Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid.

We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states g(ω) to account for this excess entropy. A corresponding peak in g(ω)/ω2 vs. frequency ω matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies.

Replication timing is regulated by the number of MCMs loaded at origins.

Replication timing is a crucial aspect of genome regulation that is strongly correlated with chromatin structure, gene expression, DNA repair, and genome evolution. Replication timing is determined by the timing of replication origin firing, which involves activation of MCM helicase complexes loaded at replication origins. Nonetheless, how the timing of such origin firing is regulated remains mysterious. Here, we show that the number of MCMs loaded at origins regulates replication timing. We show for the first time in vivo that multiple MCMs are loaded at origins. Because early origins have more MCMs loaded, they are, on average, more likely to fire early in S phase. Our results provide a mechanistic explanation for the observed heterogeneity in origin firing and help to explain how defined replication timing profiles emerge from stochastic origin firing. These results establish a framework in which further mechanistic studies on replication timing, such as the strong effect of heterochromatin, can be pursued.

How and why multiple MCMs are loaded at origins of DNA replication.

Recent work suggests that DNA replication origins are regulated by the number of multiple mini-chromosome maintenance (MCM) complexes loaded. Origins are defined by the loading of MCM - the replicative helicase which initiates DNA replication and replication kinetics determined by origin's location and firing times. However, activation of MCM is heterogeneous; different origins firing at different times in different cells. Also, more MCMs are loaded in G1 than are used in S phase. These aspects of MCM biology are explained by the observation that multiple MCMs are loaded at origins. Having more MCMs at early origins makes them more likely to fire, effecting differences in origin efficiency that define replication timing. Nonetheless, multiple MCM loading raises new questions, such as how they are loaded, where these MCMs reside at origins, and how their presence affects replication timing. In this review, we address these questions and discuss future avenues of research.

Ott1 (Rbm15) regulates thrombopoietin response in hematopoietic stem cells through alternative splicing of c-Mpl.

Thrombopoietin (Thpo) signaling through the c-Mpl receptor promotes either quiescence or proliferation of hematopoietic stem cells (HSCs) in a concentration-dependent manner; however, in vivo Thpo serum levels are responsive to platelet mass rather than HSC demands, suggesting additional regulation exists. Ott1 (Rbm15), a spliceosomal component originally identified as a fusion partner in t(1;22)-associated acute megakaryocytic leukemia, is also essential for maintaining HSC quiescence under stress. Ott1 controls the alternative splicing of a dominant negative isoform, Mpl-TR, capable of inhibiting HSC engraftment and attenuating Thpo signaling. Ott1, which associates with Hdac3 and the histone methyltransferase, Setd1b, binds to both c-Mpl RNA and chromatin and regulates H4 acetylation and H3K4me3 marks. Histone deacetylase or histone methyltransferase inhibition also increases Mpl-TR levels, suggesting that Ott1 uses an underlying epigenetic mechanism to control alternative splicing of c-Mpl. Manipulation of Ott1-dependent alternative splicing may therefore provide a novel pharmacologic avenue for regulating HSC quiescence and proliferation in response to Thpo.

Linking density functional and mode coupling models for supercooled liquids.

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Time dependent stretching of aging dynamics in a generalized hydrodynamic model for supercooled liquids.

The nonequilibrium dynamics and aging behavior of a supercooled liquid is investigated from an analysis of the correlation of density fluctuations at two different times. The dynamic correlation functions are computed by solving numerically the equations of nonlinear fluctuating hydrodynamics. The aging time dependence follows a modified stretched exponential form with a relaxation time which is dependent on the aging time. This is similar to the behavior seen in the aging data of dielectric response functions of a typical glass forming liquid.

Configurational entropy from a replica approach: A density-functional model.

We study a field-theoretic model for the metastable liquid using a nonlocal free-energy functional with density ρ(x) is the order parameter and three-point correlation effects included in the formulation. We assume fragmentation of the free-energy landscape into distinct basins of local minima and evaluate the partition function for the many-particle system through mapping into a composite system of m identical replicas. Static correlations and configurational entropy S_{c} are calculated in the m=1 limit. The Kauzman packing fraction η_{K} obtained are in agreement with other works.

Functional characterization of the Saccharomyces cerevisiae protein Chl1 reveals the role of sister chromatid cohesion in the maintenance of spindle length during S-phase arrest.

