Yıl 2016, Cilt 20 , Sayı 3, Sayfalar 617 - 625 2016-09-02

Korunumlu döngülerin stokastik simülasyon algoritmalarında kullanımı
Using conserved cycles in exact stochastic simulation algorithms

Derya Altintan [1]


Biyokimyasal reaksiyon sistemleri farklı reaksiyonlar  aracılığıyla etkileşime giren birçok farklı  türü içerir. Sistem içerisinde yer alan türlerin sayıları ve miktarları çok yüksek olduğunda, diferansiyel denklemlere dayanan saf modelleme yaklaşımları çok boyutluluktan muzdarip olurlar. Eğer bir sistem korunumlu döngüler içerirse,  bazı türlerin miktarları cebirsel bağlantılar yoluyla elde edilebilir bu da sistemin dinamiklerini  temsil eden diferansiyel denklemlerin boyutunu düşürür. Bu çalışmada, biyokimyasal reaksiyon sistemlerinde yer alan korunumlu döngüleri elde etmek için Gauss-Jordan metodunu kullanan bir nümerik algoritma öneriyoruz. Algoritmayı stokastik modelleme yaklaşımında konum vektörünün tam realizasyonlarını elde eden Direk  Metod (DM), İlk Reaksiyon Metodu (FRM) ve Sonraki Reaksiyon Metodu (FRM) içerisinde verdik. Bu üç algoritmayı korunum bağıntılarını içerecek/içermecek şekilde farklı boyutlardaki biyokimyasal sistemlere uyguladık ve   her tam lagoritmanın farklı iki versiyonunun hesaplama miktarları kıyasladık.

Biochemical reaction systems involve many different species interacting via many different reaction channels. When the number of species and the abundance of species are so high, pure modeling approaches based on differential equations suffer from curse of dimensionality. If a system involves conserved cycles, abundances of some species can be obtained via algebraic relations which in turn will reduce the dimension of differential equations representing the dynamics of the system. In the present paper, we propose a numerical algorithm that uses Gauss-Jordan method to obtain conserved cycles in biochemical systems. We give this algorithm in Direct Method (DM), First Reaction Method (FRM) and Next Reaction Method (NRM) which obtain exact realizations of the state vector in stochastic modeling approach. We apply these three algorithms with/without using conservation relations to biochemical systems in different sizes and compare the computational costs of two different versions of each exact algorithm.

 
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Bölüm Araştırma Makalesi
Yazarlar

Yazar: Derya Altintan

Tarihler

Başvuru Tarihi : 1 Ağustos 2016
Kabul Tarihi : 17 Ekim 2019
Yayımlanma Tarihi : 2 Eylül 2016

Bibtex @ { saufenbilder270018, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {}, publisher = {Sakarya Üniversitesi}, year = {2016}, volume = {20}, pages = {617 - 625}, doi = {10.16984/saufenbilder.22901}, title = {Using conserved cycles in exact stochastic simulation algorithms}, key = {cite}, author = {Altintan, Derya} }
APA Altintan, D . (2016). Using conserved cycles in exact stochastic simulation algorithms. Sakarya University Journal of Science , 20 (3) , 617-625 . DOI: 10.16984/saufenbilder.22901
MLA Altintan, D . "Using conserved cycles in exact stochastic simulation algorithms". Sakarya University Journal of Science 20 (2016 ): 617-625 <http://www.saujs.sakarya.edu.tr/tr/issue/25594/270018>
Chicago Altintan, D . "Using conserved cycles in exact stochastic simulation algorithms". Sakarya University Journal of Science 20 (2016 ): 617-625
RIS TY - JOUR T1 - Using conserved cycles in exact stochastic simulation algorithms AU - Derya Altintan Y1 - 2016 PY - 2016 N1 - doi: 10.16984/saufenbilder.22901 DO - 10.16984/saufenbilder.22901 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 617 EP - 625 VL - 20 IS - 3 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.22901 UR - https://doi.org/10.16984/saufenbilder.22901 Y2 - 2019 ER -
EndNote %0 Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi Using conserved cycles in exact stochastic simulation algorithms %A Derya Altintan %T Using conserved cycles in exact stochastic simulation algorithms %D 2016 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 20 %N 3 %R doi: 10.16984/saufenbilder.22901 %U 10.16984/saufenbilder.22901
ISNAD Altintan, Derya . "Using conserved cycles in exact stochastic simulation algorithms". Sakarya University Journal of Science 20 / 3 (Eylül 2016): 617-625 . https://doi.org/10.16984/saufenbilder.22901
AMA Altintan D . Using conserved cycles in exact stochastic simulation algorithms. SAUJS. 2016; 20(3): 617-625.
Vancouver Altintan D . Using conserved cycles in exact stochastic simulation algorithms. Sakarya University Journal of Science. 2016; 20(3): 625-617.