Molecular descriptors that influence the amount of drugs transfer into human breast milk

Abstract

Most drugs are excreted into breast milk to some extent and are bioavailable to the infant. The ability to predict the approximate amount of drug that might be present in milk from the drug structure would be very useful in the clinical setting. The aim of this research was to simplify and upgrade the previously developed model for prediction of the milk to plasma (M/P) concentration ratio, given only the molecular structure of the drug. The set of 123 drug compounds, with experimentally derived M/P values taken from the literature, was used to develop, test and validate a predictive model. Each compound was encoded with 71 calculated molecular structure descriptors, including constitutional descriptors, topological descriptors, molecular connectivity, geometrical descriptors, quantum chemical descriptors, physicochemical descriptors and liquid properties. Genetic algorithm was used to select a subset of the descriptors that best describe the drug transfer into breast milk and artificial neural network (ANN) to correlate selected descriptors with the M/P ratio and develop a QSAR. The averaged literature M/P values were used as the ANN's output and calculated molecular descriptors as the inputs. A nine-descriptor nonlinear computational neural network model has been developed for the estimation of M/P ratio values for a data set of 123 drugs. The model included the percent of oxygen, parachor, density, highest occupied molecular orbital energy (HOMO), topological indices (chiV2, chi2 and chi1) and shape indices (kappa3, kappa2), as the inputs had four hidden neurons and one output neuron. The QSPR that was developed indicates that molecular size (parachor, density) shape (topological shape indices, molecular connectivity indices) and electronic properties (HOMO) are the most important for drug transfer into breast milk. Unlike previously reported models, the QSPR model described here does not require experimentally derived parameters and could potentially provide a useful prediction of M/P ratio of new drugs only from a sketch of their structure and this approach might also be useful for drug information service. Regardless of the model or method used to estimate drug transfer into breast milk, these predictions should only be used to assist in the evaluation of risk, in conjunction with assessment of the infant's response.

Full text

Journal of Pharmaceutical and Biomedical Analysis
29 (2002) 103–119
Molecular descriptors that influence the amount of drugs
transfer into human breast milk
S. Agatonovic-Kustrin
a,
*, L.H. Ling
b
, S.Y. Tham
b
, R.G. Alany
c
a
School of Pharmaceutical,Molecular and Biomedical Science,Uni6ersity of South Australia,North Terrace,
Adelaide
5000
,Australia
b
School of Pharmaceutical Sciences,Uni6ersiti Sains Malaysia,Penang
11800
,Malaysia
c
Di6ision of Pharmacy,The Uni6ersity of Auckland,Auckland,New Zealand
Received 11 January 2001; accepted 23 December 2001
Abstract
Most drugs are excreted into breast milk to some extent and are bioavailable to the infant. The ability to predict
the approximate amount of drug that might be present in milk from the drug structure would be very useful in the
clinical setting. The aim of this research was to simplify and upgrade the previously developed model for prediction
of the milk to plasma (M/P) concentration ratio, given only the molecular structure of the drug. The set of 123 drug
compounds, with experimentally derived M/P values taken from the literature, was used to develop, test and validate
a predictive model. Each compound was encoded with 71 calculated molecular structure descriptors, including
constitutional descriptors, topological descriptors, molecular connectivity, geometrical descriptors, quantum chemical
descriptors, physicochemical descriptors and liquid properties. Genetic algorithm was used to select a subset of the
descriptors that best describe the drug transfer into breast milk and artificial neural network (ANN) to correlate
selected descriptors with the M/P ratio and develop a QSAR. The averaged literature M/P values were used as the
ANN’s output and calculated molecular descriptors as the inputs. A nine-descriptor nonlinear computational neural
network model has been developed for the estimation of M/P ratio values for a data set of 123 drugs. The model
included the percent of oxygen, parachor, density, highest occupied molecular orbital energy (HOMO), topological
indices (xV2, x2andx1) and shape indices (k3, k2), as the inputs had four hidden neurons and one output neuron.
The QSPR that was developed indicates that molecular size (parachor, density) shape (topological shape indices,
molecular connectivity indices) and electronic properties (HOMO) are the most important for drug transfer into
breast milk. Unlike previously reported models, the QSPR model described here does not require experimentally
derived parameters and could potentially provide a useful prediction of M/P ratio of new drugs only from a sketch
of their structure and this approach might also be useful for drug information service. Regardless of the model or
method used to estimate drug transfer into breast milk, these predictions should only be used to assist in the
evaluation of risk, in conjunction with assessment of the infant’s response. © 2002 Elsevier Science B.V. All rights
reserved.
Keywords
:
Milk to plasma ratio; Molecular descriptors; ANNs; GA; QSPR; QSAR
www.elsevier.com/locate/jpba
* Corresponding author. Tel.: +61-8-8302-2391; fax: +61-8-8302-2389.
E-mail address
:
nena.kustrin@unisa.edu.au (S. Agatonovic-Kustrin).
0731-7085/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S0731-7085(02)00037-7

