Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory.

Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular Ca2+ release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. This dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that (1) the dual-time structure similarly confers resistance to internal noise due to molecule number fluctuations, and (2) model variants with altered coupling, which better represent some specific biochemical systems, share all the above advantages. We also develop a similar bistable model with coupling of a fast autoactivation loop to a slow loop. This model\u27s topology was suggested by positive feedback proposed to play a role in long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance are also present in this autoactivation model. Empirically, LTP develops resistance to reversal over approximately 1h . The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback

Synchronization of Coupled Nonidentical Genetic Oscillators

The study on the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using control theory approach, we provide a theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.Comment: 16 pages, 3 figure

The Power Spectrum of Mass Fluctuations Measured from the Lyman-alpha Forest at Redshift z=2.5

We measure the linear power spectrum of mass density fluctuations at redshift z=2.5 from the \lya forest absorption in a sample of 19 QSO spectra, using the method introduced by Croft et al. (1998). The P(k) measurement covers the range 2\pi/k ~ 450-2350 km/s (2-12 comoving \hmpc for \Omega=1). We examine a number of possible sources of systematic error and find none that are significant on these scales. In particular, we show that spatial variations in the UV background caused by the discreteness of the source population should have negligible effect on our P(k) measurement. We obtain consistent results from the high and low redshift halves of the data set and from an entirely independent sample of nine QSO spectra with mean redshift z=2.1. A power law fit to our measured P(k) yields a logarithmic slope n=-2.25 +/- 0.18 and an amplitude \Delta^2(k_p) = 0.57^{+0.26}_{-0.18}, where $\Delta^2$ is the contribution to the density variance from a unit interval of lnk and k_p=0.008 (km/s)^{-1}. Direct comparison of our mass P(k) to the measured clustering of Lyman Break Galaxies shows that they are a highly biased population, with a bias factor b~2-5. The slope of the linear P(k), never previously measured on these scales, is close to that predicted by models based on inflation and Cold Dark Matter (CDM). The P(k) amplitude is consistent with some scale-invariant, COBE-normalized CDM models (e.g., an open model with \Omega_0=0.4) and inconsistent with others (e.g., \Omega=1). Even with limited dynamic range and substantial statistical uncertainty, a measurement of P(k) that has no unknown ``bias factors'' offers many opportunities for testing theories of structure formation and constraining cosmological parameters. (Shortened)Comment: Submitted to ApJ, 27 emulateapj pages w/ 19 postscript fig