Editing Partition coefficient (section)

== Prediction ==
There are many situations where prediction of partition coefficients prior to experimental measurement is useful. For example, tens of thousands of industrially manufactured chemicals are in common use, but only a small fraction have undergone rigorous [[toxicology|toxicological]] evaluation. Hence there is a need to prioritize the remainder for testing. [[QSAR]] equations, which in turn are based on calculated partition coefficients, can be used to provide toxicity estimates.<ref name="Nieto-Draghi_2015"/><ref name="pmid19479008">{{cite journal | vauthors = Judson R, Richard A, Dix DJ, Houck K, Martin M, Kavlock R, Dellarco V, Henry T, Holderman T, Sayre P, Tan S, Carpenter T, Smith E | title = The toxicity data landscape for environmental chemicals | journal = Environmental Health Perspectives | volume = 117 | issue = 5 | pages = 685–95 | date = May 2009 | pmid = 19479008 | pmc = 2685828 | doi = 10.1289/ehp.0800168 }}</ref> Calculated partition coefficients are also widely used in drug discovery to optimize [[high-throughput screening|screening libraries]]<ref name="pmid11562252">{{cite journal | vauthors = Matter H, Baringhaus KH, Naumann T, Klabunde T, Pirard B | title = Computational approaches towards the rational design of drug-like compound libraries | journal = Combinatorial Chemistry & High Throughput Screening | volume = 4 | issue = 6 | pages = 453–75 | date = September 2001 | pmid = 11562252 | doi = 10.2174/1386207013330896 }}</ref><ref name="pmid16101415">{{cite journal | vauthors = Schuffenhauer A, Ruedisser S, Marzinzik AL, Jahnke W, Blommers M, Selzer P, Jacoby E | title = Library design for fragment based screening | journal = Current Topics in Medicinal Chemistry | volume = 5 | issue = 8 | pages = 751–62 | year = 2005 | pmid = 16101415 | doi = 10.2174/1568026054637700 }}</ref> and to predict [[druglikeness]] of designed drug candidates before they are synthesized.<ref>{{cite journal | vauthors = Rutkowska E, Pajak K, Jóźwiak K | title = Lipophilicity--methods of determination and its role in medicinal chemistry | journal = Acta Poloniae Pharmaceutica | volume = 70 | issue = 1 | pages = 3–18 | year = 2013 | pmid = 23610954 | url = http://www.ptfarm.pl/pub/File/Acta_Poloniae/2013/1/003.pdf }}</ref> As discussed in more detail below, estimates of partition coefficients can be made using a variety of methods, including fragment-based, atom-based, and knowledge-based that rely solely on knowledge of the structure of the chemical. Other prediction methods rely on other experimental measurements such as solubility. The methods also differ in accuracy and whether they can be applied to all molecules, or only ones similar to molecules already studied.

===Atom-based===
Standard approaches of this type, using atomic contributions, have been named by those formulating them with a prefix letter: AlogP,<ref name="Ghose_1986"/> XlogP,<ref>{{cite journal | vauthors = Cheng T, Zhao Y, Li X, Lin F, Xu Y, Zhang X, Li Y, Wang R, Lai L | title = Computation of octanol-water partition coefficients by guiding an additive model with knowledge | journal = Journal of Chemical Information and Modeling | volume = 47 | issue = 6 | pages = 2140–8 | year = 2007 | pmid = 17985865 | doi = 10.1021/ci700257y | url = http://www.sioc-ccbg.ac.cn/?p=42&software=xlogp3 }}</ref> MlogP,<ref name="Moriguchi_1992"/> etc. A conventional method for predicting log ''P'' through this type of method is to parameterize the distribution coefficient contributions of various atoms to the overall molecular partition coefficient, which produces a [[parametric model]]. This parametric model can be estimated using constrained [[Least squares|least-squares]] [[estimation theory|estimation]], using a [[training set]] of compounds with experimentally measured partition coefficients.<ref name="Ghose_1986">{{cite journal | vauthors = Ghose AK, Crippen GM | title = Atomic Physicochemical Parameters for Three-Dimensional Structure-Directed Quantitative Structure–Activity Relationships I. Partition Coefficients as a Measure of Hydrophobicity | journal= Journal of Computational Chemistry | volume= 7 | issue= 4 | pages = 565–577 | year= 1986 | doi = 10.1002/jcc.540070419  | hdl = 2027.42/38274 | s2cid = 4272062 | url = https://deepblue.lib.umich.edu/bitstream/2027.42/38274/1/540070419_ftp.pdf | hdl-access = free }}</ref><ref name="Moriguchi_1992">{{cite journal | vauthors = Moriguchi I, Hirono S, Liu Q, Nakagome I, Matsushita Y | title = Simple method of calculating octanol/water partition coefficient | journal = Chem. Pharm. Bull. | volume=40 | issue = 1 | pages = 127–130 | year = 1992 | doi = 10.1248/cpb.40.127 | doi-access = free }}</ref><ref name="Ghose_1998">{{cite journal | vauthors = Ghose AK, Viswanadhan VN, Wendoloski JJ | title = Prediction of Hydrophobic (Lipophilic) Properties of Small Organic Molecules Using Fragmental Methods: An Analysis of AlogP and ClogP Methods | journal = Journal of Physical Chemistry A | volume = 102 | issue = 21 | pages = 3762–3772 | year = 1998 | doi = 10.1021/jp980230o | bibcode = 1998JPCA..102.3762G }}</ref> In order to get reasonable correlations, the most common elements contained in drugs (hydrogen, carbon, oxygen, sulfur, nitrogen, and halogens) are divided into several different atom types depending on the environment of the atom within the molecule. While this method is generally the least accurate, the advantage is that it is the most general, being able to provide at least a rough estimate for a wide variety of molecules.<ref name="Moriguchi_1992"/>

