Sensitivity Amplification in the Phosphorylation-Dephosphorylation Cycle: Nonequilibrium steady states, chemical master equation and temporal cooperativity

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105 585-593 (2003), Annu. Rev. Phys. Chem. 58 113-142 (2007)], emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models, and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential $\triangle G=0$, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in phosphorylation-dephosphorylation cycle respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants", which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule which can not be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein which can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.Comment: 42 pages, 13 figure

Properties of Noncommutative Renyi and Augustin Information

The scaled R\'enyi information plays a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error exponent analysis. In quantum information theory, there are three generalizations of the classical R\'enyi divergence---the Petz's, sandwiched, and log-Euclidean versions, that possess meaningful operational interpretation. However, these scaled noncommutative R\'enyi informations are much less explored compared with their classical counterpart, and lacking crucial properties hinders applications of these quantities to refined performance analysis. The goal of this paper is thus to analyze fundamental properties of scaled R\'enyi information from a noncommutative measure-theoretic perspective. Firstly, we prove the uniform equicontinuity for all three quantum versions of R\'enyi information, hence it yields the joint continuity of these quantities in the orders and priors. Secondly, we establish the concavity in the region of $s\in(-1,0)$ for both Petz's and the sandwiched versions. This completes the open questions raised by Holevo [\href{https://ieeexplore.ieee.org/document/868501/}{\textit{IEEE Trans.~Inf.~Theory}, \textbf{46}(6):2256--2261, 2000}], Mosonyi and Ogawa [\href{https://doi.org/10.1007/s00220-017-2928-4/}{\textit{Commun.~Math.~Phys}, \textbf{355}(1):373--426, 2017}]. For the applications, we show that the strong converse exponent in classical-quantum channel coding satisfies a minimax identity. The established concavity is further employed to prove an entropic duality between classical data compression with quantum side information and classical-quantum channel coding, and a Fenchel duality in joint source-channel coding with quantum side information in the forthcoming papers