Blagoj Achevski, Ljupcho Pejov
Molecular Hydrogen Acts as a Hydrogen Bond Proton Acceptor: From Protonated Betaine Tagging to the Weakest Hydrogen Bond
The journal of physical chemistry. A
fitting probability mass functions analytical solutions stochastic models gene expression singlecell count distributions mrna protein molecules yield valuable insights mechanisms underlying gene expression solutions chemical master equations available various kinetic schemes even basic onoff genetic switch take complex forms generating functions given hypergeometric functions interpretation gene expression dynamics terms bursts consistent complete range parameters functions physical insights probability mass functions essential ensure proper interpretations lacking models considering genetic switches fill gap develop urn models stochastic gene expression sample rna polymerases ribosomes master urn represents cytosol assign recipient urns two colors represent time intervals switching occurs colors recipient urns represent subsystems promoter states assignments urns specific color represent gene expression use elementary principles discrete probability theory solve range kinetic models without feedback including peccoudycart model shahrezaeiswain model models arbitrary number promoter states last case obtain novel result protein distribution activated genes show transcriptional lapses events gene inactivation short time intervals separated long active intervals quantify transcriptional dynamics better bursts show intuition gained urn models may also useful understanding existing solutions models feedback contrast models urn models related distributions discuss generalization delaporte distribution singlecell data analysis highlight limitations models