Isotopic fractionation in proteins as a measure of hydrogen bond length

If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium. It is found that the associated fractionation factor $\Phi$ is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds. Starting with a potential energy surface based on a simple diabatic state model for H-bonds we calculate $\Phi$ as a function of the proton donor-acceptor distance $R$. For numerical results, we use a parameterization of the model for symmetric O-H.... O bonds. We consider the relative contributions of the O-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunnelling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total $\Phi$ as a function of $R$ with NMR experimental results for enzymes, and in particular with an empirical parametrisation $\Phi(R)$, used previously to determine bond lengths.Comment: Final version, accepted for publication in Journal of Chemical Physics. Minor changes, including more extensive discussion of relevant of model to protein

Design of State-based Schedulers for a Network of Control Loops

For a closed-loop system, which has a contention-based multiple access network on its sensor link, the Medium Access Controller (MAC) may discard some packets when the traffic on the link is high. We use a local state-based scheduler to select a few critical data packets to send to the MAC. In this paper, we analyze the impact of such a scheduler on the closed-loop system in the presence of traffic, and show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of a scheduler with a certainty equivalent controller. This design, however, does not result in an equivalent system to the original problem, in the sense of Witsenhausen. Computing the estimate is difficult, but can be simplified by introducing a symmetry constraint on the scheduler. Based on these findings, we propose a dual predictor architecture for the closed-loop system, which ensures separation between scheduler, observer and controller. We present an example of this architecture, which illustrates a network-aware event-triggering mechanism.Comment: 17 pages, technical repor

An Experimental and Analytical Approach to Understanding the Dynamic Leaching from Municipal Solid Waste Combustion Residue

This paper describes an experimental technique involving the use of small columns for generating significant quantities of leachate data from municipal solid waste (MSW) solid residues within a relatively short amount of time. Data analysis using the discretized mass balance equations descriptive of the system results in best estimates of governing transport parameters that can, in turn, be used to predict the long-term release of leachable components (As, Cd, Cu, Fe, Ni, Pb, Zn, Ca, Mg, Na, K, Cl, SO4) from the solid matrix. Results indicate that both chemical solubility and physical transport are important factors affecting the flux of contaminants from the solid to the solution phase