Balance de masa de probetas

Of the 882 helix pairs analysed, 640 (73%) were found to have interhelical cavities of volumes greater than 0.25Â \ The mean total probe volume was found to be 9.2Â^ and the mean number of small spherical probes 5.58. Of those helix pairs that had interhelical cavities, the smallest observed volume was 0.52Â^ whereas the largest volume was 98Â^ Figure 3.20 is a histogram showing the frequency distribution of total probe volume for all helix pairs. The majority of pairs (96%) have total probe volumes less than 30Â^, however there are a few outliers.

Figure 3.20: Frequency distribution of total probe volume in interacting helix pairs

250 200^ 150 O ' 100 50 80 20 4 0 P r o b e V o l u m e

Figure 3.21 shows a 3-dimensional representation of the largest irregular interhelical cavity found. This cavity, having a volume of 98A^, comprising 36 of the small spherical probes, was found between helices 19 and 22 in a lipase

(triacylglycerol hydrolase, ITHG). The cavity is somewhat exceptional, being comparable in size to a serine residue (95A^) and 30Â^ larger than the next largest cavity observed. It is mainly hydrophobic, with 3 computationally predicted waters (1 1.5Â^). Figure 3.20 shows a more typical example of a helix pair with a large total probe volume (66Â^).

Figure 3.21: 3D representation of helices 19 and 22 from Ithg (triacylglycerol lipase)

This figure was then generated using surfnet (Laskowski, 1995). The coordinates of the interacting helix pair were extracted from the PDB file and displayed as a stick model. The interhelical cavities were generated using surfnet (Laskowski, 1995) and displayed as grey polyhedra.

Analysis o f helix-helix interactions

Figure 3.22: 3D representation of helices 3 and 4 from Ircb (Interleukin-4)

This figure was then generated using surfnet (Laskowski, 1995). The coordinates of the interacting helix pair were extracted from the PDB file and displayed as a stick model. The interhelical cavities were generated using surfnet (Laskowski, 1995) and displayed as grey polyhedra.

The cavity in Ithg was so large it was thought that it may be due to an error in the structure; Procheck (Laskowski et a i, 1993) was run on the structure and did not find any obvious anomalies in the geometric properties of the structure. The results of procheck suggested that the structure to be "better" than expected for a 1.8Â resolution structure. In addition, the helix pair was displayed on the graphics. Surfnet (Laskowski et a i, 1993) was used to generate a quanta-format mhk file of the cavity coordinates so that it could be displayed on the graphics as a brick file. Both the computational water coordinates and the complete protein structure were

superimposed on the helix pair but no clashes with the calculated cavities were found. The cavity was in the centre of the structure, adjacent to the active site.

Unless, some coordinates from part of the protein or from a co-factor were omitted from the PDB file, this cavity appears to be real. If this large cavity does exit it is likely that it would be necessary for the biological function of the protein, although none was assigned to it in the literature (Schrag & Cygler, 1993).

Figure 3.23: Scatter plots to show total probe volume versus various helical parameters

40 35 £ 30 a₀ a 25 1 15 ^ 10 5 5 10 15 2 0 25 3 0 35 40 P r o b e V o lu m e (a) 5 10 15 20 2 5 3 0 D istan ce (a n g s tro m s ) ( c ) 8 0 0 ^ 7 0 0 n 6 0 0 £ 5 0 0 I 4 0 0 ^ 3 0 0 « ? 2 0 0 Q 100 5 10 15 20 25 3 0 35 P r o b e V o lu m e (b) ■I, 0 O m eg a ( d )

The figure above shows the relationship between total probe volume (Â^) and four other helical parameters: (a) the number of spherical probes, (b) the mean loss of surface area (Â^) on packing (c) interhelical distance (A) and (d) interhelical angle (degrees). In plot (d) the shaded boxes show the mean total probe volume for angle intervals of 20°.

Analysis o f helix-helix interactions

The scatter plot of cavity volume versus mean loss on solvent accessible surface area on helix packing (ASA) shows that there is a weak correlation (coeff = 0.71). In general, the larger the surface area lost on interaction the larger the volume of interhelical cavities. There is however no correlation between the cavity volume and the distance between the two helices (coeff = -0.55); i.e. it is a function of the side chain volumes that determining packing distance with no contribution from the cavity volume that their non-perfect packing creates. The dependence of cavity volume on ASA confirms that some measure of packing efficiency that includes both a cavity volume term and ASA would be sensible.

3.4.8.a Pseudo-packing distance

As the cavity volume shows some dependency on the interhelical packing area makes it a somewhat ambiguous measure for comparing the efficiency of helix packing. Consequently, a measure designed to enable us to determine how well two interacting helices were packed was defined in Section 3 3 3 .\iii

D p s e u d o = Pvol/ASA

where Pvol is probe volume at the interface and ASA is the mean surface area lost on helix packing. The lower the value of the better packed the helices.

Figure 3.24 shows the frequency distribution of the pseudo-packing distances for all helix pairs in the data set. One third of all the helix pairs have a smaller than 0.1Â and all but 11 pairs have smaller than 0.2 Â. The cavity between helices 19 and 22 from Ithg, is again a remarkable outlier with being 0.55Â. Helices 3 and 4 from Ircb, although having a very large cavity volume (66Â^), give

a reasonable (0.129Â).

Figure 3.25 shows scatter plots of compared against other helix pair data. There is positive correlation (Figure 3.25a, coeff = 0.86) between the pseudo-

Figure 3.24: Frequency distribution of the pseudo-packing distance between helix pairs

2 5 0 2 0 0 S 150 100 5 0 20 30 4 0 50

packing distance and the total cavity volume; ie as the total cavity volume increases the is likely to be larger, suggesting the helices are less well packed. There is no correlation between and interhelical distance (Figure 3.25b, coeff = 0.05), and confirms that the quality of packing is independent of interhelical distance.

On initial inspection, it appears that there is some correlation between Dp^^^^ and the mean loss in surface area on packing (A^A) (Figure 3.25c, coeff = 0.48). However, this may be an artifact of the method. Helices which pack with very low loss of solvent accessible area tend to have zero total probe volume (0^,^^^^ = 0). This is probably a function of the solvation algorithm. When the zero terms are removed the correlation coefficient falls to 0.16. for the 640 helix pairs that remain.

Figure 3.25d shows versus interhelical angle. There is a broad range of at most angles. A plot of the mean Dp^^udo fo: angle intervals of 20° indicates that there is better quality packing at some angles. At -110°,-10° and +70°, helices appear to pack very efficiently, whereas the least well packed helices have angles at -170°. There seems to be little correlation between having a low (being well packed) with the frequency of observed angles. The most frequently

Analysis of helix-helix interactions

observed angles being-50" and +130°.

Figure 3.25: Scatter plots to show verses other helix pair parameters 601 601 4 0 30 20 201 > 10 15 20 2 5 30 D is ta n c e ( a n g s t r o m s ) P r o b e V o lu m e 8001 — 7 0 0 ' 8 0 0 ' 40l 5 0 0 ' 4 0 0 ' < 3001

I

'

The figure above shows the relationship between (*10'^Â) and four other

helical parameters: (a) total probe volume (Â^), (b) interhelical distance (A), (c) the mean loss of surface area (Â^) on packing and (d) interhelical angle (degrees). In plot (d) the shaded boxes show the mean total (*10^Â) for angle intervals of 20°.