Cancer immunotherapy, mathematical modeling and optimal control

Clinical immunologists, among other problems, routinely face a question: what is the best time and dose for a certain therapeutic agent to be administered to the patient in order to decrease/eradicate the pathological condition? In cancer immunotherapies the therapeutic agent is something able to elicit an immune response against cancer. The immune response has its own dynamics that depends on the immunogenicity of the therapeutic agent and on the duration of the immune response. The question then is "how can we decide when and how much of the drug to inject so to have a prolonged and effective immune response to the cancer?". This question can be addressed in mathematical terms in two stages: first one construct a mathematical model describing the cancer-immune interaction and secondly one applies the theory of optimal control to determine when and to which extent to stimulate the immune system by means of an immunotherapeutic agent administered in discrete variable doses within the therapeutic period. The solution of this mathematical problem is described and discussed in this article. We show that the method employed can be applied to find the optimal protocol in a variety of clinical problems where the kinetics of the drug or treatment and its influence on the physiologic/pathologic functions have been described by a system of ordinary differential equations.     

Bottom-up and cascading top-down control of macroalgae along a depth gradient

On marine rocky shores, macroalgal herbivory is often intense, such that the cascading effects of fish predation may contribute to the control of algal communities. To estimate the magnitudes of top-down and bottom-up control on a macroalgal community, we manipulated the access of carnivorous fish to macroalgal colonization substrates, as well as nutrient availability, at two sub-littoral depths. There were three levels of fish manipulation: natural fish community, no fish and the enclosure of one common species, the perch, Perca fluviatilis. We found a clear cascade effect of fish predation on both the total density and several individual species of macroalgae, which was more pronounced in deep than shallow water. The density of the dominant grazers, i.e. snails, increased in nutrient-enriched conditions; perch were inefficient in controlling herbivores, and had therefore no cascading effect on algal densities under such conditions. Although nutrients enhanced the growth of opportunistic algae, herbivores, in the absence of fish, inhibited this response. While algal diversity was higher in shallow than in deep water, the enrichment effect was opposite at the two depths with lowered diversity in the shallows and increased at depth. Our results indicate that fish predation is an efficient regulator of meso-herbivores and that its effect thereby cascades onto the producer trophic level such that both perennial and opportunistic algae benefit from the presence of fish. This cascade effect is probably stronger at depth where predation efficiency is less disturbed by wave motion.     

The use of ultraviolet-blocking films in insect pest management in the UK; effects on naturally occurring arthropod pest and natural enemy populations in a protected cucumber crop

Studies in polytunnels were conducted to investigate the effects of ultraviolet (UV)‐blocking films on naturally occurring insect pests and their arthropod natural enemies on a cucumber crop. Within tunnels clad with Antibotrytis (blocks light < 400 nm) and UVI/EVA (UV transmitting), 5.8 and 23.4 times more aphids, respectively, were recorded on traps compared with those on traps within tunnels clad with XL 385 (blocks light < 385 nm). When all plants within the UVI/EVA tunnels had become heavily infested with aphids, half of the plants in XL 385 tunnels were uninfested. More Coleoptera and thrips (approximately two times) were recorded under the UVI/EVA film than under the UV‐blocking films, but for other arthropod pests (e.g. whitefly, leafhoppers), clear conclusions could not be drawn as low numbers were recorded. Substantial numbers of chalcid parasitoids and syrphids were found under the UV‐blocking films, but further research is needed to evaluate fully the effect of such films on biological control of aphids. Higher syrphid numbers and more aphid mummies were recorded under the UVI/EVA film, probably because of the higher numbers of aphids present in tunnels clad with this film. The potential that UV‐blocking films have as an effective component of commercial Integrated Pest Management (IPM) systems, for protected horticultural crops, is discussed.     

Human pathologies associated with defective RNA transport and localization in the nervous system

RNA localization is emerging as an important process to restrict certain proteins to specific subcellular domains and thus spatially control the expression of genes within cells. It is used, for instance, to compartmentalize the developing embryo during early embryogenesis. The localization of RNA also plays important roles later during development, such as in asymmetric cell divisions, cell migration and the outgrowth and pathfinding of axons and dendrites. In differentiated cells, it serves to subdivide the cell into functionally distinct compartments. For example, in mature neurons it is believed to contribute to the plastic changes of individual synapses underlying learning and memory. In this review, we highlight the importance of subcellular RNA localization for the function of the nervous system and neurological diseases associated with defective RNA localization and translation. These diseases include fragile X mental retardation syndrome, spinocerebellar ataxia and spinal muscular atrophy.     

