We unravel how functional plasticity and redundancy are essential mechanisms underlying the ability to survive of metabolic networks. We perform an exhaustive computational screening of synthetic lethal reaction pairs in Escherichia coli in a minimal medium and we find that synthetic lethal pairs divide in two different groups depending on whether the synthetic lethal interaction works as a backup or as a parallel use mechanism, the first corresponding to essential plasticity and the second to essential redundancy. In E. coli, the analysis of pathways entanglement through essential redundancy supports the view that synthetic lethality affects preferentially a single function or pathway. In contrast, essential plasticity, the dominant class, tends to be inter-pathway but strongly localized and unveils Cell Envelope Biosynthesis as an essential backup for Membrane Lipid Metabolism. When comparing E. coli and Mycoplasma pneumoniae, we find that the metabolic networks of the two organisms exhibit a large difference in the relative importance of plasticity and redundancy which is consistent with the conjecture that plasticity is a sophisticated mechanism that requires a complex organization. Finally, coessential reaction pairs are explored in different environmental conditions to uncover the interplay between the two mechanisms. We find that synthetic lethal interactions and their classification in plasticity and redundancy are basically insensitive to medium composition, and are highly conserved even when the environment is enriched with nonessential compounds or overconstrained to decrease maximum biomass formation.

We study the propulsion of a micron-size paramagnetic colloidal doublet dispersed in water and driven above a surface by an external precessing magnetic field. The applied field forces the doublet to precess around an axis parallel to the plane of motion and the rotation of the colloidal assembly is rectified into translation due to a periodic asymmetry in dissipation close to the bounding plate. These recent experimental findings [P. Tierno, R. Golestanian, I. Pagonabarraga, and F. Sagués, Phys. Rev. Lett. 101, 218304 (2008)] are complemented here with a theoretical analysis of the system and extended to more complex magnetic modulations such as elliptical driving fields. Experimental results show a good agreement with numerical simulations with the aim to find the best conditions toward the optimization of propulsion speed and swimming efficiency.

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