Factorization of Directed Graph Describing Protein Network, Using for Research of Plants Stability to Drought and Extreme Temperatures and its Possible Development
Tsitsiashvili Gurami1*, Bulgakov Victor2 and Losev Alexandr1
1Institute for Applied Mathematics FEB RAS, Russia
2Institute of Biology and Soil Science FEB RAS, Russia
Submission: August 28, 2017; Published: September 20, 2017
*Corresponding author: Tsitsiashvili Gurami, Institute for Applied Mathematics FEB RAS, Vladivostok, Russia, Email: guram@iam.dvo.ru
How to cite this article: Tsitsiashvili G, Bulgakov V, Losev Al. Factorization of Directed Graph Describing Protein Network, Using for Research of Plants Stability to Drought and Extreme Temperatures and its Possible Development. Biostat Biometrics Open Acc J. 2017; 3(1): 555603. DOI: 10.19080/BBOAJ.2017.03.555603.
Abstract
In this paper a sequential algorithm of graph nodes classification and their partial order definition is applied to protein network using for a study of the key players required for connecting ABA signaling and ABA-mediated drought and thermo tolerance.
Keywords: A factorization; A cluster a thermo stability; A protein network
Factorization Procedure
In this paper we factorize a protein network using for a study of the key players required for connecting ABA signaling and ABA-mediated drought and thermo tolerance [1,2] (Figure 1). A choice of this network is in accordance with a definition of functional protein sub networks approaches [3,4]. The sequential algorithm of graph nodes classification and their partial order definition is applied to protein network using for a study of the key players required for connecting ABA signaling and ABA-mediated drought and thermo tolerance [5,6].
Suggested classification procedure allows finding in the network proteins the most important for thermo stability and impacts to provide them conditions that are more convenient. In this network, we define one node clusters: input, output, intermediary, and two multi node intermediary clusters (encircled by blue and red color curves).
Output proteins DREB2C, ABA receptors PYLs, which are the most important for thermo stability of plants by their biochemical characteristics. Multi node cluster encircled by red color curve (Figure 1) does not have edges connected with these proteins. The most interesting is multi node intermediary cluster encircled by blue color curve. It has edges connected with output nodes DREB2C, ABA receptors PYLs. In this multi node cluster there are the following centers ABF4, ABF2/AREB1, PP2CA protein phosphatases, which are the most important for further biochemical tests. This statement is confirmed by biochemists hypotheses also. To make more comfortable situation for DREB2C, ABA receptors PYLs stimulation it is possible to inhibit proteins HSFA6a, AREB3, HSF A3 which connect intermediary cluster encircled by blue color with intermediary cluster encircled by red color.
Possible Development of Factorization Procedure
This procedure allows making more detailed consideration of protein sub networks, connected with a calculation of stationary mass intensities of flows (from their nodes) by a solution of balance equations. Analogous problem is widely used in the product theorem of the queuing networks theory [7] and different economical applications. Our problem is how to decompose solution of this system. Main idea of this procedure is to order clusters with cyclically equivalent nodes by their maximal distance from input clusters so that direct edges may be only from clusters with smaller to clusters with larger distances [8]. Then a solution of balance equations system is divided into solutions of sub systems for clusters with cyclically equivalent nodes so that these sub systems may be solved sequentially in accordance with their ordering by maximal distances [9]. Partially supported by Russian Fund of Basic Researches (project 17-07-00177), and by Far Eastern Branch of Russian Academy Sciences, grant «Far East» (project 15-I-4-001 o, subproject 15- I-4-030).
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