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1. Introduction
Breastfeeding is an essential physiologic process
that provides nutrition and protects a child
against infection and immunologic disorders. The
frequency of various diseases and metabolic disor-
ders are less in a breastfed infant. When drugs are
administered to a nursing mother, a small part of
them may appear in her milk [1]. Most drugs pass
into breast milk, but the dose is reduced and
usually does not produce a pharmacological ef-
fect. Certain drugs, however, do reach greater
levels in milk than in the mother. Because of the
infant’s small size and the difference in
metabolism between infants and adults, occasion-
ally this transfer of medication can be harmful to
the infant [2–4]. The amount of drug excreted
into milk depends on a number of kinetic factors:
(1) lipid solubility of the drug; (2) molecular size
of the drug; (3) blood level attained in the mater-
nal circulation; (4) protein binding in the maternal
circulation; (5) oral bioavailability in the infant
and the mother; and (6) half-life in the maternal
and infant’s plasma compartments.
Human milk is a suspension of protein and fat
globules in a carbohydrate-based solution [5]. The
mechanisms by which medications are transferred
into breast milk are no different than those gov-
erning passage into any other maternal body fluid
or organ system. Drugs enter milk primarily by
passive diffusion reaching concentration equi-
librium with the concentration in the blood, but
also by active secretory methods that can concen-
trate the drug in the breast milk [6–8].
The most important determinant of drug pene-
tration into milk is the mother’s plasma level.
Drugs enter milk and, in most cases, exit milk as
a function of the mother’s plasma level. Of the
many factors, perhaps the two most important
and useful are the degree of protein binding and
lipid solubility. Drugs that are extremely lipid
soluble penetrate milk in higher concentrations
(i.e. CNS active drugs). Protein binding also plays
a very important role. Drugs that have high ma-
ternal protein binding almost invariably produce
lesser levels in milk. Most drugs circulate in the
maternal plasma bound to a large molecular
weight protein called albumin. An unbound com-
ponent remains freely soluble in the plasma and
transfers into milk, while the bound fraction stays
in the maternal plasma unable to reach the tis-
sues. For weak acids and bases, excretion into
breast milk is governed by factors such as their
pK
a
, their concentration in plasma and the pH of
the milk and plasma. In some instances, drugs
become ion trapped in milk. Due to the lower pH
of human milk, the physicochemical structure of
the drug changes and prevents its perfusion back
into the maternal circulation. Hence, they become
ion trapped in the milk. Also, drugs may concen-
trate in the milk due to specialized transport
systems, which ‘pump’substances into the milk.
In addition, a small water-soluble molecule, such
as alcohol, may pas into the milk through
aqueous pores in the membrane.
Assessing the risk of maternal medication to the
breast-feed infant requires knowledge of the con-
centration of drug that might be present in the
milk. This concentration can be calculated for a
particular drug if the milk to plasma (M/P) con-
centration ratio is known for the drug. The M/P
value is an attempt to identify the equilibrium
concentration between breast milk and blood. It is
equivalent to the drug concentration in the breast
milk divided by the maternal serum concentra-
tion. As almost all drugs pass into milk from
maternal plasma by passive diffusion, the M/P
ratio is affected by the composition of the milk
(aqueous, lipid, protein and pH) and the physico-
chemical characteristics of the drug (degree of
ionization, molecular weight protein binding and
lipophilicity).
Lower molecular weight drugs with high
lipophilicity that are less protein-bound, nonion-
ized, are more likely to diffuse into breast milk.
The more lipid-soluble a medication, the more
likely it will diffuse into milk. Breast milk has a
lower pH (7.08) than plasma (7.42), causing weak
bases to pass more readily into the milk than
weak acids. Drugs that tend to concentrate in
milk are weak bases, with low plasma protein
binding and high lipid solubility. Additionally,
medications may be transferred into breast milk
incorporated within fat globules or bound to
proteins, primarily casein and lactalbumin. Highly
protein-bound drugs, though, are unlikely to cross

