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kernel (mostly used in image analysis) and the hyperbolic tangent kernel [318] (that
often plays the role of proxy in neural networks).
Once the kernel has been chosen, the best hyperplane to separate the two groups
has to be determined. In SVM, the maximum-margin hyperplane is chosen. This
hyperplane is the best one with regard to the Vapnik–Chervonenkis theory. This is
limiting overfitting (i.e., making a very precise definition of the lea rning sample but
losing any ability to generalize to new data), which is a risk when involved with very
high dimensional spaces.
A tolerance to misclassifications on either side of the hyperplane has to be
introduced since it is rare to have perfectly linearly separable observations. This is
performed through the introduction of an error penalty, which is chosen by the user
and allows a trade-off between a large margin and a small number of errors. This is
called the soft margin. The final optimization issue is a classical one solved by usual
optimization algorithms.
Possible Extensions SVM can be extended to classify more than two groups.
Generalizing a method designed to classify two groups consists in reducing the
multiclass problem into several two-class problems. There are two approaches: the
one-versus-one where each group is compared to each other and the one-versus-all
comparing each group to the other ones. The former one is the most frequently used. In
this approach, each comparison outputs a vote for one class and the majority class is
assigned. SVM can also be used to perform regression. SVM principle has been used
in several other contexts to perform nonlinear transformations before applying other
methods (kernel-PCA, kernel-PLS, etc.).
2.6.4 Decision Trees
2.6.4.1 Aim A decision tree is a simple supervised model, which explains and
predicts one response variable (discrete or continuous) taking into account numerous
descriptors/features. DTs are based on tree diagrams where leaves or nodes represent
classifications and branches represent conjunctions of features that lead to those
classifications. DTs correspond to a binary recursive partitioning process since parent
nodes are split into two child nodes and recursive because it can be repeated by treating
each child node as a parent. The first step of DT is splitting each parent node in two
children nodes using some split index, and then deciding when a tree is complete. A
splitting rule showing maximal index value is regarded as the best rule among possible
splittingrules. Each terminal node of the tree is assigned to a class outcome or predicted
value. Pruning can be used to avoid overfitting. Pruning cuts deepest subtrees of the
built decision tree according to their potential generalization performance.
Classification tree analysis is possible when the predicted outcome is the class to
which the data belong (discrete outcome, e.g., active versus inactive compounds).
Regression tree analysis is when the predicted outcome can be considered as a real
number (continuous outcome as solubility, permeability values of drugs). Classification and regression tree (CART) analysis, first introduced by Breiman et al. [319],
is used to refer to both the above procedures. Figure 2.32 represents an example of
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a diagram tree to predict molecules of three types Y ¼ (YA, YB, YC) using three
descriptors (X
1
, X2, X3). DT creates a branching structure in which the branch at each
intersection is determined by a rule relating to one of the three descriptors for the
molecules and final leaves are assigned to the dominant type among the observations
falling in each leaf. DT is a simple method, easy to understand and interpret.
2.6.4.2 Examples of ADME/Tox Application DT approach has been applied in
combinatorial library design, prediction of “drug-likeness” as a general property,
prediction of specific biological activities, and on some specific compound profiling.
With discrete outcome, decision trees are used for the identification of substructures that discriminate activity from nonactivity within a given collection of compounds [320–323]. DT approach allows to estimate the conditional probability of
activity given the combination of substructures present (or absent) in a given
collection of compounds while accounting for the abundance of substructures within
the library [323]. Once identified, each of these discriminating substructur es are tested
statistically for enriched activity and compared to the privileged substructures
reported in the literature. DTs are also used for the classification of chemical
compounds into drug and nondrugs [111, 324]. In Schneider et al., DT interpretation
suggested the main criteria for separating drugs from nondrugs. These were a
molecule weight higher than 230 Da, a molar refractivity higher than 40, and the
presence of ring(s) as well as one or more functional groups. This approach resulted
in at least 39% of the nondrugs filtered out, while retaining more than 83% of the
actual drugs.
Figure 2.32 DT example. Diagram tree predict molecules of three types Y ¼ (YA, YB, YC) using
three descriptors (X
1
, X2, X3). First discriminant descriptor is X1, related to threshold t1; for
branch X
1
> t1: discriminant descriptor is X2, related to threshold t2, allowing to predict
Y
A(X2
> t2) else YC(X2 t2); for other branch (X1 t1): descriptor X3, related to t3, predict
Y
c(X3
> t3); and else (X3 t3), descriptor X1predict YA(X1> t12), either YB(X1 t12).