Mitochondrial DNA sequence diversity and origin of Chinese domestic yak

In order to clarify the origin and genetic diversity of yak in China, we analysed mitochondrial DNA (mtDNA) control region sequences (approximately 891 bp) in 52 individuals from four domestic yak (Poephagus grunniens) breeds, as well as from a hybrid between yak and cattle (Pianniu). Twenty-five samples were further selected for partial (420 bp) cytochrome b sequencing based on control region sequence information. Two yak samples shared sequences with Chinese cattle (Bos taurus); the remaining yak mtDNAs converged into two major clades in the phylogenetic analysis. Genetic diversity varied substantially among the breeds, with the hybrid Pianniu yak demonstrating the highest diversity. Our results suggest that the Chinese yak was domesticated from two distinct matrilineal sources or from a heterogeneous pool containing both divergent lineages, with occasional gene introgression from cattle.     

Association of MT-ND5 gene variation with mitochondrial respiratory control ratio and NADH dehydrogenase activity in Tibet chicken embryos

NADH dehydrogenase (complex I) couples the oxidation of NADH for the reduction of ubiquinone with the generation of a proton gradient that can be used for the synthesis of ATP. We have found a missense mutation in the MT-ND5 subunit of NADH dehydrogenase in the Tibet chicken breed. In the present study, the mitochondrial respiratory control ratio (RCR) and NADH dehydrogenase activity in Tibet chicken embryonic brain with different genotypes were measured. Significant differences between animals carrying mitochondria with the EF493865.1:m.1627A vs. EF493865.1:m.1627C alleles were observed for RCR and enzyme activity.     

Less is more: restricted application of insecticide to cattle to improve the cost and efficacy of tsetse control

Studies were carried out in Zimbabwe of the responses of tsetse to cattle treated with deltamethrin applied to the parts of the body where most tsetse were shown to land. Large proportions of Glossina pallidipes Austen (Diptera: Glossinidae) landed on the belly ( approximately 25%) and legs ( approximately 70%), particularly the front legs ( approximately 50%). Substantial proportions of Glossina morsitans morsitans Westwood landed on the legs ( approximately 50%) and belly (25%), with the remainder landing on the torso, particularly the flanks ( approximately 15%). Studies were made of the knockdown rate of wild, female G. pallidipes exposed to cattle treated with a 1% pour-on or 0.005% suspension concentrate of deltamethrin applied to the (a) whole body, (b) belly and legs, (c) legs, (d) front legs, (e) middle and lower front legs, or (f) lower front legs. The restricted treatments used 20%, 10%, 5%, 2% or 1% of the active ingredient applied in the whole-body treatments. There was a marked seasonal effect on the performance of all treatments. With the whole-body treatment, the persistence period (knockdown > 50%) ranged from approximately 10 days during the hot, wet season (mean daily temperature > 30 degrees C) to approximately 20 days during the cool, dry season (< 22 degrees C). Restricting the application of insecticide reduced the seasonal persistence periods to approximately 10-15 days if only the legs and belly were treated, approximately 5-15 days if only the legs were treated and < 5 days for the more restricted treatments. The restricted application did not affect the landing distribution of tsetse or the duration of landing bouts (mean = 30 s). The results suggest that more cost-effective control of tsetse could be achieved by applying insecticide to the belly and legs of cattle at 2-week intervals, rather than using the current practice of treating the whole body of each animal at monthly intervals. This would cut the cost of insecticide by 40%, improve efficacy by 27% and reduce the threats to non-target organisms and the enzootic stability of tick-borne diseases.     