===Fragment-based===
The most common of these uses a [[group contribution method]] and is termed cLogP. It has been shown that the log ''P'' of a compound can be determined by the sum of its non-overlapping molecular fragments (defined as one or more atoms covalently bound to each other within the molecule). Fragmentary log ''P'' values have been determined in a statistical method analogous to the atomic methods (least-squares fitting to a training set). In addition, [[Hammett equation|Hammett-type corrections]] are included to account of [[Inductive effect|electronic]] and [[steric effects]]. This method in general gives better results than atomic-based methods, but cannot be used to predict partition coefficients for molecules containing unusual functional groups for which the method has not yet been parameterized (most likely because of the lack of experimental data for molecules containing such functional groups).<ref name="Hansch"/>{{rp|125ff}}<ref name="Leo2"/>{{rp|1–193}}

===Knowledge-based===
A typical [[data-mining]]-based prediction uses [[support-vector machine]]s,<ref name="pmid17031534">{{cite journal | vauthors = Liao Q, Yao J, Yuan S | title = SVM approach for predicting LogP | journal = Molecular Diversity | volume = 10 | issue = 3 | pages = 301–9 | date = August 2006 | pmid = 17031534 | doi = 10.1007/s11030-006-9036-2 | s2cid = 1196330 }}</ref> [[Decision tree learning|decision trees]], or [[Artificial neural network|neural networks]].<ref name="pmid15012980">{{cite journal | vauthors = Molnár L, Keseru GM, Papp A, Gulyás Z, Darvas F | title = A neural network based prediction of octanol-water partition coefficients using atomic5 fragmental descriptors | journal = Bioorganic & Medicinal Chemistry Letters | volume = 14 | issue = 4 | pages = 851–3 | date = February 2004 | pmid = 15012980 | doi = 10.1016/j.bmcl.2003.12.024 }}</ref> This method is usually very successful for calculating log ''P'' values when used with compounds that have similar chemical structures and known log ''P'' values. [[Molecule mining]] approaches apply a similarity-matrix-based prediction or an automatic fragmentation scheme into molecular substructures. Furthermore, there exist also approaches using [[Maximum common subgraph isomorphism problem|maximum common subgraph]] searches or [[Molecule mining|molecule kernels]].

===Log ''D'' from log ''P'' and p''K''<sub>a</sub>===
For cases where the molecule is un-ionized:<ref name="Scherrer"/><ref name="Manners_1998"/>
: <math>\log D \cong \log P.</math>

For other cases, estimation of log ''D'' at a given pH, from log ''P'' and the known [[mole fraction]] of the un-ionized form, <math>f^0</math>, in the case where partition of [[Partition coefficient#Relationship to log P (logP)|ionized forms]] into non-polar phase can be neglected, can be formulated as<ref name="Scherrer"/><ref name="Manners_1998"/>
: <math>\log D \cong \log P + \log \left(f^0\right).</math>

