Thesis Title: Subtitle - NMR Spectroscopy Research Group

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14 Chapter 1. Introduction. Figure 1.9 Flow-chart of the Echidna algorithm. Both these two automatic <strong>NMR</strong> assignment techniques require partial initial assignments. In the case of Echidna, the whole diamagnetic spectrum needs to be assigned, while Platypus required the connectivity between the paramagnetic and the diamagnetic cross peak. In both cases, those prerequisites reduced the computational problem to a 2D Multi-dimensional Assignment Problem (MAP, Figure 1.10.a). A 2D-MAP is easily solved with the Hungarian method. More challenging and attractive would be to shortcut any initial manual assignment and start directly from the chemical shift lists of the diamagnetic and paramagnetic states. Such a method could be applied to automate the side chain assignment of a protein, once the preliminary and easier task of assigning the backbone chemical shifts and determining the Δχ-tensor has been done, for example with
1.3 Computational study of paramagnetic proteins. 15 Echidna. Computationally, the problem becomes a 3D-MAP (Figure 1.10.b) with the number of possibilities increasing by (n!) 2 . This problem can no longer be solved in a polynomial time since a MAP problem of dimension larger or equal to three is proven to be NP-hard 1 (Karp, 1972). Instead, a heuristic method has to be used to find a good assignment, but without any guarantee of reaching the optimal assignment. An approach that tries to cope with the computational challenges (by means of additional experimental information) led to the development of a software dubbed Possum (Figure 1.11), which is described in Chapter 2. Figure 1.10 Examples of the MAP problem. (a) When calculated and predicted PCSs have to be matched, the cost function c(i, j) can be defined as the square deviation of the two values. The aim is to minimize the sum Q. The binary variables xi,j are defined to ensure that each element i and j is chosen exactly once. (b) The experimental PCSs are not directly available, but the paramagnetic and chemical shifts are measured. Their differences give possible experimental PCSs. 1 The time required to solve a NP-Hard problem drastically increases with the size of the problem which is, in this context, the number n of residue to assign. Some problems with low n value (< 12) could be easily solved in a few minutes. The same problem, with just one extra peak to assign, remained unsolved after days of calculation. This illustrates that, independently of the algorithm used, NP-Hard problem becomes practically and suddenly insolvable for a given size n.which is, in this context, the number n of residue to assign. Some problems with low n value (< 12) could be easily solved in a few minutes. The same problem, with just one extra peak to assign, remained unsolved after days of calculation. This illustrates that, independently of the algorithm used, NP- Hard problem becomes practically and suddenly insolvable for a given size n.
Page 1 and 2: Computational study of proteins wit
Page 3 and 4: iii Schmitz C, Stanton-Cook MJ, Su
Page 5 and 6: v Acknowledgements I would like to
Page 7 and 8: vii Keywords paramagnetic nmr, pseu
Page 9 and 10: ix 2.3.3 Manual resonance assignmen
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Chapter 3 Numbat: new user-friendly
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3.4 Introduction 3.4 Introduction.
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3.5 Algorithm. 79 rhombic component
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3.6 Program Features. 81 each fitti
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3.6 Program Features. 83 A new PCS
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3.6 Program Features. 85 Carlo prot
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3.7 Study case. 87 The coordinates
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3.7 Study case. 89 illustrates how
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3.7 Study case. 91 can be used to a
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3.9 Acknowledgment. 93 variables, t
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3.10 References. 95 Galassi M, Davi
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3.11 Supporting information. 97 Zwe
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Chapter 5 Conclusion and perspectiv
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5.1 The use of PCS for structure de
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5.3 The use of PCS for protein dock
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Thesis Title: Subtitle - NMR Spectroscopy Research Group

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