Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $\rho$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.Comment: to appear in Physical Review

Charge Oscillations in Debye-Hueckel Theory

The recent generalized Debye-Hueckel (GDH) theory is applied to the calculation of the charge-charge correlation function G_{ZZ}(r). The resulting expression satisfies both (i) the charge neutrality condition and (ii) the Stillinger-Lovett second-moment condition for all T and rho_N, the overall ion density, and (iii) exhibits charge oscillations for densities above a "Kirkwood line" in the (rho_N,T) plane. This corrects the normally assumed DH correlations, and, when combined with the GDH analysis of the density correlations, leaves the GDH theory as the only complete description of ionic correlation functions, as judged by (i)-(iii), (iv) exact low-density (rho_N,T) variation, and (v) reasonable behavior near criticality.Comment: 6 pages, EuroPhys.sty (now available on archive), 1 eps figur

On the Adsorption of Two-State Polymers

Monte Carlo(MC) simulations produce evidence that annealed copolymers incorporating two interconverting monomers, P and H, adsorb as homopolymers with an effective adsorption energy per monomer, $\epsilon_{eff}$, that depends on the PH equilibrium constants in the bulk and at the surface. The cross-over exponent, $\Phi,$ is unmodified. The MC results on the overall PH ratio, the PH ratio at the surface and in the bulk as well as the number of adsorbed monomers are in quantitative agreement with this hypothesis and the theoretically derived $\epsilon_{eff}$. The evidence suggests that the form of surface potential does not affect $\Phi$ but does influence the PH equilibrium.Comment: 22 pages, 10 figure

Universality class of criticality in the restricted primitive model electrolyte

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using temperature-density, (T, rho), loci of inflections, Q = ^2/ maxima, canonical and C_V criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with potentials phi(r)>Phi/r^{4.9} when r \to \infty

Application of machine learning methods to histone methylation ChIP-Seq data reveals H4R3me2 globally represses gene expression

<p>Abstract</p> <p>Background</p> <p>In the last decade, biochemical studies have revealed that epigenetic modifications including histone modifications, histone variants and DNA methylation form a complex network that regulate the state of chromatin and processes that depend on it including transcription and DNA replication. Currently, a large number of these epigenetic modifications are being mapped in a variety of cell lines at different stages of development using high throughput sequencing by members of the ENCODE consortium, the NIH Roadmap Epigenomics Program and the Human Epigenome Project. An extremely promising and underexplored area of research is the application of machine learning methods, which are designed to construct predictive network models, to these large-scale epigenomic data sets.</p> <p>Results</p> <p>Using a ChIP-Seq data set of 20 histone lysine and arginine methylations and histone variant H2A.Z in human CD4⁺T-cells, we built predictive models of gene expression as a function of histone modification/variant levels using Multilinear (ML) Regression and Multivariate Adaptive Regression Splines (MARS). Along with extensive crosstalk among the 20 histone methylations, we found H4R3me2 was the most and second most globally repressive histone methylation among the 20 studied in the ML and MARS models, respectively. In support of our finding, a number of experimental studies show that PRMT5-catalyzed symmetric dimethylation of H4R3 is associated with repression of gene expression. This includes a recent study, which demonstrated that H4R3me2 is required for DNMT3A-mediated DNA methylation--a known global repressor of gene expression.</p> <p>Conclusion</p> <p>In stark contrast to univariate analysis of the relationship between H4R3me2 and gene expression levels, our study showed that the regulatory role of some modifications like H4R3me2 is masked by confounding variables, but can be elucidated by multivariate/systems-level approaches.</p

Quantum computing at the frontiers of biological sciences

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences