Biomedical Engineering Reference
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Fig. 4
As predicted by the
inverse C
h
rule, capsids with
high hexamer complexity are
underrepresented in nature as
evident in the observed versus
unbiased capsid abundances
(% of families that display
capsids of specific C
h
)
The subunit-subunit angles present within the pentamers (which we call endo
angles) impose constraints on the adjacent hexameric angles, an effect that is
termed endo angle propagation [
36
]. While the shape and number of pentamers
is fixed for all T number capsids, the number of hexamers (and therefore the
shape) is not. The hexamers experience different environments based upon their
adjacency to neighboring pentamers/hexamers. As a result, the angle patterns
produced by interacting endo angles within the capsid ensure the emergence of
three general morphological classes of capsids that can be differentiated by their
h-k relationship [
37
]:
class 1
(described by the relationship h>k
D
0),
class
2
(h>k>0), and
class 3
(h
D
k). We have identified the minimum number
of distinct hexamer shapes (which we call hexamer complexity C
h
) required to
form a canonical capsid of specific capsid size (T -number). Each canonical capsid
of specific h and k is described by a single C
h
value. Thus, C
h
is very useful
in systematically predicting properties of a group of capsids that were previously
thought to be unrelated viruses.
C
h
is also an indicator of the ease with which a capsid can be assembled,
i.e., a larger number of distinct hexamer shapes would require a more complex
assembly mechanism. Indeed, our modeling studies show that the capsids with
ahighC
h
value require more auxiliary control mechanism for their assembly
while the capsids with a low C
h
value and low T
n
u
mber (T
D
3; 4; or 7)
display the ability to assemble with no auxiliary requirements [
46
,
47
]. Thus, the
hexamer complexity number (C
h
) can be used as tool to predict if a particular capsid
assembly requires auxiliary mechanisms or proteins. Accordingly, we predicted
that canonical capsids with larger C
h
must be present with a lower frequency in
nature since they require complex auxiliary assembly mechanisms. This hypothesis
is corroborated by surveying all available capsid structures in the literature and virus
structure databases. In the scenario that all T number capsids were equally probable,
it would be expected that the complex capsids with C
h
>2 would represent the
majority of the virus families observed in the nature (63%) (Fig.
4
Unbiased
).
However, in actuality, capsids with C
h
>2represent only 5% of the observed
capsid structures (Fig.
4
Observed
). This suggests the existence of an evolutionary
pressure which discriminates against viruses with a high hexamer complexity.
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