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extensively into breast milk, since these drugs
bind preferentially to serum albumin [9,10]. Fi-
nally, large molecules are not able to diffuse
passively into the milk.
There is a tremendous need for more informa-
tion on the safety of drugs while breastfeeding.
The milk to plasma drug concentration ratios has
been determined experimentally for many drugs.
This ratio is most reliable when it comes from
studies where the area under the concentration–
time profiles has been measured over a whole dose
interval. Unfortunately, most of the data on
breastfeeding and drugs is based on single case
reports or small case series. M/P data based on
single time point concentration measurements in
the two phases can be misleading because the time
course of concentrations in milk and plasma may
not parallel each other. Using these experimental
data, empirical regression equations have been
developed relating milk plasma ratio to the drug
pK
a
, the octanol water partition coefficient and
plasma protein binding [11]. A log-transformed
phase-distribution model appears to have good
predictive performance [12]. The disadvantage of
these methods is that plasma protein binding for
the drug must be known or experimentally deter-
mined. Since these physico-chemical drug proper-
ties are not always available, a theoretical method
that could predict the milk plasma ratio from the
drug structure would be of interest.
The aim of this research was to simplify and
upgrade a previously developed genetic neural
network (GNN) model for prediction of M/P
ratio given only the molecular structure of the
drug [13]. The model is based only on theoretical
molecular descriptors that can be calculated di-
rectly from molecular structure. This approach
has potential use for drug information services
when experimental physico-chemical properties of
the drug are not available and experimental milk
plasma ratios have not been investigated.
1
.
1
.Artificial neural network
(
ANN
)
An artificial neural network is a biologically
inspired computer program designed to simulate
the way in which the human brain processes
information. ANNs are composed of hundreds of
single processing elements (PE). Each PE has
weighted inputs, transfer function and one output.
PEs are connected with coefficients (weights) and
are organized in a layered feed forward topology,
the input layer, the output layer and the hidden
layers between them. The number of layers and
the number of units in each layer determines the
function complexity.
Neural networks gather their knowledge by de-
tecting the patterns and relationships in data and
learn (or are trained) through experience with
appropriate learning exemplars. The input layer
neurons receive data from a data file. The output
neurons provide the ANN’s response to the input
data. Units in the input layer do not process.
They simply pass an output value onto units in
the second layer. Each hidden or output unit
performs a biased weighted sum of inputs and
passes this activation signal through an activation
function (also known as a transfer function) to
produce their output.
Multilayer perceptron (MLP) is the most com-
monly used type of feed-forward network. MLPs
use a linear activation signal or post synaptic
potential (PSP) to combine incoming inputs and
usually a non-linear activation function (also
known as a transfer function). PEs are defined by
their weights and threshold. Linear PSP units
perform a weighted sum of their inputs, biased by
the threshold value. Thus, a parameterized model
is formed, with the weights and thresholds (biases)
as the free parameters of the model. The standard
activation function for MLPs is the logistic func-
tion. It is an S-shaped (sigmoid) curve, with out-
put in the range (0.1).
When the network is executed, the input vari-
able values are placed in the input units and then
the hidden and output layer units are progres-
sively executed. Each unit in the proceeding layers
calculates its PSP of the neuron by taking the
weighted sum of the outputs of the units in the
preceding layer and subtracting the threshold. The
activation signal is than passed through the acti-
vation function to produce the output of the
neuron. When the entire network has been exe-
cuted, the outputs of the output layer act as the
output of the entire network.

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2. Experimental
Neural Networks TM (StatSoft Inc., Tulsa) was
used for building the QSAR model. For calculat-
ing drug properties from molecular structure,
BioMed CAChe Project leader (Fujitsu America,
Inc.) and ACD/ChemSketch (Toronto, Canada)
were used.
2
.
1
.Network training
The set of 123 structurally different compounds
and their experimentally derived M/P values used
in this study were collected from the literature.
The M/P values were used as the ANN’s output
and 71 calculated molecular descriptors as the
inputs. Before each training run, data sets were
split randomly into three separate groups: training
(83 data sets), testing (20 data sets) and validation
(20 data sets) and both weights and biases were
initialized with random values. The results of five
runs were averaged. During training, the perfor-
mance of the ANN was evaluated with testing
data. The training set was used to train the net-
work and the testing set was used to monitor
overtraining the network. Training was stopped
when the training root mean squared error (RMS)
failed to improve over a given number of training
cycles and when the testing RMS error started to
increase. Validation set was used to evaluate the
trained model.
The number of input and output neurons is
defined by the problem. Input variables were se-
lected based on their significance and physico-
chemical meaning. The number of hidden layers
and neurons was optimized. A network with more
input and hidden neurons has more weights, and
models a more complex function and is likely to
suffer from the over-fitting. A network with fewer
weights may not be sufficiently powerful to model
the underlying function. A network with no hid-
den layers models a simple linear function. Once
the number of layers and the number of units in
each layer was selected, the network’s weights and
thresholds were set in order to minimize the pre-
diction error of the network. This is the role of
the training algorithms.
2
.
2
.Input 6ariables selection
A neural network is usually treated as a black-
box system, i.e. inputs are fed forward, weights
are adjusted by back-propagation of the error and
the outputs are saved. However, we wanted to
look inside the box and to select significant
inputs.
Inputs sensitivity analysis was used to specify
significance of individual molecular descriptor
and to select descriptors that are considered as
most important. Variables with constant low sen-
sitivity and high rating and uncertain variables
with variable ratings that probably carry equally
redundant information were regarded as insignifi-
cant and eliminated from the network.
Sensitivity analysis rates variables according to
the deterioration in modeling performance that
occurs if that variable is not included in the
model. However, input variables are not indepen-
dent and sensitivity analysis does not rate the
significance of inputs in an absolute manner. It
assigns a single rating value to each variable that
cannot reflect the complexity and interdependence
between variables. For that reason, a number of
models with different topology were studied and
variables that always had high sensitivity were
identified as significant.
In addition, inputs activation was used to ex-
amine the activation level (outputs) of the input
neurons. Inputs whose activation was equal to
zero were eliminated.
2
.
3
.Network design
Initial network configuration with one hidden
layer and the number of hidden units set to half
of the sum of the number of input and output
units was generated. The number of hidden neu-
rons and layer was optimized. Five experiments
were conducted iteratively, with each configura-
tion retaining the best network with the smallest
validation error. Repeated training with each
configuration was necessary to avoid undertrain-
ing of the network and stopping at the local
minima. If the network did not achieve an accept-
able performance level due to undertraining, more
neurons or an additional hidden layer were added

