A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Polymeric human Fc-fusion proteins with modified effector functions

The success of Fc-fusion bio-therapeutics has spurred the development of other Fc-fusion products for treating and/or vaccinating against a range of diseases. We describe a method to modulate their function by converting them into well-defined stable polymers. This strategy resulted in cylindrical hexameric structures revealed by tapping mode atomic force microscopy (AFM). Polymeric Fc-fusions were significantly less immunogenic than their dimeric or monomeric counterparts, a result partly owing to their reduced ability to interact with critical Fc-receptors. However, in the absence of the fusion partner, polymeric IgG1-Fc molecules were capable of binding selectively to FcγRs, with significantly increased affinity owing to their increased valency, suggesting that these reagents may prove of immediate utility in the development of well-defined replacements for intravenous immunoglobulin (IVIG) therapy. Overall, these findings establish an effective IgG Fc-fusion based polymeric platform with which the therapeutic and vaccination applications of Fc-fusion immune-complexes can now be explored

Probing Molecular Mechanisms of the Hsp90 Chaperone: Biophysical Modeling Identifies Key Regulators of Functional Dynamics

Deciphering functional mechanisms of the Hsp90 chaperone machinery is an important objective in cancer biology aiming to facilitate discovery of targeted anti-cancer therapies. Despite significant advances in understanding structure and function of molecular chaperones, organizing molecular principles that control the relationship between conformational diversity and functional mechanisms of the Hsp90 activity lack a sufficient quantitative characterization. We combined molecular dynamics simulations, principal component analysis, the energy landscape model and structure-functional analysis of Hsp90 regulatory interactions to systematically investigate functional dynamics of the molecular chaperone. This approach has identified a network of conserved regions common to the Hsp90 chaperones that could play a universal role in coordinating functional dynamics, principal collective motions and allosteric signaling of Hsp90. We have found that these functional motifs may be utilized by the molecular chaperone machinery to act collectively as central regulators of Hsp90 dynamics and activity, including the inter-domain communications, control of ATP hydrolysis, and protein client binding. These findings have provided support to a long-standing assertion that allosteric regulation and catalysis may have emerged via common evolutionary routes. The interaction networks regulating functional motions of Hsp90 may be determined by the inherent structural architecture of the molecular chaperone. At the same time, the thermodynamics-based “conformational selection” of functional states is likely to be activated based on the nature of the binding partner. This mechanistic model of Hsp90 dynamics and function is consistent with the notion that allosteric networks orchestrating cooperative protein motions can be formed by evolutionary conserved and sparsely connected residue clusters. Hence, allosteric signaling through a small network of distantly connected residue clusters may be a rather general functional requirement encoded across molecular chaperones. The obtained insights may be useful in guiding discovery of allosteric Hsp90 inhibitors targeting protein interfaces with co-chaperones and protein binding clients

The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes

A new coarse-grain model for molecular dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid molecules are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielectric constant of unity (). Second, water molecules are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water molecule is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main physical properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liquid crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liquid crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or experimental methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 microseconds were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodology's inherent multiscale capabilities

Single-Molecule Force Spectroscopy: Experiments, Analysis, and Simulations

International audienceThe mechanical properties of cells and of subcellular components are important to obtain a mechanistic molecular understanding of biological processes. The quantification of mechanical resistance of cells and biomolecules using biophysical methods matured thanks to the development of nanotechnologies such as optical and magnetic tweezers, the biomembrane force probe and atomic force microscopy (AFM). The quantitative nature of force spectroscopy measurements has converted AFM into a valuable tool in biophysics. Force spectroscopy allows the determination of the forces required to unfold protein domains and to disrupt individual receptor/ligand bonds. Molecular simulation as a computational microscope allows investigation of similar biological processes with an atomistic detail. In this chapter, we first provide a step-by-step protocol of force spectroscopy including sample preparation, measurement and analysis of force spectroscopy using AFM and its interpretation in terms of available theories. Next, we present the background for molecular dynamics (MD) simulations focusing on steered molecular dynamics (SMD) and the importance of bridging of computational tools with experimental technique

Molecular dynamics simulation of humic substances

© 2014, Orsi. Humic substances (HS) are complex mixtures of natural organic material which are found almost everywhere in the environment, and particularly in soils, sediments, and natural water. HS play key roles in many processes of paramount importance, such as plant growth, carbon storage, and the fate of contaminants in the environment. While most of the research on HS has been traditionally carried out by conventional experimental approaches, over the past 20 years complementary investigations have emerged from the application of computer modeling and simulation techniques. This paper reviews the literature regarding computational studies of HS, with a specific focus on molecular dynamics simulations. Significant achievements, outstanding issues, and future prospects are summarized and discussed

Residual structures, conformational fluctuations, and electrostatic interactions in the synergistic folding of two intrinsically disordered proteins

To understand the interplay of residual structures and conformational fluctuations in the interaction of intrinsically disordered proteins (IDPs), we first combined implicit solvent and replica exchange sampling to calculate atomistic disordered ensembles of the nuclear co-activator binding domain (NCBD) of transcription coactivator CBP and the activation domain of the p160 steroid receptor coactivator ACTR. The calculated ensembles are in quantitative agreement with NMRderived residue helicity and recapitulate the experimental observation that, while free ACTR largely lacks residual secondary structures, free NCBD is a molten globule with a helical content similar to that in the folded complex. Detailed conformational analysis reveals that free NCBD has an inherent ability to substantially sample all the helix configurations that have been previously observed either unbound or in complexes. Intriguingly, further high-temperature unbinding and unfolding simulations in implicit and explicit solvents emphasize the importance of conformational fluctuations in synergistic folding of NCBD with ACTR. A balance between preformed elements and conformational fluctuations appears necessary to allow NCBD to interact with different targets and fold into alternative conformations. Together with previous topology-based modeling and existing experimental data, the current simulations strongly support an ‘‘extended conformational selection’’ synergistic folding mechanism that involves a key intermediate state stabilized by interaction between the C-terminal helices of NCBD and ACTR. In addition, the atomistic simulations reveal the role of long-range as well as short-range electrostatic interactions in cooperating with readily fluctuating residual structures, which might enhance the encounter rate and promote efficient folding upon encounter for facile binding and folding interactions of IDPs. Thus, the current study not only provides a consistent mechanistic understanding of the NCBD/ACTR interaction, but also helps establish a multi-scale molecular modeling framework for understanding the structure, interaction, and regulation of IDPs in general