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After modifying the 4HNA coordinates as described in the main text (deletion of neck-linker residues and ATP), we equilibrated this system to allow water into the newly vacated nucleotide pocket, and then introduced an cryo-EM steering potential (linear ramp over 10 ns, as was done for the ATP state model) in order to bias the coordinates toward the conformation observed in our no-nucleotide map.
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The point α RθBmaxe i θB lies on the edge of or inside the unit square for 0 ≤ α ≤ 1 and the following definition for RθBmax: The bias coordinates (B0, B∞) in the square along the vector defined by θB represent a family of hyperbolae for which tan. Define a mapping from the unit square, the points with bias coordinates (B0, B∞) = α RθBmaxe i θB by: for 0 ≤ α ≤ 1, 0 ≤ θB ≤ 2π, and 0 ≤ θY ≤ π/2.
The root mean square (RMS) of the coordinates bias, which is an important internal precision indicator of SPP, was calculated and shown in Table 3.
Bias factors are simple consequences of the map and the novel distance metric of the disk, and the distance between bias coordinates in the disk provides a quantitative means of characterizing and sorting ligands.
In this formulation, hyperbolae represent the comparative responses of test ligands, and signaling biases are described by mappings of bias coordinates representing the hyperbolae from the unit square to a stack of Poincare unit disks.
Two optimality criteria are developed, the one relating to precision and based on the sum of the first-order approximations to the asymptotic variances and the other to accuracy and based on the sum of squares of the second-order approximations to the asymptotic biases of the estimates of the coordinates of the extremal point.
The polar bias coordinates (β,θB,θY) are shown below where β is the polar distance and θB the polar angle.
This means that the MAPR does not bias the solution by using a coordinate direction-by-direction approach to the reconstruction, which is highly desirable when unstructured meshes consisting of elements with (almost) arbitrary geometry are used.
Therefore, indicating all bias coordinates in the neighborhood of z1 within the distance d z 1 represent response functions g2 and f2 having ratios within.
Figure 4B displays the unit square bias coordinates, Poincare disk mapped coordinates, transducer ratio parameters, and relative distances (βL) from the angle equivalent quinpirole coordinates.
The coordinates are fixed.
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