Table 1 Typical enzyme–substrate kinetics along with their respective average enzyme occupancy as a function of time and the spatial two-point connected correlation functions
From: Scaling and self-similarity in the formation of the embryonic epigenome
Description | Interaction kernel, K(i, j) | First moment, 〈m〉 | Correlation function, 〈mimj〉 − 〈mi〉〈mj〉 |
|---|---|---|---|
Non-local interactions (involving topological changes in the DNA) | ∝ ∣i − j∣−λ, λ < 1 | \(\propto {t}^{\displaystyle \frac{1}{1-\lambda }}\) | \(\begin{array}{l}|i-j{|}^{{-\lambda }^{1+\langle m\rangle }},\,|i-j|\ll 1/\langle m\rangle \\ |i-j{|}^{-{\left[\frac{2}{3}(2-\lambda )\right]}^{1+\langle m\rangle }},\,|i-j|\gg 1/\langle m\rangle \end{array}\) |
Oligomerization with rate α | αδi,i±1 | αt2 | e−α∣i−j∣ |
Independent binding | αδij | αt2 | δ(∣i − j∣) |
Processivity with rate α | No interaction kernel | αt3/2 | e−α∣i−j∣ |
