part2

• QSAR


  Quantitative structure-activity relationships that correlate, within congeneric series of compounds, affinities of ligands to their binding sites, inhibition constants, rate constants, and other biological activities, either with certain structural features or with atomic, group or molecular properties

  
• 3D QSAR


  Methods, especially comparative molecular field analysis, that consider the three-dimensional structures and the binding modes of protein ligands

  
• Quantitative similarity-activity relationships


  Derive correlations between the similarities of individual compounds and their biological activities
• Classical QSAR methods describe structure-activity relationships in terms of physicochemical parameters and steric properties (Hansch analysis, extrathermodynamic approach), or certain structural features (Free Wilson analysis)

  
• 3D QSAR methods, especially comparative molecular field analysis, consider the three-dimensional structures and the binding modes of protein ligands
• Quantitative structure-activity relationships (QSAR) have been used to describe thousands of biological activities within different series of drugs and drug candidates

  
• Enzyme inhibition data have been successfully correlated with physicochemical properties of the ligands
• In certain cases, where X-ray structures of the proteins became available, the results of QSAR regression models could be interpreted with the additional information from the three-dimensional (3D) structures

  
• Comparative molecular field analysis (CoMFA)

  A molecular field-based 3D QSAR method that was published in 1988 and has had many successful applications, especially in cases where classical QSAR methods fail

  
• In contrast to Hansch or Free Wilson analysis, CoMFA is better suited to describe ligand-receptor interactions, because it considers the properties of the ligands in their (supposed) bioactive conformations
• As the result of a CoMFA analysis, regions in space are identified that are favorable or unfavorable for the ligand-receptor interaction
• QSAR analyses are based on the assumption of linear additive contributions of the different structural properties or features of a compound to its biological activity, provided that there are no nonlinear dependences of transport or binding on certain physicochemical properties

  
• Eqn 1 holds for a wide range of energy values and its standard deviation corresponds to a mean error of about 1.4 log units in the prediction of ligand binding constants
• Free Wilson analysis


  A mathematical model that describes the presence and absence of certain structural features by values of 1 or 0 and correlates the resulting structural matrix with biological activity values

  
• Free Wilson analysis has several shortcomings, including the need for at least two different positions of substitution to be chemically modified, and the inability to make predictions for new combinations of substituents not included in the analysis

  
• Hansch analysis

  A linear free-energy-related model that combines the description of transport and binding affinity in one mathematical model, using lipophilicity, electronic properties, and other linear free-energy-related properties
• Equations 8 and 9 demonstrate the use of Hansch analysis to correlate the antiadrenergic activities of N,N-dimethyl-α-bromophenethylamine derivatives with lipophilicity, electronic, and steric parameters
• Parameters


  Substituents X
• Partition coefficient P


  Equilibrium constant, similar to dissociation or reaction constants K
• Hansch analysis


  • Superiority over Free Wilson analysis
  • Only a few properties needed to correlate biological activities
  • Model can be directly interpreted in physicochemical terms

  
• Free Wilson analysis results are confirmed in all details but predictions for compounds with other substituents can be made

  
• Predictions that are too far outside the range of investigated parameters will most probably fail
• Mixed approach


  Combines advantages of Hansch and Free Wilson analyses and widens the applicability of both methods
• Transport rate constants k1 and k2

  Depend on lipophilicity in a nonlinear manner
• Parabolic Hansch model (Equation 5) may be considered as a good approximation to the bilinear model
• Nonlinear dependences of binding affinities or biological activities on the volumes of the substituents are relatively common
• pH-absorption profiles should be parallel to the pH-partition profiles
• Deviations from the simple pH partition hypothesis, called pH shifts, are obtained for highly lipophilic compounds
• CoMFA (Comparative Molecular Field Analysis)


  A 3D QSAR approach that uses partial least squares (PLS) analysis to correlate molecular field values with biological activities

  
• Steps in CoMFA


  1. Select a group of chemically related compounds with a common pharmacophore

  2. Convert 2D/2.5D structures to 3D structures

  3. Align the 3D structures based on the common pharmacophore
• Alignment is one of the most critical and difficult steps in a CoMFA study
• Similarities and affinities of molecules can be properly described even if they are studied in geometries different from the correct bioactive conformations
• Theoretically, this problem severely limits the applicability of CoMFA; on the other hand, some investigations give evidence that the similarities (and correspondingly the affinities) of molecules are properly described, even if they are studied in geometries that are different from the correct bioactive conformations
• In addition, 3D approaches have been developed that do not depend on a common alignment of the molecules
• Although 'chemically' related, the different pattern of hydrogen bond donor and acceptor distribution in MTX, when compared with the lead structure DHF, demands a completely different orientation

  
• This different binding mode was predicted from the 3D structure of the DHF/dihydrofolate reductase complex and later experimentally confirmed by the X-ray structure determination of the MTX complex
• SEAL (Similarity Index)


  Defines a 'similarity index' between two molecules A and B in any relative orientation to each other

  
• The data set is separated into a training set for which a CoMFA model is derived and a test set that will prove the external predictivity of the resulting model
• A box is placed around the superimposed molecules in such a manner that the box is in all directions several Å larger than the combined volume of all molecules
• A regular lattice is laid over the molecules to calculate different molecular fields in each grid point