10,303 research outputs found
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
, 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
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
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