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to the hidden layer. In case of over-training (in-
crease of the testing error), the number of hidden
units or layers was reduced.
3. Results and discussion
The first step in developing QSAR was to cal-
culate molecular descriptors. Seventy-one calcu-
lated structural features, including constitutional,
topological, geometrical, quantum chemical and
physicochemical descriptors, were generated for
each drug molecule. The next step was to select
descriptors that effect drug passage into breast
milk.
Selection of the important molecular descrip-
tors and examination of the variable contribution
to the model through output sensitivity is an
important aspect of QSRR study, not only for
ranking the relative importance of each variable
and calculating its statistical significance, but also
asameansofrefining the model by variable
selection. Initially, MLP models with different
topology were trained and tested. Best models,
with low testing error and good predictive perfor-
mance, were selected to perform sensitivity and to
examine the activation level (outputs) of the input
neurons. Inputs whose average activation was
equal to zero and inputs with low sensitivity were
eliminated. New MLP model with 32 inputs was
established. Following this procedure, 14 inputs
were selected in the same way for the next model,
the number of inputs was reduced to 14 and
finally to nine inputs (Table 1). The final model
included percent of oxygen, parachor, density,
highest occupied molecular orbital energy
(HOMO), topological indices (xV2, x2andx1)
and shape indices (k3, k2), as the inputs had four
hidden neurons and one output neuron. The
QSPR that was developed indicates that molecu-
lar size (parachor, density) shape (topological
shape indices, molecular connectivity indices) and
electronic properties (HOMO) are the most im-
portant for the drug transfer into breast milk.
The octanol–water partition coefficient (log P)
is frequently used in quantitative structure–activ-
ity relationships [14]. Partition coefficients thor-
oughly influence drug transport characteristics
and the way drugs reach the site of action from
the site of application (e.g. injection site, gas-
trointestinal tract, etc.). Since drugs are dis-
tributed via the blood, they must penetrate and
traverse many cells to reach the site of action.
Hence, the partition coefficient will determine
what tissues a given compound can reach. Ex-
tremely water-soluble drugs may be unable to
cross lipid barriers and gain access to organs rich
in lipids, such as the brain and other neuronal
tissues. Naturally, the partition coefficient is one
of several physico-chemical parameters influenc-
ing drug transport and distribution, which itself is
only one aspect of drug activity. Lipophilicity is
basically a constitutive property. However, there
is some degree of additivity and lipophilicity (log
P) can be considered as an additive constitutive
property. The contribution of each functional
group and their structural arrangement influences
the polarity and therefore the lipophilic or hy-
drophilic character of the molecule. Any given
moiety with known lipophilicity can serve as a
basic fragment from which the total lipophilicity
can be construed by simple addition of the proper
values. A correction term may be necessary to
account for the constitutive changes introduced
by the substituents, such as branching, double
bonds, folding, intramolecular hydrogen-bonding,
ring joining, etc. However, log Pvalue contains
limited information and becomes insufficient
when topological or stereochemical features of
molecules are analyzed in the context of inter-
Table 1
A subset of selected descriptors used as inputs in QSAR
model, their sensitivity rating report and inputs activation
values
Input activationSensitivity ratingDescriptor
4.0 0.60Oxygen (%)
Parachor 7.5 0.17
8.0Density 0.84
xV2 3.5 0.17
0.162.0k3
k2 1.0 0.22
4.5 0.75HOMO
6.5 0.26x2
0.298.0x1

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molecular interactions with receptors. The model
that was developed did not include lipophilicity,
since the contribution of log Pwas smaller than
that of other descriptors. Parameters that repre-
sent bulk properties, such as parachor and molec-
ular connectivity indices that are directly
correlated with log Pwere included.
The steric effects characterize bulk properties of
a molecule and can be described with molecular
mass, surface area, density and molar volume.
The density of a substance is the ratio of its
molecular mass to its volume and molar volume
can be measured by determination of density of
dilute solutions. Diffusion coefficients for hydro-
carbon systems were successfully estimated from
the molar density [15]. It is shown that the in-
crease in density increases drug transfer to milk,
perhaps due to a decrease in molar volume and
hence molecular size. On the other hand, the
lower the molecular mass of a medication, the
more likely it is to penetrate into human milk,
simply because diffusion through the alveolar ep-
ithelial cell is much easier. Medications with
molecular weights B300 are considered smaller
and will tend to penetrate milk in higher concen-
trations than those with higher molecular weights.
An example of a low molecular weight drug is
ethanol (Alcohol). With a molecular weight of
120, it rapidly equilibrates between the plasma
and milk compartments. Many of the am-
phetamines and diet medications unfortunately
have low molecular weights as well. Drugs with
molecular weights of 600 or greater are unlikely to
penetrate milk in high concentrations. Typical
examples of drugs with high molecular weights
that are basically excluded from milk would in-
clude heparin (30,000) and insulin (6000).
Parachor [16] is an additive physical property
of a substance also related to its molar volume
and is determined by the kind and number of
atoms in a molecule, as well as their manner of
arrangement and binding. Increase in the para-
chor decreases M/P ratio. Small lipid insoluble
substances penetrate cell membranes via the pores
between aqueous phases on both sides of the
membrane. The rate of such passive diffusion
depends on the size of the pores, the molecular
volume of the solute and the solute concentration
gradient.
Over the last 10 years, a variety of topological
and shape descriptors for the characterization of
the molecular structure in combination with
molecular dynamic analysis emerged as alterna-
tive descriptors in quantitative structure-activity
studies [17,18]. The advantage of such descriptors
is that they can be calculated for any chemical
structure, real or hypothetical. Topological in-
dices or numerical graph invariants constitute an
important subset of these theoretical descriptors.
They are suitable for describing similarity or dis-
similarity of molecules. If two compounds have
close values of a number of indices, they can be
regarded as similar. Topological indices are
derived from different classes of weighted graphs,
representing various levels of chemical structural
information. They are numerical quantifiers of
molecular topology and encode information re-
garding the size, shape, branching pattern, cyclic-
ity and symmetry of molecular graphs. A
developed ANN model included topological shape
descriptors of the second and third order, (k2and
k3), connectivity indices of the first and second
order (x0–x2) and valence connectivity index of
the second order.
Topological shape indices [19] are the basis of a
method of molecular structure quantification in
which attributes of molecular shape and size are
encoded into three indices (kvalues 1–3). These
indices are useful in quantification of shape simi-
larity in contrast to the absolute quantification of
size. The kvalues permit a rational prediction of
which molecule has a high degree of shape simi-
larity. Electronic structure is encoded into other
indices. A second application of the kindices is its
use to predict candidate molecule to fill molecular
cavities. With the increasing use of molecular
graphics, the fit docking or intercalation of
molecules into cavities in macromolecular simula-
tions, become an important consideration in drug
design. First order shape attribute provides struc-
tural information related to complexity, or more
precisely, on cyclicity of a molecule. The k2 index
value encodes information related to the degree of
star graph-likeness and linear graph-likeness. It
encodes information about the spatial density of
atoms in a molecule. The k3 values are larger
when branching is non-existent or located at the

