Nutrigonometry I: using right-angle triangles to quantify nutritional trade-offs in performance landscapes

AbstractAnimals regulate their food intake to maximize the expression of fitness traits but are forced to trade off the optimal expression of some fitness traits because of differences in the nutrient requirements of each trait ("nutritional trade-offs"). Nutritional trade-offs have been experimentally uncovered using the geometric framework for nutrition (GF). However, current analytical methods to measure such responses rely on either visual inspection or complex models of vector calculations applied to multidimensional performance landscapes, making these approaches subjective or conceptually difficult, computationally expensive, and, in some cases, inaccurate. Here, we present a simple trigonometric model to measure nutritional trade-offs in multidimensional landscapes (nutrigonometry) that relies on the trigonometric relationships of right-angle triangles and thus is both conceptually and computationally easier to understand and use than previous quantitative approaches. We applied nutrigonometry to a landmark GF data set for comparison of several standard statistical models to assess model performance in finding regions in the performance landscapes. This revealed that polynomial (Bayesian) regressions can be used for precise and accurate predictions of peaks and valleys in performance landscapes, irrespective of the underlying structure of the data (i.e., individual food intakes vs. fixed diet ratios). We then identified the known nutritional trade-off between life span and reproductive rate in terms of both nutrient balance and concentration for validation of the model. This showed that nutrigonometry enables a fast, reliable, and reproducible quantification of nutritional trade-offs in multidimensional performance landscapes, thereby broadening the potential for future developments in comparative research on the evolution of animal nutrition.

An integrative approach to dietary balance across the life course

Animals require specific blends of nutrients that vary across the life course and with circumstances, e.g., health and activity levels. Underpinning and complicating these requirements is that individual traits may be optimized on different dietary compositions leading to nutrition-mediated trade-offs among outcomes. Additionally, the food environment may constrain which nutrient mixtures are achievable. Natural selection has equipped animals for solving such multi-dimensional, dynamic challenges of nutrition, but little is understood about the details and their theoretical and practical implications. We present an integrative framework, nutritional geometry, which models complex nutritional interactions in the context of multiple nutrients and across levels of biological organization (e.g., cellular, individual, and population) and levels of analysis (e.g., mechanistic, developmental, ecological, and evolutionary). The framework is generalizable across different situations and taxa. We illustrate this using examples spanning insects to primates and settings (laboratory, and the wild), and demonstrate its relevance for human health.

The Ol1mpiad: concordance of behavioural faculties of stage 1 and stage 3 Drosophila larvae

Mapping brain function to brain structure is a fundamental task for neuroscience. For such an endeavour, the Drosophila larva is simple enough to be tractable, yet complex enough to be interesting. It features about 10,000 neurons and is capable of various taxes, kineses and Pavlovian conditioning. All its neurons are currently being mapped into a light-microscopical atlas, and Gal4 strains are being generated to experimentally access neurons one at a time. In addition, an electron microscopic reconstruction of its nervous system seems within reach. Notably, this electron microscope-based connectome is being drafted for a stage 1 larva – because stage 1 larvae are much smaller than stage 3 larvae. However, most behaviour analyses have been performed for stage 3 larvae because their larger size makes them easier to handle and observe. It is therefore warranted to either redo the electron microscopic reconstruction for a stage 3 larva or to survey the behavioural faculties of stage 1 larvae. We provide the latter. In a community-based approach we called the Ol1mpiad, we probed stage 1 Drosophila larvae for free locomotion, feeding, responsiveness to substrate vibration, gentle and nociceptive touch, burrowing, olfactory preference and thermotaxis, light avoidance, gustatory choice of various tastants plus odour–taste associative learning, as well as light/dark–electric shock associative learning. Quantitatively, stage 1 larvae show lower scores in most tasks, arguably because of their smaller size and lower speed. Qualitatively, however, stage 1 larvae perform strikingly similar to stage 3 larvae in almost all cases. These results bolster confidence in mapping brain structure and behaviour across developmental stages.

