Mini Map Aide: Difference between revisions

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~~Mini~~ map aide ~~in use showing a threonine residue at~~ the ~~centre~~ of the ~~screen with a symmetry-related molecule, shown with its bonds drawn green~~. ~~The bonds~~ of ~~main molecule are coloured dark yellow and individual atoms are coloured according~~ to ~~type, red for oxygen and blue for nitrogen~~.

A tyrosine side chain being rebuilt in mini map aide. The moveable atoms are drawn as green squares and have been dragged slightly to the right of the ring's current position. Use of the "Tidy" button will allow the geometry to be regularised.

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[[Image:Cooper-jon-~~minimap1~~.jpg|200px]]

[[Image:Cooper-jon-minimap2.jpg|200px]]

</td></tr></table>

The option to tidy the geometry does so in a very simple stochastic way which is based on a table of approximate interatomic distances found in high resolution crystal structures of amino acids and polypeptides. These are all rounded to the nearest 0.1 Å. The method calculates all of the deviations from the ideal distances within the rebuilt residue and the atom-pair with the worst distance deviation is targeted for correction. Consider two atoms that should be covalently bonded. Since we know the direction of the bond in 3D and how much the bond length needs to increased or decreased to correct it, we could move both atoms inwards or outwards along the bond vector by half the distance violation and get a perfect bond length, at the risk of worsening the geometry of other bonds which these atoms are involved in. Instead, the algorithm takes a slightly different approach which is to take one of the two atoms at random and move it by half of the calculated distance correction in the right direction and leave the other atom unmoved. At this point the deviations from ideal geometry for the whole residue are recalculated and the worst distance violation found and corrected in exactly the same way as before. The whole process is repeated until the worst distance violation is less than 0.1 Å. The reason for choosing which of the two atoms to move completely at random is simply to stop the process becoming stuck trying to correct correlated distance violations cycle after cycle <i>ad infinitum</i>. It helps to prevent the algorithm getting stuck making the same two conflicting distance corrections over and over again.

Similar distance targets can be used to maintain the planarity of groups with a central trigonal atom (*e.g.* carboxylates and amides) by calculating the distance between the centroid of the three outer atoms and the central atom. This should be less than 0.1 Å and bad violations can be corrected exactly as for the interatomic distance violations, although in this case it is only the central atom (not the centroid!) which can be moved. For tetrahedral groups, such as the Cα atom of all residues except Gly and the Cβ atoms of Thr and Ile, the central atom has to be almost exactly 0.5 Å from the centroid of the three outer non-hydrogen atoms bonded to it. The vector between the central atom and the centroid is the direction along which any shifts to the central atom can be applied in 3D.

It is also possible to construct similar target positions for the atoms to help maintain the planarity and chirality of amino acids. For example in Phe and Tyr, the Cβ - Cγ bond will be parallel, well within experimental error, to the Cδ - Cε bonds in the aromatic ring. Given the slight difference in length between single and double bonds (which is known from atomic resolution studies), we can calculate a target position for each of the Cε atoms from the direction of the Cβ - Cγ bond and the current Cδ atom positions. The distance between each Cε atom and its target position is fed into the list of distance violations and will be corrected by the algorithm when it becomes the worst one. Longer-range constraints, such as ensuring the phenolic C-OH bond of Tyr is also parallel to these bonds helps to maintain planarity. In addition, we can correct main chain and side chain chirality errors by using math.js to calculate the signed volume of these groups. When the chiral volume is negative, the group needs to be inverted. The program uses a fairly crude way of doing this which is to move the central atom to the centroid of the three outer non-hydrogen atoms and one of the outer atoms is shifted the same distance but in exactly the opposite direction in 3D. Subsequent iterations to correct the interatomic distances seem to sort out any remaining anomalies introduced by flipping the hand of the group in this way.

Whilst this is a far cry from molecular mechanics (something best left to computational chemists!) it does seem to give reasonable geometry to the amino acids and usually takes only 1 or 2 seconds at most on a humble Android smartphone.

In future versions, it is planned to allow simple mutations to be made.

