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Algorithmic analysis of functional pathways affected by typical and atypical antipsychotics Arsen Arakelyan, Anna Boyajian, Levon Aslanyan, David Muradian, and Hasmik Sahakyan "Laboratory of Information Biology" Project of the Institute of Molecular Biology and Institute for Informatics and Automation Problems National Academy of Sciences of Republic of Armenia Yerevan, Armenia e-mail: [email protected]

A different situation appears in area of pattern recognition The advantages of atypical vs. typical neuroleptics have been (PR). There is no satisfactory statistics in this case. These demonstrated in a number of clinical trials. Differences in heuristics are more responsible and conditional. Learning set functional pathways affected by typical and atypical is given as a limited number of known classifications but it antipsychotics in the brain have been assessed using Gene Set has to be large enough to describe the class properties in Enrichment Analysis. Data on gene expression, obtained from application area. A number of basic approaches are known in Gene Expression Omnibus, is a numerical array of size PR - Metric Algorithms, Logic Separation (LS), Neural 4x17000, which can be treated directly neither by statistical Networks, etc. One of the well-known classes of metric approach nor by means of classification and pattern algorithms is the voting (or estimation calculation) model [1]. recognition regular theory. Extended logic-combinatorial This is an algorithmic model with a number of additional scheme is designed for the treatment of this kind data set. parameters, requiring optimization during the learning stage. Applied results show that atypical neuroleptics have less The dataset of gene expression, being considered, structurally effect on pathways related to neurodegeneration, cognition, obeys neither statistical requirements nor – of pattern neuronal architectonics, as well as stimulation of recognition. Two classes are given, two learning examples in inflammatory processes. each. Instead, the features set is very large. All these raise a novel very specific situation for data analysis, when it is necessary to recover the limited and valuable knowledge Keywords
contained in such structures. ANOVA methods are the typical Pattern Recognition, Functional Pathway, Gene Set tool being proposed to determine the gene sets that are Enrichment Analysis, Neuroleptics diffrentially expressed over different experimental conditions. However, only a few studies have been concerned with the 1. INTRODUCTION
use of ANOVA when the number of genes is large and the number of observations is small. The strong normality, and The functional pathway analysis affected by second- independence assumptions, that traditional ANOVA imposes, generation atypical antipsychotics (atypical neuroleptics; AN) makes it impractical and not powerful enough. Several over those from the first generation (typical neuroleptics; TN) improvements and alternative approaches were developed [8]. become a hot research topic. Promising studies suggest that Biclustering or simultaneous clustering [9], where both genes atypical antipsychotics have less pronounced extrapyramidal, and conditions is challenging particularly to find subgroups of anticholinergic, parkinsonian and dystonic side effects [3-5]. genes and subgroups of conditions where the genes exhibit However, more detailed studies are needed for complete highly correlated activities over a range of conditions. Next to assessment of preponderance over the TN. Since the frontal mention is the branch of pattern recognition name Logical cortex is one of the most important regions for antipsychotics Combinatorial Pattern Recognition [1], which works action, in this study we compare the effects of treatment by effectively with nonstandard classification problems. We typical and atypical neuroleptics on functional pathways in design and extend logic-combinatorial scheme to overcome frontal cortex of the brain. The "Typical and atypical the difficulty raised by our practical problem. Elementary antipsychotic drugs effect on brain" dataset ℑ of Gene classifiers, cluster analysis, testing and greedy solvers are Expression Omnibus (GEO) repository considered and applied. has been used. This dataset contains gene expressions from frontal cortex of 13-week male mice treated for 28 days with 2. ALGORITHM
