The development of multicellular organisms such as Drosophila
is both precise and reproducible. Understanding the origin of precise and reproducible behavior, in development and in other biological processes, is fundamentally a quantitative question. We can distinguish two broad classes of ideas (Schrödinger 1944
). In one view, each step in the process is noisy and variable, and this biological variability is suppressed only through averaging over many elements or through some collective property of the whole network of elements. In the other view, each step has been tuned to enhance its reliability, perhaps down to some fundamental physical limits. These very different views lead to different questions and to different languages for discussing the results of experiments.
Our goal has been to locate the initial stages of Drosophila development on the continuum between the ‘precisionist’ view and the ‘noisy input, robust output’ view. To this end we have measured the absolute concentration of Bcd proteins, and used these measurements to estimate the physical limits to precision that arise from random arrival of these molecules at their targets. We then measured the input/output relation between Bcd and Hb, and found that Hb expression provides a readout of the Bcd concentration with better than 10% accuracy, very close to the physical limit. The mean input/output relation is reproducible from embryo to embryo, and direct measurements of the Bcd concentration profiles demonstrates that these too are reproducible from embryo to embryo at the ~ 10% level. Thus, the primary morphogen gradient is established with high precision, and it is transduced with high precision.
Our analysis of the Bcd/Hb input/output relations is similar in spirit to measurements of noise in gene expression that have been done in unicellular organisms (Elowitz et al 2002
; Raser & O’Shea 2004
; Rosenfeld et al 2005
). The morphogen gradients in early embryos provide a naturally occurring range of transcription factor concentrations to which cells respond, and the embryo itself provides an experimental “chamber” in which many factors that would be considered extrinsic to the regulatory process in unicellular organisms are controlled. Perhaps analogous to the distinction between intrinsic and extrinsic noise in single cells, we have distinguished between noise in the responses of individual nuclei to morphogens within a single embryo and the reproducibility of these input signals across embryos. Although there are many reasons why antibody staining might not provide a quantitative indicator of protein concentration, our results [see also Gregor et al (2007)
] show that coupling classical antibody staining methods with quantitative image analysis allows a quantitative characterization of noise in the potentially more complex metazoan context. This approach should be more widely applicable.
A central result of our work is the matching of the different measures of precision and reproducibility. We have seen that, near its point of half-maximal activation, the expression level of hb
provides a readout of Bcd concentration with better than 10% accuracy. At the same time, the reproducibility of the Bcd profile from embryo to embryo, and from one cycle of nuclear division to the next within one embryo (Gregor et al 2007
), is also at the ~ 10% level. Importantly, these different measures of precision and reproducibility must be determined by very different mechanisms. For the readout, there is a clear physical limit which may set the scale for all steps. This limiting noise level is sufficient to provide reliable discrimination between neighboring nuclei, thus providing sufficient positional information for the system to specify each “pixel” of the final pattern.
Previous work has shown that the Bcd profile scales to compensate for the large changes in embryo length across related species of flies (Gregor et al 2005
), but evidence for scaling across individuals within a species has been elusive, perhaps because the relevant differences are small. We find that the Bcd profile is sufficiently reproducible that it can specify position along the anterior-posterior axis within 1–2% when we express position in units relative to the length of the embryo ( & ). But embryos, for example in our ensemble of 15 that provide the data for , have a standard deviation of lengths δLrms
= 4.1%. Even if the Bcd profile were perfectly reproducible as concentration vs position in microns, this would mean that knowledge of relative position would be uncertain by 4%, more than what we see. This suggests that the Bcd profile exhibits some degree of scaling to compensate for length differences. New experiments will be required to test this more directly.
Our results suggest that communication among nearby nuclei, perhaps through a diffusable messenger, plays a role in the suppression of noise. The messenger could be Hb itself, since in the blastoderm stages the protein is free to diffuse between nuclei and hence the Hb protein concentration in one nucleus could reflect the Bcd-dependent mRNA translation levels of many neighboring nuclei. This model predicts that precision will depend on the local density of nuclei, and hence will be degraded in earlier nuclear cycles unless there are compensating changes in integration time. Such averaging mechanisms might be expected to smooth the spatial patterns of gene expression, which seems opposite to the goal of morphogenesis; the fact that Hb can activate its own expression (Margolis et al 1995
) may provide a compensating sharpening of the output profile. There is a theoretically interesting tradeoff between suppressing noise and blurring of the pattern, with self-activation shifting the balance. Note that the idea of spatial averaging, although employed here in a syncitial embryo, can be extended to non-syncitial systems, e.g. via autocrine signaling or via small molecules that can freely pass through cell membranes or gap junctions.
The reproducibility of absolute Bcd concentration profiles from embryo to embryo literally means that the number of copies of the protein is reproducible at the ~ 10% level. Understanding how the embryo achieves reproducibility in Bcd copy number is a significant challenge. Feedback mechanisms, explored for other morphogens (Eldar et al 2004
), could compensate for variations in mRNA levels, but the linear response of the Bcd profile to halving the dosage of the Bcd-eGFP transgene argues against such compensation. The simplest view consistent with all these data is that mRNA levels themselves are reproducible at the ~ 10% level, and this should be tested directly.
At a conceptual level our results on Drosophila
development have much in common with a stream of results on the precision of signaling and processing in other biological systems. There is a direct analogy between the approach to the physical limits in the Bcd/Hb readout and the sensitivity of bacterial chemotaxis (Berg & Purcell 1977
) or the ability of the visual system to count single photons (Rieke & Baylor 1998
; Bialek 2002
). In each case the reliability of the whole process is such that the randomness of essential molecular events dominates the reliability of the macroscopic output. There are several examples in which the reliability of neural processing reaches such limits (de Vries 1957, Barlow 1981
, Bialek 1987
), and it is attractive to think that developmental decision making operates with a comparable degree of reliability. The approach to physical limits places important constraints on the dynamics of the decision making circuits.
Finally, we note that the precision and reproducibility which we have observed in the embryo is disturbingly close to the resolution afforded by our measuring instruments.