Ligand-Controlled Assembly of Hexamers, Dihexamers, and Linear Multihexamer Structures by the Engineered Acylated Insulin Degludec

Insulin degludec, an engineered acylated insulin, was recently reported to form a soluble depot after subcutaneous injection with a subsequent slow release of insulin and an ultralong glucose-lowering effect in excess of 40 h in humans. We describe the structure, ligand binding properties, and self-assemblies of insulin degludec using orthogonal structural methods. The protein fold adopted by insulin degludec is very similar to that of human insulin. Hexamers in the R₆ state similar to those of human insulin are observed for insulin degludec in the presence of zinc and resorcinol. However, under conditions comparable to the pharmaceutical formulation comprising zinc and phenol, insulin degludec forms finite dihexamers that are composed of hexamers in the T₃R₃ state that interact to form an R₃T₃–T₃R₃ structure. When the phenolic ligand is depleted and the solvent condition thereby mimics that of the injection site, the quaternary structure changes from dihexamers to a supramolecular structure composed of linear arrays of hundreds of hexamers in the T₆ state and an average molar mass, <i>M</i>₀, of 59.7 × 10³ kg/mol. This novel concept of self-assemblies of insulin controlled by zinc and phenol provides the basis for the slow action profile of insulin degludec. To the best of our knowledge, this report for the first time describes a tight linkage between quaternary insulin structures of hexamers, dihexamers, and multihexamers and their allosteric state and its origin in the inherent propensity of the insulin hexamer for allosteric half-site reactivity

A Scalable High-performance Topographic Flow Direction Algorithm for Hydrological Information Analysis

Hydrological information analyses based on Digital Elevation Models (DEM) provide hydrological properties derived from high-resolution topographic data represented as an elevation grid. Flow direction is one of the most computationally intensive functions in the current implementation of TauDEM, a broadly used high-performance hydrological analysis software in hydrology community. Hydrologic flow direction defines a flow field on the DEM that directs flow from each grid cell to one or more of its neighbors. This is a local computation for the majority of grid cells, but becomes a global calculation for the geomorphologically motivated procedure in TauDEM to route flow across flat regions. As the resolution of DEM becomes higher, the computational bottleneck of this function hinders the use of these DEM data in large-scale studies. This paper presents an efficient parallel flow direction algorithm that identifies spatial features (e.g., flats) and reduces the number of sequential and parallel iterations needed to compute their geomorphologically motivated flow direction. Numerical experiments show that our algorithm outperformed the existing parallel D8 algorithm in TauDEM by two orders of magnitude. The new parallel algorithm exhibited desirable scalability on Stampede and ROGER supercomputers

Data collection and refinement statistics.

a<p> <i>R_merge = Σ|I_i−I|/ΣI where I_i is an individual intensity measurement and I is the mean intensity for this reflection.</i></p>b<p> <i>R value = crystallographic R-factor = Σ|F_obs|−|F_calc|/Σ|F_obs|, where Fobs and Fcalc are the observed and calculated structure factors respectively. R_free value is the same as R value but calculated on 5% of the data not included in the refinement.</i></p>c<p> <i>Root-mean-square deviations of the parameters from their ideal values.</i></p

Cartoon representation of the crystal structure of the B25C-dimer.

<p><b>A:</b> The A chain is coloured in green and the B chain is shown in blue. The additional disulphide bond is shown by stick representation (yellow). An omit map was calculated by omitting the Sulphur atom of B25C. The resulting difference electron density Fo-Fc map is coloured in orange at σ-level = 3.0. It is clear from the structure that the two monomers are linked by a disulfide bond between the two adjoining B25C. <b>B:</b> Comparison of the B25C structure (blue) with that of the porcine in-sulin (PDB code 1B2E) (grey). The Cα trace shows that the two structures have a high resemblance with minor deviations in Cα positions at residue B21E and B29K.</p

Measurements of <i>in vitro</i> activity of the B25C-dimer compared to HI.

