL/6 mice (45 and 50 pg/ml, respectively). When arthritis was induced using other arthritogenic triggers than immune complexes (zymosan, SCW), all the mouse strains tested (DBA/1, FcR γ-chain(-/-), and C57BL/6) showed similar inflammation, indicating that the differences described above are found only when immune complexes are used to elicit arthritis. We next compared articular cartilage damage in arthritic joints of the three mouse strains FcR γ-chain(-/-), C57BL/6 (intermediate basal expression of FcγRs), and DBA/1 (high basal expression of FcγRs). Three indicators of cartilage damage were investigated: depletion of PGs, chondrocyte death, and erosion of the cartilage matrix. At day 3 after induction of ICA, there was no PG depletion in FcR γ-chain(-/-) mice, whereas PG depletion in the matrix of the C57BL/6 mice was marked and that in the arthritic DBA/1 mice was even greater. PG depletion was still massive at days 7 and 14 in the DBA/1 mice, whereas by day 14 the PG content was almost completely restored in knee joints of the C57BL/6 mice. Chondrocyte death and erosion of cartilage matrix, two indicators of more severe cartilage destruction, were significantly higher in the DBA/1 than in the C57BL/6 mice, while both indicators were completely absent in the FcR γ-chain(-/-) mice. Again, when arthritis was induced using other triggers (SCW, zymosan), all strains showed similar PG depletion and no chondrocyte death or matrix erosion. These findings underline the important role of immune complexes and FcγRs in irreversible cartilage damage. DISCUSSION: Our findings indicate that inflammation and subsequent cartilage damage caused by immune complexes may be related to the occurrence of FcγRs on macrophages. The absence of functional FcγRI and RIII prevented inflammation and cartilage destruction after induction of ICA, whereas high basal expression of FcγRs on resident joint macrophages of similarly treated mice susceptible to autoimmune arthritis was correlated with markedly more synovial inflammation and cartilage destruction. The difference in joint inflammation between the three strains was not due to different susceptibilities to inflammation per se, since intra-articular injection of zymosan or SCW caused comparable inflammation. Although extensive inflammatory cell mass was found in the synovium of all strains after intra-articular injection of zymosan, no irreversible cartilage damage (chondrocyte death or matrix erosion) was found. ICA induced in C57BL/6 and DBA/1 mice did cause irreversible cartilage damage at later time points, indicating that immune complexes and FcγRs play an important role in inducing irreversible cartilage damage. Macrophages communicate with immune complexes via Fcγ receptors. Absence of functional activating receptors completely abrogates the synovial inflammation, as was shown after ICA induction in FcR γ-chain(-/-) mice. However, the γ-chain is essential not only in FcγRI and RIII but also for FcεRI (found on mast cells) and the T cell receptor (TcR)-CD3 (Tcells) complex of γδT cells. However, T, B, or mast cells do not play a role in this arthritis that is induced by passive immunisation. Furthermore, this effect was not caused by a difference in clearance of IgG or complement deposition in the tissue. In this study, DBA/1 mice, which are susceptible to collagen-induced autoimmune arthritis and in a recent study have been shown to react hypersensitively to immune complexes, are shown to express higher levels of FcγRs on both synovial and peritoneal macrophages. Because antibodies directed against the different subclasses of FcγR are not available, no distinction could be made between FcγRII and RIII. Genetic differences in DBA/1 mice in genes coding for or regulating FcγRs may be responsible for altered FcγR expression. If so, these mouse strains would have a heightened risk for immune-complex-mediated diseases. To provide conclusive evidence for the roles of the various classes of FcγR during ICA, experiments are needed in which FcγRs are blocked with specific antibodies, or in which knockout mice lacking one specific class of FcγR are used. The only available specific antibody to FcγR (2.4G2) has a stimulatory effect on cells once bound to the receptor, and therefore cannot be used in blocking experiments. Experiments using specific knockout mice are now being done in our laboratory. Macrophages are the dominant type of cell present in chronic inflammation during RA and their number has been shown to correlate well with severe cartilage destruction. Apart from that, in humans, these synovial tissue macrophages express activating FcRs, mainly FcγIIIa, which may lead to activation of these macrophages by IgG-containing immune complexes. The expression of FcRs on the surface of these cells may have important implications for joint inflammation and severe cartilage destruction and therefore FCRs may constitute a new target for therapeutic intervention

Iflavirus increases its infectivity and physical stability in association with baculovirus

Virus transmission and the prevalence of infection depend on multiple factors, including the interaction with other viral pathogens infecting the same host. In this study, active replication of an iflavirus, Spodoptera exigua iflavirus 1 (order Picornavirales) was observed in the offspring of insects that survived following inoculation with a pathogenic baculovirus, Spodoptera exigua multiple nucleopolyhedrovirus. Tracking the origin of the iflavirus suggested the association of this virus with the occlusion bodies of the baculovirus. Here we investigated the effect of this association on the stability and infectivity of both viruses. A reduction in baculovirus pathogenicity, without affecting its infectivity and productivity, was observed when associated with the iflavirus. In contrast, viral association increased the infectivity of the iflavirus and its resistance to ultraviolet radiation and high temperature, two of the main factors affecting virus stability in the field. In addition, electron microscopy analysis revealed the presence of particles resembling iflavirus virions inside the occlusion bodies of the baculovirus, suggesting the possible co-occlusion of both viruses. Results reported here are indicative of facultative phoresis of a virus and suggest that virus virus interactions may be more common than currently recognized, and may be influential in the ecology of baculovirus and host populations and in consequence in the use of baculoviruses as biological insecticides.This study received financial support from the Spanish Ministry for Science and Technology (AGL2011-30352-C02 and AGL2014-57752-C2)