The following approximate expressions are valid only for [[Acid dissociation constant|monoprotic acids and bases]]:<ref name="Scherrer">{{cite journal | vauthors = Scherrer RA, Howard SM | title = Use of distribution coefficients in quantitative structure-activity relationships | journal = Journal of Medicinal Chemistry | volume = 20 | issue = 1 | pages = 53–8 | date = January 1977 | pmid = 13215 | doi = 10.1021/jm00211a010 }}</ref><ref name="Manners_1998">{{cite journal | vauthors = Manners CN, Payling DW, Smith DA | title = Distribution coefficient, a convenient term for the relation of predictable physico-chemical properties to metabolic processes | journal = Xenobiotica; the Fate of Foreign Compounds in Biological Systems | volume = 18 | issue = 3 | pages = 331–50 | date = March 1988 | pmid = 3289270 | doi = 10.3109/00498258809041669 }}</ref>
: <math>\begin{align}
  \log D_\text{acids} &\cong \log P + \log\left[\frac{1}{1 + 10^{\mathrm{p}H - \mathrm{p}K_a}}\right], \\
  \log D_\text{bases} &\cong \log P + \log\left[\frac{1}{1 + 10^{\mathrm{p}K_a - \mathrm{pH}}}\right].
\end{align}</math>

Further approximations for when the compound is largely ionized:<ref name="Scherrer"/><ref name="Manners_1998"/>
* for acids with <math>\mathrm{pH} - \mathrm{p}K_a > 1</math>, <math>\log D_\text{acids} \cong \log P + \mathrm{p}K_a - \mathrm{pH}</math>,
* for bases with <math>\mathrm{p}K_a - \mathrm{pH} > 1</math>, <math>\log D_\text{bases} \cong \log P - \mathrm{p}K_a + \mathrm{pH}</math>.

For [[acid dissociation constant#Prediction|prediction of p''K''<sub>a</sub>]], which in turn can be used to estimate log&nbsp;''D'', [[Hammett equation|Hammett type equations]] have frequently been applied.<ref name="Perrin">{{cite book | vauthors = Perrin DD, Dempsey B, Serjeant EP | title = pK<sub>a</sub> Prediction for Organic Acids and Bases | publisher = Chapman & Hall | year = 1981 | location = London | isbn = 978-0-412-22190-3 | doi = 10.1007/978-94-009-5883-8 | chapter = Chapter 3: Methods of pK<sub>a</sub> Prediction | pages = 21–26 }}</ref><ref name="RMC_2013">{{cite encyclopedia | vauthors = Fraczkiewicz R | encyclopedia = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering [Online] | veditors = Reedijk J | volume = 5 | publisher = Elsevier | location = Amsterdam, the Netherlands | year = 2013 | doi = 10.1016/B978-0-12-409547-2.02610-X | title = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering | isbn = 9780124095472 | chapter = In Silico Prediction of Ionization }}</ref>

===Log ''P'' from log ''S''===
If the solubility, ''S'', of an organic compound is known or predicted in both water and 1-octanol, then log&nbsp;''P'' can be estimated as<ref name="Nieto-Draghi_2015">{{cite journal | vauthors = Nieto-Draghi C, Fayet G, Creton B, Rozanska X, Rotureau P, de Hemptinne JC, Ungerer P, Rousseau B, Adamo C | title = A General Guidebook for the Theoretical Prediction of Physicochemical Properties of Chemicals for Regulatory Purposes | journal = Chemical Reviews | volume = 115 | issue = 24 | pages = 13093–164 | date = December 2015 | pmid = 26624238 | doi = 10.1021/acs.chemrev.5b00215 }}</ref><ref>{{cite journal | vauthors = Pinsuwan S, Li A, Yalkowsky SH | title = Correlation of Octanol/Water Solubility Ratios and Partition Coefficients | journal = Journal of Chemical & Engineering Data | date = May 1995 | volume = 40 | issue = 3 | pages = 623–626 | doi = 10.1021/je00019a019 }}</ref>
: <math>\log P = \log S_\text{o} - \log S_\text{w}.</math>
There are a variety of approaches to [[Solubility#Solubility prediction|predict solubilities]], and so log ''S''.<ref name="pmid21470182">{{cite journal | vauthors = Wang J, Hou T | title = Recent advances on aqueous solubility prediction | journal = Combinatorial Chemistry & High Throughput Screening | volume = 14 | issue = 5 | pages = 328–38 | date = June 2011 | pmid = 21470182 | doi = 10.2174/138620711795508331 }}</ref><ref name="pmid25660403">{{cite journal | vauthors = Skyner RE, McDonagh JL, Groom CR, van Mourik T, Mitchell JB | title = A review of methods for the calculation of solution free energies and the modelling of systems in solution | journal = Physical Chemistry Chemical Physics | volume = 17 | issue = 9 | pages = 6174–91 | date = March 2015 | pmid = 25660403 | doi = 10.1039/c5cp00288e | url = https://research-repository.st-andrews.ac.uk/bitstream/10023/6096/1/c5cp00288e.pdf | bibcode = 2015PCCP...17.6174S | doi-access = free }}</ref>