Propagation of fluctuations in biochemical systems, I: Linear SSC networks

We investigate the propagation of random fluctuations through biochemical networks in which the number of molecules of each species is large enough so that the concentrations are well modeled by differential equations. We study the effect of network topology on the emergent properties of the reaction system by characterizing the behavior of variance as fluctuations propagate down chains and studying the effect of side chains and feedback loops. We also investigate the asymptotic behavior of the system as one reaction becomes fast relative to the others. © 2007 Springer Science+Business Media, Inc

A Switch in the Control of Growth of the Wing Imaginal Disks of Manduca sexta

Background: Insulin and ecdysone are the key extrinsic regulators of growth for the wing imaginal disks of insects. In vitro tissue culture studies have shown that these two growth regulators act synergistically: either factor alone stimulates only limited growth, but together they stimulate disks to grow at a rate identical to that observed in situ. It is generally thought that insulin signaling links growth to nutrition, and that starvation stops growth because it inhibits insulin secretion. At the end of larval life feeding stops but the disks continue to grow, so at that time disk growth has become uncoupled from nutrition. We sought to determine at exactly what point in development this uncoupling occurs. Methodology: Growth and cell proliferation in the wing imaginal disks and hemolymph carbohydrate concentrations were measured at various stages in the last larval instar under experimental conditions of starvation, ligation, rescue, and hormone treatment. Principal Findings: Here we show that in the last larval instar of M. sexta, the uncoupling of nutrition and growth occurs as the larva passes the critical weight. Before this time, starvation causes a decline in hemolymph glucose and trehalose and a cessation of wing imaginal disks growth, which can be rescued by injections of trehalose. After the critical weight the trehalose response to starvation disappears, and the expression of insulin becomes decoupled from nutrition. After the critical weight the wing disks loose their sensitivity to repression by juvenile hormone, and factors from the abdomen, bu

A model for selection of eyespots on butterfly wings

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell

Spatial variation in boundary conditions can govern selection and location of eyespots in butterfly wings

Despite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reaction-diffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.Publisher PD

Effect of Dietary Components on Larval Life History Characteristics in the Medfly (Ceratitis capitata: Diptera, Tephritidae)

Background: The ability to respond to heterogenous nutritional resources is an important factor in the adaptive radiation of insects such as the highly polyphagous Medfly. Here we examined the breadth of the Medfly’s capacity to respond to different developmental conditions, by experimentally altering diet components as a proxy for host quality and novelty. Methodology/Principal Findings: We tested responses of larval life history to diets containing protein and carbohydrate components found in and outside the natural host range of this species. A 40% reduction in the quantity of protein caused a significant increase in egg to adult mortality by 26.5%±6% in comparison to the standard baseline diet. Proteins and carbohydrates had differential effects on larval versus pupal development and survival. Addition of a novel protein source, casein (i.e. milk protein), to the diet increased larval mortality by 19.4%±3% and also lengthened the duration of larval development by 1.93±0.5 days in comparison to the standard diet. Alteration of dietary carbohydrate, by replacing the baseline starch with simple sugars, increased mortality specifically within the pupal stage (by 28.2%±8% and 26.2%±9% for glucose and maltose diets, respectively). Development in the presence of the novel carbohydrate lactose (milk sugar) was successful, though on this diet there was a decrease of 29.8±1.6 µg in mean pupal weight in comparison to pupae reared on the baseline diet. Conclusions: The results confirm that laboratory reared Medfly retain the ability to survive development through a wide range of fluctuations in the nutritional environment. We highlight new facets of the responses of different stages of holometabolous life histories to key dietary components. The results are relevant to colonisation scenarios and key to the biology of this highly invasive species

Color changes upon cooling of Lepidoptera scales containing photonic nanoarchitectures, and a method for identifying the changes

The effects produced by the condensation of water vapor from the environment in the various intricate nanoarchitectures occurring in the wing scales of several Lepidoptera species were investigated by controlled cooling (from 23° C, room temperature to -5 to -10° C) combined with in situ measurements of changes in the reflectance spectra. It was determined that all photonic nanoarchitectures giving a reflectance maximum in the visible range and having an open nanostructure exhibited alteration of the position of the reflectance maximum associated with the photonic nanoarchitectures. The photonic nanoarchitectures with a closed structure exhibited little to no alteration in color. Similarly, control specimens colored by pigments did not exhibit a color change under the same conditions. Hence, this method can be used to identify species with open photonic nanoarchitectures in their scales. For certain species, an almost complete disappearance of the reflectance maximum was found. All specimens recovered their original colors following warming and drying. Cooling experiments using thin copper wires demonstrated that color alterations could be limited to a width of a millimeter or less. Dried museum specimens did not exhibit color changes when cooled in the absence of a heat sink due to the low heat capacity of the wings

Artificially induced changes of butterfly wing colour patterns: dynamic signal interactions in eyespot development

Eyespot formation in butterfly wings has been explained by the concentration gradient model. However, this model has recently been questioned, and dynamic interactions between the black-inducing signal and its inhibitory signal have been proposed. Here, the validity of these models was examined using a nymphalid butterfly Junonia almana. Early focal damage to the major eyespots often made them smaller, whereas the late damage made the outer ring larger and the inner ring smaller in a single eyespot. Non-focal damage at the outer ring not only attracted the whole eyespot structure toward the damaged site but also reduced the overall size of the eyespot. Surprisingly, a reduction of the major eyespot was accompanied by an enlargement of the associated miniature eyespots. These results demonstrate limitations of the conventional gradient model and support a dynamic interactive nature of morphogenic signals for colour-pattern determination in butterfly wings

A Reversible Color Polyphenism in American Peppered Moth (Biston betularia cognataria) Caterpillars

Insect body color polyphenisms enhance survival by producing crypsis in diverse backgrounds. While color polyphenisms are often indirectly induced by temperature, rearing density, or diet, insects can benefit from immediate crypsis if they evolve polyphenisms directly induced by exposure to the background color, hence immediately deriving protection from predation. Here, we examine such a directly induced color polyphenism in caterpillars of the geometrid peppered moth (Biston betularia). This larval color polyphenism is unrelated to the genetic polymorphism for melanic phenotypes in adult moths. B. betularia caterpillars are generalist feeders and develop body colors that closely match the brown or green twigs of their host plant. We expand on previous studies examining the proximal cues that stimulate color development. Under controlled rearing conditions, we manipulated diets and background reflectance, using both natural and artificial twigs, and show that visual experience has a much stronger effect than does diet in promoting precise color matching. Their induced body color was not a simple response to reflectance or light intensity but instead specifically matched the wavelength of light to which they were exposed. We also show that the potential to change color is retained until the final (sixth) larval instar. Given their broad host range, this directly induced color polyphenism likely provides the caterpillars with strong protection from bird predation