MEDLA method

An Application of the MEDLA Method for the Direct Computation of Electron Densities of Functional Groups... 

The additive fuzzy electron density fragmentation scheme of Mezey is the basis of the Molecular Electron Density Lego Assembler (MEDLA) method [67,70-72], reviewed in section 4. of this report, where additional details and applications in local shape analysis are discussed. The MEDLA method was used for the generation of the first ab initio quality electron densities for macromolecules such as proteins [71,72] and other natural products such as taxol [66],... 

The application of the additive fuzzy electron density fragments for the building of electron densities of large molecules is called the Molecular Electron Density Lego Assembler method, or MEDLA method [5,37,66,67,70-72],... 

Both of the natural requirements of additivity and fuzziness are fulfilled by Mezey s fragmentation scheme that has served as the basis of the MEDLA method. 

In all tests, the MEDLA method performed consistently better than standard ab initio SCF 3-21G basis computations, consequently, the claim of "ab initio quality" appears justified. 

By combining the results of two of these tests, one may conclude that the MEDLA method does not appear to show a bias concerning the joining of various density domains. This is an important concern for the analysis of functional groups. 

The MEDLA method does not impose any size limitation on the fragments only the feasibilty of traditional ab initio calculations limits the actual size of the fragments and the size of the "coordination shell" around them in the small molecule imitating the actual surroundings within the target molecule. Electron densities of satisfactory accuracy have been obtained in all the test calculations. 

Whereas density functional theory guaranties that for the ground electronic state of molecules the electron density determines the energy, the actual construction of such energy functions from first principles is a problem of considerable complexity. The electron densities computed by the MEDLA method suggest various approximations to the molecular energy of large systems. 

It is now possible to analyze macromolecular electron densities at a resolution far exceeding the resolution of current x-ray diffraction and other experimental and macromolecular computational techniques. The MEDLA method presents a new perspective for the analysis of global and local shape, molecular similarity, and complementarity. 

FIGURE 1 The fuzzy body of the electron density of a bovine insulin molecule is represented by three molecular isodensity contour surfaces (MlDCOs), for the density thresholds of 0.1, 0.01, and 0.001 a.u. (atomic unit), respectively, as computed using the MEDLA method. Bovine insulin was among the proteins selected for the first ab initio quality electron density computations for macromolecules. ... 

Since the introduction of the MEDLA method, three more recent developments have extended the applications of the Mulliken-Mezey and the more general AFDF schemes. These developments, all utilizing various representations of additive fuzzy subsets of molecular electron densities, are the... 

Within the quantum chemical description of molecular electron density clouds, a natural criterion, the Density Domain criterion, provides a quantum chemical definition for functional groups [14-18]. Furthermore, techniques that generate fuzzy electron density contributions for local molecular moieties that are analogous to the fuzzy electron density clouds of complete molecules, determined by the analytic Additive Fuzzy Density Fragmentation (AFDF) method [19-21], or the earlier numerical-grid MEDLA method [22,23], are also... 

The MEDLA method is based on the following electron density fragment additivity principle. A natural scheme for the implementation of this principle has been d cribed in [12]. Consider an LCAO ab initio wavefunction of a small molecule of some fixed conformation K. If n is the number of atomic orbitals three-dimensional position vector variable, and P is the n X n density matrix, then the electronic density p(r) of the molecule is given by... 

Some recent developments concerning macromolecular quantum chemistry, especially the first linear-scaling method applied successfully for the ab initio quality quantum-chemistry computation of the electron density of proteins, have underlined the importance and the applicability of quantum chemistry-based approaches to molecular similarity. These methods, the linear-scaling numerical Molecular Electron Density Lego Approach (MEDLA) method [6 9] and the more advanced and more generally applicable linear-scaling macromolecular density matrix method called Adjustable Density Matrix Assembler or ADMA method [10,11], have been employed for the calculation of ab initio quality protein electron densities and other... 

Note that the simplest, Mulliken-Mezey fragmentation scheme employed in the MEDLA method, and in the more advanced macromolecular density matrix approach of the ADMA method [34-37], corresponds to the special choice of v/y =... 

Besides the possibilities of the computation of all molecular properties expressible in terms of density matrices, the ADMA method has other advantages. For example, if electron density computations are compared, then the accuracy of the electron density obtained using the ADMA macromolecular density matrix P((p(A0) corresponds to the ideal MEDLA result that could be obtained using an infinite resolution numerical grid. The memory requirements of the ADMA method is also substantially lower than that of the numerical MEDLA method since it takes much less memory to store density matrices than three-dimensional numerical grids of electron densities, especially if reasonably detailed electron densities are required. 

According to detailed tests, ° the MEDLA method generates ab initio quality electronic densities at a level better than standard SCF calculations using 3-2IG bases. The MEDLA electronic densities are virtually indistinguishable from electronic densities obtained by standard SCF calculations at the 6-3IG basis set level. ... 

The MEDLA method, based on numerical electronic density data base, the more advanced, geometry-adjustable ALDA method,based on a fragment density matrix data base, and the ADMA method, " generating macromolecular density... 

---