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extremities of the graph. The k3 value encodes
information about the centrality of branching.
The second order is defined by the count of
two-bond paths and is related to the shape ex-
tremes represented by star graph or linear graph.
A developed model shows that an increase in k2
decreases M/P ratio due to an increase in molecu-
lar size and lipid solubility, while the increase in
k3 (branching) promote drug transfer into breast
milk. Molecular branching decreases molecular
size, decreases molecular length and increases
molecular complexity and perhaps decreases
protein binding.
Molecular connectivity is a method of molecu-
lar structure quantification based only on bonding
and branching patterns rather than physical or
chemical characteristics. Weighted counts of sub-
structure fragments are incorporated into numeri-
cal indices. Structural features, such as size,
branching, unsaturation, heteroatom content and
cyclicity are encoded. These indices are related to
the number of atoms and how they are connected
in a molecule. Only the carbon or heavy atoms
are taken into consideration and the connectivity
indices are derived from the hydrogen-suppressed
graph of the molecule. Each atom is represented
by a vertex in the graph, while the bonds becomes
edges. Valence connectivity index [20] uses the
same invariant but modifies vertex degrees to
account for heteroatoms by using the number of
valence electrons in the corresponding atom.
The molecular connectivity indices, xvalues,
describe the extent of skeletal branching. Connec-
tivity indices are descriptor of molecular struc-
ture, a descriptor of size and shape based on a
count of groupings of skeletal atoms, weighted by
degree of skeletal branching. Each carbon atom in
a molecular skeleton is assigned a number accord-
ing to its number of neighboring carbon. The
molecular skeleton is then fragmented into all its
two carbon atom bonds. The sum of these values
over the structure forms the xindex. Molecules
could be further dissected into two bond frag-
ments, three bond fragments and so on. Molecu-
lar structure is quantified so that weighted counts
of substructure fragments are incorporated into
numerical indices and an index is derived from a
consideration of pairs of atoms forming bonds.
The x0, zeroth order (atomic) connectivity index,
conveys information about the number of atoms
in a molecule. The x1 index encodes size and
branching information. The x2 encodes even more
specific information about skeletal branching.
These indices are correlated to molar volume [21].
Increase in x1, (bond) and x2 (path) connectivity
indices decreases drugs transfer into milk. Molec-
ular connectivity index of the first order, x1,
encodes single bond properties. It is a weighted
count of bonds, related to the types and position
of branching in the molecule. Molecular connec-
tivity index of the second order, x2, is derived
from fragments of two-bond length. It also pro-
vides information about types and position of
branching and may be an indication of the
amount of structural flexibility. An increase in
branching increases surface area and molecular
volume [22] and results in the increase of solubil-
ity and lower partition coefficient. A statistical
analysis has shown that x1 and x2 are covariant
to an extent. However, there is enough difference
between the information in x1andx2toreflect
structural features contributing in a different way
to the numerical value. The x2 can differentiate
between structural isomers, while x1 values are
identical. Low values of x1 and x2 are found for
more elongated molecules or those with only one
branching atom. An increase in the length of the
carbon chain, non-polar portion of the molecule,
results in the increase in lipid-solubility (log P)
and an increase in molecular length.
Although solubility parameters, topological
shape and connectivity indices are often successful
in rationalizing solubilities and partition coeffi-
cients, they cannot account for conformational
changes and they do not provide information
about electronic influence through bonds or
across space. For that reason, quantum chemical
descriptors are used in developing QSAR. Quan-
tum chemical descriptors can give great insight
into structure and reactivity and can be used to
establish and compare the conformational stabil-
ity, chemical reactivity and inter-molecular inter-
actions. They include thermodynamic properties
(system energies) and electronic properties
(LUMO or HOMO energy). Electronic properties
may play a role in the magnitude in a biological

