Meshless Methods in Conformation Dynamics by Weber M.

By Weber M.

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Conformational changes can be modeled as monomolecular reactions. For all pairs of conformations χ1 , . . , χnC we have a reaction of the type χi χj , i, j = 1, . .

NC . Proof: From (17) we get s wi = χi π s = χdisc (j, i) ξj π nC = X(j, k)A(k, i) ξj π . j=1 j=1 k=1 Due to (21) the eigenvectors X(:, k) for k = 2, . . e. s X(j, k) ξj π . 0 = X(:, k) D e = j=1 Hence nC s A(k, i) wi = s X(j, k) ξj π = A(1, i) j=1 k=1 s = A(1, i) ξj X(j, 1) ξj j=1 π π =1 = A(1, i). 6 metastability I2 becomes: nC nC λi I2 (A) = i=1 j=1 A(i, j)2 . A(1, j) Note that for I1 and I2 the eigenproblem data X and λ is fixed and A consists of the optimization variables. There are many other possibilities for objective functions.

8 In [131] the notion “indecomposable membership function” was introduced, which is nothing else but a discretization matrix χdisc = XA for A ∈ v(FA ). 3(iii) in [131]. 2) is active. Therefore, one can define a subset FA ⊂ FA with v(FA ) ⊂ FA by the following constraints: nC (1) A(j, 1) = δj,1 − A(j, i), j = 1, . . ,s j=2 A(j, i)X(l, j), i = 1, . . , nC . This subset FA of the feasible set FA , which includes an optimal vertex A of FA , is very important in the following, because it is defined via equations, which reduces the dimension of the search space.

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