Conformational search space, molecular

Here, we consider RNA three-dimensional structure as the assembly of its constituent nucleotides in three-dimensional space. We introduce a RNA conformational search space defined by molecular contacts (or constraints). The molecular contacts are used in operators that position and orient the nucleotides in three-dimensional space. 

In the following, we first present how contact graphs define the conformational search space of RNAs, to position and orient all nucleotides in three-dimensions. Then, a database of spatial relations based on molecular contacts, as observed among pairs of nucleotides in known structures, is introduced. 

RNA Conformational Search Space Defined by Molecular Contacts. The premise to use molecular contacts in defining the conformational space of RNAs relies on the fact that molecular contacts contain all the information critical to the global fold of the molecule. Consider the best characterized case of an RNA double-helix. The spatial relation between two bases involved in a Watson-Ciick pairing can be used, in conjunction with a canonical base stacking geometry, as a good approximation to position and orient double-helical strands in three-dimensions. 

The number of spanning trees, pairs of nucleotide contacts and homogeneous transformation matrices associated with a contact graph determine the conformational search space size of a RNA. The number of homogeneous transformation matrices associated with a molecular contact type is given by the number of occurrences observed in all available RNA three-dimensional structures in the Protein DataBank (PDB) (7), Nucleic acids DataBase (NDB) (5) and other personally communicated structures. 

For a conformation in a relatively deep local minimum, a room temperature molecular dynamics simulation may not overcome the barrier and search other regions of conformational space in reasonable computing time. To overcome barriers, many conformational searches use elevated temperatures (600-1200 K) at constant energy. To search conformational space adequately, run simulations of 0.5-1.0 ps each at high temperature and save the molecular structures after each simulation. Alternatively, take a snapshot of a simulation at about one picosecond intervals to store the structure. Run a geometry optimization on each structure and compare structures to determine unique low-energy conformations. 

The choice of heating time depends on the purpose of the molecular dynamics simulation. If the simulation is for conformational searches, the heating step is not critical for a successful calculation. The heating step may be rapid to induce large structural changes that provide access to more of the conformational space. 

Virtual screening applications based on superposition or docking usually contain difficult-to-solve optimization problems with a mixed combinatorial and numerical flavor. The combinatorial aspect results from discrete models of conformational flexibility and molecular interactions. The numerical aspect results from describing the relative orientation of two objects, either two superimposed molecules or a ligand with respect to a protein in docking calculations. Problems of this kind are in most cases hard to solve optimally with reasonable compute resources. Sometimes, the combinatorial and the numerical part of such a problem can be separated and independently solved. For example, several virtual screening tools enumerate the conformational space of a molecule in order to address a major combinatorial part of the problem independently (see for example [199]). Alternatively, heuristic search techniques are used to tackle the problem as a whole. Some of them will be covered in this section. 

Model building, manipulation. Stick, ball-and-stick, space-filling, and dot surface display. Semiempirical calculations by extended Hiickel, CNDO, INDO/1, INDO/S, MINDO/3, MNDO, AMI PM3, ZINDO/1, and ZINDO/S. UV, IR, electrostatic potential, and molecular orbital plots. 2D-to-3D conversion. Protein and DNA fragment libraries. MM4-, BIO-I- (implementations of MM2 and CHARMM, respectively), OPTS, and AMBER molecular mechanics and dynamics. Solvent box. ChemPlus for 3D rendering, conformational searching, modeling biomolecules, computing log P and other QSAR properties. PCs under DOS and Windows. 

Exhaustive conformational search is a simple and practical way to explore the entire conformational space available to a peptide (or molecular segment) with fewer than a dozen rotatable bonds. A search is performed by systematically varying each rotatable bond in the peptide. Rotations are made about backbone dihedrals (<]) and v) and/or side chain torsions (%). In our work, bond lengths and angles are held rigid. After each rotation, the molecule is checked for steric overlap. If overlap occurs, the conformer is discarded otherwise it is... 

Constraint A constraint in a target function such as the energy function in molecular mechanics is defined as a degree of freedom that is fixed or not allowed to vary during the molecular simulation. This reduces the amount of space to be searched in conformational searching. 

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