Enhancement of the stability of genetic switches by overlapping upstream regulatory domains

We study genetic switches formed from pairs of mutually repressing operons. The switch stability is characterised by a well defined lifetime which grows sub-exponentially with the number of copies of the most-expressed transcription factor, in the regime accessible by our numerical simulations. The stability can be markedly enhanced by a suitable choice of overlap between the upstream regulatory domains. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons, that regulate each other, together in the course of evolution.Comment: 4 pages, 5 figures, RevTeX

Analysis of cool DO-type white dwarfs from the Sloan Digital Sky Survey Data Release 10

We report on the identification of 22 new cool DO-type white dwarfs (WD) detected in Data Release 10 (DR10) of the Sloan Digital Sky Survey (SDSS). Among them, we found one more member of the so-called hot-wind DO WDs, which show ultrahigh excitation absorption lines. Our non-LTE model atmosphere analyses of these objects and two not previously analyzed hot-wind DO WDs, revealed effective temperatures and gravities in the ranges Teff=45-80kK and log g= 7.50-8.75. In eight of the spectra we found traces of C (0.001-0.01, by mass). Two of these are the coolest DO WDs ever discovered that still show a considerable amount of C in their atmospheres. This is in strong contradiction with diffusion calculations, and probably, similar to what is proposed for DB WDs, a weak mass-loss is present in DO WDs. One object is the most massive DO WD discovered so far with a mass of 1.07 M_sun if it is an ONe-WD or 1.09 M_sun if it is a CO-WD. We furthermore present the mass distribution of all known hot non-DA (pre-) WDs and derive the hot DA to non-DA ratio for the SDSS DR7 spectroscopic sample. The mass distribution of DO WDs beyond the wind limit strongly deviates from the mass distribution of the objects before the wind limit. We address this phenomenon by applying different evolutionary input channels. We argue that the DO WD channel may be fed by about 13% by post-extreme-horizontal branch stars and that PG1159 stars and O(He) stars may contribute in a similar extent to the non-DA WD channel.Comment: 13 pages, accepted for publication in A&

Sampling rare switching events in biochemical networks

Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by calculating the spontaneous flipping rate of a symmetric model of a genetic switch consisting of two mutually repressing genes. The rate constant can be obtained orders of magnitude more efficiently than using brute-force simulations. For this model switch, we show that the switching mechanism, and consequently the switching rate, depends crucially on whether the binding of one regulatory protein to the DNA excludes the binding of the other one. Our technique could also be used to study rare events and non-equilibrium processes in soft condensed matter systems.Comment: 9 pages, 6 figures, last page contains supplementary informatio

Stochastic model of transcription factor-regulated gene expression

We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes: Gene A and Gene B which synthesize the TFs and the target gene proteins respectively. We show through analytic calculations that the TF fluctuations have a significant effect on the distribution of the target gene protein levels when the mean TF level falls in the highest sensitive region of the dose-response curve. We further study the effect of reducing the copy number of Gene A from two to one. The enhanced TF fluctuations yield results different from those in the deterministic case. The probability that the target gene protein level exceeds a threshold value is calculated with a knowledge of the probability density functions associated with the TF and target gene protein levels. Numerical simulation results for a more detailed stochastic model are shown to be in agreement with those obtained through analytic calculations. The relevance of these results in the context of the genetic disorder haploinsufficiency is pointed out. Some experimental observations on the haploinsufficiency of the tumour suppressor gene, Nkx3.1, are explained with the help of the stochastic model of TF-regulated gene expression.Comment: 17 pages, 11 figures. Accepted for publication in Physical Biolog

Correlation of internal representations in feed-forward neural networks

Feed-forward multilayer neural networks implementing random input-output mappings develop characteristic correlations between the activity of their hidden nodes which are important for the understanding of the storage and generalization performance of the network. It is shown how these correlations can be calculated from the joint probability distribution of the aligning fields at the hidden units for arbitrary decoder function between hidden layer and output. Explicit results are given for the parity-, and-, and committee-machines with arbitrary number of hidden nodes near saturation.Comment: 6 pages, latex, 1 figur

Noise Characteristics of Feed Forward Loops

A prominent feature of gene transcription regulatory networks is the presence in large numbers of motifs, i.e, patterns of interconnection, in the networks. One such motif is the feed forward loop (FFL) consisting of three genes X, Y and Z. The protein product of x of X controls the synthesis of protein product y of Y. Proteins x and y jointly regulate the synthesis of z proteins from the gene Z. The FFLs, depending on the nature of the regulating interactions, can be of eight different types which can again be classified into two categories: coherent and incoherent. In this paper, we study the noise characteristics of FFLs using the Langevin formalism and the Monte Carlo simulation technique based on the Gillespie algorithm. We calculate the variances around the mean protein levels in the steady states of the FFLs and find that, in the case of coherent FFLs, the most abundant FFL, namely, the Type-1 coherent FFL, is the least noisy. This is however not so in the case of incoherent FFLs. The results suggest possible relationships between noise, functionality and abundance.Comment: 17 page

Evidence from K2 for rapid rotation in the descendant of an intermediate-mass star

Using patterns in the oscillation frequencies of a white dwarf observed by K2, we have measured the fastest rotation rate, 1.13(02) hr, of any isolated pulsating white dwarf known to date. Balmer-line fits to follow-up spectroscopy from the SOAR telescope show that the star (SDSSJ0837+1856, EPIC 211914185) is a 13,590(340) K, 0.87(03) solar-mass white dwarf. This is the highest mass measured for any pulsating white dwarf with known rotation, suggesting a possible link between high mass and fast rotation. If it is the product of single-star evolution, its progenitor was a roughly 4.0 solar-mass main-sequence B star; we know very little about the angular momentum evolution of such intermediate-mass stars. We explore the possibility that this rapidly rotating white dwarf is the byproduct of a binary merger, which we conclude is unlikely given the pulsation periods observed.Comment: 5 pages, 4 figure, 1 table; accepted for publication in The Astrophysical Journal Letter

An asteroseismic test of diffusion theory in white dwarfs

The helium-atmosphere (DB) white dwarfs are commonly thought to be the descendants of the hotter PG1159 stars, which initially have uniform He/C/O atmospheres. In this evolutionary scenario, diffusion builds a pure He surface layer which gradually thickens as the star cools. In the temperature range of the pulsating DB white dwarfs (T_eff ~ 25,000 K) this transformation is still taking place, allowing asteroseismic tests of the theory. We have obtained dual-site observations of the pulsating DB star CBS114, to complement existing observations of the slightly cooler star GD358. We recover the 7 independent pulsation modes that were previously known, and we discover 4 new ones to provide additional constraints on the models. We perform objective global fitting of our updated double-layered envelope models to both sets of observations, leading to determinations of the envelope masses and pure He surface layers that qualitatively agree with the expectations of diffusion theory. These results provide new asteroseismic evidence supporting one of the central assumptions of spectral evolution theory, linking the DB white dwarfs to PG1159 stars.Comment: 7 pages, 3 figures, 3 tables, accepted for publication in A&

Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation functions that although being formally down by powers of $N$ (the population size) nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher-order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.Comment: Revtex, 15 pages, + 4 embedded PS figure