The effects of symmetry on the dynamics of antigenic variation

In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the dynamics of immune escape of other parasites, as well as for the dynamics of multi-strain diseases.     

Effect of weight loss and exercise on angiogenic factors in the circulation and in adipose tissue in obese subjects

Background:

Vascular growth is a prerequisite for adipose tissue (AT) development and expansion. Some AT cytokines and hormones have effects on vascular development, like vascular endothelial growth factor (VEGF‐A), angiopoietin (ANG‐1), ANG‐2 and angiopoietin‐like protein‐4 (ANGPTL‐4).

Methods:

In this study, the independent and combined effects of diet‐induced weight loss and exercise on AT gene expression and proteins levels of those angiogenic factors were investigated. Seventy‐nine obese males and females were randomized to: 1. Exercise‐only (EXO; 12‐weeks exercise without diet‐restriction), 2. Hypocaloric diet (DIO; 8‐weeks very low energy diet (VLED) + 4‐weeks weight maintenance diet) and 3. Hypocaloric diet and exercise (DEX; 8‐weeks VLED + 4‐weeks weight maintenance diet combined with exercise throughout the 12 weeks). Blood samples and fat biopsies were taken before and after the intervention.

Results:

Weight loss was 3.5 kg in the EXO group and 12.3 kg in the DIO and DEX groups. VEGF‐A protein was non‐significantly reduced in the weight loss groups. ANG‐1 protein levels were significantly reduced 22‐25% after all three interventions (P < 0.01). The ANG‐1/ANG‐2 ratio was also decreased in all three groups (P < 0.05) by 27‐38%. ANGPTL‐4 was increased in the EXO group (15%, P < 0.05) and 9% (P < 0.05) in the DIO group. VEGF‐A, ANG‐1, and ANGPTL‐4 were all expressed in human AT, but only ANGPTL‐4 was influenced by the interventions.

Conclusions:

Our data show that serum VEGF‐A, ANG‐1, ANG‐2, and ANGPTL‐4 levels are influenced by weight changes, indicating the involvement of these factors in the obese state. Moreover, it was found that weight loss generally was associated with a reduced angiogenic activity in the circulation.     

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases.     

Mean-field models for non-Markovian epidemics on networks

Journal of Mathematical Biology - This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general...     

Immunological serotype interactions and their effect on the epidemiological pattern of dengue

Long-term epidemiological data reveal multi-annual fluctuations in the incidence of dengue fever and dengue haemorrhagic fever, as well as complex cyclical behaviour in the dynamics of the four serotypes of the dengue virus. It has previously been proposed that these patterns are due to the phenomenon of the so-called antibody-dependent enhancement (ADE) among dengue serotypes, whereby viral replication is increased during secondary infection with a heterologous serotype; however, recent studies have implied that this positive reinforcement cannot account for the temporal patterns of dengue and that some form of cross-immunity or external forcing is necessary. Here, we show that ADE alone can produce the observed periodicities and desynchronized oscillations of individual serotypes if its effects are decomposed into its two possible manifestations: enhancement of susceptibility to secondary infections and increased transmissibility from individuals suffering from secondary infections. This decomposition not only lowers the level of enhancement necessary for realistic disease patterns but also reduces the risk of stochastic extinction. Furthermore, our analyses reveal a time-lagged correlation between serotype dynamics and disease incidence rates, which could have important implications for understanding the irregular pattern of dengue epidemics.     

Iron and iron/manganese ratio in forage from Icelandic sheep farms: relation to scrapie

This study was undertaken in order to examine whether any connection existed between the amounts of iron in forage and the sporadic occurrence of scrapie observed in certain parts of Iceland. As iron and manganese are considered antagonistic in plants, calculation of the Fe/Mn ratios was also included by using results from Mn determination earlier performed in the same samples. Forage samples (n = 170) from the summer harvests of 2001–2003, were collected from 47 farms for iron and manganese analysis. The farms were divided into four categories: 1. Scrapie-free farms in scrapie-free areas (n = 9); 2. Scrapie-free farms in scrapie-afflicted areas (n = 17); 3. Scrapie-prone farms (earlier scrapie-afflicted, restocked farms) (n = 12); 4. Scrapie-afflicted farms (n = 9). Farms in categories 1 and 2 are collectively referred to as scrapie-free farms. The mean iron concentration in forage samples from scrapie-afflicted farms was significantly higher than in forage samples from farms in the other scrapie categories (P = 0.001). The mean Fe/Mn ratio in forage from scrapie-afflicted farms was significantly higher than in forage from scrapie-free and scrapie-prone farms (P < 0.001). The results indicated relative dominance of iron over manganese in forage from scrapie-afflicted farms as compared to farms in the other categories. Thus thorough knowledge of iron, along with manganese, in soil and vegetation on sheep farms could be a pivot in studies on sporadic scrapie.     

Scanning electron microscopy and gramicidin patch clamp recordings of microvillous receptor neurons dissociated from the rat vomeronasal organ

Vomeronasal organs from female rats were dissociated and isolated microvillous receptor neurons were studied. The isolated receptor neurons kept the typical bipolar shape which they have in situ as observed by scanning electron microscopy. We applied the perforated patch-clamp technique using the cation-selective ionophore gramicidin on freshly isolated and well differentiated receptor neurons. The mean resting potential was -58+/-14 mV (n=39). The contribution of the sodium pump current to the resting potential was demonstrated by lowering the K+ concentration in the bath or by application of 100 microM dihydro-ouabain. The input resistance was in the range of 1-6 GOmega and depolarizing current pulses of a few pA were sufficient to trigger overshooting action potentials. In voltage clamp conditions a fast transient sodium inward current and a sustained outward potassium current were activated by membrane depolarization. These observations indicate that freshly isolated vomeronasal receptor neurons of rats can be recorded, using gramicidin, with little modification of the intracellular content. Their electrophysiological properties are very similar to those observed in situ. Four out of eight female vomeronasal receptor cells were depolarized by diluted rat male urine.      

Stability and bifurcations in a model of antigenic variation in malaria

We examine the properties of a recently proposed model for antigenic variation in malaria which incorporates multiple epitopes and both long-lasting and transient immune responses. We show that in the case of a vanishing decay rate for the long-lasting immune response, the system exhibits the so-called “bifurcations without parameters” due to the existence of a hypersurface of equilibria in the phase space. When the decay rate of the long-lasting immune response is different from zero, the hypersurface of equilibria degenerates, and a multitude of other steady states are born, many of which are related by a permutation symmetry of the system. The robustness of the fully symmetric state of the system was investigated by means of numerical computation of transverse Lyapunov exponents. The results of this exercise indicate that for a vanishing decay of long-lasting immune response, the fully symmetric state is not robust in the substantial part of the parameter space, and instead all variants develop their own temporal dynamics contributing to the overall time evolution. At the same time, if the decay rate of the long-lasting immune response is increased, the fully symmetric state can become robust provided the growth rate of the long-lasting immune response is rapid. This work was partially supported by the ATRJVVO grant from the James Martin 21st Century School, University of Oxford.