Biomedical Engineering Reference
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a
b
c
Nup84
Sec13
Fig. 1.13 Toleranced model of the entire NPC. ( a ) The four canonical configurations, 18 balls
each, illustrated with protein types Nup84 and Sec13. ( b ) The toleranced model at λ
=0
corresponds to inner balls .( c ) The toleranced model at λ =1 corresponds to outer balls
of these two types. Having painted all the proteins types in red, let us consider
the Hasse diagram for the range of λ -values [0 max ], as discussed in Sect. 1.3.4 .
As soon as k pairwise contacts between distinct pairs of instances of these types
are observed, say at λ = λ ( p i ,p j ), the contact probability p ( k )
is set as p ( k )
ij
=
ij
1 −λ ( p i ,p j ) max ; if the two types make strictly less than k contacts, then p ( k )
=0.
ij
For a given probability b ,thesetof k -significant contacts S ( k )
b
is the set of contacts
such that p ( k )
ij
≥ b and p ( k +1)
ij <b .
An illustration of k -significant contacts is provided in Fig. 1.14 . To appreciate
the “value added” by this figure, recall that the NPC is composed of 16 half-spokes,
and that the stoichiometry of all protein types is either 8, 16 or 32. In particular,
for a large number of protein pairs, 16 copies of the corresponding complexes are
expected. Remarkably, the size four cliques of this graph show five quadruples
of proteins, two of which correspond to the intensively studied Y-complex and
T -complex. The remaining ones are under scrutiny, and together with the remaining
k -significant contacts, have captured the attention of biologists specializing in the
architecture of the NPC.
Global assessment w.r.t. a collection of types: stoichiometry, symmetry, sta-
bility. Assume that the red proteins are instances of types prescribed in a set T ,
e.g. a TAP pullout as discussed in Sect. 1.3.1.2 . The following parameters can be
assessed.
Stoichiometry. Analyzing the complexes of the Hasse diagram is of interest for
several reasons: first, one sees whether the set T corresponds to a single complex
or to a mixture of complexes; second, one can spot the copies associated with the
set T ;third,if T corresponds to a TAP experiment, one can check whether each
complex contains the tagged protein.
Symmetry. For an assembly that exhibits symmetries, one can compare the
number of complexes with the expected number. For example, in the NPC, the
multiplicity of selected complexes is expected to be 16.
 
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