Serially-regulated biological networks fully realize a constrained set of functions

We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends only on the direct path from the input to the target, even when there is a feedback loop allowing for multiple interaction pathways. Using a stochastic model for a set of small transcriptional regulatory networks that have been studied experimentally, we further find that all networks can achieve all functions permitted by this constraint under reasonable settings of biochemical parameters. This underscores the functional versatility of the networks.Comment: 9 pages, 3 figure

Multiple breast cancer risk variants are associated with differential transcript isoform expression in tumors.

Genome-wide association studies have identified over 70 single-nucleotide polymorphisms (SNPs) associated with breast cancer. A subset of these SNPs are associated with quantitative expression of nearby genes, but the functional effects of the majority remain unknown. We hypothesized that some risk SNPs may regulate alternative splicing. Using RNA-sequencing data from breast tumors and germline genotypes from The Cancer Genome Atlas, we tested the association between each risk SNP genotype and exon-, exon-exon junction- or transcript-specific expression of nearby genes. Six SNPs were associated with differential transcript expression of seven nearby genes at FDR < 0.05 (BABAM1, DCLRE1B/PHTF1, PEX14, RAD51L1, SRGAP2D and STXBP4). We next developed a Bayesian approach to evaluate, for each SNP, the overlap between the signal of association with breast cancer and the signal of association with alternative splicing. At one locus (SRGAP2D), this method eliminated the possibility that the breast cancer risk and the alternate splicing event were due to the same causal SNP. Lastly, at two loci, we identified the likely causal SNP for the alternative splicing event, and at one, functionally validated the effect of that SNP on alternative splicing using a minigene reporter assay. Our results suggest that the regulation of differential transcript isoform expression is the functional mechanism of some breast cancer risk SNPs and that we can use these associations to identify causal SNPs, target genes and the specific transcripts that may mediate breast cancer risk

Relation between stress heterogeneity and aftershock rate in the rate-and-state model

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A is a parameter of the rate-and-state friction law, and \sigma_n the normal stress. Omori exponent p thus decreases if the stress "heterogeneity" tau_0 decreases. We also invert the stress distribution P(tau) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant "k^2" slip model [Herrero and Bernard, 1994]. We generate synthetic aftershock catalogs from this stress change.The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault.This stochastic slip model gives a Gaussian stress distribution, but nevertheless produces an aftershock rate which is very close to Omori's law, with an effective p<=1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs, when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of A\sigma_n can also modify the parameters p and c of Omori's law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.Comment: In press in JG

Dynamic Fluctuation Phenomena in Double Membrane Films

Dynamics of double membrane films is investigated in the long-wavelength limit including the overdamped squeezing mode. We demonstrate that thermal fluctuations essentially modify the character of the mode due to its nonlinear coupling to the transversal shear hydrodynamic mode. The corresponding Green function acquires as a function of the frequency a cut along the imaginary semi-axis. Fluctuations lead to increasing the attenuation of the squeezing mode it becomes larger than the `bare' value.Comment: 7 pages, Revte

Efficient LZ78 factorization of grammar compressed text

We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string. Given an SLP of size $n$ representing a text $S$ of length $N$, our algorithm computes the LZ78 factorization of $T$ in $O(n\sqrt{N}+m\log N)$ time and $O(n\sqrt{N}+m)$ space, where $m$ is the number of resulting LZ78 factors. We also show how to improve the algorithm so that the $n\sqrt{N}$ term in the time and space complexities becomes either $nL$, where $L$ is the length of the longest LZ78 factor, or $(N - \alpha)$ where $\alpha \geq 0$ is a quantity which depends on the amount of redundancy that the SLP captures with respect to substrings of $S$ of a certain length. Since $m = O(N/\log_\sigma N)$ where $\sigma$ is the alphabet size, the latter is asymptotically at least as fast as a linear time algorithm which runs on the uncompressed string when $\sigma$ is constant, and can be more efficient when the text is compressible, i.e. when $m$ and $n$ are small.Comment: SPIRE 201

Traffic jams and ordering far from thermal equilibrium

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.Comment: Contribution to the Niels Bohr Summer Institute on Complexity and Criticality; to appear in a Per Bak Memorial Issue of PHYSICA

Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension

We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.Comment: Latex file; with three postscript figures; .ps available at http://dept.physics.upenn.edu/~nelson/pull.p

Factorised Steady States in Mass Transport Models

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and random sequential dynamics and includes models such as the Zero-range process and Asymmetric random average process as special cases. We derive a necessary and sufficient condition for the steady state to factorise, which takes a rather simple form.Comment: 6 page

The mechanisms of spatial and temporal earthquake clustering

The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent spatial and temporal clustering features of earthquakes are not reproduced by this kind of modeling. We show that when a spring-block model is complemented with a mechanism allowing for structural relaxation, realistic earthquake patterns are obtained. The proposed model does not need to include a phenomenological velocity weakening friction law, as traditional spring-block models do, since this behavior is effectively induced by the relaxational mechanism as well. In this way, the model provides also a simple microscopic basis for the widely used phenomenological rate-and-state equations of rock friction.Comment: 7 pages, 10 figures, comments welcom