Self-tuning to the Hopf bifurcation in fluctuating systems

The problem of self-tuning a system to the Hopf bifurcation in the presence of noise and periodic external forcing is discussed. We find that the response of the system has a non-monotonic dependence on the noise-strength, and displays an amplified response which is more pronounced for weaker signals. The observed effect is to be distinguished from stochastic resonance. For the feedback we have studied, the unforced self-tuned Hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum. The implications of our general results are briefly discussed in the context of sound detection by the inner ear.Comment: 37 pages, 7 figures (8 figure files

PTBP1 Is Required for Embryonic Development before Gastrulation

Polypyrimidine-tract binding protein 1 (PTBP1) is an important cellular regulator of messenger RNAs influencing the alternative splicing profile of a cell as well as its mRNA stability, location and translation. In addition, it is diverted by some viruses to facilitate their replication. Here, we used a novel PTBP1 knockout mouse to analyse the tissue expression pattern of PTBP1 as well as the effect of its complete removal during development. We found evidence of strong PTBP1 expression in embryonic stem cells and throughout embryonic development, especially in the developing brain and spinal cord, the olfactory and auditory systems, the heart, the liver, the kidney, the brown fat and cartilage primordia. This widespread distribution points towards a role of PTBP1 during embryonic development. Homozygous offspring, identified by PCR and immunofluorescence, were able to implant but were arrested or retarded in growth. At day 7.5 of embryonic development (E7.5) the null mutants were about 5x smaller than the control littermates and the gap in body size widened with time. At mid-gestation, all homozygous embryos were resorbed/degraded. No homozygous mice were genotyped at E12 and the age of weaning. Embryos lacking PTBP1 did not display differentiation into the 3 germ layers and cavitation of the epiblast, which are hallmarks of gastrulation. In addition, homozygous mutants displayed malformed ectoplacental cones and yolk sacs, both early supportive structure of the embryo proper. We conclude that PTBP1 is not required for the earliest isovolumetric divisions and differentiation steps of the zygote up to the formation of the blastocyst. However, further post-implantation development requires PTBP1 and stalls in homozygous null animals with a phenotype of dramatically reduced size and aberration in embryonic and extra-embryonic structures

Resolving early mesoderm diversification through single-cell expression profiling.

In mammals, specification of the three major germ layers occurs during gastrulation, when cells ingressing through the primitive streak differentiate into the precursor cells of major organ systems. However, the molecular mechanisms underlying this process remain unclear, as numbers of gastrulating cells are very limited. In the mouse embryo at embryonic day 6.5, cells located at the junction between the extra-embryonic region and the epiblast on the posterior side of the embryo undergo an epithelial-to-mesenchymal transition and ingress through the primitive streak. Subsequently, cells migrate, either surrounding the prospective ectoderm contributing to the embryo proper, or into the extra-embryonic region to form the yolk sac, umbilical cord and placenta. Fate mapping has shown that mature tissues such as blood and heart originate from specific regions of the pre-gastrula epiblast, but the plasticity of cells within the embryo and the function of key cell-type-specific transcription factors remain unclear. Here we analyse 1,205 cells from the epiblast and nascent Flk1(+) mesoderm of gastrulating mouse embryos using single-cell RNA sequencing, representing the first transcriptome-wide in vivo view of early mesoderm formation during mammalian gastrulation. Additionally, using knockout mice, we study the function of Tal1, a key haematopoietic transcription factor, and demonstrate, contrary to previous studies performed using retrospective assays, that Tal1 knockout does not immediately bias precursor cells towards a cardiac fate.We thank M. de Bruijn, A. Martinez-Arias, J. Nichols and C. Mulas for discussion, the Cambridge Institute for Medical Research Flow Cytometry facility for their expertise in single-cell index sorting, and S. Lorenz from the Sanger Single Cell Genomics Core for supervising purification of Tal1−/− sequencing libraries. ChIP-seq reads were processed by R. Hannah. Research in the authors’ laboratories is supported by the Medical Research Council, Cancer Research UK, the Biotechnology and Biological Sciences Research Council, Bloodwise, the Leukemia and Lymphoma Society, and the Sanger-EBI Single Cell Centre, and by core support grants from the Wellcome Trust to the Cambridge Institute for Medical Research and Wellcome Trust - MRC Cambridge Stem Cell Institute and by core funding from Cancer Research UK and the European Molecular Biology Laboratory. Y.T. was supported by a fellowship from the Japan Society for the Promotion of Science. W.J. is a Wellcome Trust Clinical Research Fellow. A.S. is supported by the Sanger-EBI Single Cell Centre. This work was funded as part of Wellcome Trust Strategic Award 105031/D/14/Z ‘Tracing early mammalian lineage decisions by single-cell genomics’ awarded to W. Reik, S. Teichmann, J. Nichols, B. Simons, T. Voet, S. Srinivas, L. Vallier, B. Göttgens and J. Marioni.This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nature1863

Uncovering cell identity through differential stability with Cepo

The use of single-cell RNA-sequencing (scRNA-seq) allows observation of different cells at multi-tiered complexity in the same microenvironment. To get insights into cell identity using scRNA-seq data, we present Cepo, which generates cell-type-specific gene statistics of differentially stable genes from scRNA-seq data to define cell identity. When applied to multiple datasets, Cepo outperforms current methods in assigning cell identity and enhances several cell identification applications such as cell-type characterisation, spatial mapping of single cells and lineage inference of single cells