ABSTRACT
Transcription in eukaryotes involves complex biological processes, like transcription factors (TF) binding and chromatin remodelling, which are dynamical in nature. The preceding sections focus on chemical equilibrium, where the steady state is described by some probability measure π, as described in section 5.2. We assume in this section that https://www.w3.org/1998/Math/MathML"> π = π β https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429086663/acb7e1d1-9bf9-43aa-8a26-560ac513e49b/content/eq1251.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is a Gibbs-Boltzmann distribution associated with some free energy function H. These distributions should coincide with steady state distributions of Markov chains describing chemical kinetics. Cooperativity is quite often introduced using dynamical arguments. We hence focus on basic Markov chains describing binding processes. Assume that the binding process is such that only one ligand molecule can bind per unit time (sequential binding), that is, suppose that the possible transitions are of the form, for https://www.w3.org/1998/Math/MathML"> i = 1 , ⋯ , N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429086663/acb7e1d1-9bf9-43aa-8a26-560ac513e49b/content/eq1252.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , https://www.w3.org/1998/Math/MathML"> n = ( n 1 , ⋯ , n i − 1 , 0 , n i + 1 , ⋯ , n N ) → n ′ = ( n 1 , ⋯ , n i − 1 , 1 , n i + 1 , ⋯ , n N ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429086663/acb7e1d1-9bf9-43aa-8a26-560ac513e49b/content/eq1253.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