Deltamethrin-impregnated bednets reduce human landing rates of sandfly vector Lutzomyia longipalpis in Amazon households

The entomological efficacy of using 25% deltamethrin EC insecticide-treated bednets (ITNs) was evaluated against the sandfly Lutzomyia longipalpis Lutz and Neiva (Diptera: Psychodidae), the principal vector of zoonotic visceral leishmaniasis (ZVL) in Latin America. A crossover field study in Amazon Brazil (Marajó Island, Pará State) demonstrated that, compared with untreated nets, the insecticide increased the barrier effect of nets by 39% (95% confidence interval [CI] 34-44%), reduced human landing rates by 80% (95% CI 62-90%) and increased the 24-h mortality rate from 0% to 98% (95% CI 93-99%) inside ITNs. The presence of an ITN also reduced the human landing rate on unprotected persons outside the net in the same room by 56% (95% CI 52-59%), and increased 24-h mortality to 68% (95% CI 62-73%) compared to 0.4% (0.1-2.0%) in untreated houses. The reduction in human landing rates in ITN rooms was associated with a doubling in the proportion of sandflies alighting on walls compared with that in untreated rooms, which was attributed to insecticide-induced excito-repellency. There was no evidence that sandflies were diverted onto unprotected hosts. Human landing catches inside houses peaked between 19.00 hours and 23.00 hours and declined steadily to zero at 02.00 hours and thereafter. House-to-house questionnaires established that only 34% of households owned at least one net (median two, range 1-8), only 20% of the population slept under a net (33% of 0-5-year-old children), and the majority (73%) of the population slept in hammocks. Combined data pertaining to sleeping times for children and sandfly activity period indicate that > 50% of sandfly bites inside houses, and substantially more outside houses, were taken before a third of children were potentially protected by a net. This study demonstrates the clear entomological efficacy of ITNs against Lu. longipalpis in this endemic region. The effectiveness of ITNs at preventing ZVL infection and disease has still to be evaluated.     

Allosteric control model of bone remodelling containing periodical modes

To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodelling process prevalent in native bone. We have formulated a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo and could set a basis for the more detailed allosteric models. The model is extended towards a bio-cybernetic vision of basic multicellular unit (BMU) action, when some of the regulation loops have been modified to reflect the allosteric control mechanisms, developed by Michaels-Menten, Hill, Koshland-Nemethy-Filmer, Monod-Wyman-Changeux. By implementation of this approach a four-dimensional system was obtained that shows steady cyclic behaviour using a wide range of constants with clear biological meaning. We have observed that a local steady state appears as a limiting cycle in multi-dimensional phase space and this is discussed in this paper. Physiological interpretation of this limiting four-dimension cycle possibly related to a conservative-like value has been proposed. Analysis and simulation of the model has shown an analogy between this conservative value, as a kind of substrate-energy regenerative potential of the bone remodelling system with a molecular nature, and to the classical physical value--energy. This dynamic recovery potential is directed against both mechanical and biomechanical damage to the bone. Furthermore, the current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Hill mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This result indicates the viability of the proposed existence of a conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. Linear stability analysis has been performed in order to determine the robustness of the basic state, however, additional work is required to study a wider range of constants.     

Modeling competition for infection sites on roots by nonpathogenic strains of Fusarium oxysporum

By use of plane and solid geometry and probability models, efficiencies of infection and competition for nutrients and infection sites by a nonpathogenic strain of Fusarium oxysporum (C14) with F. oxysporum f. sp. cucumerinum on the rhizoplane of cucumber were calculated. The model is derived from previously published data. Efficiencies for successful infection were 0.04 chlamydospores per infection site for both pathogen and nonpathogen. Observed successful infections by the pathogen in competition with the nonpathogen were close in values to the competition ratio (CR) calculated as the number of chlamydospores on the infection court of the pathogen divided by the total number of both pathogen and nonpathogen at relatively low densities. When total chlamydospores were, on average, closer than 175 μm apart, however, competition for nutrients/mutual inhibition occurred. At such densities there was an overestimation of the effect of competition for infection sites. These relationships were modeled at inoculum densities of pathogen and/or nonpathogen of 5000 chlamydospores per g soil and above, however, in the field, maximum densities of 1000 colony forming units/g (cfu) were observed. Most likely models of competition for infection sites at this density of the pathogen revealed that infection efficiency was only approximately halved, even when 0.98 of the possible 30 infection sites were occupied by the nonpathogen. It is conclude that competition for nutrients and/or infection sites is an insignificant factor in biocontrol of Fusarium wilt diseases by nonpathogenic fusaria.