Amir Bar

Epigenetic polymorphism and the stochastic formation of differentially methylated regions in normal and cancerous tissues

DNA methylation has been comprehensively profiled in normal and cancer cells, but the dynamics that form, maintain and reprogram differentially methylated regions remain enigmatic. Here, we show that methylation patterns within populations of cells from individual somatic tissues are heterogeneous and polymorphic. Using in vitro evolution of immortalized fibroblasts for over 300 generations, we track the dynamics of polymorphic methylation at regions developing significant differential methylation on average. The data indicate that changes in population-averaged methylation occur through a stochastic process that generates a stream of local and uncorrelated methylation aberrations. Despite the stochastic nature of the process, nearly deterministic epigenetic remodeling emerges on average at loci that lose or gain resistance to methylation accumulation. Changes in the susceptibility to methylation accumulation are correlated with changes in histone modification and CTCF occupancy. Characterizing epigenomic polymorphism within cell populations is therefore critical to understanding methylation dynamics in normal and cancer cells.

Widespread Compensatory Evolution Conserves DNA-Encoded Nucleosome Organization in Yeast

Evolution maintains organismal fitness by preserving genomic information. This is widely assumed to involve conservation of specific genomic loci among species. Many genomic encodings are now recognized to integrate small contributions from multiple genomic positions into quantitative dispersed codes, but the evolutionary dynamics of such codes are still poorly understood. Here we show that in yeast, sequences that quantitatively affect nucleosome occupancy evolve under compensatory dynamics that maintain heterogeneous levels of A+T content through spatially coupled A/T-losing and A/T-gaining substitutions. Evolutionary modeling combined with data on yeast polymorphisms supports the idea that these substitution dynamics are a consequence of weak selection. This shows that compensatory evolution, so far believed to affect specific groups of epistatically linked loci like paired RNA bases, is a widespread phenomenon in the yeast genome, affecting the majority of intergenic sequences in it. The model thus derived suggests that compensation is inevitable when evolution conserves quantitative and dispersed genomic functions.

Loop dynamics in DNA denaturation.

The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases (either closed or open) is calculated. The long-time decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.

Dynamics of DNA melting.

The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using single-molecule experiments such as fluorescence correlation spectroscopy.

Denaturation of circular DNA: supercoil mechanism.

The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double-stranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent c. However the first-order transition displayed by the PS model for c>2 in linear DNA is replaced by a continuous transition with arbitrarily high order as c approaches 2, while the second-order transition found in the linear case in the regime 1<c≤2 disappears. In addition, our analysis reveals that melting under fixed linking number is a condensation transition, where the condensate is a macroscopic loop which appears above the critical temperature.

Macroscopic loop formation in circular DNA denaturation.

The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed at the expense of (i) overtwist or (ii) supercoils. Recent work has shown that the supercoiling mechanism results in a picture similar to Bose-Einstein condensation where a macroscopic loop appears at T{c} and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above T{c}, with a cusp at the critical point.

Mixed order transition and condensation in an exactly soluble one dimensional spin model

Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far from thermal equilibrium. In a recent paper [1], an exactly soluble spin model with long-range interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to form a bridge between two classes of 1D models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper, we elaborate on the calculations performed in [1]. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins and also consider a broader class of interactions that decay with distance using a power law different from 2.

Denaturation of circular DNA: supercoils and overtwist.

The denaturation transition of circular DNA is studied within a Poland-Scheraga-type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant κ associated with the overtwisting energy for any given loop entropy exponent c. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for c ≤ 2. For c > 2 and κ = 0 we find that the model exhibits a first-order transition. The transition becomes of higher order for any κ > 0. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent c.

Exact extreme-value statistics at mixed-order transitions.

We study extreme-value statistics for spatially extended models exhibiting mixed-order phase transitions (MOT). These are phase transitions that exhibit features common to both first-order (discontinuity of the order parameter) and second-order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising model, which is a prototypical model exhibiting MOT, and study analytically the extreme-value statistics of the domain lengths The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size L. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length l_{max} converges, in the large L limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of l_{max} are governed by novel distributions, which we compute exactly. Our main analytical results are verified by numerical simulations.

Constrained thermal denaturation of DNA under fixed linking number

A DNA molecule with freely fluctuating ends undergoes a sharp thermal denaturation transition upon heating. However, in circular DNA chains and some experimental setups that manipulate single DNA molecules, the total number of turns (linking number) is constant at all times. The consequences of this additional topological invariant on the melting behaviour are nontrivial. Below, we investigate the melting characteristics of a homogeneous DNA where the linking number along the melting curve is preserved by supercoil formation in duplex portions. We obtain the mass fraction and the number of loops and supercoils below and above the melting temperature. We also argue that a macroscopic loop appears at Tc and calculate its size as a function of temperature.