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110
activity, along with structural features encoded in
indexes. The developed model contained HOMO
energy. Electronic effects are quantified explicitly
by the use of molecular orbital calculations to
estimate HOMO energy. In the case of an unsatu-
rated compound, HOMO energy is a good de-
scriptor that presents the distribution of p
electron and explains p–pcharge transfer interac-
tion. The high electronic density and high frontier
orbitals are present in molecules with high elec-
tron delocalization and can be used to predict
biological reactivity. An increase in molecular re-
activity also increases metabolic processes. There-
fore, higher reactivity is to be expected for the
molecules with higher HOMO energies. The
HOMO energy plays a very important role in the
nucleophylic behavior and it represents molecular
reactivity as a nucleophyle. Good nucleophyles
are those where the electron residue is high lying
orbital. As expected, molecules with lower LUMO
energy have a higher M/P ratio.
Chemical composition (weight percent of oxy-
gen in molecular mass) also plays an important
role. Presumably, weight percent of oxygen is
related to the presence of the polar functional
group. Polar functional groups account for many
of the dipole–dipole, dipole-induced dipole and
hydrogen bond interactions. They accommodate
additional interaction in polar and in hydrogen-
bonding compounds. Hydrogen bonding can be
facilitated by the presence of hydroxyl groups.
Dipole interactions are related to dipole moment
of a whole molecule or part of a molecule, such as
functional group, e.g. nitro. An increase in the
weight percent of oxygen resulting in the increase
in the high charge-transfer properties (dipole, ni-
tro group) and hydrogen bonding, decreases drug
transfer into milk and M/P ratio.
Predicted M/P values were within the range or
close to the experimentally measured M/P ratio
values (Table 2). In order to evaluate predictive
performance of the final model, percent of testing
and validation data set was gradually increased
on account of the training data set and the rela-
tive error in prediction was monitored. Increasing
the testing data up to 30% and validation data set
up to 45% did not influence the network
performance.
The predictive performance of the upgraded
ANN model was better for basic drugs (cime-
tidine, mefloquine, morphine, methadone,
nadolol) than that with the logarithmically trans-
formed phase distribution model. For the loga-
rithmically transformed phase distribution model,
examinations of residual plot for acidic drugs
indicated that penicillin was an outlier. The model
also predicted lower M/P ratio for sertraline than
the experimentally derived value taken from the
literature. Study on the infants’serum sertraline
concentrations show that the concentration of
detectable sertraline is below the detection limit of
most commercial laboratories [23]. The absence of
detectable serum sertraline levels in the infant
suggests that if medication were present in infant
serum, its concentration would be extremely low
[24]. Future studies of breast milk and infant
serum samples should address these issues. Higher
M/P values were predicted for ethanol, propra-
nolol, oxprenolol, phenacetin, paracetamol, rox-
ithromycin, minoxidil, zolpiderm, zonisamide,
verapamil.
Alcohol can pass into a mother’s milk very
quickly and then out of the blood system (and
milk) in a relatively short time, depending on the
amount consumed. Alcohol levels in the milk
peak 30–60 min after drinking or 60 –90 min if
the drink is taken with food. Beer has been used
for years as a stimulant to breast milk production.
This may be due to beer’s ability to increase
prolactin in men and non-lactating women. The
active ingredient in beer is reported to be various
B vitamins or ‘Brewer’s yeast’. Conversely, alco-
hol can inhibit milk ejection reflex in a dose
dependent manner [25]. Several factors influence
how much of a given drug, such as alcohol, will
pass from the maternal circulation into the breast
milk. Those factors include the pharmacokinetic
properties of the drug and its metabolism, as well
as the drug’s solubility in water, pH, molecular
weight and degree with which it binds to proteins
[26]. Alcohol concentration in milk is similar to
that in the blood and alcohol’s elimination from
blood and milk is closely correlated.
The fat and protein composition of human milk
changes dramatically in the first several weeks
postpartum. Milk whey and total proteins content

