Spline-based parallel nonlinear optimization of function sequences

Ben-Nun, Tal; Barak, Amnon; Raviv, Uri

doi:10.1016/j.jpdc.2016.04.011

Cited by 6 publications

(6 citation statements)

References 42 publications

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“…The values of p n s,c (t i ) should continuously vary with time. As was discussed in our earlier paper, 70 when fitting a data series the continuity assumption may help to speed-up convergence.…”

Section: ■ Materials and Methodsmentioning

confidence: 99%

Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly

et al. 2020

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There are ∼ 10 30 possible intermediates on the assembly path from hepatitis B capsid protein dimers to the 120-dimer capsid. If every intermediate was tested, assembly would often get stuck in an entropic trap and essentially every capsid would follow a unique assembly path. Yet, capsids assemble rapidly with minimal trapped intermediates, a realization of the Levinthal paradox. To understand the fundamental mechanisms of capsid assembly it is critical to resolve the early stages of the reaction. We have used Time-Resolved Small Angle X-ray Scattering, which is sensitive to solute size and shape and has millisecond temporal resolution. Scattering curves were fit to a thermodynamically curated library of assembly intermediates, using the principle of maximum entropy. Maximum entropy also provides a physical rationale for the selection of species. We found that the capsid assembly pathway was exquisitely sensitive to 1 initial assembly conditions. With the mildest conditions tested, the reaction appeared two-state from dimer to 120-dimer capsid with some dimers-of-dimers and trimers-ofdimers. In slightly more aggressive conditions, we observed transient accumulation of a decamer-of-dimers and appearance of 90-dimer capsids. In conditions where there is measurable kinetic trapping, we found that a highly diverse early intermediates accumulated within a fraction of a second and propagated into long-lived kinetically trapped states (≥ 90-mer). In all cases, intermediates between 35 and 90 subunits did not accumulate. These results are consistent with the presence of low barrier paths that connect early and late intermediates and direct the ultimate assembly path to late intermediates where assembly can be paused.

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Section: ■ Materials and Methodsmentioning

confidence: 99%

Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly

et al. 2020

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“…The scattering intensity, I , as a function of the magnitude of the momentum transfer vector, q , was then analyzed to determine the repeat distance, D , of the lamellar phase. The analysis was done using X+ software () developed in our laboratory ,, as explained. ,,, WAXS data analysis was done as explained . SAXS measurements were also performed at the X33 beamline (Desy synchrotron, Hamburg) and at beamlines BM26B and ID02 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, described elsewhere …”

Section: Methodsmentioning

confidence: 99%

Structure and Interactions between Charged Lipid Membranes in the Presence of Multivalent Ions

et al. 2019

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When aqueous salt solutions contain multivalent ions (like Ca 2+ or Mg 2+ ), strong correlation effects may lead to ionbridging, net attraction, and tight-coupling between like-charged interfaces. To examine the effects of surface charge density, temperature, salt type, and salt concentration on the structures of tightly coupled charged interfaces, we have used mixed lipid membranes, containing either saturated or unsaturated tails in the presence of multivalent ions. We discovered that tightly coupled membrane lamellar phases, dominated by attractive interactions, coexisted with weakly coupled lamellar phases, dominated by repulsive interactions. To control the membrane charge density, we mixed lipids with negatively charged headgroups, DLPS and DOPS, with their zwitterionic analogue having the same tails, DLPC and DOPC, respectively. Using solution X-ray scattering we measured the lamellar repeat distance, D, at different ion concentrations, temperatures, and membrane charge densities. The multivalent ions tightly coupled the mixed lipid bilayers whose charged lipid molar fraction was between 0.1 and 1. The repeat distance of the tightly coupled phase was about 4 nm for the DLPS/DLPC mixtures and about 5 nm for the DOPS/DOPC mixtures. In this phase, the repeat distance slightly increased with increasing temperature and decreased with increasing charge density. When the molar fraction of charged lipid was 0.1 or 0.25, a less tightly coupled phase coexisted with the tightly coupled phase. The weakly coupled lamellar phase had significantly larger D values, although they were consistently shorter than the D values in monovalent salt solutions with similar screening lengths.

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“…To analyze the data, we simulated the real-space structure of the flagellar bundle and the interactions between neighboring filaments, and calculated the bundle's scattering intensity, I, as a function of q, which is the magnitude of the momentum transfer vector (or scattering vector),q (24)(25)(26)(27)(28). By comparing the simulation results with the data, we determined the structural parameters and physical properties of the bundles.…”

Section: Solution X-ray Scattering Data Analysismentioning

confidence: 99%

Structure and Intermolecular Interactions between L-Type Straight Flagellar Filaments

Louzon

Ginsburg

Schwenger

et al. 2017

Biophysical Journal

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Bacterial mobility is powered by rotation of helical flagellar filaments driven by rotary motors. Flagellin isolated from the Salmonella Typhimurium SJW1660 strain, which differs by a point mutation from the wild-type strain, assembles into straight filaments in which flagellin monomers are arranged in a left-handed helix. Using small-angle x-ray scattering and osmotic stress methods, we investigated the structure of SJW1660 flagellar filaments as well as the intermolecular forces that govern their assembly into dense hexagonal bundles. The scattering data were fitted to models, which took into account the atomic structure of the flagellin subunits. The analysis revealed the exact helical arrangement and the super-helical twist of the flagellin subunits within the filaments. Under osmotic stress, the filaments formed two-dimensional hexagonal bundles. Monte Carlo simulations and continuum theories were used to analyze the scattering data from hexagonal arrays, revealing how the bundle bulk modulus and the deflection length of filaments in the bundles depend on the applied osmotic stress. Scattering data from aligned flagellar bundles confirmed the theoretically predicated structure-factor scattering peak line shape. Quantitative analysis of the measured equation of state of the bundles revealed the contributions of electrostatic, hydration, and elastic interactions to the intermolecular forces associated with bundling of straight semi-flexible flagellar filaments.

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Spline-based parallel nonlinear optimization of function sequences

Cited by 6 publications

References 42 publications

Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly

Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly

Structure and Interactions between Charged Lipid Membranes in the Presence of Multivalent Ions

Structure and Intermolecular Interactions between L-Type Straight Flagellar Filaments

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