Relative entropy and exponential deviation bounds for general markov chains

We develop explicit, general bounds for the probability that the normalized partial sums of a function of a Markov chain on a general alphabet will exceed the steady-state mean of that function by a given amount. Our bounds combine simple information-theoretic ideas together with techniques from optimization and some fairly elementary tools from analysis. In one direction, we obtain a general bound for the important class of Doeblin chains; this bound is optimal, in the sense that in the special case of independent and identically distributed random variables it essentially reduces to the classical Hoeffding bound. In another direction, motivated by important problems in simulation, we develop a series of bounds in a form which is particularly suited to these problems, and which apply to the more general class of "geometrically ergodic" Markov chains

Sleeping Beauty transposase structure allows rational design of hyperactive variants for genetic engineering

Sleeping Beauty (SB) is a prominent Tc1/mariner superfamily DNA transposon that provides a popular genome engineering tool in a broad range of organisms. It is mobilized by a transposase enzyme that catalyses DNA cleavage and integration at short specific sequences at the transposon ends. To facilitate SB’s applications, here we determine the crystal structure of the transposase catalytic domain and use it to model the SB transposase/transposon end/target DNA complex. Together with biochemical and cell-based transposition assays, our structure reveals mechanistic insights into SB transposition and rationalizes previous hyperactive transposase mutations. Moreover, our data enables us to design two additional hyperactive transposase variants. Our work provides a useful resource and proof-of-concept for structure-based engineering of tailored SB transposases

Structural basis for retroviral integration into nucleosomes

Retroviral integration is catalysed by a tetramer of integrase (IN) assembled on viral DNA ends in a stable complex, known as the intasome1, 2. How the intasome interfaces with chromosomal DNA, which exists in the form of nucleosomal arrays, is currently unknown. Here we show that the prototype foamy virus (PFV) intasome is proficient at stable capture of nucleosomes as targets for integration. Single-particle cryo-electron microscopy reveals a multivalent intasome–nucleosome interface involving both gyres of nucleosomal DNA and one H2A–H2B heterodimer. While the histone octamer remains intact, the DNA is lifted from the surface of the H2A–H2B heterodimer to allow integration at strongly preferred superhelix location ±3.5 positions. Amino acid substitutions disrupting these contacts impinge on the ability of the intasome to engage nucleosomes in vitro and redistribute viral integration sites on the genomic scale. Our findings elucidate the molecular basis for nucleosome capture by the viral DNA recombination machinery and the underlying nucleosome plasticity that allows integration