antipsychotics. Chlorpromazine and thioridazine were used as Pattern recognition deals with classes given by limited sets of typical antipsychotics, and olanzapine and quetiapine as classified examples and possibly by some hypotheses of the atypical antipsychotics. Gene expression profiles in GEO classes themselves. The main goal is to find an algorithm- dataset were obtained using Agilent 011978 Mouse classifier which extends the known classification to the area Microarray G4121A (GEO Platform ID: GPL891, Agilent of unclassified objects. Formally, conditions of correct classification of all objects might be composed and then the Generally the basic approach of diverse type of analysis of problem of maximization of number of satisfied conditions multidimensional experimental data sets is mathematical appears. For linear hyperplane classifiers for example we statistics (MS). Having satisfactory amount of experimental receive systems of linear inequalities, - unnecessarily data (statistics) it helps to form conclusions that some compatible in general. The question is in determining the properties and postulations take place in some probabilistic maximal compatible subset of such systems, which is level. Simple correlation, regression and hypothesis computationally a known NP hard problem. The situation estimation algorithms are components of the statistical with classes of typical and atypical antipsychotics given by data ℑ is relatively different. ℑ , containing data on gene expression, is a numerical array of four 1700 long numerical ℑ = {S ,S ,S ,S }. Classes consist of two Generally k -classifiers examine k columns, construct convex hulls in areas of two considered classes, consider the members each: S , S - typical, and S , S - atypical. It is geometrical centers and balanced middle point, which serves as the value for classification. In our case convex hulls are evident that almost any unique column S (i), S (i), just intervals of a multidimensional vector space. The force S (i), S (i) of ℑ can correctly classify the two drug sets f (i ,.,i ) is defined through the projections of intervals even using a simple hyperplane. And the number of such into the separating hyperplans. The projection area, divided columns might be very large among the 17000. The same on length of interval projections, provides a comparable for time, it is realistic that different sets of columns are all k measure of force of separation. classifying the classes differently. Formally, a collection of Future Work – Growing Support Systems.
subsets of the set n is known as a set of support Among 2 elementary classifiers defined above, we intend systems Ω [1]. Support system is the unit used in comparison to find those ones for which corresponding subsets of genes of a pair of object descriptions. This is when a set of are most differentially expressed by drug groups. The simplest distances, - each by a member of Ω is defined. The way is to start by a 1-classifier, and growing it step by step to application counterpart is that a set of features – not smaller k -classifiers so that the forces are strictly increasing, with and not larger than a support system is very effective in interruption in the k th step. Any k-classifier may be describing a particular classification. This brings us to the problems of determining the proper column subsets (support considered as a composition of one k − 1 -classifier together systems), which provide the maximal difference between with one new column. Concepts c (i ,., i ) and classes (quality vs. accuracy of classification). In doing this we will eliminate the equivalent (in some sense) columns f (i ,.,i ) in this way introduce monotonity relation from one side; and will compose the sets of columns between gene sets, put into 1-1 correspondences to the representing different equivalency subsets as approximations vertices of an n dimensional unit cube. However, this might to the proper support systems. Last general note we bring is that for classes we consider, support systems are presented - be rather hard to fulfill because of for some large values of k by two vectors in each class. We connect these two vectors it will become impossible to consider all 2 sub-classifiers. into the intervals and consider the best hyperplane separation The search area for these subsets is very large, and of these two intervals. We receive a simplest geometry appropriate heuristics to combat this complexity is necessary. separation problem. The advantage is that we are able to We consider several heuristics: compare support systems finding the most effective ones among them. Sorting 1-classifiers by decreasing forces f (i) , Classifiers
and eliminating from the further treatment columns with At first we define Elementary classifiers.
