Kinetic energy-free Hartree–Fock equations: an integral formulation

We have implemented a self-consistent feld solver for Hartree–Fock calculations, by making use of Multiwavelets and Multiresolution Analysis. We show how such a solver is inherently a preconditioned steepest descent method and therefore a good starting point for rapid convergence. A distinctive feature of our implementation is the absence of any reference to the kinetic energy operator. This is desirable when Multiwavelets are employed, because diferential operators such as the Laplacian in the kinetic energy are challenging to represent correctly. The theoretical framework is described in detail and the implemented algorithm is both presented in the paper and made available as a Python notebook. Two simple examples are presented, highlighting the main features of our implementation: arbitrary predefned precision, rapid and robust convergence, absence of the kinetic energy operator

DeltaProt: a software toolbox for comparative genomics

Abstract Background Statistical bioinformatics is the study of biological data sets obtained by new micro-technologies by means of proper statistical methods. For a better understanding of environmental adaptations of proteins, orthologous sequences from different habitats may be explored and compared. The main goal of the DeltaProt Toolbox is to provide users with important functionality that is needed for comparative screening and studies of extremophile proteins and protein classes. Visualization of the data sets is also the focus of this article, since visualizations can play a key role in making the various relationships transparent. This application paper is intended to inform the reader of the existence, functionality, and applicability of the toolbox. Results We present the DeltaProt Toolbox, a software toolbox that may be useful in importing, analyzing and visualizing data from multiple alignments of proteins. The toolbox has been written in MATLAB™ to provide an easy and user-friendly platform, including a graphical user interface, while ensuring good numerical performance. Problems in genome biology may be easily stated thanks to a compact input format. The toolbox also offers the possibility of utilizing structural information from the SABLE or other structure predictors. Different sequence plots can then be viewed and compared in order to find their similarities and differences. Detailed statistics are also calculated during the procedure. Conclusions The DeltaProt package is open source and freely available for academic, non-commercial use. The latest version of DeltaProt can be obtained from http://services.cbu.uib.no/software/deltaprot/. The website also contains documentation, and the toolbox comes with real data sets that are intended for training in applying the models to carry out bioinformatical and statistical analyses of protein sequences. Equipped with the new algorithms proposed here, DeltaProt serves as an auxiliary analysis tool capable of visualizing and comparing orthologus protein sequences. The framework of the algorithms also enables easy incorporation of extra information on structure, if such data is available.</p

Dynamical models of mutated chronic myelogenous leukemia cells for a postimatinib treatment scenario: Response to dasatinib or nilotinib therapy

Targeted inhibition of the oncogenic BCR-ABL1 fusion protein using the ABL1 tyrosine kinase inhibitor imatinib has become standard therapy for chronic myelogenous leukemia (CML), with most patients reaching total and durable remission. However, a significant fraction of patients develop resistance, commonly due to mutated ABL1 kinase domains. This motivated development of second-generation drugs with broadened or altered protein kinase selectivity profiles, including dasatinib and nilotinib. Imatinib-resistant patients undergoing treatment with second-line drugs typically develop resistance to them, but dynamic and clonal properties of this response differ. Shared, however, is the observation of clonal competition, reflected in patterns of successive dominance of individual clones. We present three deterministic mathematical models to study the origins of clinically observed dynamics. Each model is a system of coupled first-order differential equations, considering populations of three mutated active stem cell strains and three associated pools of differentiated cells; two models allow for activation of quiescent stem cells. Each approach is distinguished by the way proliferation rates of the primary stem cell reservoir are modulated. Previous studies have concentrated on simulating the response of wild-type leukemic cells to imatinib administration; our focus is on modelling the time dependence of imatinib-resistant clones upon subsequent exposure to dasatinib or nilotinib. Performance of the three computational schemes to reproduce selected CML patient profiles is assessed. While some simple cases can be approximated by a basic design that does not invoke quiescence, others are more complex and require involvement of non-cycling stem cells for reproduction. We implement a new feedback mechanism for regulation of coupling between cycling and non-cycling stem cell reservoirs that depends on total cell populations. A bifurcation landscape analysis is also performed for solutions to the basic ansatz. Computational models reproducing patient data illustrate potential dynamic mechanisms that may guide optimization of therapy of drug resistant CML

Linear scaling Coulomb interaction in the multiwavelet basis, a parallel implementation

We present a parallel and linear scaling implementation of the calculation of the electrostatic potential arising from an arbitrary charge distribution. Our approach is making use of the multi-resolution basis of multiwavelets. The potential is obtained as the direct solution of the Poisson equation in its Green’s function integral form. In the multiwavelet basis, the formally non local integral operator decays rapidly to negligible values away from the main diagonal, yielding an effectively banded structure where the bandwidth is only dictated by the requested accuracy. This sparse operator structure has been exploited to achieve linear scaling and parallel algorithms. Parallelization has been achieved both through the shared memory (OpenMP) and the message passing interface (MPI) paradigm. Our implementation has been tested by computing the electrostatic potential of the electronic density of long-chain alkanes and diamond fragments showing (sub)linear scaling with the system size and efficent parallelization. Keywords: Multiwavelets; electrostatic potentials; Poisson equation; integral operators; linear scaling; parallel implementation