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

An effective likelihood-free approximate computing method with statistical inferential guarantees

Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference conducted from this method with a non-sufficient summary statistic. In this paper, we seek to re-frame approximate Bayesian computing within a frequentist context and justify its performance by standards set on the frequency coverage rate. In doing so, we develop a new computational technique called approximate confidence distribution computing, yielding theoretical support for the use of non-sufficient summary statistics in likelihood-free methods. Furthermore, we demonstrate that approximate confidence distribution computing extends the scope of approximate Bayesian computing to include data-dependent priors without damaging the inferential integrity. This data-dependent prior can be viewed as an initial `distribution estimate' of the target parameter which is updated with the results of the approximate confidence distribution computing method. A general strategy for constructing an appropriate data-dependent prior is also discussed and is shown to often increase the computing speed while maintaining statistical inferential guarantees. We supplement the theory with simulation studies illustrating the benefits of the proposed method, namely the potential for broader applications and the increased computing speed compared to the standard approximate Bayesian computing methods

A Context-aware Attention Network for Interactive Question Answering

Neural network based sequence-to-sequence models in an encoder-decoder framework have been successfully applied to solve Question Answering (QA) problems, predicting answers from statements and questions. However, almost all previous models have failed to consider detailed context information and unknown states under which systems do not have enough information to answer given questions. These scenarios with incomplete or ambiguous information are very common in the setting of Interactive Question Answering (IQA). To address this challenge, we develop a novel model, employing context-dependent word-level attention for more accurate statement representations and question-guided sentence-level attention for better context modeling. We also generate unique IQA datasets to test our model, which will be made publicly available. Employing these attention mechanisms, our model accurately understands when it can output an answer or when it requires generating a supplementary question for additional input depending on different contexts. When available, user's feedback is encoded and directly applied to update sentence-level attention to infer an answer. Extensive experiments on QA and IQA datasets quantitatively demonstrate the effectiveness of our model with significant improvement over state-of-the-art conventional QA models.Comment: 9 page

Transition magnetic moment of Majorana neutrinos in the μν\mu\nuSSM

The nonzero vacuum expectative values of sneutrinos induce spontaneously R-parity and lepton number violation, and generate three tiny Majorana neutrino masses through the seesaw mechanism in the $\mu\nu$SSM, which is one of Supersymmetric extensions beyond Standard Model. Applying effective Lagrangian method, we study the transition magnetic moment of Majorana neutrinos in the model here. Under the constraints from neutrino oscillations, we consider the two possibilities on the neutrino mass spectrum with normal or inverted ordering.Comment: 20 pages, 2 figures, accepted for publication in JHEP. arXiv admin note: text overlap with arXiv:1305.4352, arXiv:1304.624