Matlab Functions and Scripts:
- hw3.m
- HW3 Matlab script
- approxCurv.m
- Computes the numerical approximation of the curvature
- computeCurv.m
- Computes the curvature analytically
Graphs and Figures:
- Figure 1
- The plot of deviations from the ideal distance of 3.8A
- Figure 2
- Cubic spline interpolation of 1MBC coordinates
- Figure 3
- The plot of approximate curvature at all points on the interval tt (in red),
and the analytical curvature at all points on the interval t (in blue),
where t=1:153 and tt=1:0.01:153. Note the overlap of the two graphs
at integer values on the horizontal axis.
- Figure 4
- The plot of the contact map for 1MBC
Curvature and Structural Analysis:
As we can see from Figure 3, for several regions of the protein,
the curvature at integer coordinates (corresponsing to amino acid indices), fluctuates
relatively slowly, mostly retaining values between 1.5 and 2.5. This suggest a somewhat curved
overall shape for those regions of the protein, a shape consistent with that of alpha-helices.
This observation is consistent with the spline plot of protein coordinates in
Figure 2 and the contact map in
Figure 4, both of which indicate that the protein consists mostly of alpha-helices, with
no truly discernible beta strands. In addition, there are several points in the curvature graph
where the curvature spikes up suddenly. These points correspond naturally to turns in the
protein chain, where we expect the protein structure to have a high degree of curvature.