RESUMO
We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those extracted from experiment. The influence of periodic orbits on spectra in the case of two-dimensional curved geometries is thereby demonstrated, where the parameter corresponding to Planck's constant in quantum systems involves the wave number and the curvature radius. We use these findings to explain the marked clustering of levels when the shell is hemispherical.
RESUMO
The behavior of living systems is dependent on large dynamical gene regulatory networks (GRNs). However, the functioning of even the smallest GRNs is difficult to predict. The bistable GRN of bacteriophage lambda is able to count to make a decision between lysis and lysogeny on the basis of the number of phages infecting the cell, even though replication of the phage genome eliminates this initial difference. By simulating the behavior of a large number of random transcriptional GRNs, we show that a surprising variety of GRNs can carry out this complex task, including simple CI-Cro-like mutual repression networks. Thus, our study extends the repertoire of simple GRNs. Counterintuitively, the major effect of the addition of CII-like regulation, generally thought to be needed for counting by lambda, was to improve the ability of the networks to complete a simulated prophage induction. Our study suggests that additional regulatory mechanisms to decouple Cro and CII levels may exist in lambda and that infection counting could be widespread among temperate bacteriophages, many of which contain CI-Cro-like circuits.
