make gridspacing finer

README.txt

@@ -6,4 +6,40 @@ RNA: 'polyribonucleotide'
 DNA: 'polydeoxyribonucleotide'
 protein: 'polypeptide(L)'
 
-There is more exotic stuff such as DNA/RNA hybrid, which we can ignore.
+There is more exotic stuff such as DNA/RNA hybrid, which we can ignore.
\ No newline at end of file
+
+Initial conclusion
+Single-ring stacking interactions (PHE/TYR - U/C)
+
+In translational space: 886 grid points that fulfill the criteria
+Note that in the typical case, half of them can be discarded immediately because
+they are on the wrong side (above/below) of the ring.
+
+In rotational space: 8.3 % of plane-plane orientations is kept. 
+In addition, 75 % of dihedral space is kept, for a total of 6.2 % of rotational space.
+
+The trinucleotide library has typically 40k rotamers per conformer. 
+6.2 % of rotational space is about 2.5k rotamers per conformer kept.
+
+With 4k conformers per library, this is 10 million rotaconformers, 
+ or about 9 billion potential docking solutions.
+
+For double stacking:
+A test has been done in the 1B7F-stack folder in a different project
+The plane angle reduction is independent, i.e. 
+  8.3 % of 8.3 % of 40k = 275 rotamers per conformer
+In fact, in the 1B7F test, this is confirmed,
+ as ~220 rotamers per conformer, or 800k rotaconformers in total.
+The dihedral filter (75 % per stacking, or 56 % for two stackings) is also 
+ approx. independent, selecting 450k rotaconformers in total.
+
+pseudo-crocodile: this leads to approximately 19 million poses.
+However, distance criteria need to be relaxed by 0.5 to account for grid spacing, bringing
+the number of poses to 130 million. However, the best RMSD is 0.43 A!
+
+NOTE: Instead of filtering at sin(angle)<0.4, one might consider a stricter cutoff.
+For example, angle<15 degrees corresponds only to 3.4 % instead of 8.3 % 
+ of the rotamers, a factor 2.44. For the double stacking, the factor would be squared
+ too, i.e. an factor 6 in reduction of conformational space.
+However, one must consider that filtering at 15 degrees only covers 62.9 % of stackings instead of 94.6 %.
+In fact, for the 1B7F test, all rotaconformers are lost!
\ No newline at end of file

plot-angle-corrected-vector.out

@@ -40,13 +40,14 @@ Under 0.4: 2362, 79.0 percent
 Under 0.5: 2662, 89.1 percent
 
 Rotational space: distribution of sin(ring-ring plane angle) for random planes
-Under 0.4: 8.5 percent
-Under 0.5: 13.6 percent
+Under 0.4: 8.2 percent
+Under 0.5: 13.2 percent
 
 Translational space
-Define a grid of 1.0 Angstroms spacing.
-This will give a maximum distance from the center of 0.87 A
- and a mean square distance from the center of sqrt(1/4) = 0.5 A
+Define a grid of 1/3*sqrt(3) Angstroms spacing.
+This will give a maximum distance from the center of 0.5 A
+ and a mean square distance from the center of sqrt(a**2/4) = 0.29 A
 Filtering: center-center distance <= 5.0 A
   and corrected center-center distance between 2.3 and 3.8 A
-Number of grid points: 162
+8.0 0.5773502691896257
+Number of grid points: 886

plot-angle-corrected-vector.py

@@ -18,6 +18,7 @@ corrected_dis = corrected_dis[mask]
 sin_angle = sin_angle[mask]
 center_dis = center_dis[mask]
 
+np.random.seed(0)
 r1 = Rotation.random(200).as_matrix()[:, 2]
 r2 = Rotation.random(200).as_matrix()[:, 2]
 random_cross = np.cross(r1[:, None, :], r2[None, :, :])
@@ -92,15 +93,16 @@ print("Under 0.4: {:.1f} percent".format((random_sin_ang < 0.4).sum()/len(random
 print("Under 0.5: {:.1f} percent".format((random_sin_ang < 0.5).sum()/len(random_sin_ang) * 100))
 print()
 print("Translational space")
-print("Define a grid of 1.0 Angstroms spacing.")
-print("This will give a maximum distance from the center of 0.87 A")
-print(" and a mean square distance from the center of sqrt(1/4) = 0.5 A")
+print("Define a grid of 1/3*sqrt(3) Angstroms spacing.")
+print("This will give a maximum distance from the center of 0.5 A")
+print(" and a mean square distance from the center of sqrt(a**2/4) = 0.29 A")
 print("Filtering: center-center distance <= 5.0 A")
 print("  and corrected center-center distance between 2.3 and 3.8 A")
 lateral_slope = 1.78966
-a = 1.0
+a = 1.0/3 * np.sqrt(3)
 max_dist = 5   # max center-center distance
 max_steps = np.floor(max_dist / a)
+print(max_steps, a)
 space = np.arange(-max_steps, max_steps+1) * a
 grid = np.stack(np.meshgrid(space, space, space, indexing='ij'), axis=-1)
 grid_center_dis = norm(grid, axis=3)