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With continuous outcome, decision trees are also used to predict ADME/Tox
properties such as absorption properties [317, 325], solubility or permeability of
drugs [326], distribution properties [327], P-glycoprotein [328] or BBB penetration
[329], and metabolic stability [330]. For toxicity properties, DTs are used to predict
hERG inhibition [202] and toxicity involving cytochrome P450 such as six CYP
isoforms [331], 2D6 and 1A2 isoforms [193, 312], or the 3A4 isoform [332].
2.6.4.3 Usage Warning The main issue with DT is to choose the “best” appropriate index to split parent node into two child nodes and to decide when a tree is
complete. If the target is a classification outcome, different measures of node impurity
for splitting nodes and pruning the tree can be used as misclassification errors. Gini
index and cross-entropy or deviance are the most common measures of error [88].
For regression, the squared-error node impurity measure can be used.
The preferred strategy for pruning is to grow a large tree T0, stopping the splitting
process only when some minimum node size is reached. The large tree is pruned using
cost-complexity pruning. By using five- or ten-fold cross-validation, the subtree
(obtained by pruning T0 that is collapsing any number of the internal nodes) is
established, which minimizes the cost complexity.
One major problem with trees is their high variance. Often a small change in the
data can result in a very different series of splits, complicating the interpretation. This
instability is due to the hierarchical nature of the process: the effect of an error in the
top split is propagated down to all the splits below.
DTs are valuable even with complex data or with a few observations (pruning). It
is an appropriate choice from even a very large set of input descriptors due to the
recursive partitioning strategy. It results in a descriptive means for calculating
conditional probabilities and does not need any preselection of informative variables.
To conclude, decision trees are conceptually simple yet powerful and, easy to
understand. Classification scheme can be easily interpretable with the most significant
descriptors usually appearing at early decision nodes.
2.6.4.4 Technical Description
Input Data Data come in records of the form (x, y) ¼ (x
1
, x2, x3, ..., xp, y): the
description of n individuals by p descriptors (x
1
, x2, x3, ..., xp) and the vector y of
length n containing the data to be predicted (either discrete or any continuous
variable).
Output The dependent variable, y, is the target variable to understand, classi fy, or
predict. To follow the decision tree (with binary decisions obtained on most
significant descriptors) allows assigning one y value to each leaf, indicating either
the predicted group or the predicted value of the target variable. DT can describe or
predict continuous output or discrete one (for two or more groups).
Description The goal is to create a model that predicts the value of a target variable
based on several input variables. Each interior node is split according to a dichot-
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omous decision based on one of the input variables. There are two edges to children
for each of the possible types of values of that input variable. Each leaf is assigned a
value that is the predicted one for observations following the path leading to this leaf.
A tree can be “learned” by splitting the source set into subsets based on an attribute
value test.
A decision criterion based on maximal purity results in a mixture of classes in the
children nodes that are lower than in the parent node. To construct the tree, the “best”
division in term of purity criterion is chosen for the p descriptors x. The descriptor
(associated to its best division), which results in the best decision in term of purity
criterion among all descriptors, is chosen for the first branching. A splitting rule
showing a maximal Gini index value is regarded as the best. This process is repeated
on each derived subset or node in a recursive manner and is called recursive
partitioning. The recursion is completed when the subset at a node has the same
value as the target variable, or when splitting no longer adds value to the predictions.
Each node of the tree is assigned to a class outcome or predicted value regression. To
avoid excessive partitioning, there exist some techniques of pruning to optimize the
tree. The pruning component of CART is analogous to the backward elimination
approach in regression analysis. This idea provides a control for tree sizes, thus
reducing the prediction error of the tree for new data not seen in the learning process.
In the CART pruning process, Breiman et al. [333] use a linear combination of the
expected loss of the decisions by the tree and the total number of the terminal nodes
of the tree. A new observation follows the tree with a particular path and is affected to
the corresponding final node.
Possible Extension The other popular methodology is C5.0, which uses a different
scheme for deriving rule sets resulting in simpler trees [334]. A random forest
combines many decision trees, in order to improve the classification rate. It is a
relatively new technique introduced by Breiman in 2001 [335]. In random forest,
training data are randomly selected for replacement from the original training data.
The forest chooses the most popular class having most votes over all the trees in the
forest.
