Novel Methods for the Prediction of logP, pKa and logD

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Novel Methods for the Prediction of logP, pKa and
logD

• Li Xing and Robert C. Glen
• J. Chem. Inf. Comput. Sci. 2002, 42, 796-805

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Outline

• Introduction
• logP prediction
• pKa prediction
• logD calculation
• Conclusions
• Discussion

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Introduction
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Introduction The Motivation

• Important for rational drug design
• Bioavailability of a drug
• The drugs access to the therapeutic target
• Factors determing the environment the compound is
  exposed to
• Route of administration of the drug
• Location of the target
• Interest in quantification of
• the drugs affinity for the target
• the ability to partition into a lipophilic
  environment at different pH values

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Introduction The Motivation

• Example of oral administration
• Drug is exposed to a large variety
• of pH values
• Saliva pH 6.4
• Stomach pH 1.0 3.5
• Duodenum pH 5 7.5
• Jejunum pH 6.5 8
• Colon pH 5.5 6.8
• Blood pH 7.4
• Liver-first-pass-effect

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Introduction The Motivation

• Applications
• ADME/Tox screening of virtual libraries
• Lipinskis rule of five
• Quantitative structure-activity relationships
  (QSAR)
• Protein active site determination
• Goal Proper prediction of the drugs ability to
  interact with the biological target

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Introduction The Descriptors

• logP gives the distribution coefficient
• of a substance in the 2 phase system
• 1-octanol/water and thus is a mea-
• sure of lipophilicity
• The ionization constant pKa defines the strength
  of acidity
• LogD is a pH dependent distribution coefficient
  and can be described using logP and pKa

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logP Prediction
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logP The Model

• Use of only three parameters
• Polarizability a
• Partial charges
• for oxygen atoms qO
• for nitrogen atoms qN
• Description of molecular size and dispersion
  interactions empirically by molecular
  polarizability
• Charge estimation using Gasteiger-Hückel-Method

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logP The Data Set

• Measured logP values for 449 molecules under
  standard conditions from CRC Handbook
• 157 logP values, a collection of measured and
  predicted logP values
• No account for stereochemistry cis/trans
  isomers represented by one of both with average
  logP assigned to it
• In total 592 non-redundant molecules

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logP The Model Fit

• Sum of squared charges on nitrogen and oxygen
  atoms more effective than the corresponding
  absolute charges
• The resulting equation by multiple linear
  regression
• LogP 0.287(0.066) 0.190(0.004) a
  14.862(0.545) qN2 8.445(0.216) qO2
• 10-fold cross-validition gives average q2 0.877

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logP The Model Fit

• Quality of the fit
• r2 0.893,
• r 0.945,
• s 0.653,
• F 1631,
• n 592

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logP The Test Set

• 40 molecules from literature composed of five
  pharmacological classes
• Quantitative evaluation of the diversity of the
  test set using Tanimoto index
• Mean Tanimoto index 0.75
• 70 below value of 0.85 (close neighborship)
• Experimental values from 0.42 to 5.99

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logP Predictive Power

• LogP values for 40 drug molecules predicted by
  the model and CLogP vs. The experimental values

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logP Predictive Power

• Summary of statistics of the logP prediction on
  40 drug molecules
• When breaking down the test set into therapeutic
  subsets
• Class I antiarrhytmics are modeled by far the
  worst
• (SE 1 log unit)
• ß-blockers stand out as the best modeled class

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pKa Prediction
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pKa The Model

• Molecular fragments precomputed as a general
  metalayer
• Nitro, cyano, carbonyl, hydroxyl, amino groups
• Amino groups divided by hybridization state
  (sp2/sp3)
• Explicit handling of atom types

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pKa The Model

• Hypothesis of ionization state dependence upon
  immediate subenvironment
• Hierarchical tree constructed from ionized atom
  outward up to five levels

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pKa The Model

• At each tree level 33 (24 atom and nine group
  types) atom/group type bins
• Maximum number of bins over five levels
• 5 levels 33 types/level 24 ionizable types
  189
• The model
• pKc0 base dissociation constant
• xi and yj number of occurences of corresponding
  subclass
• zi class-specific indicator variables
• ai, bj, qk coefficients obtained from
  Partial-Least-Squares along with Sybyl and
  cross-validation

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pKa The Data Set

• Data set derived from Langes Handbook of
  Chemistry by careful inspection for dubious
  entries
• pKa values in the range from -6.94 to 12.48 for
  bases and from -2.8 to 14.22 for acids
  respectively
• In total 384 bases and 645 acids

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pKa The Model Fit

• Bases Acids
• Summary

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pKa The Test Set

• 25 molecules of different chemical classes
  (Perrins examples)
• Test set includes few molecules containing
  multiple ionizable centers
• pKa values range from 1.8 to 10.23

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pKa Predictive Power

• Prediction and Perrins
• values vs. experimental
• Summary statistics

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logD Calculation
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logD The Calculation

• LogD may simply be calculated from predicted logP
  and pKa of the singly ionized species at certain
  pH
• For acids
• logD(pH) logP log1 10(pH - pKa)
• For bases
• logD(pH) logP log1 10(pKa - pH)

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Conclusions
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Conclusions

• Fast and simple methods with significant
  development potential
• Usage of natural descriptors provides insights
  into mechanisms of partitioning and acid/base
  properties
• Only 86(acids) and 80(bases) of training(!)
  samples predicted within one log unit of accuracy
• No account for cis/trans isomers
• Models seem to be overfitted since for all models
  slope and intercept of the regression are 1.0 and
  0.0 respectively

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Thank you for your attention!
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Discussion
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Gasteiger-Hückel-Method

• Description of atomic charges by partial charges
• only uses information about atom type and bonds
• partial equalisation of orbital electronegativity
• Computes a grid for the molecule in question
• For each grid point a partial charge is
  calculated
• s-electrons by Gasteiger
• p-electrons by Hückel
• From this the atomic charges for the whole
  molecule are estimated

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Cross-Validation (CV)

• In K-fold cross-validation (here 10-fold), the
  original sample is partitioned into K subsamples
• Of the K subsamples, a single subsample is
  retained as the validation data to validate the
  model
• The remaining K - 1 subsamples are used as
  training data
• The CV process is then repeated K times with each
  of the K samples used exactly once as the
  validation data
• The K results from the folds then can be
  averaged to produce a single estimation.

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Tanimoto Index

• Also known as Jaccard similarity
• Can be interpreted as the intersection of the
  properties of x and y divided by the union of
  their properties
• If x and y are equal, then the Tanimoto index is
  1, if they are orthogonal, then it is 0

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Partial-Least-Squares

• Goal of ordinary least squares regression
• Minimizing prediction error
• Seeking linear functions of the predictors
  exhibiting as much variation as possible
• Additional goal of Partial-Least-Squares
• Accounting for variation in the predictors, under
  the assumption that directions with high variance
  provide better prediction for new observations
  when the predictors are highly correlated with
  the outcome

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Partial-Least-Squares

• Seeks directions that have high variance in
  predictors xj and high correlation with outcome y
• The Algorithm
• Compute univariate regression coefficients of y
  on each xj
• Construct the first PLS direction
• Regress y on z1 yielding
• Orthogonalize x1,,xp with respect to z1
• Continue with Step 1 until M p directions have
  been obtained