Using conserved cycles in exact stochastic simulation algorithms

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.

Korunumlu döngülerin stokastik simülasyon algoritmalarında kullanımı

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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