<p><b>A:</b> Representative insulin receptor binding curves for HI(black), B25C-NEM1 (dark gray) B25C-NEM2(gray)and the B25C dimer(light gray). <b>B:</b> Representative metabolic dose response curves for HI(black) and the B25C-dimer (dark gray). Each point on the graph represents the mean ± SD, n = 4 within one assay.</p

AUC results for the B25C-dimer.

<p><b>A:</b> SV Analysis of the B25C-dimer in the presence of 2 Zn²⁺/hexamer (insulin normals). In the top part of the figure, open circles represent the g(s*)/s-curve derived from a dcdt-analysis. For clarity, only every 10^th data point is shown. The solid red line represents the fit to a model of a single ideal species, resulting in the parameters shown in Tabel 2. The bottom part of the figure represents the local deviations between the experimental and simulated data (residuals). Every data point is shown. The rmsd of the shown fit is 9.83×10⁻³. <b>B:</b> Representative data of a SE experiment used to determine the self-association model of B25C. In the top part of the figure, open circles represent experimental concentration distributions at apparent thermo- and hydrodynamic equilibrium for one concentration (out of five) at 15 krpm (black), 24 krpm (red) and 36 krpm (green). For clarity, only every 10^th data point is shown. The solid like-colored lines represent the global fit to all measured conditions to a model of a reversible monomer-dimer model, resulting in the equilibrium coefficient mentioned in the text. The bottom part of the figure represents the local deviations between the experimental and simulated data (residuals). Every data point is shown. The molar mass parameter was fixed to its expected value and the global rmsd of the fit is 7.4×10⁻³.</p

Assessing the stability of the B25C-dimer compared to HI.

<p><b>A:</b> DSC of HI and the B25C-dimer. <b>B:</b> ThT fibrillation assay of 0.3 mM B25C-dimer (grey diamonds) and 0.6 mM HI (black diamonds) with incubation at 37°C and vigorous shaking as described in “<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030882#s2" target="_blank">Methods</a>”. Both samples contained 7 mM phosphate adjusted to pH 7.4.</p

The experimental parameters determined from the fit in Figure 2 and results previously determined for hexameric insulin of human and porcine origin.

*<p> <i>Measured value.,</i></p>**<p> <i>Probably affected by non-ideality because of high concentration.</i></p

Examples for the determination of radial magnification errors.

<p>(A) Radial intensity profile measured in scans of the precision mask. Blue lines are experimental scans, and shaded areas indicate the regions expected to be illuminated on the basis of the known mask geometry. In this example, the increasing difference between the edges corresponds to a calculated radial magnification error of -3.1%. (B—D) Examples for differences between the experimentally measured positions of the light/dark transitions (blue circles, arbitrarily aligned for absolute mask position) and the known edge distances of the mask. The solid lines indicate the linear or polynomial fit. (B) Approximately linear magnification error with a slope corresponding to an error of -0.04%. Also indicated as thin lines are the confidence intervals of the linear regression. (C) A bimodal shift pattern of left and right edges, likely resulting from out-of-focus location of the mask, with radial magnification error of -1.7%. (D) A non-linear distortion leading to a radial magnification error of -0.53% in the <i>s</i>-values from the analysis of back-transformed data. The thin grey lines in C and D indicate the best linear fit through all data points.</p

Analysis of the rotor temperature.

<p>(A) Temperature values obtained in different instruments of the spinning rotor, as measured in the iButton at 1,000 rpm after temperature equilibration, while the set point for the console temperature is 20°C (indicated as dotted vertical line). The box-and-whisker plot indicates the central 50% of the data as solid line, with the median displayed as vertical line, and individual circles for data in the upper and lower 25% percentiles. The mean and standard deviation is 19.62°C ± 0.41°C. (B) Correlation between iButton temperature and measured BSA monomer <i>s</i>-values corrected for radial magnification, scan time, scan velocity, but not viscosity (symbols). In addition to the data from the present study as shown in (A) (circles), also shown are measurements from the pilot study [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126420#pone.0126420.ref027" target="_blank">27</a>] where the same experiments were carried out on instruments not included in the present study (stars). The dotted line describes the theoretically expected temperature-dependence considering solvent viscosity.</p