We apply techniques from complexity theory to a model of biological cellular membranes known as membrane systems or P-systems. Like Boolean circuits, membrane systems are defined as uniform families of computational devices. To date, polynomial time uniformity has been the accepted uniformity notion for membrane systems. Here, we introduce the idea of using AC 0-uniformity and investigate the computational power of membrane systems under these tighter conditions. It turns out that the computational power of some systems is lowered from P to NL when using AC 0-semi-uniformity, so we argue that this is a more reasonable uniformity notion for these systems as well as others. Interestingly, other P-semi-uniform systems that are known to be lower-bounded by P are shown to retain their P lower-bound under the new tighter semi-uniformity condition. Similarly, a number of membrane systems that are known to solve PSPACE-complete problems retain their computational power under tighter uniformity conditions.
Stochastic pulsing of gene expression can generate phenotypic diversity in a genetically identical population of cells, but it is unclear whether it has a role in the development of multicellular systems. Here, we show how stochastic pulsing of gene expression enables spatial patterns to form in a model multicellular system, Bacillus subtilis bacterial biofilms. We use quantitative microscopy and time-lapse imaging to observe pulses in the activity of the general stress response sigma factor σB in individual cells during biofilm development. Both σB and sporulation activity increase in a gradient, peaking at the top of the biofilm, even though σB represses sporulation. As predicted by a simple mathematical model, increasing σB expression shifts the peak of sporulation to the middle of the biofilm. Our results demonstrate how stochastic pulsing of gene expression can play a key role in pattern formation during biofilm development.
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