PMC:1635054 / 10782-13943
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{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1635054","sourcedb":"PMC","sourceid":"1635054","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1635054","text":"The protein model\nThe HSE and CN energy functions only depend on the positions of the Cα atoms in the protein backbone. This allows us to simplify the problem by considering a protein as a chain of connected points representing the positions of the Cα atoms. Furthermore, to reduce and discretize the conformational space of the protein, we require the Cα atoms of the chain to be positioned on a 3D lattice. A lattice can be defined as a set of basis vectors corresponding to the directions to the neighbouring nodes. The basis vectors of the simple cubic lattice (SCC) are the cyclic permutations of [± 1,0,0] ([1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1]) and the basis vectors of the face centered cubic lattice (FCC) are the cyclic permutations of [± 1, ± 1,0] ([1,1,0], [1,0,1], [1,-1,0], [1,0,-1], [-1,1,0], [-1,0,1], [-1,-1,0], [-1,0,-1], [0,1,1], [0,1,-1], [0,-1,1], [0,-1,-1]). This gives 6 basis vectors for SCC and 12 for FCC as illustrated in Figure 3. The length of an edge between two neighbouring nodes is taken to be 3.8 Å which is the average distance between two consecutive Cα atoms in proteins.\nFigure 3 Lattices. Interior nodes of the SCC and FCC lattices are connected to respectively 6 and 12 neighbouring nodes. Nodes of high coordination lattices have many neighbours because of variable edge size. Lattice models are widely used for studying the fundamental properties of protein structure[17]. Such models have for example provided invaluable insights on topics such as the validity of pairwise energy functions[18], the evolution of protein superfamilies[19] and the importance of local structural bias in the determination of a protein's fold[20]. Many lattice models have been proposed and evaluated in the literature. Not surprisingly, experiments show a high correlation between the number of basis vectors of a lattice and its ability to represent a protein backbone[21,22]. When deciding on a lattice model, one must always consider the trade-off between the reduction of the conformational space and the quality of the structure representation. Therefore, in section Lattice experiments we evaluate four different lattices of various complexity: The SCC lattice, the FCC lattice and two high coordination (HC) lattices with 54 and 390 basis vectors, respectively.\nA high coordination lattice has an underlying cubic lattice with unit length less than 3.8/N Å for some integer N \u003e 1. Cubic lattice points are connected in the high coordination lattice if their Euclidean distance is between 3.8 ± ε for some ε \u003e 0. The high coordination lattices used here are named HC4 and HC8 corresponding to their N value (4 and 8). The ε value is 0.2 for all HC lattices. Figure 3 shows an illustration of a 2D high coordination lattice with N = 3 and ε = 0.4. High coordination lattices have previously been used for protein structure prediction[23,24]. Note that the SCC and FCC lattices both have the excluded volume property, meaning that atoms at two different lattice points will never collide. This property does not necessarily hold for high coordination lattices, and collisions must therefore be detected explicitly.","divisions":[{"label":"title","span":{"begin":0,"end":17}},{"label":"p","span":{"begin":18,"end":1126}},{"label":"figure","span":{"begin":1127,"end":1336}},{"label":"label","span":{"begin":1127,"end":1135}},{"label":"caption","span":{"begin":1137,"end":1336}},{"label":"p","span":{"begin":1137,"end":1336}},{"label":"p","span":{"begin":1337,"end":2311}}],"tracks":[{"project":"2_test","denotations":[{"id":"17069644-7613459-1690267","span":{"begin":1429,"end":1431},"obj":"7613459"},{"id":"17069644-8609636-1690268","span":{"begin":1552,"end":1554},"obj":"8609636"},{"id":"17069644-16483605-1690269","span":{"begin":1596,"end":1598},"obj":"16483605"},{"id":"17069644-16488978-1690270","span":{"begin":1685,"end":1687},"obj":"16488978"},{"id":"17069644-7783205-1690271","span":{"begin":1916,"end":1918},"obj":"7783205"},{"id":"17069644-11504922-1690272","span":{"begin":2882,"end":2884},"obj":"11504922"},{"id":"17069644-12885659-1690273","span":{"begin":2885,"end":2887},"obj":"12885659"}],"attributes":[{"subj":"17069644-7613459-1690267","pred":"source","obj":"2_test"},{"subj":"17069644-8609636-1690268","pred":"source","obj":"2_test"},{"subj":"17069644-16483605-1690269","pred":"source","obj":"2_test"},{"subj":"17069644-16488978-1690270","pred":"source","obj":"2_test"},{"subj":"17069644-7783205-1690271","pred":"source","obj":"2_test"},{"subj":"17069644-11504922-1690272","pred":"source","obj":"2_test"},{"subj":"17069644-12885659-1690273","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"2_test","color":"#e593ec","default":true}]}]}}