2.6.5 Neural Networks
2.6.5.1 Aim Neural network (NN) attempts to mimic a network or circuit of
biological neurons [336]. Each unit represents a neuron, and the connections represent
synapses. The modern usage of the term often refers to artificial neural networks,
which are composed of interconnecting artificial neurons or nodes (programming
constructs that mimic the properties of biological neurons). NN result in powerful
nonlinear statistical models. The central idea of NN is to extract linear combinations
of the inputs as derived features, and then model the target as a nonlinear function of
these features. An NN is a two-stage regression or classification model, typically
represented by a network diagram (Figure 2.33). Derived features Z
m
are created from
linear combinations of the inputs, and then the target Y
q
is modeled as a nonlinear
function of Z
m
, using an activation function. This function performs a linear
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transformation for small coefficients but progressively implies nonlinear transformation when the coefficient values increase. The units in the middle of the networks,
computing the derived features Z
m
, are called hidden units because the values Zmare
not directly observed. In general there can be more than one hidden layer. The result is
a powerful learning method with widespread applications in many fields. It is often
difficult to decode the final model to identify the changes to molecular structure
needed to obtain a desired property. NNs also have a tendency to “memorize” rather
than learn and are particularly susceptible to overfitting, especially if the training data
are noisy.
2.6.5.2 Examples of ADME/Tox Applications The application of NNs in the field
of ADME/Tox predictions was initiated in the 1990s to predict physicochemical
properties of molecules such as aqueous solubility [337] and lipophilicity [338]. In
the early 2000s, more sophisticated NN techniques have gradually emerged and
been applied to this area [339]. With discrete outcome, filter programs have been
established that use large databases of drug and nondrugs [111, 340]. These programs
used NN approaches together with topological descriptors to encode the molecular
structures.In these papers, the NN classificationmethod has been found to discriminate
between drug-like chemical matter (represented by databases such as CMC, MDDR,
WDI) and nondrug-like chemical matter (represented by dataset such as ACD). The
result was 80–90% of the compounds were correctly classified as drugs or nondrugs.
With continuous outcome, NNs are used for prediction of lipophilicity and aqueous
solubility of chemical compounds [341]. The ALOGPS 2.1 package, based on
associative neural networks, combines k-nearest-neighbor and ANN methods on
several datasets to careful ly analyze the associative neural network parameters. The
predictive ability of associative neural network for the training sets was estimated
using the leave-one-out method.
For ADME/Tox properties, NN have been used to predict solubility, distribution [327], P-glycoprotein [183], for QSAR modeling of human serum protein
binding [342], or absorption [343, 344]. For Toxicity properties, NN have been
Figure 2.33 Left: Schematic representation of a single hidden layer, feed-forward neural
network. Right: The sigmoid function, the red zone shows that for x values near from 0, the
sigmoid function is approximately linear.
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used to predict P450 1A2 inhib ition [312], P450 2D6 [345], P450 3A4 inhibition [346, 347], and to predict whenever a compound might be cytotoxic [348].
2.6.5.3 Usage Warning Training neural networks is quite an art. As NNs are
iterative processes, initialization of the coefficients is required. Usually, small
coefficients are initially provided leading to a model that is not far from the linear
one. It aims at providing a simple model that is not overfitting the training data. More
complex transformations are derived during the training process if regularization is
well controlled. In order to facilitate the coefficient initialization, a prior scaling of
inputs (leading to zero mean and unit variance) is recommended (see PCA for more
details about data scaling). In addition, the objective function often possesses many
local minima. Different initializations can lead to different solutions. Several initial
parameter sets to obtain a more reliable final solution should be attempted.
The number of hidden layers and of units generally has to be provided by the user.
With too few hidden units, the model might not have enough flexibility to capture
the nonlinearities in the data. Too many hidden layers are likely to produce overfitting
models. However if regularization is well controlled, useless layers will simply
reproduce the results obtained in the previous ones. Choosing a high number of hidden
layers should not be a problem if the required work on regularization has been
performed (see Section 2.6.5.4 for more details). Typically the number of hidden units
is in the range of 5–100, with the number increasing with the number of inputs and
number of training cases. Choice of the number of hidden layers is guided by
background knowledge and experimentation.
Finally, neural networks are complex models but they are likely to be very efficient
if well tuned. The model is generally overparameterized, and the optimization
problem is nonconvex and unstable unless certain guidelines are followed. Similar
to SVMs, NN models cannot be interpreted in terms of relationships between input
and output variables.
These tools are especially effective in problems with a high signal-to-noise ratio
and settings where prediction without interpretation is the goal. They are not effective
to describe a process and the roles of individual inputs. Each input enters the model
in many places in a nonlinear fashion.
2.6.5.4 Technical Description
Input Data This method is based on the description of n individuals by p descriptors
collected in a matrix having n rows and p columns, called X, and of the values of q
response variables measured on the same n individuals and collected in Y.
Output The predicted values of Y are provided. The final coefficients applied to each
input variable and internal node are generally given.