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Table 2
Predictive performance of the developed model
Drug Experimental M/PPredicted M/P
Average Minimum Maximum
2.35Acyclovir [29,30] 0.62.31 4.1
Amitriptyline [31–34] 1.28 1.53 0.5 1.93
Amoxycillin [35] 0.0280.089 0.013 0.043
5.15 2.85.18 7.5Amphetamine [36]
0.295 0.01Ampicillin [37] 0.580.15
1.63 0.061.05 3.2Aspirin [38–40]
4.08Astemizole [41] 4.4 4.4 4.4
2.1 1.12.16 3.1Atenolol [42,43]
0.36Bupivacaine [44] 0.34 0.10 0.58
Bupropion [45] 5.5455.43 5.545 5.545
0.711 0.610.77 0.812Caffeine [46,47]
4.24 0.08Cannabis [48] 8.43.88
0.79 0.790.85 0.79Carbamazepine 10,11-epoxide [49,50]
0.74Carbamazepine [50,51] 0.465 0.24 0.69
0.02 0.020.058 0.02Carbenicillin [51]
0.08Cefotaxime [52,53] 0.16 0.16 0.16
00Cefoxitin [54] 00.04
0.045 0.030.08 0.06Ceftriaxone [55]
0.012 0.01Cephalexin [56] 0.014−0.03
0.655 0.6550.65 0.655Chloramphenicol [57]
2.08Chlorprothixene [58] 1.48 0.38 2.58
1.7 1.71.74 1.7Cimetidine [59–61]
1.5Ciprofloxacin [62] 1.495 0.85 2.14
2.1 1.2 3.0Citalopram [63] 1.06
0.375 0.250.54 0.5Clemastine [64]
1.35 1.35Clofazim 1.351.46
1.03 0.840.92 1.22Clomipramine [65]
0.33 0.33Clonazepam [66,67] 0.370.23
3.555 2.793.84 4.32Clozapine [68]
2.16 2.16Codeine [69] 2.162.28
0.78 0.780.74 0.78Cotinine [70]
0.89Decarboetoxyloratadine [71] 0.8 0.8 0.8
1.75 1.01.92 2.5Demethylcitalopram [64]
0.915 0.63Desipramine [72,73] 1.20.92
1.275 1.021.32 1.53Desmethyldoxepin [74]
0.86Diazepam [75,76] 0.7 0.1 1.3
0.98 0.980.93 0.98Diltiazem [77]
1.04Disopyramide [78,79] 0.9 0.9 0.9
1.63Dothiepin [80] 1.59 1.27 1.91
1.18 0.891.12 1.47Dothiepsulfoxide [80]
1.37 0.4Doxepin [75] 1.651.24
0.34 0.320.49 0.36Doxycycline [42]
0.39Erythromycin [42] 0.455 0.41 0.5
0.9 0.92.72 0.9Ethanol [81,82]
0.83Ethosuximide [83,84] 0.8 0.8 0.8
0.54 0.54Flunitrazepam [85] 0.540.54
0.68 0.521.07 0.84Fluoxetine [86]
0.44 0.44Gentamicin [87] 0.440.47
0.64 0.590.50 0.69Holoperidol [88,89]
0.14Ibuprofen [90,91] 0 0 0
0.76 0.761.25 0.76Imipramine [42,74]

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Table 2
(
continued
)
Predicted M/P Experimental M/PDrug
Average Minimum Maximum
0.01Indomethacin [92] 0.37−0.11 0.19
Labetalol [93] 1.7 0.8 2.62.0
Lamotrigine [94] 0.40.25 0.450.425
0.25 1.891.07Lidocaine [45] 1.27
1.2 1.2Loratadine [72] 1.07 1.2
0.15 0.260.205Lorazepam [95] 0.23
0.721.99 0.72 0.72Medroxyprogesterone [96]
0.13 0.160.1450.18Mefloquine [97]
2.63.4 1.0 4.2Mepindolol [98]
Methadone [99,100] 0.240.95 0.640.44
0.04 0.040.040.08Methotrexate [101]
0.265 0.265Methyldopa [102] 0.34 0.265
2.0 3.12.55Metoprol [103] 2.48
0.951.11 0.9 1Metronidazole [104–106]
0.79 1.891.341.55Mexiletine [107]
2.21.99 2.2 2.2Mianserin [42]
0.76 0.76Minoxidil [108] 2.49 0.76
0.69 0.750.72Moclobemide [109] 0.97
2.46 2.46Morphine [110,111] 2.59 2.46
4.6 4.64.6Nadolol [112] 4.65
1.641.01 1.64 1.64N-desmethylsertraline [113]
1.2 1.21.21.61Nefopam [114]
2.251.7 1.5 3.0Nicotine [71,115]
Nitrazepam [42] 0.270.15 0.270.27
0.35 0.350.35Nitredipin [116] 0.62
2.25 2.25Nitrofuranthoin [117] 1.32 2.25
0.69 1.010.85Nordothiepin [81] 1.39
1.861.69 1.57 2.15Nordothiepsulfoxide [81]
0.19 0.190.191.19Norethindron [42]
0.560.63 0.56 0.56Norfluexetine [87]
0.35 0.77Norfluoxetine [87] 0.81 0.56
0.50 1.621.18Nortriptyline [118,119] 0.98
0.29 0.29Noscapine [120] 0.96 0.29
2.8 3.83.3O-desmethylvenlafaxine [121] 5.27
0.11 0.1 0.33Oxazepam [122,123]
0.37 0.370.371.42Oxprenolol [124]
0.885.28 0.76 1.0Paracetamol [125,126]
0.39 1.11Paroxetine [127–129] 1.09 0.75
0.37 0.370.370.39Penicillin V [130]
0.06 0.57Penicillin G 0.17 0.315
0.7 1.10.9Perfenazine [131] 0.9
0.672.85 0.67 0.67Phenacetine [132]
0.4 0.60.5−0.14Phenobarbitone [133]
0.3630.03 0.142 0.584Phenytoin [134,135]
0.13 0.13Prednisolone [136,137] 0.14 0.13
3.2 3.23.2Procainamide [138] 1.53
0.107 0.699Propranolol [139,140] 2.99 0.403
4.13 4.134.13Quazepam [141] 1.21
0.120.42 0.12 0.12Quinapril [142]
0.12 0.120.12Rosaramicin [143] 1.42

