No abstract

Cells switch between various stable genetic programs (attractors) to accommodate environmental conditions. Signal transduction machineries efficiently convey environmental changes to the gene regulation apparatus in order to express the appropriate genetic program. However, since the number of environmental conditions is much larger than that of available genetic programs so that the cell may utilize the same genetic program for a large set of conditions, it may not have evolved a signaling pathway for every environmental condition, notably those that are rarely encountered. Here we show that in the absence of signal transduction, switching to the appropriate attractor state expressing the genes that afford adaptation to the external condition can occur. In a synthetic bistable gene switch in Escherichia coli in which mutually inhibitory operons govern the expression of two genes required in two alternative nutritional environments, cells reliably selected the “adaptive attractor” driven by gene expression noise. A mathematical model suggests that the “non-adaptive attractor” is avoided because in unfavorable conditions, cellular activity is lower, which suppresses mRNA metabolism, leading to larger fluctuations in gene expression. This, in turn, renders the non-adaptive state less stable. Although attractor selection is not as efficient as signal transduction via a dedicated cascade, it is simple and robust, and may represent a primordial mechanism for adaptive responses that preceded the evolution of signaling cascades for the frequently encountered environmental changes.

Mutual information function, which is an alternative to correlation function for symbolic sequences, and a esymbolic spectrum, are calculated for a human DNA sequence containing mostly intron segments, those that do not code for proteins. It is observed that the mutual information function of this sequence decays very slowly, and the correlation length is extremely long (at least 800 bases). The symbolic spectrum of the sequence at very low frequencies can be approximated by llf", where f is the frequency and t( ranges from 0.5 to 0.85. It is suggested that the existence of the repetitive patterns in the sequence is mainly responsible for the observed long-range correlation. A possible connection between this long-range correlation and those in music notes is also briefly discussed.