A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield.
All data was generated from stochastic simulations in C++ and deterministic simulations in Matlab. The Source File Codes are uploaded with the manuscript files.
- Patrick Wilke
- Florian M Gartner
- Isabella R Graf
- Erwin Frey
- Erwin Frey
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
- Frank Jülicher, Max Planck Institute for the Physics of Complex Systems, Germany
© 2020, Gartner et al.
This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.
Cells convert electrical signals into chemical outputs to facilitate the active transport of information across larger distances. This electrical-to-chemical conversion requires a tightly regulated expression of ion channels. Alterations of ion channel expression provide landmarks of numerous pathological diseases, such as cardiac arrhythmia, epilepsy, or cancer. Although the activity of ion channels can be locally regulated by external light or chemical stimulus, it remains challenging to coordinate the expression of ion channels on extended spatial–temporal scales. Here, we engineered yeast Saccharomyces cerevisiae to read and convert chemical concentrations into a dynamic potassium channel expression. A synthetic dual-feedback circuit controls the expression of engineered potassium channels through phytohormones auxin and salicylate to produce a macroscopically coordinated pulses of the plasma membrane potential. Our study provides a compact experimental model to control electrical activity through gene expression in eukaryotic cell populations setting grounds for various cellular engineering, synthetic biology, and potential therapeutic applications.
Animal migration is highly sensitised to environmental cues, but plant dispersal is considered largely passive. The common dandelion, Taraxacum officinale, bears an intricate haired pappus facilitating flight. The pappus enables the formation of a separated vortex ring during flight; however, the pappus structure is not static but reversibly changes shape by closing in response to moisture. We hypothesised that this leads to changed dispersal properties in response to environmental conditions. Using wind tunnel experiments for flow visualisation, particle image velocimetry, and flight tests we characterised the fluid mechanics effects of the pappus morphing. We also modelled dispersal to understand the impact of pappus morphing on diaspore distribution. Pappus morphing dramatically alters the fluid mechanics of diaspore flight. We found that when the pappus closes in moist conditions, the drag coefficient decreases and thus the falling velocity is greatly increased. Detachment of diaspores from the parent plant also substantially decreases. The change in detachment when the pappus closes increases dispersal distances by reducing diaspore release when wind speeds are low. We propose that moisture-dependent pappus-morphing is a form of informed dispersal allowing rapid responses to changing conditions.