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Table 2
(
continued
)
Drug Experimental M/PPredicted M/P
Average Minimum Maximum
0.035 0.031.85 0.04Roxithromycin [144]
6.58Satalol [145,146] 5.4 5.4 5.4
0.28Sertraline [147,148] 1.275 0.62 1.93
0.1 0.12.59 0.1Sulfamethoxazole
Sumatriptan [149] 4.94.11 4.1 5.7
0.014 0.0140.0001 0.014Suprofen [150]
0.95Temazepam [151] 0.14 0.14 0.14
0.03Tetracycline [42] 0.95 0.6 1.3
0.82 0.820.89 0.82Theobromine [152]
0.0001Theophylline [153] 0.7 0.7 0.7
0.44 0.430.41 0.45Tiapamil [154]
0.8 0.8Timolol [125] 0.81.4
1.005 1.0053.36 1.005Tinidazole [155]
0.15Tolmetin [156] 0.005 0.005 0.005
0.53 0.51.21 0.56Triprolidine [157]
0.72Valproic acid [158] 0.053 0.01 0.096
3.84Venlafaxine [122] 3.8 2.8 4.8
0.6 0.62.55 0.6Verapamil [159]
Vigabatrin [160] 10.60 1.0 1.0
0.13 0.131.21 0.13Zolpidem [161]
0.93 0.84 1.02Zonisamide [162] 3.47
0.555 0.41 0.700.17Zopiclone [163]
decreases as lactation progresses, but changes in fat
levels are usually not statistically significant. Beta-
adrenergic antagonists are one of the most com-
monly used class of agents in the treatment of
hypertension, angina pectoris and certain arrhyth-
mias. Experiments show that M/P ratio of propra-
nolol increases during the first several weeks
postpartum, due to changes in milk pH and total
serum protein content [27]. The issue of prescrip-
tion of analgesics during lactation is also complex.
Most of the information available is based on single
dose or short term studies and for many drugs only
a single or a few case reports have been published.
Minoxidil has not been studied in pregnant
women. However, there have been reports of babies
born with extra thick or dark hair on their bodies
after the mothers took minoxidil during pregnancy.
Minoxidil passes into breast milk, it has not been
reported to cause problems in nursing babies.
Norethindrone is a progestational agent. Al-
though progestins pass into the breast milk, they
have not been shown to cause problems in nursing
babies. However, progestins may change the qual-
ity or amount (increase or decrease) of the mother’s
breast milk.
Roxithromycin, a new macrolide antibiotic is
rapidly absorbed after oral administration. Peak
plasma levels following 150 and 300 mg doses occur
within 2 h. Steady state is reached within 4 days
with doses of 150 mg twice a day or 300 mg once
daily. The plasma half-life is :12 h.
Verapamil is known as a calcium channel
blocker. Calcium channel blocking agents have not
been studied in pregnant women. However, studies
in animals have shown that large doses of calcium
channel blocking agents cause birth defects, pro-
longed pregnancy, poor bone development in the
offspring and stillbirth. Verapamil is excreted in
breast milk. It may be necessary to change therapy
or provide an alternate to breast milk.
All of the psychotropic medications studied to
date pass into breast milk. The data regarding the
degree of passage to the infant and the subsequent
effects of this exposure on infant growth and
development are very limited. The apparent elimi-
nation half life for zolpidem is 2.6 h. Experimen-

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tal value for M/P ratio of the zolpidem 3 h after
administration is 0.13 and no detectable zolpidem
can be found in the milk at subsequent sampling
times. Zolpidem belongs to the central nervous
system (CNS) depressants. It is used to treat
insomnia. Zonisamide, anticonvulsant is used in
the treatment of epilepsy. It passes into breast
milk. However, it is not known whether this
medicine causes problems in nursing babies. Psy-
chotropic medications pass into breast milk to
some degree, mostly through the process of pas-
sive diffusion [15,16]. However, a drug’s protein
binding, lipid solubility, degree of ionization (or
pK
a
), and molecular weight also influence the
extent of passage of a compound and the amount
that remains in breast milk.
In addition, predicted M/P ratio for ibuprofen
was slightly higher than the experimentally deter-
mined ratio. The absorption of ibuprofen is rapid
and complete when given orally. The area under
the plasma concentration–time curve (AUC) of
ibuprofen is dose-dependent. Ibuprofen binds ex-
tensively, in a concentration-dependent manner,
to plasma albumin. At doses \600 mg, there is
an increase in the unbound fraction of the drug,
leading to an increased clearance of ibuprofen and
a reduced AUC of the total drug.
4. Conclusion
A nine-descriptor nonlinear computational neu-
ral network model has been developed for the
estimation of M/P ratio values for a data set of
123 drugs. Unlike previously reported models, the
QSPR model described here does not require ex-
perimental parameters and could potentially
provide useful prediction of M/P ratio of new
drugs and reduce the need for actual compound
synthesis and M/P ratio measurements. Model
can be used to estimate the activities of other
molecules only from a sketch of their structure
and this approach might also be useful for drug
information service.
Regardless of the model or method used to
estimate drug transfer into breast milk, these pre-
dictions should only be used to assist in the
evaluation of risk, in conjunction with assessment
of the infant’s response.
Toxicity in the infant is not the only potential
adverse effect of maternal medication use. Recent
research has revealed an effect on infant
metabolism. Maternal use of medications, which
induce hepatic metabolism, appears to stimulate
the breastfeeding infant’s liver as well as the
mother’s. In a similar manner, drugs that inhibit
metabolism have been found to slow function in
both mother and child [28].
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