==See Also==

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@@ Line 24: / Line 24: @@
 <table class="wikitable" align="right"><tr><td width="150">
-Mini map aide in use showing a threonine residue at the centre of the screen with a symmetry-related molecule, shown with its bonds drawn green. The bonds of main molecule are coloured dark yellow and individual atoms are coloured according to type, red for oxygen and blue for nitrogen.
+A tyrosine side chain being rebuilt in mini map aide. The moveable atoms are drawn as green squares and have been dragged slightly to the right of the ring's current position. Use of the "Tidy" button will allow the geometry to be regularised.
 </td><td width="200">
-[[Image:Cooper-jon-minimap1.jpg|200px]]
+[[Image:Cooper-jon-minimap2.jpg|200px]]
 </td></tr></table>
+The option to tidy the geometry does so in a very simple stochastic way which is based on a table of approximate interatomic distances found in high resolution crystal structures of amino acids and polypeptides. These are all rounded to the nearest 0.1 &#8491;. The method calculates all of the deviations from the ideal distances within the rebuilt residue and the atom-pair with the worst distance deviation is targeted for correction. Consider two atoms that should be covalently bonded. Since we know the direction of the bond in 3D and how much the bond length needs to increased or decreased to correct it, we could move both atoms inwards or outwards along the bond vector by half the distance violation and get a perfect bond length, at the risk of worsening the geometry of other bonds which these atoms are involved in. Instead, the algorithm takes a slightly different approach which is to take one of the two atoms at random and move it by half of the calculated distance correction in the right direction and leave the other atom unmoved. At this point the deviations from ideal geometry for the whole residue are recalculated and the worst distance violation found and corrected in exactly the same way as before. The whole process is repeated until the worst distance violation is less than 0.1 &#8491;. The reason for choosing which of the two atoms to move completely at random is simply to stop the process becoming stuck trying to correct correlated distance violations cycle after cycle <i>ad infinitum</i>. It helps to prevent the algorithm getting stuck making the same two conflicting distance corrections over and over again.
+Similar distance targets can be used to maintain the planarity of groups with a central trigonal atom (*e.g.* carboxylates and amides) by calculating the distance between the centroid of the three outer atoms and the central atom. This should be less than 0.1 &#8491; and bad violations can be corrected exactly as for the interatomic distance violations, although in this case it is only the central atom (not the centroid!) which can be moved. For tetrahedral groups, such as the C&alpha; atom of all residues except Gly and the C&beta; atoms of Thr and Ile, the central atom has to be almost exactly 0.5 &#8491; from the centroid of the three outer non-hydrogen atoms bonded to it. The vector between the central atom and the centroid is the direction along which any shifts to the central atom can be applied in 3D.
+It is also possible to construct similar target positions for the atoms to help maintain the planarity and chirality of amino acids. For example in Phe and Tyr, the C&beta; - C&gamma; bond will be parallel, well within experimental error, to the C&delta; - C&epsilon; bonds in the aromatic ring. Given the slight difference in length between single and double bonds (which is known from atomic resolution studies), we can calculate a target position for each of the C&epsilon; atoms from the direction of the C&beta; - C&gamma; bond and the current C&delta; atom positions. The distance between each C&epsilon; atom and its target position is fed into the list of distance violations and will be corrected by the algorithm when it becomes the worst one. Longer-range constraints, such as ensuring the phenolic C-OH bond of Tyr is also parallel to these bonds helps to maintain planarity. In addition, we can correct main chain and side chain chirality errors by using math.js to calculate the signed volume of these groups. When the chiral volume is negative, the group needs to be inverted. The program uses a fairly crude way of doing this which is to move the central atom to the centroid of the three outer non-hydrogen atoms and one of the outer atoms is shifted the same distance but in exactly the opposite direction in 3D. Subsequent iterations to correct the interatomic distances seem to sort out any remaining anomalies introduced by flipping the hand of the group in this way.
+Whilst this is a far cry from molecular mechanics (something best left to computational chemists!) it does seem to give reasonable geometry to the amino acids and usually takes only 1 or 2 seconds at most on a humble Android smartphone.
+In future versions, it is planned to allow simple mutations to be made.
 ==See Also==