Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.

11 12 1. Introduction 14Astronomical emission or absorption sources have an enormous range of densities. 15 Two examples include the intergalactic medium, with n e ∼ 10 −4 cm −3 , and the broad 16 emission-line regions of Active Galactic Nuclei, with n e ∼ 10 10 cm −3 . The gas producing 17 the spectrum is not in thermodynamic equilibrium (Osterbrock & Ferland 2006), so 18 microphysical processes determine the physical conditions. 19 The two common cases encountered for ionization are photoionization and collisional 20 (e.g., electron-impact) ionization. In both cases, ions are recombined by dielectronic 21 and radiative recombination, with dielectronic recombination (DR) usually the dominant 22 process for elements heavier than helium. Databases give ionization and recombination 23 rates that are the sum of several contributing processes. Examples include Voronov (1997) 24 for electron impact ionization, Verner & Yakovlev (1995) for photoionization, and the 25 DR project (Badnell et al. 2003) for dielectronic recombination and Badnell (2006a) for 26 radiative recombination; it is these latter data 1 which will be of primary interest to us in 27 the present study. 28The collisional ionization and recombination rate coefficients used in astrophysics are 29 frequently assumed to depend on temperature but to have no density dependence. The 30 rigorous treatment of density dependent ionization and recombination rate coefficients is 31 via collisional-radiative modeling. This was introduced by Bates et al. (1962) for radiative 32 recombination only and extended to treat the much more complex case of dielectronic 33 recombination by Burgess & Summers (1969). Summers applied their techniques to 34 determine density dependent ionization and recombination rate coefficients, and the 35 consequential ionization balance for collisional plasmas, for H-like thru Ar-like ions.36 1 http://amdpp.phys.strath.ac.uk/tamoc/DATA/ Graphical results were presented for the elements C, O and Ne (Summers 1972) and then 37 N, Mg and Si (Summers 1974). Reduced temperatures and densities were used so as to 38 enable easy interpolation for other elements. Tables of such recombination rate coefficients 39 were made available only via a Laboratory Report -Summers (1974 & 1979) -due to 40 their voluminous nature at that point in history. The 'difficulty' in utilizing this pioneering 41 data led to some modelers attempting to develop simplified approaches. For example, 42 Jordan (1969) used an approach which was based on truncating the zero-density DR sum 43 over Rydberg states using a simple density dependent cut-off which itself was based on 44 early collisional-radiative calculations by Burgess & Summers (1969); a suppression factor 45 was formed from its ratio to the zero-density value and then used more generally. Also, 46 Davidson (1975) simplified the collisional-radiative approach of Burgess & Summers (1969) 47 and, using hydrogenic atomic data, determined suppression factors for Li-like C IV and 48 O VI. New calculations for C IV ...

Experimental measurements of the center of the H_{beta} Stark profile on three different installations have been done to study its asymmetry in wide ranges of electron density, temperature, and plasma conditions. Theoretical calculations for the analysis of experimental results have been performed using the standard theory and computer simulations and included separately quadrupolar and quadratic Stark effects. Earlier experimental results and theoretical calculations of other authors have been reviewed as well. The experimental results are well reproduced by the calculations at high and moderate densities.

We explore a new approach in the rational design of specificity in molecular recognition of small molecules based on statistical-mechanical integral equation theory of molecular liquids in the form of the three-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH). The numerically stable iterative solution of conventional 3D-RISM equations includes the fragmental decomposition of flexible ligands, which are treated as distinct species in solvent mixtures of arbitrary complexity. The computed density functions for solution (including ligand) molecules are obtained as a set of discrete spatial grids that uniquely describe the continuous solvent-site distribution around the protein solute. Potentials of mean force derived from these distributions define the scoring function interfaced with the AutoDock program for an automated ranking of docked conformations. As a case study in terms of solvent composition, we analyze cooperative interactions encountered in the binding of a flexible thiamine molecule to the prion protein at near-physiological conditions. The predicted location and residency times of computed binding modes are in excellent agreement with the available experimental data.