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3-n3ndeb6 (n=0-3)


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Supplementary Information 3.2:

Curve Fitting Procedure for Mixed Assemblies 23-n3nDEB6 (n=0-3).
The equilibrium between assemblies and individual building blocks is described by


3K(n=0)=K(n=1)=K(n=2)=3K(n=3), as a result of the three possibilities of forming an assembly with composition 223 (223, 232, and 322) and 233 (233, 323, and 332). It is assumed that free components 2 and 3 are not present and therefore K(n) is assigned a value of 1E10.

Assemblies with P-chirality are only formed from combinations of building blocks with P-conformation, e.g. P-2 and P-3. The enthalpy of formation is identical for all assemblies (homomeric and heteromeric).


Based on these assumptions the mass balances for [2tot] and [3tot] are :
[2]tot = 3[P-23DEB6] + 2[P-223DEB6] + [P-232DEB6] +

3[M-23DEB6] + 2[M-223DEB6] + [M-232DEB6].


[2]tot = 3K(n=3)[P-2]3 + 2K(n=2)[P-2]2[P-3] + K(n=1)[P-2][P-3]2 +

3K(n=3)[M-2]3 + 2K(n=2)[M-2]2[M-3] + K(n=1)[M-2][M-3]2.


[2]tot = 3K(n=3)[P-2]3 + 6K(n=3)[P-2]2[P-3] + 3K(n=3)[P-2][P-3]2 +

3K(n=3)[M-2]3 + 6K(n=3)[M-2]2[M-3] + 3K(n=3)[M-2][M-3]2.


[2]tot/3K(n=3)= [P-2]3 + 2[P-2]2[P-3] + [P-2][P-3]2 +

[M-2]3 + 2[M-2]2[M-3] + [M-2][M-3]2.


[M-2] = K2 x [P-2] and

[M-3] = K3 x [P-3] gives:


[2]tot/3K(n=3)= [P-2]3(1+K23) + 2[P-2]2[P-3](1+K22K3) + [P-2][P-3]2(1+K2K32).

With K3 = 1/K2:



= [P-2]3(1+K23) + 2[P-2]2[P-3](1+K2) + [P-2][P-3]2(1+1/K2).
This equation expresses [P-3] as a function of K2 and [P-2].
[3]tot = 3[P-33DEB6] + 2[P-232DEB6] + [P-223DEB6] +

3[M-33DEB6] + 2 [M-232DEB6] + [M-223DEB6].


[3]tot = 3K(n=0)[P-3]3 + 2K(n=1)[P-2][P-3]2 + K(n=2)[P-2]2[P-3] +

3K(n=0)[M-3]3 + 2K(n=1)[M-2][M-3]2 + K(n=2)[M-2]2[M-3].


[3]tot = 3K(n=0)[P-3]3 + 6K(n=0)[P-2][P-3]2 + 3K(n=0)[P-2]2[P-3] +

3K(n=0)[M-3]3 + 6K(n=0)[M-2][M-3]2 + 3K(n=0)[M-2]2[M-3].


[3]tot/3K(n=0)= [P-3]3 + 2[P-2][P-3]2 + [P-2]2[P-3] +

[M-3]3 + 2[M-2][M-3]2 + [M-2]2[M-3].


[M-2] = K2 x [P-2] and

[M-3] = K3 x [P-3] gives:


[3]tot/3K(n=0)= [P-3]3(1+K33) + 2[P-3]2[P-2](1+K32K2) + [P-3][P-2]2(1+K3K22).
With K3 = 1/K2:

= [P-3]3(1+1/K23) + 2[P-3]2[P-2](1+1/K2) + [P-3][P-2]2(1+K2).
This equation expresses [P-2] as a function of K2 and [P-3].
From these two equations [P-2] and [P-3] can be calculated numerically for a specific value of K2.
From [P-2] and [P-3] a CD-signal is calculated using:
[P-23DEB6] = K(n=3)[P-2]3

[M-23DEB6] = K(n=3)[M-2]3 = K(n=3)K23[P-2]3 = K23[P-23DEB6]

[P-223DEB6] = 3K(n=3)[P-2]2[P-3]

[M-223DEB6] = 3K(n=3)[M-2]2[M-3] = 3K(n=3)K22[P-2]2K3[P-3] = K2[P-223DEB6]

[P-232DEB6] = 3K(n=3)[P-2][P-3]2

[M-232DEB6] = 3K(n=3)[M-2][M-3]2 = 3K(n=3)K2[P-2]K32[P-3]2 = (1/K2)[P-232DEB6]

[P-33DEB6] = K(n=3)[P-3]3

[M-33DEB6] = K(n=3)[M-3]3 = K(n=3)K33[P-3]3 = (1/K2)3[P-33DEB6]


resulting in:
calc.= SF ([M-23DEB6]-[P-23DEB6]+[M-223DEB6]-[P-223DEB6]+

[M-232DEB6]-[P-232DEB6]+[M-33DEB6]-[P-33DEB6]+)

([M-23DEB6]+[P-23DEB6]+[M-223DEB6]+[P-223DEB6]+

[M-232DEB6]+[P-232DEB6]+[M-33DEB6]+[P-33DEB6])
= SF (d.e.6R[23DEB6] + d.e.4R/2S[223DEB6] + d.e.2R/4S[232DEB6]+ d.e.6S[33DEB6]) x (23DEB6)

(n=0-3) [23-n3nDEB6]


SF: Scaling Factor
The experimental CD-curve can now be fitted by variation of K2. ([P-2] and [P-3] are numerically solved for each K2 in a subroutine) using least rms fit analysis.


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