Scaling Behavior of Quantum Nanosystems: Emergence of Quasi-particles, Collective Modes, and Mixed Exchange Symmetry States

Quantum nanosystems such as graphene nanoribbons or superconducting nanoparticles are studied via a multiscale approach. Long space-time dynamics is derived using a perturbation expansion in the ratio of the nearest-neighbor distance to a nanometer-scale characteristic length, and a theorem on the equivalence of long-time averages and expectation values. This dynamics is shown to satisfy a coarse-grained wave equation (CGWE) which takes a Schr\"odinger-like form with modified masses and interactions. The scaling of space and time is determined by the orders of magnitude of various contributions to the N-body potential. If the spatial scale of the coarse-graining is too large, the CGWE would imply an unbounded growth of gradients; if it is too short, the system's size would display uncontrolled growth inappropriate for the bound states of interest, i.e., collective motion or migration within a stable nano-assembly. The balance of these two extremes removes arbitrariness in the choice of the scaling of space-time. Since the long-scale dynamics of each fermion involves its interaction with many others, we hypothesize that the solutions of the CGWE have mean-field character to good approximation, i.e., can be factorized into single-particle functions. This leads to a Coarse-grained Mean-field (CGMF) approximation that is distinct in character from traditional Hartree-Fock theory. A variational principle is used to derive equations for the single-particle functions. This theme is developed and used to derive an equation for low-lying disturbances from the ground state corresponding to long wavelength density disturbances or long-scale migration. An algorithm for the efficient simulation of quantum nanosystems is suggested.Comment: Copyright 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics; Keywords: Quantum nanosystems, coarse-grained wave equation, mean field theory, multiscale analysi

Block network mapping approach to quantitative trait locus analysis

BACKGROUND: Advances in experimental biology have enabled the collection of enormous troves of data on genomic variation in living organisms. The interpretation of this data to extract actionable information is one of the keys to developing novel therapeutic strategies to treat complex diseases. Network organization of biological data overcomes measurement noise in several biological contexts. Does a network approach, combining information about the linear organization of genomic markers with correlative information on these markers in a Bayesian formulation, lead to an analytic method with higher power for detecting quantitative trait loci? RESULTS: Block Network Mapping, combining Similarity Network Fusion (Wang et al., NM 11:333-337, 2014) with a Bayesian locus likelihood evaluation, leads to large improvements in area under the receiver operating characteristic and power over interval mapping with expectation maximization. The method has a monotonically decreasing false discovery rate as a function of effect size, unlike interval mapping. CONCLUSIONS: Block Network Mapping provides an alternative data-driven approach to mapping quantitative trait loci that leverages correlations in the sampled genotypes. The evaluation methodology can be combined with existing approaches such as Interval Mapping. Python scripts are available at http://lbm.niddk.nih.gov/vipulp/ . Genotype data is available at http://churchill-lab.jax.org/website/GattiDOQTL . BMC Bioinformatics 2016 Dec 22; 17(1):544

Computer-Aided Design of Nanocapsules for Therapeutic Delivery

The design of nanocapsules for targeted delivery of therapeutics presents many, often seemingly self-contradictory, constraints. An algorithm for predicting the physico-chemical characteristics of nanocapsule delivery and payload release using a novel all-atom, multiscale technique is presented. This computational method preserves key atomic-scale behaviours needed to make predictions of interactions of functionalized nanocapsules with the cell surface receptors, drug, siRNA, gene or other payload. We show how to introduce a variety of order parameters with distinct character to enable a multiscale analysis of a complex system. The all-atom formulation allows for the use of an interatomic force field, making the approach universal and avoiding recalibration with each new application. Alternatively, key parameters, which minimize the need for calibration, are also identified. Simultaneously, the methodology enables predictions of the supra-nanometer-scale behaviour, such as structural transitions and disassembly of the nanocapsule accompanying timed payload release or due to premature degradation. The final result is a Fokker–Planck equation governing the rate of stochastic payload release and structural changes and migration accompanying it. A novel “salt shaker” effect that underlies fluctuation-enhancement of payload delivery is presented. Prospects for computer-aided design of nanocapsule delivery system are discussed

The slopes within the networks of each 3-node topology divided into 7 categories.

<p>Within each topology , the overall robustness to parameters in category is shown versus , the slope of the regression line between and , for <i>j</i> = 1 (A), 2 (B), 3 (C), 4 (D), 5 (E), 6 (F), and 7 (G).</p

A Network Characteristic That Correlates Environmental and Genetic Robustness

<div><p>As scientific advances in perturbing biological systems and technological advances in data acquisition allow the large-scale quantitative analysis of biological function, the robustness of organisms to both transient environmental stresses and inter-generational genetic changes is a fundamental impediment to the identifiability of mathematical models of these functions. An approach to overcoming this impediment is to reduce the space of possible models to take into account both types of robustness. However, the relationship between the two is still controversial. This work uncovers a network characteristic, transient responsiveness, for a specific function that correlates environmental imperturbability and genetic robustness. We test this characteristic extensively for dynamic networks of ordinary differential equations ranging up to 30 interacting nodes and find that there is a power-law relating environmental imperturbability and genetic robustness that tends to linearity as the number of nodes increases. Using our methods, we refine the classification of known 3-node motifs in terms of their environmental and genetic robustness. We demonstrate our approach by applying it to the chemotaxis signaling network. In particular, we investigate plausible models for the role of CheV protein in biochemical adaptation via a phosphorylation pathway, testing modifications that could improve the robustness of the system to environmental and/or genetic perturbation.</p></div

All possible sets of interactions for links a, b, c in Fig. 11.

<p>All possible sets of interactions for links a, b, c in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003474#pcbi-1003474-g011" target="_blank">Fig. 11</a>.</p

Variations in the Pearson test within individual networks.

<p>When the Pearson test is performed using two different definitions of and , small variations can be observed within individual networks. In (A) we show an example where a network's time-course (blue) is deemed TR when the definition, (red) and (green) of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003474#pcbi.1003474.e233" target="_blank">equations (6)</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003474#pcbi.1003474.e234" target="_blank">(7)</a> is used (), but NP when the definition, (pink) and (gray) of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003474#pcbi.1003474.e283" target="_blank">equations (10)</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003474#pcbi.1003474.e284" target="_blank">(11)</a> is used instead (). (B) is an example where the two tests agree ( and ). In (C) we show all (red), (green), (pink), and (gray) values over the space of networks. Networks where the two tests (i.e., Pearson test using the two different definitions) differ are shown in black (note that only their values are colored in black to avoid showing the same network 4 times).</p