forces lower than the threshold selected. Let the columns in These are hyperplane classifiers by small number of columns. sorted sequence are as i , i ,.,i ,.,i . An important 1-classifier is defined through a single column (let say the
i th) and its expression values S (i), S (i), and property of this sequence is the first index i so that forces S (i), S (i) . Denote by t ( ) and a (i) the average f (i ,.,i ) are increasing for i < i and this increase values on the intervals (S (i), S (i)) and interrupts at the point i . Besides, sorting may also be (S (i), S (i)) applied to the mixed sets of classifiers because of the note on respectively, and let t (i) and a (i) is comparability of forces for different k 's. the lengths of these intervals. 1-classifier c (i) by i th
Consider an arbitrary hyperplane elementary column, i ∈ , 1 n ( n is the number of gene expressions), is classifier c (i ,., i ) . Compose n -dimensional binary defined as the balanced (by values t (i) and a (i) ) vector, evaluating coordinates i ,.,i as 1. Completing by 0 middle point of interval (t (i), a (i)) , and all the coordinates, not used in c (i ,., i ) we create a 1-1 correspondence between classifiers and n -cube vertices. t (i) − a (i) = f (i) is called the power/force of Applying hierarchical clustering in n-cube layers we split k- c (i) . classifiers by the equivalency relation (after some cut of dendrogram). Similarity measure used is some correlation 2-classifier considers pair of genes and expression values.
between the hyperplanes (their coefficient vectors). We Logically 2-classifiers are to be composed by pairs of genes, consider the representatives sets of clusters. Some of them higher ranked by corresponding 1-classifiers. Arranging
may give the same force of classifying drug groups by gene columns by decreasing order of values f (i) we rank the expressions as the whole descriptive table does. In this way gene expressions by their forces for differentiating two drug we reduce the dimensionality combating the exponential explosion for large n . groups. 2-classifiers and in general k -classifiers consider any As it was mentioned, 1-classifiers might be directly k columns, construct average values on corresponding sorted by their forces. Any k -classifier may be considered as intervals in classes (intervals by row vector pairs) and define a composition of one k − 1-classifier c (i ,.,i structures c (i ,., i ) and f (i ,.,i ) . c (i ,., i ) defines the hyperplane, separating the average expressions by together with one new column i . In terms of class vectors drug groups and gene collections, and f (i ,.,i ) defines this change means concatenation of a new dimension in the quality of this separation. direction i . Concepts c (i ,., i ) and f (i ,.,i ) in this way introduce monotonity relation between gene sets in the same way as the vertices of n dimensional unit cube which are in 1-1 correspondence to elementary classifiers. Considering subsets of different n-cube layers and taking into account monotonity we may apply the chain split technology [10] in finding the best separating gene sets. It is important to note that chain split (and other known frequent subsets growing algorithms of association rule mining) work with random objects otherwise with overall structure of all objects which is computationally hard. Instead, the representatives set mentioned above are a valuable heuristic that may help in reducing the computational complexity in growing. The results obtained suggest that AN, as compared to TN, Consider the convex hull Ξ of all classifiers have less influence on regulatory pathways contributing to neurodegeneration (Huntington's disease) and neuronal c , j ∈ , 1 2 in n dimensional vector space. The volume architectonics (Axon guidance, Gap junction), cell and shape of Ξ appears as a sophisticated measure of drug proliferation (Glioma). Moreover, according to our findings, groups' differences, characterized by the gene expressions. TN strongly affects GnRH signaling pathway, as well as immune response regulatory reactions (Focal adhesion and Approximation of Ξ by smaller groups of genes might be Cell adhesion molecules), whereas AN have very week achieved in different ways. Such smaller subsets are effective influence on these processes. In addition, our study revealed candidates for separating the drug group-driven expression that AN possess less pronounced effects on cognition, differences. These subsets might be compared to functional particularly related to learning memory (Long-term gene subsets describing the drug influences. A satisfactory potentiation, Long-term depression) than TN do. approximation of Ξ by gene sets or by classifiers sets shows that these subsets keep the diversity of drug groups. The approximation we considered is greedy algorithm, given in 5. CONCLUSION
The benefit of AN, compared to TN, includes less side effects related to functional pathways of brain frontal cortex. 3. APPLIED MODEL
Extended classification algorithms are designed to analyze the To generate ranked gene list, first, average intragroup (TN applied data which are of very specific structure. and AN) expression levels for each gene were calculated. Then, for each gene the average level for TN group was REFERENCES
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