Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

Response to comment on 'Valid molecular dynamics simulations of human hemoglobin require a surprisingly large box size'

We recently reported that molecular dynamics simulations for hemoglobin require a surprisingly large box size to stabilize the T(0) state relative to R(0), as observed in experiments (El Hage et al., 2018). Gapsys and de Groot have commented on this work but do not provide convincing evidence that the conclusions of El Hage et al., 2018 are incorrect. Here we respond to these concerns, argue that our original conclusions remain valid, and raise our own concerns about some of the results reported in the comment by Gapsys and de Groot that require clarification

Valid molecular dynamics simulations of human hemoglobin require a surprisingly large box size

Recent molecular dynamics (MD) simulations of human hemoglobin (Hb) give results in disagreement with experiment. Although it is known that the unliganded (T 0 ) and liganded (R 4 ) tetramers are stable in solution, the published MD simulations of T 0 undergo a rapid quaternary transition to an R-like structure. We show that T 0 is stable only when the periodic solvent box contains ten times more water molecules than the standard size for such simulations. The results suggest that such a large box is required for the hydrophobic effect, which stabilizes the T 0 tetramer, to be manifested. Even in the largest box, T 0 is not stable unless His146 is protonated, providing an atomistic validation of the Perutz model. The possibility that extra large boxes are required to obtain meaningful results will have to be considered in evaluating existing and future simulations of a wide range of systems

Theory of Anomalous Hall Effect in a Heavy fermion System with a Strong Anisotropic Crystal Field

In a heavy fermion system, there exists the anomalous Hall effect caused by localized $f$-orbital freedom, in addition to the normal Hall effect due to the Lorentz force. In 1994, we found that the Hall coefficient caused by the anomalous Hall effect ($R_H^{AHE}$) is predominant and the relation $R_H^{AHE} \propto \rho^2$ ($\rho$ is the electrical resistivity) holds at low temperatures in many compounds. In this work, we study the system where the magnetic susceptibility is highly anisotropic due to the strong crystalline electric field on $f$-orbitals. Interestingly, we find that $R_H^{AHE}$ is nearly isotropic in general. This tendency is frequently observed experimentally, which has casted suspicion that the anomalous Hall effect may be irrelevant in real materials. Our theory corresponds to corrections and generalizations of the pioneering work on ferromagnetic metals by Karplus and Luttinger.Comment: 4 pages, revtex, to be published in J. Phys. Soc. Jpn. (No.8

Role of framework mutations and antibody flexibility in the evolution of broadly neutralizing antibodies

Eliciting antibodies that are cross reactive with surface proteins of diverse strains of highly mutable pathogens (e.g., HIV, influenza) could be key for developing effective universal vaccines. Mutations in the framework regions of such broadly neutralizing antibodies (bnAbs) have been reported to play a role in determining their properties. We used molecular dynamics simulations and models of affinity maturation to study specific bnAbs against HIV. Our results suggest that there are different classes of evolutionary lineages for the bnAbs. If germline B cells that initiate affinity maturation have high affinity for the conserved residues of the targeted epitope, framework mutations increase antibody rigidity as affinity maturation progresses to evolve bnAbs. If the germline B cells exhibit weak/moderate affinity for conserved residues, an initial increase in flexibility via framework mutations may be required for the evolution of bnAbs. Subsequent mutations that increase rigidity result in highly potent bnAbs. Implications of our results for immunogen design are discussed

Sequencing of folding events in Go-like proteins

We have studied folding mechanisms of three small globular proteins: crambin (CRN), chymotrypsin inhibitor 2 (CI2) and the fyn Src Homology 3 domain (SH3) which are modelled by a Go-like Hamiltonian with the Lennard-Jones interactions. It is shown that folding is dominated by a well-defined sequencing of events as determined by establishment of particular contacts. The order of events depends primarily on the geometry of the native state. Variations in temperature, coupling strengths and viscosity affect the sequencing scenarios to a rather small extent. The sequencing is strongly correlated with the distance of the contacting aminoacids along the sequence. Thus $\alpha$-helices get established first. Crambin is found to behave like a single-route folder, whereas in CI2 and SH3 the folding trajectories are more diversified. The folding scenarios for CI2 and SH3 are consistent with experimental studies of their transition states.Comment: REVTeX, 12 pages, 11 EPS figures, J. Chem. Phys (in press

Pokefind: a novel topological filter for use with protein structure prediction

Motivation: Our focus has been on detecting topological properties that are rare in real proteins, but occur more frequently in models generated by protein structure prediction methods such as Rosetta. We previously created the Knotfind algorithm, successfully decreasing the frequency of knotted Rosetta models during CASP6. We observed an additional class of knot-like loops that appeared to be equally un-protein-like and yet do not contain a mathematical knot. These topological features are commonly referred to as slip-knots and are caused by the same mechanisms that result in knotted models. Slip-knots are undetectable by the original Knotfind algorithm. We have generalized our algorithm to detect them, and analyzed CASP6 models built using the Rosetta loop modeling method

A Score of the Ability of a Three-Dimensional Protein Model to Retrieve Its Own Sequence as a Quantitative Measure of Its Quality and Appropriateness

BACKGROUND: Despite the remarkable progress of bioinformatics, how the primary structure of a protein leads to a three-dimensional fold, and in turn determines its function remains an elusive question. Alignments of sequences with known function can be used to identify proteins with the same or similar function with high success. However, identification of function-related and structure-related amino acid positions is only possible after a detailed study of every protein. Folding pattern diversity seems to be much narrower than sequence diversity, and the amino acid sequences of natural proteins have evolved under a selective pressure comprising structural and functional requirements acting in parallel. PRINCIPAL FINDINGS: The approach described in this work begins by generating a large number of amino acid sequences using ROSETTA [Dantas G et al. (2003) J Mol Biol 332:449-460], a program with notable robustness in the assignment of amino acids to a known three-dimensional structure. The resulting sequence-sets showed no conservation of amino acids at active sites, or protein-protein interfaces. Hidden Markov models built from the resulting sequence sets were used to search sequence databases. Surprisingly, the models retrieved from the database sequences belonged to proteins with the same or a very similar function. Given an appropriate cutoff, the rate of false positives was zero. According to our results, this protocol, here referred to as Rd.HMM, detects fine structural details on the folding patterns, that seem to be tightly linked to the fitness of a structural framework for a specific biological function. CONCLUSION: Because the sequence of the native protein used to create the Rd.HMM model was always amongst the top hits, the procedure is a reliable tool to score, very accurately, the quality and appropriateness of computer-modeled 3D-structures, without the need for spectroscopy data. However, Rd.HMM is very sensitive to the conformational features of the models' backbone