The developmental control of size in insects

The mechanisms that control the sizes of a body and its many parts remain among the great puzzles in developmental biology. Why do animals grow to a species-specific body size, and how is the relative growth of their body parts controlled to so they grow to the right size, and in the correct proportion with body size, giving an animal its species-characteristic shape? Control of size must involve mechanisms that somehow assess some aspect of size and are upstream of mechanisms that regulate growth. These mechanisms are now beginning to be understood in the insects, in particular in Manduca sexta and Drosophila melanogaster. The control of size requires control of the rate of growth and control of the cessation of growth. Growth is controlled by genetic and environmental factors. Insulin and ecdysone, their receptors, and intracellular signaling pathways are the principal genetic regulators of growth. The secretion of these growth hormones, in turn, is controlled by complex interactions of other endocrine and molecular mechanisms, by environmental factors such as nutrition, and by the physiological mechanisms that sense body size. Although the general mechanisms of growth regulation appear to be widely shared, the mechanisms that regulate final size can be quite diverse.

The Role of the Prothoracic Gland in Determining Critical Weight for Metamorphosis in Drosophila melanogaster

BACKGROUND

The timely onset of metamorphosis in holometabolous insects depends on their reaching the appropriate size known as critical weight. Once critical weight is reached, juvenile hormone (JH) titers decline, resulting in the release of prothoracicotropic hormone (PTTH) at the next photoperiod gate and thereby inducing metamorphosis. How individuals determine when they have reached critical weight is unknown. We present evidence that in Drosophila, a component of the ring gland, the prothoracic gland (PG), assesses growth to determine when critical weight has been achieved.

RESULTS

We used the GAL4/UAS system to suppress or enhance growth by overexpressing PTEN or Dp110, respectively, in various components of the ring gland. Suppression of the growth of the PG and CA, but not of the CA alone, produced larger-than-normal larvae and adults. Suppression of only PG growth resulted in nonviable larvae, but larvae with enlarged PGs produced significantly smaller larvae and adults. Rearing larvae with enlarged PGs under constant light enhanced these effects, suggesting a role for photoperiod-gated PTTH secretion. These larvae are smaller, in part as a result of their repressed growth rates, a phenotype that could be rescued through nutritional supplementation (yeast paste). Most importantly, larvae with enlarged PGs overestimated size so that they initiated metamorphosis before surpassing the minimal viable weight necessary to survive pupation.

CONCLUSIONS

The PG acts as a size-assessing tissue by using insulin-dependent PG cell growth to determine when critical weight has been reached.

Ecdysteroid control of metamorphosis in the differentiating adult leg structures of Drosophila melanogaster

During insect metamorphosis, the steroid hormone 20-hydroxyecdysone (20E) is responsible for coordinating the differentiation of adult structures. Several structures of the Drosophila melanogaster adult leg, the six distalmost joints, the bristles, and the pretarsal claws, were examined to investigate how 20E controls their development in vitro. Joints, bristles, and claws were dependent on 20E for differentiation between 20-22 and 24-26 h after puparium formation (APF). After 26-28 h APF, differentiation became hormone independent. Tissue-specific markers in 20E-free cultures showed that the bristle and joint cells had not undergone any further morphogenetic progression. In contrast, the pretarsi underwent partial differentiation. The concentration of 20E required for differentiation was structure specific; tarsal joints required higher concentrations of 20E (greater than 400 ng 20 E/ml) than pretarsal claws, bristles, and other joints (greater than 40 ng 20E/ml). The 20E precursor ecdysone (E) was also able to induce differentiation at concentrations over 700 ng E/ml, but did not show any synergistic interactions with 20E. Lastly, leg structures had a finite ability to respond to 20E; tarsal joints lost competence to respond after 32-34 h APF, while the remaining structures became incompetent after 44-46 h APF.

Joint development in the Drosophila leg: cell movements and cell populations

Flexible joints separate the rigid sections of the insect leg, allowing them to move. In Drosophila, the initial patterning of these joints is apparent in the larval imaginal discs from which the adult legs will develop. Here, we describe the later patterning and morphogenesis of the joints, which occurs after pupariation (AP). In the tibial/tarsal joint, the apodeme insertion site provides a fixed marker for the boundary between proximal and distal joint territories (the P/D boundary). Cells on either side of this boundary behave differently during morphogenesis. Morphogenesis begins with the apical constriction of distal joint cells, about 24 h AP. Distal cells then become columnar, causing distal tissue nearest the P/D boundary to fold into the leg. In the last stage of joint morphogenesis, the proximal joint cells closest to the P/D boundary align and elongate to form a "palisade" (a row of columnar cells) over the distal joint cells. The proximal and distal joint territories are characterised by the differential organisation of cytoskeletal and extracellular matrix proteins, and by the differential expression of enhancer trap lines and other gene markers. These markers also define a number of more localised territories within the pupal joint.