Mesh-free hierarchical clustering methods for fast evaluation of electrostatic interactions of point multipoles.

Electrostatic interactions involving point multipoles are being increasingly implemented to achieve higher accuracy in molecular simulations. A major drawback of multipolar electrostatics is the increased computational cost. Here we develop and compare two Cartesian tree algorithms which employ Taylor approximations and hierarchical clustering to speed up the evaluation of point multipole interactions. We present results from applying the algorithms to compute the free space Coulomb potential and forces of different sets of interacting point multipoles with different densities. The methods achieve high accuracy and speedup of more than an order of magnitude over direct sum calculations and scale well in parallel.

Arbitrary order permanent Cartesian multipolar electrostatic interactions.

Recently, there has been a concerted effort to implement advanced classical potential energy surfaces by adding higher order multipoles to fixed point charge electrostatics in a bid to increase the accuracy of simulations of condensed phase systems. One major hurdle is the unwieldy nature of the expressions which in part has limited developers mostly to including only dipoles and quadrupoles. In this paper, we present a generalization of the Cartesian formulation of electrostatic multipolar interactions that enables the specification of an arbitrary order of multipoles. Specifically, we derive formulas for arbitrary order implementation of the particle mesh Ewald method and give a closed form formula for the stress tensor in the reciprocal space. In addition, we provide recurrence relations for common electrostatic potentials employed in molecular simulations, which allows for the generalization to arbitrary order and guarantees a computational cost that scales as O(p(3)) for Cartesian multipole interactions of order p.

The incidence of malaria and the comparison of hematological and biochemical indices of Plasmodium falciparum-parasitemic and aparasitemic sickle cell disease (SCD) patients.

Hemolytic anemia is common in sickle cell disease (SCD), but the course and extent differ, depending on genetic, epigenetic, and environmental factors. In the malaria-endemic tropical environment, some vulnerable subjects would be infected and the impact of infection would vary. Therefore, this study was to find malaria incidence and the associated changes in some laboratory indices in 330 SCD subjects. Following blood smear preparation for falciparum detection, hematological and biochemical indices were measured for a comparison of parasitemic and age-matched, genotype-matched, and sex-matched nonparasitemics. For sixty-nine parasitemics, constituting about 21% of all subjects studied, and sixty-six matched nonparasitemics, hematological indices (hemoglobin, white-cell count, red-cell count, mean cellular volume, reticulocyte count, and HbF) as well as biochemical indices (LDH, total bilirubin, AST, and ALT) were determined. For all quantities, except the reticulocyte count (12.3% ± 12.4% for parasitemics and 23.6% ± 17.7% for nonparasitemics), no statistically significant differences were observed. Classification of both cohorts according to their genotypes showed some intergenotypic differences for hemoglobin and WBC counts. Mathematical modeling of the reticulocyte counts shows the distribution in the parasitemics followed an exponential pattern, while the nonparasitemic showed a polynomial distribution, with each model characterized by an equation of best fit. The study has shown about 21% incidence of parasitemia. All differences in the indices can be seen as normal variations, unattributable to the malaria infection. However, the lower reticulocyte count in the parasitemic is a reflection of lowered erythropoietic activity because of the infection.