Some species of bacteria exhibit quorum sensing, a phenomenon in which gene expression and resultant behavior undergo a phase change at some threshold population density. We show here that even very simple nanodevices , modeled as chemical reaction networks, can by a different mechanism also sense their own population densities and change their behaviors dramatically at certain thresholds. Moreover, the magnitudes of these thresholds can thwart attempts to use  model checking, simulation, or approximation by differential equations to formally verify the behaviors of such nanodevices at realistic population densities . We show how formal theorem provers can successfully verify some such systems at sizes where other verification methods fail.
We show that very simple molecular systems , modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts to use simulation, model checking, or approximation by differential equations to formally verify the behaviors of such systems at realistic populations . We show how formal theorem provers can successfully verify some such systems at populations where other verification methods fail.
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Some species of bacteria exhibit quorum sensing, a phenomenon in which gene expression and resultant behavior undergo a phase change at some threshold population density. We show here that even very simple nanodevices
We show that very simple molecular systems
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by a different mechanism also sense their own population densities and change their behaviors dramatically at certain
have behaviors that exhibit dramatic phase transitions at certain population
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simulation,
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simulation,
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nanodevices at realistic population densities
systems at realistic populations
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sizes
populations