A quantitative analysis of the mechanism that controls body size in Manduca sexta

Abstract

Background: Body size is controlled by mechanisms that terminate growth when the individual reaches a species-specific size. In insects, it is a pulse of ecdysone at the end of larval life that causes the larva to stop feeding and growing and initiate metamorphosis. Body size is a quantitative trait, so it is important that the problem of control of body size be analyzed quantitatively. The processes that control the timing of ecdysone secretion in larvae of the moth Manduca sexta are sufficiently well understood that they can be described in a rigorous manner.

Results: We develop a quantitative description of the empirical data on body size determination that accurately predicts body size for diverse genetic strains. We show that body size is fully determined by three fundamental parameters: the growth rate, the critical weight (which signals the initiation of juvenile hormone breakdown), and the interval between the critical weight and the secretion of ecdysone. All three parameters are easily measured and differ between genetic strains and environmental conditions. The mathematical description we develop can be used to explain how variables such as growth rate, nutrition, and temperature affect body size.

Conclusion: Our analysis shows that there is no single locus of control of body size, but that body size is a system property that depends on interactions among the underlying determinants of the three fundamental parameters. A deeper mechanistic understanding of body size will be obtained by research aimed at uncovering the molecular mechanisms that give these three parameters their particular quantitative values.

Figure 1

Flow chart for the mechanism that controls body size in Manduca. During the last larval instar there are three physiological decision points (diamonds) that control the timing of the cessation of growth. The amount of growth in the intervals between these conditional events determines the final size. PCG, growth prior to the critical weight; during this period the larva achieves approximately half its final mass. ICG, the interval to cessation of growth, which corresponds to the delay period between attainment of the critical weight and the secretion of prothoracicotropic hormone (PTTH) (see Figure 2).

Figure 2

Method for establishing the critical weight and the delay time for PTTH secretion. Larvae are starved at various weights and the onset of wandering is determined and compared with that of larvae of similar weights that are allowed to continue feeding. The critical weight is the smallest weight at which there is no difference between starved and feeding larvae in the time required to initiate PTTH secretion and enter the wandering phase. The delay time is the time between achieving the critical weight and the actual secretion of PTTH, which corresponds to the ICG in Figure 1. Thus at the critical weight a series of events are set in motion that lead to PTTH secretion and that are not affected by subsequent nutrition. The critical weight occurs in about the middle of the growth phase of the fifth larval instar, so a larva can approximately double its mass after passing the critical weight.

Figure 3

Growth trajectory of a typical larva. Growth occurs during five larval instars, separated by brief periods of molting during which no growth occurs. (a) Linear plot: the peak on day 18 is the maximum size the larva attained and marks the time at which the larva stopped feeding and growing. Decreasing mass after this time is due to the purge of gut contents. (b) Semilogarithmic plot: dashed lines are exponential regressions on the growth phases of each of the five larval instars. The inset shows a plot of the exponents of the regressions in (b) showing a linear decrease with instar (the regression is: exponent = 1.01 - 0.098*instar; R² = 0.92).

Figure 4

Final sizes of the five larval instars of Manduca sexta. The size of the first four instars increase exponentially, but the final size of the fifth instar is about twice (10.75 g) what would be expected (5.39 g) from the regression on the earlier instars. The regression is: weight = 0.0014*e^1.66*instar (R² = 0.999).

Figure 5

Relationship between the empirically measured critical weight of a fifth-instar larva and the predicted weight at which a fifth instar would have molted to a sixth larval instar. The predicted weight is based on the projected terminal weight of the last larval instar deduced from the exponential increase from instar to instar (Dyar's rule), as shown in Figure 4. The fit to a slope of 1 is excellent.

Figure 6

Growth of a fifth-instar larva with a critical weight of 5.2 g. The vertical dotted line is drawn through the time point at which the critical weight is passed. The growth trajectory before this time is concave upward and the trajectory after this time is concave downward, and the best-fitting equations for each of these segments of the growth trajectory are indicated.

Figure 7

Growth trajectories of normal and JH-treated larvae of Manduca. JH-treated larvae (open circles) received a topical application of 50 μg methoprene (a stable JH analog) when they reached a weight of 3 g and again when they reached a weight of 6 g. Untreated larvae (filled circles) ceased feeding, purged their gut and entered the wandering stage on day 4. JH-treated larvae continued to feed for more than 2 weeks, but stopped growing after about 10–12 days, indicating that there is a physical limitation to the maximal size to which they can grow. Each curve is the mean of five larvae.

Figure 8

Relationship between the mass of the larva at the beginning of the last larval instar and the critical weight (CW), at which the decision to initiate the endocrine events that lead to metamorphosis is made. Each point is from a different genetic strain of Manduca that differs in body size and development time (G.D., D.A.R. and H.F.N., unpublished observations). The regression is: CW = 5.3*initial mass - 0.8 (R² = 0.95).

Figure 9

Derivation of growth exponent from growth rate on day 3. (a) The relationship between growth rate and growth exponent for larvae with the same initial weight. The relationship is best fit by a logarithmic regression where k = 0.2*ln(GR) + C, where C is a constant that depends on the initial weight of the instar. In this regression the initial weight was 1.5 g, which gives C = 0.25. (b) The relationship between C and the initial weight. An exponential regression gives the best fit. Substituting the equation in (b) for the constant C in k = 0.2*ln(GR) + C gives k = 0.2*ln(GR) + . So k can be deduced from the initial weight of the instar and the growth rate on the third day of the instar.

Figure 10

Variation in growth rate constant. Empirical growth data for three different strains: H (filled circles), B (triangles) and D (open circles), shows that all have the same rate of decay of the growth constant.

Figure 11

Predicted body sizes. Model predictions of peak weight of larvae of four different genetic strains of Manduca that differ in their growth parameters. 'Empirical data' are from Table 1. Bars are standard deviations.

Figure 12

Simulation of population variation in body size and development time. One thousand individuals were generated with small amounts of random variation in all parameter values of the model. (a) Frequency distribution of peak sizes; (b) frequency distribution of times at which peak size was reached and wandering stage began. Hatched areas are photoperiodic gates.

Figure 13

Model predictions of the effect of growth rate on body size. (a) Predicted effect of variation in growth rate on peak size; (b) predicted effect of variation in growth rate on peak size in the presence of a small amount of random variation in all other parameter values. Variation in the generating parameters masks the sawtooth character of the 'ideal' relationship. The line is a linear regression.

Figure 14

Relationship between body size and development time. Variation was introduced by allowing growth rate, critical weight and the ICG to vary with a standard deviation of 10% of the mean values of strain B in Table 1. The line is a linear regression on the data from 20,000 individuals (circles, many of which overlap in this plot).

Figure 15

Body size as a simultaneous function of the three fundamental parameters. The three parameters describe a volume of parameter space in which body size is depicted on a color scale. The two panels show different views of the same graph. The cutout is made to illustrate some of the data within the volume. The sawtooth-like discontinuities arise from the photoperiodic gating of PTTH and ecdysone secretion (see Figure 12a for a one-dimensional representation). ICG, the interval to cessation of growth.