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In this paper we investigate properties of continuous time chiral quantum walks, which possess complex valued edge weights in the underlying graph structure, together with an initial Gaussian wavefunction spread over a number of vertices. We demonstrate that, for certain graph topology and phase matching conditions, we are able to direct the flow of probability amplitudes in a specific direction inside the graph network. We design a quantum walk graph analogue of an optical circulator which is a combination of a cycle and semi-infinite chain graphs. Excitations input into the circulator from a semi-infinite chain are routed in a directionally biased fashion to output to a different semi-infinite chain. We examine in detail a two port circulator graph which spatially separates excitations flowing back in forth between the two semi-finite chains to directionally occupy the top or bottom half of the cycle portion of the circulator. This setup can be used, for example, to detect non-Markovian processes, which leads to information and energy back-flow from the bath back into the system.

We investigate novel transport properties of chiral continuous-time quantum walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate that CTQWs on chiral chains are equivalent to those on non-chiral chains, but with additional momenta from initial wave packets. This explains the novel transport phenomenon numerically studied in (Khalique et al 2021 New J. Phys. 23 083005). Building on this, we delve deeper into the analysis of chiral CTQWs on the Y-junction graph, introducing phases to account for the chirality. The phase plays a key role in controlling both asymmetric transport and directed complete transport among the chains in the Y-junction graph. We systematically analyze these features through a comprehensive examination of the chiral CTQW on a Y-junction graph. Our analysis shows that the CTQW on Y-junction graph can be modeled as a combination of three wave functions, each of which evolves independently on three effective open chains. By constructing a lattice scattering theory, we calculate the phase shift of a wave packet after it interacts with the potential-shifted boundary. Our results demonstrate that the interplay of these phase shifts leads to the observed enhancement and suppression of quantum transport. The explicit condition for directed complete transport or 100 % efficiency is analytically derived. Our theory has applications in building quantum versions of binary tree search algorithms.

The conversion of light energy into ion gradients across biological membranes is one of the most fundamental reactions in primary biological energy transduction. Recently, the structure of the first light-activated Na⁺ pump, Krokinobacter eikastus rhodopsin 2 (KR2), was resolved at atomic resolution [Kato HE, et al. (2015) Nature 521:48–53]. To elucidate its molecular mechanism for Na⁺ pumping, we perform here extensive classical and quantum molecular dynamics (MD) simulations of transient photocycle states. Our simulations show how the dynamics of key residues regulate water and ion access between the bulk and the buried light-triggered retinal site. We identify putative Na⁺ binding sites and show how protonation and conformational changes gate the ion through these sites toward the extracellular side. We further show by correlated ab initio quantum chemical calculations that the obtained putative photocycle intermediates are in close agreement with experimental transient optical spectroscopic data. The combined results of the ion translocation and gating mechanisms in KR2 may provide a basis for the rational design of novel light-driven ion pumps with optogenetic applications.

Complex I functions as a redox-linked proton pump in the respiratory chains of mitochondria and bacteria, driven by the reduction of quinone (Q) by NADH. Remarkably, the distance between the Q reduction site and the most distant proton channels extends nearly 200 Å. To elucidate the molecular origin of this long-range coupling, we apply a combination of large-scale molecular simulations and a site-directed mutagenesis experiment of a key residue. In hybrid quantum mechanics/molecular mechanics simulations, we observe that reduction of Q is coupled to its local protonation by the His-38/Asp-139 ion pair and Tyr-87 of subunit Nqo4. Atomistic classical molecular dynamics simulations further suggest that formation of quinol (QH₂) triggers rapid dissociation of the anionic Asp-139 toward the membrane domain that couples to conformational changes in a network of conserved charged residues. Site-directed mutagenesis data confirm the importance of Asp-139; upon mutation to asparagine the Q reductase activity is inhibited by 75%. The current results, together with earlier biochemical data, suggest that the proton pumping in complex I is activated by a unique combination of electrostatic and conformational transitions.

Developing low-cost and high-catalytic photocatalysts is momentous to achieve efficient photocatalytic splitting of water to produce hydrogen. In this study, a 0D–3D structure ZnCdS–NiCoP composite was synthesized by a simple physical mixing method. A series of characterization results show that the close bonding of ZnCdS nanoparticles and NiCoP nanorods is conducive to electron transfer between the ZnCdS and NiCoP interface. The sea-urchin-structure NiCoP composed of nanorods could be as an electron acceptor to accelerate the directed migration of electrons. Thereby achieving separation of electrons and holes in space. Sea-urchin-structure NiCoP provides spatial support for ZnCdS, greatly reducing the degree of agglomeration of ZnCdS nanoparticles and increasing the specific surface area of the catalyst. The performance of the visible-light-driven photocatalyst showed that the ZnCdS–NiCoP10 composite had the highest photocatalytic hydrogen production activity, and the amount of hydrogen evolution in the reaction for 5 h was 789.7 μmol, which reached 5.2 times that of pure ZnCdS. The apparent quantum efficiency (AQE) of the ZnCdS–NiCoP10 composite was 6.28% at a wavelength of 475 nm. After 5 cycles of reaction, the composite ZnCdS–NiCoP10 maintained long-term stability. Based on the characterization analysis results, a possible mechanism of hydrogen production of by ZnCdS–NiCoP composite catalyst is proposed, which will help to understand the enhance photocatalytic hydrogen evolution activity of ZnCdS–NiCoP and may stimulate the synthesis of other 0D–3D catalytic systems. Graphic Abstract

Porous protein cages are supramolecular protein self-assemblies presenting pores that allow the access of surrounding molecules and ions into their core in order to store and transport them in biological environments. Protein cages' pores are attractive channels for the internalisation of inorganic nanoparticles and an alternative for the preparation of hybrid bioinspired nanoparticles. However, strategies based on nanoparticle transport through the pores are largely unexplored, due to the difficulty of tailoring nanoparticles that have diameters commensurate with the pores size and simultaneously displaying specific affinity to the cages' core and low non-specific binding to the cages' outer surface. We evaluated the specific internalisation of single small gold nanoparticles, 3.9 nm in diameter, into porous protein cages via affinity binding. The E2 protein cage derived from the Geobacillus stearothermophilus presents 12 pores, 6 nm in diameter, and an empty core of 13 nm in diameter. We engineered the E2 protein by site-directed mutagenesis with oligohistidine sequences exposing them into the cage's core. Dynamic light scattering and electron microscopy analysis show that the structures of E2 protein cages mutated with bis- or penta-histidine sequences are well conserved. The surface of the gold nanoparticles was passivated with a self-assembled monolayer made of a mixture of short peptidols and thiolated alkane ethylene glycol ligands. Such monolayers are found to provide thin coatings preventing non-specific binding to proteins. Further functionalisation of the peptide coated gold nanoparticles with Ni2+ nitrilotriacetic moieties enabled the specific binding to oligohistidine tagged cages. The internalisation via affinity binding was evaluated by electron microscopy analysis. From the various mutations tested, only the penta-histidine mutated E2 protein cage showed repeatable and stable internalisation. The present work overcomes the limitations of currently available approaches and provides a new route to design tailored and well-controlled hybrid nanoparticles.