The last decade has seen an exponential expansion of interest in conjugating multiple enzymes of cascades in close proximity to each other, with the overarching goal being to accelerate the overall reaction rate. However, some evidence has emerged that there is no effect of proximity channeling on the reaction velocity of the popular GOx-HRP cascade, particularly in the presence of a competing enzyme (catalase). Herein, we rationalize these experimental results quantitatively. We show that, in general, proximity channeling can enhance reaction velocity in the presence of competing enzymes, but in steady state a significant enhancement can only be achieved for diffusion-limited reactions or at high concentrations of competing enzymes. We provide simple equations to estimate the effect of channeling quantitatively and demonstrate that proximity can have a more pronounced effect under crowding conditions in vivo, particularly that crowding can enhance the overall rates of channeled cascade reactions.

Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion and water desalination. Exactly solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly solvable, one-dimensional off-lattice model for charging single-file pores. Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, by changing cation–anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, C ∼ u−2. This dependence follows from hard-core interactions and is not captured by the lattice model.

We present a theoretical analysis of charge storage in electrochemical capacitors with electrodes based on carbon nanotubes. Using exact analytical solutions supported by Monte Carlo simulations, we show how the limitations of the electron density of states in such low-dimensional electrode materials may help boost the energy stored at increased voltages. While these counterintuitive predictions await experimental verification, they suggest exciting opportunities for enhancing energy storage by rational engineering of the electronic properties of low-dimensional electrodes.

Please cite this article in press as: A.R. Kuzmak, V.M. Tkachuk, The quantum brachistochrone problem for an arbitrary spin in a magnetic field, Phys. Lett. A (2015), http://dx. Highlights• The Fubini-Study metrics of rotational manifolds of spin-s system are considered.• It is shown that they are spheres.• The brachistochrone problem for a spin-s system on rotational manifolds is examined. We consider quantum brachistochrone evolution for a spin-s system on rotational manifolds. Such manifolds are determined by the rotation of the eigenstates of the operator of projection of spin-s on some direction. The Fubini-Study metrics of these manifolds are those of spheres with radii dependent on the value of the spin and on the value of the spin projection. The conditions for optimal evolution of the spin-s system on rotational manifolds are obtained.

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