BACKGROUND: Metaphase cells have short spindles for efficient bi-orientation of chromosomes. The cohesin proteins hold sister chromatids together, creating Sister Chromatid Cohesion (SCC) that helps in the maintenance of short spindle lengths in metaphase. The budding yeast protein Chl1p, which has human homologs, is required for DNA damage repair, recombination, transcriptional silencing and aging. This protein is also needed to establish SCC between sister chromatids in S-phase. RESULTS: In the present study we have further characterized Chl1p for its role in the yeast Saccharomyces cerevisiae when cells are under replication stress. We show that when DNA replication is arrested by hydroxyurea (HU), the chl1 mutation causes growth deficiency and a mild loss in cell viability. Although both mutant and wild-type cells remained arrested with undivided nuclei, mutant cells had mitotic spindles, which were about 60-80% longer than wild-type spindles. Spindle extension occurred in S-phase in the presence of an active S-phase checkpoint pathway. Further, the chl1 mutant did not show any kinetochore-related defect that could have caused spindle extension. These cells were affected in the retention of SCC in that they had only about one-fourth of the normal levels of the cohesin subunit Scc1p at centromeres, which was sufficient to bi-orient the chromosomes. The mutant cells showed defects in SCC, both during its establishment in S-phase and in its maintenance in G2. Mutants with partial and pericentromeric cohesion defects also showed spindle elongation when arrested in S-phase by HU. CONCLUSIONS: Our work shows that Chl1p is required for normal growth and cell viability in the presence of the replication block caused by HU. The absence of this protein does not, however, compromize the replication checkpoint pathway. Even though the chl1 mutation gives synthetic lethal interactions with kinetochore mutations, its absence does not affect kinetochore function; kinetochore-microtubule interactions remain unperturbed. Further, chl1 cells were found to lose SCC at centromeres in both S- and G2 phases, showing the requirement of Chl1p for the maintenance of cohesion in G2 phase of these cells. This work documents for the first time that SCC is an important determinant of spindle size in the yeast Saccharomyces cerevisiae when genotoxic agents cause S-phase arrest of cells.

Fluctuating nonlinear hydrodynamics does not support an ergodic-nonergodic transition.

Despite its appeal, real and simulated glass forming systems do not undergo an ergodic-nonergodic (ENE) transition. We reconsider whether the fluctuating nonlinear hydrodynamics (FNH) model for this system, introduced by us in 1986, supports an ENE transition. Using nonperturbative arguments, with no reference to the hydrodynamic regime, we show that the FNH model does not support an ENE transition. Our results support the findings in the original paper. Assertions in the literature questioning the validity of the original work are shown to be in error.

Nonequilibrium dynamics in an amorphous solid.

The nonequilibrium dynamics of an amorphous solid is studied with a soft-spin model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts form similar to that obtained in Lunkenheimer [Phys. Rev. Lett. 95, 055702 (2005)] from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem violation is also studied in time as well as correlation windows.

Fluctuating nonlinear hydrodynamics of flocking.

Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or "particles" is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH). The latter are the equations used frequently for describing active systems on the basis of intuitive arguments. The transport coefficients which appear in the macroscopic FNH equations are determined in terms of the parameters of the microscopic dynamics.

Fragility and elastic behavior of a supercooled liquid.

A model for the supercooled liquid is considered by taking into account its solidlike properties. We focus on how the long time dynamics is affected due to the coupling between the slowly decaying density fluctuations and the local displacement variables in the frozen liquid. Results from our model agree with the recent observation of Novikov and Sokolov [Nature (London) 431, 961 (2004)] that the fragility index m of a glass forming material is linearly related to the corresponding ratio KG of the bulk and the shear moduli.

Glassy aging with modified Kohlrausch-Williams-Watts form.

In this paper, we address the question of whether aging in the nonequilibrium glassy state is controlled by the equilibrium alpha-relaxation process, which occurs at temperatures above T(g) . Recently, Lunkenheimer [Phys. Rev. Lett. 95, 055702 (2005)] proposed a model for the glassy aging data of dielectric relaxation using a modified Kohlrausch-Williams-Watts form exp[-(t(age)/tau(age)(beta(age))] . The aging time t(age) dependence of the relaxation time tau(age) is defined by these authors through a functional relation involving the corresponding frequency nu(t(age))=1/(2pi tau(age)) , but the stretching exponent beta(age) is the same as beta(alpha), the alpha-relaxation stretching exponent. We present here an alternative functional form for tau(age)(t(age)) directly involving the relaxation time itself. The proposed model fits the data of Lunkenheimer perfectly with a stretching exponent beta(age) different from beta(alpha) .

Characteristic temperatures of glassy behaviour in a simple liquid.

