Epigenetic regulation of Mash1 expression

Mash1 is a proneural gene important for specifying the neural fate. The Mash1 locus undergoes specific epigenetic changes in ES cells following neural induction. These include the loss of repressive H3K27 trimethylation and acquisition of H3K9 acetylation at the promoter, switch to an early replication timing and repositioning of the locus away from the nuclear periphery. Here I examine the relationship between nuclear localization and gene expression during neural differentiation and the role of the neuronal repressor REST in silencing Mash1 expression in ES cells. Following neural induction of ES cells, I observed that relocation of the Mash1 locus occurs from day 4-6 whereas overt expression begins at day 6. Mash1 expression was unaffected by REST removal in ES cells as well as the locus localization at the nuclear periphery. In contrast bona fide REST target genes were upregulated in REST -/- cells. Interestingly, among REST targets, loci that were more derepressed upon REST removal showed an interior location (Sthatmin, Synaptophysin), while those more resistant to REST withdrawal, showed a peripheral location (BDNF, Calbidin, Complexin). To ask whether the insulator protein CTCF together with the cohesin complex might be involved in regulating Mash1 in ES cells, I performed ChIP analysis of CTCF and cohesin binding across the Mash1 locus in ES cells and used RNAi to deplete CTCF and cohesin expression. A slight increase in the transcription of Mash1 was seen in cells upon Rad21 knock down, although it was not possible to exclude this was a consequence of delayed cell cycle progression. Finally ES cell lines that carried a Mash1 transgene were created as a tool to look at whether activation of Mash1 can affect the epigenetic properties of neighbouring genes

Nonlinear Quantum Evolution Equations to Model Irreversible Adiabatic Relaxation with Maximal Entropy Production and Other Nonunitary Processes

We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.Comment: To appear in Reports on Mathematical Physics. Presented at the The Jubilee 40th Symposium on Mathematical Physics, "Geometry & Quanta", Torun, Poland, June 25-28, 200

Addendum to "Nonlinear quantum evolution with maximal entropy production"

The author calls attention to previous work with related results, which has escaped scrutiny before the publication of the article "Nonlinear quantum evolution with maximal entropy production", Phys.Rev.A63, 022105 (2001).Comment: RevTex-latex2e, 2pgs., no figs.; brief report to appear in the May 2001 issue of Phys.Rev.

Maximal-entropy-production-rate nonlinear quantum dynamics compatible with second law, reciprocity, fluctuation-dissipation, and time-energy uncertainty relations

In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, in this paper, together with a review of the general features of the nonlinear quantum (thermo)dynamics I proposed in a series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)], I show its exact equivalence with the maximal-entropy-production variational-principle formulation recently derived in S. Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on the formalism of general interest I developed for the analysis of composite systems, I show how the variational derivation can be extended to the case of a composite system to obtain the general form of my equation of motion, that turns out to be consistent with the demanding requirements of strong separability. Moreover, I propose a new intriguing fundamental ansatz: that the time evolution along the direction of steepest entropy ascent unfolds at the fastest rate compatible with the time-energy Heisenberg uncertainty relation. This ansatz provides a possible well-behaved general closure of the nonlinear dynamics, compatible with the nontrivial requirements of strong separability, and with no need of new physical constants. In any case, the time-energy uncertainty relation provides lower bounds to the internal-relaxation-time functionals and, therefore, upper bounds to the rate of entropy production.Comment: RevTeX; 19 pages; submitted to Phys.Rev.A on Feb.9, 2001; revised version submitted on Sept.14, 2001 with slightly modified derivation in Section III, improved discussion on strong separability in Sections X and IX, added Eqs. 64b, 64c and 11

Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of non-equilibrium dynamics into a unified formulation, which extends to such frameworks the concept of Steepest Entropy Ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. The present formulation constitutes a generalization also for the quantum thermodynamics framework. In the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near equilibrium limit, the metric tensor is related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far non-equilibrium domain, most of the existing theories of non-equilibrium thermodynamics can be cast in such a way that the state exhibits a spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. Non-negativity of the entropy production is a readily proved general feature of SEA dynamics. In several of the different approaches to non-equilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called Maximum Entropy Production Principle. It is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far non-equilibrium states.Comment: 15 pages, 4 figures, to appear in Physical Review

Quantum thermodynamic Carnot and Otto-like cycles for a two-level system

From the thermodynamic equilibrium properties of a two-level system with variable energy-level gap $\Delta$, and a careful distinction between the Gibbs relation $dE = T dS + (E/\Delta) d\Delta$ and the energy balance equation $dE = \delta Q^\leftarrow - \delta W^\to$, we infer some important aspects of the second law of thermodynamics and, contrary to a recent suggestion based on the analysis of an Otto-like thermodynamic cycle between two values of $\Delta$ of a spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the celebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in principle with no need of an infinite number of infinitesimal processes, provided we cycle smoothly over at least three (in general four) values of $\Delta$, and we change $\Delta$ not only along the isoentropics, but also along the isotherms, e.g., by use of the recently suggested maser-laser tandem technique. We derive general bounds to the net-work to high-temperature-heat ratio for a Carnot cycle and for the 'inscribed' Otto-like cycle, and represent these cycles on useful thermodynamic diagrams.Comment: RevTex4, 4 pages, 1 figur