Structural inheritance

Abstract: Y1,Y2,. . . be a sequence of independent two-valued random variables, Yn+i = -s or f3 + ns with probabilities (1 W) and W, where s is a small positive number and W is then determined by the condition -E(Y.) = aV(Yn). Verify that the probability that for some n, 3 + Y, + . . . + Yn > 0 converges to 1/(1 + ad) as s -. 0, and let X,, = Yn E(Yn). This completes the proof. The theorem can be extended to say that for each y > 0, if rT is the least n if any for which (Xi + . . . + Xn) . -yT +GI + . . . + An) + .(V. + * * * + Vn). then the probability that there is some n < rz for which (1) holds is less than (,y/(( + 3))(1/(1 + ac)); and this bound is sharp. The material of this note, including proofs of Lemmas 1 and 2, will appear as part of our forthcoming book, How to Gamble If You Must (New York: McGrawHill), Theorems 2.12.1 and 9.4.1, and an illustrative application of the theorem will appear in the forthcoming article, \"A sharper form of the Borel-Cantelli lemma and the strong law\" by L. E. Dubins and D. A. Freedman.

Abstract: Genome-wide association studies of complex physiological traits and diseases consistently found that associated genetic factors, such as allelic polymorphisms or DNA mutations, only explained a minority of the expected heritable fraction. This discrepancy is known as “missing heritability”, and its underlying factors and molecular mechanisms are not established. Epigenetic programs may account for a significant fraction of the “missing heritability.” Epigenetic modifications, such as DNA methylation and chromatin assembly states, reflect the high plasticity of the genome and contribute to stably alter gene expression without modifying genomic DNA sequences. Consistent components of complex traits, such as those linked to human stature/height, fertility, and food metabolism or to hereditary defects, have been shown to respond to environmental or nutritional condition and to be epigenetically inherited. The knowledge acquired from epigenetic genome reprogramming during development, stem cell differentiation/de-differentiation, and model organisms is today shedding light on the mechanisms of (a) mitotic inheritance of epigenetic traits from cell to cell, (b) meiotic epigenetic inheritance from generation to generation, and (c) true transgenerational inheritance. Such mechanisms have been shown to include incomplete erasure of DNA methylation, parental effects, transmission of distinct RNA types (mRNA, non-coding RNA, miRNA, siRNA, piRNA), and persistence of subsets of histone marks.

Abstract: This review will first recall the phenomena of “cortical inheritance” observed and genetically demonstrated in Paramecium 40 years ago, and later in other ciliates (Tetrahymena, Oxytricha, Paraurostyla), and will analyze the deduced concept of “cytotaxis” or “structural memory”. The significance of these phenomena, all related (but not strictly restricted ) to the properties of ciliary basal bodies and their mode of duplication, will be interpreted in the light of present knowledge on the mechanism and control of basal body/centriole duplication. Then other phenomena described in a variety of organisms will be analyzed or mentioned which show the relevance of the concept of cytotaxis or structural memory to other cellular processes, mainly (1) cytoskeleton assembly and organization with examples on ciliates, trypanosome, mammalian cells and plants, and (2) transmission of polarities with examples on yeast, trypanosome and metazoa. Finally, I will discuss some aspects of this particular type of non DNA inh...