A model for the metastable liquid in terms of holes present in the amorphous structure is considered using the classical density functional theory (DFT). For a one component Lennard-Jones liquid we obtain the temperature dependence of the free volume v(f) in the metastable state. A temperature T(0), similar to that of the characteristic transition of the free volume theory, is identified by extrapolating v(f)(T) to zero. The Kauzmann temperature T(K) is also obtained here by extrapolating the entropy difference between the supercooled state and that of the crystal to zero. We compare the temperatures T(0) and T(K) obtained in our model with other two characteristic temperatures for glassy behaviour, namely (a) the dynamic transition temperature T(c) of the mode coupling theory (MCT) and (b) the glass transition temperature T(g) which was obtained by Leonardo et al (2000 Phys. Rev. Lett. 84 6054) from studying the violation of the fluctuation-dissipation theorem. All the four temperatures, obtained from independent routes, are located with respect to the melting temperature T(m) in a manner which is in agreement with experiments.

Dependence of the configurational entropy on amorphous structures of a hard-sphere fluid.

The free energy of a hard-sphere fluid for which the average energy is trivial signifies how its entropy changes with packing. The packing η_{f} at which the free energy of the crystalline state becomes lower than that of the disordered fluid state marks the freezing point. For packing fractions η>η_{f} of the hard-sphere fluid, we use the modified weighted density functional approximation to identify metastable free energy minima intermediate between uniform fluid and crystalline states. The distribution of the sharply localized density profiles, i.e., the inhomogeneous density field ρ(x) characterizing the metastable state is primarily described by a pair function g_{s}(η/η_{0}). η_{0} is a structural parameter such that for η=η_{0} the pair function is identical to that for the Bernal random structure. The configurational entropy S_{c} of the metastable hard-sphere fluid is calculated by subtracting the corresponding vibrational entropy from the total entropy. The extrapolated S_{c} vanishes as η→η_{K} and η_{K} is in agreement with other works. The dependence of η_{K} on the structural parameter η_{0} is obtained.

Mrg19 depletion increases S. cerevisiae lifespan by augmenting ROS defence.

Caloric restriction (CR) is the most compelling example of lifespan extension by external manipulation. Although the molecular mechanisms remain unknown, the theory of hormesis has been invoked to explain the life promoting effects of CR. Hormesis is defined as the beneficial effects of low intensity stressor on a cell or organism. Mrg19 is a putative transcription factor that regulates carbon and nitrogen metabolism in yeast. In this study, we have found that deletion of MRG19 gene causes metabolic shift in yeast cells, leading to higher intracellular reactive oxygen species, augmentation of scavenging enzymes and longer lifespan compared to wild-type cells. All these results together suggest that similar to CR, depletion of Mrg19 leads to a condition of mild stress which in turn enhances vitality.

Optimum vacancy concentration in a crystal.

The importance of the presence of a small fraction of vacancies in a crystal structure is demonstrated from considerations of thermodynamic stability. We include in the density functional theory the effects due to the distortion of the lattice structure surrounding the vacancy and show that the free energy is less when vacancies are present. Near freezing point, our theoretical model obtains the equilibrium vacancy fraction in the hard sphere crystal to be approximately 10(-5) and it decreases with increase of the density.

Renormalized dynamics of the Dean-Kawasaki model.

We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ(x,t) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ. The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ,θ}, linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D(0) to D(R) is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997)]. D(R) sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with D(R)=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.

Slow dynamics of a tagged particle in a supercooled liquid.

The ergodicity-nonergodicity (ENE) transition of the self-consistent mode-coupling theory (MCT) is marked by the point at which the time correlation of collective density fluctuations is not zero in the long-time limit. The nonergodic state, reaching beyond the ENE transition of simple MCT, is characterized by a finite shear modulus. The MCT, formulated in the current set of papers, predicts that the single-particle density correlation, unlike the collective density correlation, decays to zero at long times on either side of the ENE transition. The self-diffusion coefficient remains finite. This differs from the existing MCT results in which both collective and single-particle correlations are simultaniously frozen at the ENE transition. We discuss in this paper mechanisms by which a sharp fall in self-diffusion coefficient may occur within the present model. This overdamping or the so-called adiabatic approximation for the supercooled state does not maintain microscopic momentum conservation. Within this approximation, the self-diffusion constant approaches zero at the ENE transition point. This approximate result, which is similar to the prediction of the existing MCT models, further illustrates the process of cage formation with increase of density. At a qualitative level, our analysis shows that the self-diffusion process depends on the structure as well as short-time transport properties of the supercooled liquid. We solve the integral equations for the nonergodicity parameters to analyze the full implications of the adiabatic approximation.