Small regulatory RNAs are central players in the regulation of many cellular processes across all kingdoms of life. Experiments in mouse and human have shown that a typical small RNA may regulate the expression of many different genes, suggesting that small RNAs act as global regulators. It is noted though that most targets respond only weakly to the presence of the small RNA. At the same time, evidence in bacteria and animals suggest that the phenotypes associated with small RNA mutants are only due to a few of their targets. Here we assume that targets regulated by a small RNA to control function is in fact small, and propose that the role of the many other weak targets is to confer robustness to the regulation of these few principal targets. Through mathematical modeling we show that auxiliary targets may significantly buffer both number and kinetic fluctuations of the principal targets, with only minor slowdown in the kinetics of response. Analysis of genomic data suggests that auxiliary targets experience a nonspecific evolutionary pressure, playing a role at the system level. Our work is of importance for studies on small RNA functions, and impacts on the understanding of small RNA evolution.

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We have developed an analytical model of angle-dependent magnetoresistance oscillations (AMROs) in a quasi-two-dimensional metal in which magnetic breakdown occurs. The model takes account of all the contributions from quasiparticles undergoing both magnetic breakdown and Bragg reflection at each junction and allows extremely efficient simulation of data which can be compared with recent experimental results on the organic metal κ-(BEDT-TTF)2Cu(NCS)2. AMROs resulting from both closed and open orbits emerge naturally at low field, and the model enables the transition to breakdown-AMROs with increasing field to be described in detail.The measurement of angle-dependent magnetoresistance oscillations (AMROs) is a powerful technique in the determination of details of the Fermi surfaces (FSs) in various reduced-dimensionality metals [1,2,3,4]. In many cases the angle-dependence originates in correlations in the time-dependent interplanar velocity of quasiparticles which traverse the FS under the influence of the magnetic field B and hence can be efficiently simulated by integrating up such correlations for all quasiparticle trajectories [5,6,7,8,9,10,11]. In high B, the additional effect of magnetic breakdown (MB) can substantially complicate this picture. This effect occurs in the FSs of quasi-two-dimensional metals such as that illustrated in Fig. 1(a) which is described by the dispersion E(k) =h 2 (k 2 x + k 2 y )/2m * with effective mass m * , Fermi wave vector k F and Brillouin zone edges at k y = ±k F cos ξ. Because of the periodic potential, small gaps in the dispersion open up at the Brillouin zone edge, splitting the FS into distinct open and closed sections. Quasiparticles orbit around the FS with constant k z when B lies along the interlayer direction. In very low B, because of Bragg reflection, only open orbits [ Fig. 1(b)] and small closed orbits [ Fig. 1(c)] occur around the distinct sections of the FS. In high B, mixing between the states on the two FS sections leads to MB at the four filled points shown in Fig. 1(a) which we term MB junctions. At these junctions a quasiparticle "tunnels" in k-space between the FS sections [12], resulting in a single large closed orbit [ Fig. 1(d)].In fact for general values of the magnetic field there should be a superposition of all the orbits in Fig. 1(b)-(d) as well as many other intermediate possibilities in which MB occurs at some of the MB junctions and Bragg reflection occurs at the others. The probability p = exp(−B 0 /B) of MB at each MB junction is parameterized by B 0 , the characteristic breakdown field [12,13,14]. For all finite, non-zero values of B (for which 0 < p < 1) there is a hierarchy of complex trajectories that must be summed to account for all possible contributions to the conductivity in which MB either does or does not occur at each MB junction. If a quasiparticle crosses N MB junctions, one has to consider 2 N possible trajecto- ries with their correct probabilistic weightings, and this complicates a direct computation of AMROs since one has ...

We derive an analytical expression which allows efficient computation of the effect of all the Fermi-surface trajectories induced by a combination of Bragg scattering and magnetic breakdown on the in-plane components of the resistivity tensor. The particular network of coupled orbits which we consider was first formulated by Falicov and Sievert, who studied the problem numerically. Our approach, based upon a method used previously to derive an analytical solution for interlayer transport, allows us to show that the conductivity tensor can be written as a sum of a matrix representing the effect of total magnetic breakdown and one representing a combination of complex electronic trajectories, and we find a compact expression for the in-plane components of the resistivity tensor that can be evaluated straightforwardly.

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