An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is selected to capture the slow, macroscopic behavior of the system, and the family of quasi-equilibrium probability densities on phase space corresponding to these resolved variables is employed as a statistical model. The macroscopic dynamics of the mean resolved variables is determined by optimizing over paths of these probability densities. Specifically, a cost function is introduced that quantifies the lack-of-fit of such paths to the underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of the residual that results from submitting a path of trial densities to the Liouville equation. The evolution of the macrostate is estimated by minimizing the time integral of the cost function. The value function for this optimization satisfies the associated Hamilton-Jacobi equation, and it determines the optimal relation between the statistical parameters and the irreversible fluxes of the resolved variables, thereby closing the reduced dynamics. The resulting equations for the macroscopic variables have the generic form of governing equations for nonequilibrium thermodynamics, and they furnish a rational extension of the classical equations of linear irreversible thermodynamics beyond the near-equilibrium regime. In particular, the value function is a thermodynamic potential that extends the classical dissipation function and supplies the nonlinear relation between thermodynamics forces and fluxes

Chromatin conversations: Mechanisms and implications of paramutation

Paramutation is a widespread epigenetic phenomenon that was first described in pea and then extensively studied in maize, whereby combining two specific alleles results in a heritable change in the expression of one of the alleles. Far from being restricted to endogenous plant genes, paramutation-like interactions have been described in several kingdoms, in which they can occur between homologous transgenes or between transgenes and homologous endogenous genes at allelic or non-allelic positions. In this review, we discuss potential mechanisms underlying paramutation, compare paramutation to several other trans-sensing phenomena, and speculate on the potential roles and evolutionary implications of these intriguing homology-sensing mechanisms

Differential chromatin structure within a tandem array 100 kb upstream of the maize b1 locus is associated with paramutation.

Recombination mapping defined a 6-kb region, 100 kb upstream of the transcription start site, that is required for B-I enhancer activity and paramutation—a stable, heritable change in transcription caused by allele interactions in maize (Zea mays). In this region, B-I and B‘ (the only b1 alleles that participate in paramutation) have seven tandem repeats of an 853-bp sequence otherwise unique in the genome; other alleles have one. Examination of recombinant alleles with different numbers of tandem repeats indicates that the repeats are required for both paramutation and enhancer function. The 6-kb region is identical in B-I and B‘, showing that epigenetic mechanisms mediate the stable silencing associated with paramutation. This is the first endogenous gene for which sequences required for paramutation have been defined and examined for methylation and chromatin structure. The tandem repeat sequences are more methylated in B-I (high expressing) relative to B‘ (low expressing), opposite of the typical correlation. Furthermore, the change in repeat methylation follows establishment of the B‘ epigenetic state. B-I has a more open chromatin structure in the repeats relative to B‘. The nuclease hypersensitivity differences developmentally precede transcription, suggesting that the repeat chromatin structure could be the heritable imprint distinguishing the two transcription states