Bayesian Inference of the Complex MAPK Pathway Under the Structural Dependency

Öz

The MAPK pathway is one of the main signal transaction system in all eukaryotes which regulates the cellular growth control. Because of its vital role, the regulation of the pathway is conducted via many proteins, thereby constitutes a complex structure. In inference of this system via MCMC techniques based on the Euler approximation, we have observed that there are many proteins which indicate high structural dependencies on other proteins and these species have caused singular diffusion matrices, hereby resulted in infeasible acceptance probabilities. Therefore, we have discarded these problematic substrates at the beginning of the inference and estimated the parameters by using merely linearly independent species in the system. However in that case, the accuracy of the estimation has been highly affected by the underlying exclusion, particularly, when the number of dependent species was big. The elimination of those proteins has led to a significant rise in the number of current missing components in MCMC. In this study, we implicitly include these proteins in our computation via an alternative approach which simulates dependent terms as a linear combination of linearly independent species. In that way, we can add the effect of dependent species in the calculation of acceptance probabilities of reaction rates and states. From the analysis, we conclude that the highlighted innovation decreases the average error of estimates and suggests less computational cost in inference of the MAPK pathway.

Anahtar Kelimeler

• Bayesian inference
• Diffusion approximation
• MAPK pathway

Yapısal Bağımlılık Altında Karmaşık MAPK Yolunun Bayesci Tahmini

Öz

MAPK yolu, tüm ökaryotlarda bulunan hücresel büyüme kontrolünü düzenleyen başlıca sinyal iletim sistemlerinden biridir. Hayati görevinden dolayı sistemin idaresi çok sayıda protein vasıtasıyla yürütülür, buna bağlı olarak karmaşık bir yapı oluşturur. Çalışmada, Euler yaklaşımına dayalı MCMC teknikleriyle bu sistemin tahmininde diğer proteinlerle yüksek yapısal bağımlılıklar gösteren birçok proteinin varolduğu gözlenmiştir. Bu proteinler kabul edilme olasılıklarını imkansız yapan tekil difüzyon/varyans matrislerine neden olmuşlardır. Bu nedenle bu sorunlu proteinler tahmin hesabının başında çıkarılmış ve parametreler sadece sistemdeki doğrusal bağımsız türler kullanarak tahmin edilmiştir. Ancak bu durumda da özellikle bağımlı türlerin sayısı arttıkça, tahminin doğruluğu bahsedilen eliminasyondan oldukça etkilenmektedir. Bu proteinlerin elenmesi MCMC’deki mevcut kayıp terim sayısının belirgin derecede artmasına neden olmaktadır. Bu çalışmada dolaylı yoldan bu proteinler, bağımlı terimlerin bağımsız türlerin doğrusal kombinasyonu şeklinde simülasyon eden alternatif bir yaklaşımla hesaplamaların içine katılmaktadır. Bu şekilde reaksiyon oranlarının ve durumlarının kabul edilme olasılıklarını hesaplamada bağımlı türlerin etkileri ilave edilebilmektedir. Analizlerden, bahsedilen yeniliğin tahminlerin ortalama hatalarını azalttığı ve MAPK yolunun tahmininde daha az hesaplama maliyeti önerdiği sonucuna varılmıştır.

Anahtar Kelimeler

• Bayesci tahmin
• Difüzyon yaklaşımı
• MAPK yolu

Kaynakça

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