Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation.

Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.

Thermodynamic Cost, Speed, Fluctuations, and Error Reduction of Biological Copy Machines.

Due to large fluctuations in cellular environments, transfer of information in biological processes without regulation is error-prone. The mechanistic details of error-reducing mechanisms in biological copying processes have been a subject of active research; however, how error reduction of a process is balanced with its thermodynamic cost and dynamical properties remain largely unexplored. Here, we study the error reducing strategies in light of the recently discovered thermodynamic uncertainty relation (TUR) that sets a physical bound to the cost-precision trade-off for dissipative processes. We found that the two representative copying processes, DNA replication by the exonuclease-deficient T7 DNA polymerase and mRNA translation by the E. coli ribosome, reduce the error rates to biologically acceptable levels while also optimizing the processes close to the physical limit dictated by TUR.

Energy budget of Drosophila embryogenesis.

Eggs of oviparous animals must be prepared to develop rapidly and robustly until hatching. The balance between sugars, fats, and other macromolecules must therefore be carefully considered when loading the egg with nutrients. Clearly, packing too much or too little fuel would lead to suboptimal conditions for development. While many studies have measured the overall energy utilization of embryos, little is known of the identity of the molecular-level processes that contribute to the energy budget in the first place [1]. Here, we introduce Drosophila embryos as a platform to study the energy budget of embryogenesis. We demonstrate through three orthogonal measurements - respiration, calorimetry, and biochemical assays - that Drosophila melanogaster embryogenesis utilizes 10 mJ of energy generated by the oxidation of the maternal glycogen and triacylglycerol (TAG) stores (Figure 1). Normalized for mass, this is comparable to the resting metabolic rates of insects [2]. Interestingly, alongside data from earlier studies, our results imply that protein, RNA, and DNA polymerization require less than 10% of the total ATPs produced in the early embryo.