Description NNs are a wide category of methods aiming at performing nonlinear
regression and classification. In general, they tend to imitate biological neurons
behavior. Simple units receive information and produce other information in order to
achieve a given goal.
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Figure 2.33 outlines the main features of a very simple NN. Input variables are
combined in one layer of hidden units via linear combinations. Inside these hidden
nodes, an activation function is applied to the result of the linear combination
producing one value. This activation function is typically a sigmoid one (or sometimes
radical basis function). As shown in Figure 2.33 (right), the sigmoid function is
approximately linear at approximately zero. If the norm of the vectors containing
the coefficients applied in the linear combination is not far from zero (i.e., if all the
coefficients are small), the corresponding hidden unit can be considered as only
performing linear transformation. To the contrary, higher coefficients imply a
nonlinear transformation. The values provided by the hidden layers are linearly
combined in each output variable and the obtained value is transformed by the output
function. This function is usually the identity function for regression (the value
remains unchanged) and the softmax function for classification (allowing one to
obtain a probability for each class). There may be several hidden layers performing
successive transformations.
In order to train a neural network an objective function is required. For regression,
the sum of squared differences between the true and predicted values is used. The
same method can be applied in classification as well as other functions such as crossentropy (which measures the quantity of disagreement between true and predicted
values). In order to minimize these objective functions, back propagation (also called
gradient descent) is used. It consists in adapting the coefficients applied to each hidden
unit (to obtain the output values) according to their contribution to the global error. It is
possible to propagate these contributions to the linear combinations implying the
input variables and to perform similar coefficient corrections. This process is repeated
until convergence (there are no more changes in the coefficients) or a user-defined
maximum number of iterations is reached. In this correction step, a penalty is applied
to control regularization (the ability to generalize to new observations). This consists
in penalizing high coefficients, which lead to highly nonlinear functions and thus to
potential overfitting. This tuning parameter is often chosen through cross-validation.
Possible Extensions Many extensions have been proposed. They generally rely on
changes concerning topology of connections between units (cycles can be allowed),
using combination functions (weighted linear combinations, for example), activation
and output functions, and learning algorithm.
2.7 CONCLUSIONS
In summary, although many currently developed molecules tend to challenge known
rules, the alliance of medicinal chemistry and drug-metabolism pharmacokineticsADME/Tox has made a substantial impact on quality of drug candidates [125]. As
new regions of the chemical space are explored, there will be a need to continue to
explore the boundaries of the drug-like chemical space in order to be able to rationally
design and balance the physicochemical properties of a drug candidate. Here, in silico
tools greatly assist the decision-making process [198, 349, 350]. A major challenge is
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to forge a comparable partnership with preclinical pharmacology such that concentration–effect relationships equal the pharmacokinetic structure–activity relationships in lead optimization. Many other obstacles await such as designing better drugs
for children and the elderly using ADME/Tox issues [351–353] and better assessment
of interindividual variability [354, 355]. Pharmacogenomics, genotyping, toxicogenomics, proteomics, metabonimics and metabolomics, chemogenomics, structural
biology, chemical systems biology, mapping adverse drug reactions in chemical
space, integration and annot ation of the data, merging chemical and biological space,
generation of drug–target networks, new algorithms, will all play a key role in
understanding drug responses in different patients relative to their genetic constitution
and in improving the predictive character of in silico methods [151, 356–362]. New
experimental approaches and computer technologies will contribute to this process
[67, 191, 363]. Better understanding of serious adverse drug reactions (SADRs)
already allows for the development of the web-hosted tool such as SePreSA [364]
http://sepresa.bio-x.cn/. SADRs are caused by unexpected drug–human protein
interactions, and some polymorphisms within binding pockets make these populations more susceptible to drug attack (e.g., Vioxx, 2004 or Avandia, 2007). While
automating every modeling task, it will be important to not transform the in silico
processes into black boxes. Ultimately, new predictive methods will be developed in
the coming years integrating new experimental data and theoretical concepts.
Mutations or single nucleotide polymorphisms in drug-metabolizing enzymes and
for other ADME/Tox involved proteins, age, pathology-dependent variations will be
considered. From a patient and clinician perspective, it is imperative that new
predictive methods are pursued to administer inherently less toxic drugs coupled to
the identification of genetically susceptible patient groups. All these will take time
and require important financial investment. Further, this should be accomplished
while limiting as much as possible animal experimentations. We do hope that this
chapter provides the readers with a global picture of different concepts currently used
or emerging in the field of in silico ADME/Toxpredictions. Definitively, this area will
remain a challenge for at least the next 20–50 years.
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Соседние файлы в папке Библиотека им академика М.И. Перельмана
