On Hypercomplex Extensions of Quantum Theory

This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.Comment: 17 page

Marked changes in electron transport through the blue copper protein azurin in the solid state upon deuteration

Measuring electron transport (ETp) across proteins in the solid-state offers a way to study electron transfer (ET) mechanism(s) that minimizes solvation effects on the process. Solid state ETp is sensitive to any static (conformational) or dynamic (vibrational) changes in the protein. Our macroscopic measurement technique extends the use of ETp meas-urements down to low temperatures and the concomitant lower current densities, because the larger area still yields measurable currents. Thus, we reported previously a surprising lack of temperature-dependence for ETp via the blue copper protein azurin (Az), from 80K till denaturation, while ETp via apo-(Cu-free) Az was found to be temperature de-pendent \geq 200K. H/D substitution (deuteration) can provide a potentially powerful means to unravel factors that affect the ETp mechanism at a molecular level. Therefore, we measured and report here the kinetic deuterium isotope effect (KIE) on ETp through holo-Az as a function of temperature (30-340K). We find that deuteration has a striking effect in that it changes ETp from temperature independent to temperature dependent above 180K. This change is expressed in KIE values between 1.8 at 340K and 9.1 at \leq 180K. These values are particularly remarkable in light of the previously reported inverse KIE on the ET in Az in solution. The high values that we obtain for the KIE on the ETp process across the protein monolayer are consistent with a transport mechanism that involves through-(H-containing)-bonds of the {\beta}-sheet structure of Az, likely those of am-ide groups.Comment: 15 pages, 3 figures, 2 Supplementary figure

Direct evidence for heme-assisted solid-state electronic conduction in multi-heme c-type cytochromes

Multi-heme cytochrome c (CytC) proteins are key for transferring electrons out of cells, to enable intracellular oxidation to proceed, also in the absence of O2. In these proteins most of the hemes are arranged in a linear array suggesting a facile path for electronic conduction. To test this, we studied solvent free electron transport across two multi-heme CytC-type: MtrF (deca-heme CytC) and STC (tetra-heme CytC). Transport is measured across monolayers of these proteins in solid state configuration between Au electrodes. Both proteins showed 1,000x higher conductance than single heme, or heme-free proteins, but similar to monolayers of conjugated organics. Conductances are found to be temperature-independent (320-80K), suggesting tunneling as the transport mechanism based on present experimental data. This mechanism is consistent with modelling the I-V curves, results of which could be interpreted by having protein-electrode coupling as rate limiting, rather than transport within the proteins

Temperature and force dependence of nanoscale electron transport via the Cu protein Azurin

The mechanisms of solid-state electron transport (ETp) via a monolayer of immobilized Azurin (Az) was examined by conducting probe atomic force microscopy (CP-AFM), both as function of temperature (248 - 373K) and of applied tip force (6-12 nN). By varying both temperature and force in CP-AFM, we find that the ETp mechanism can alter with a change in the force applied via the tip to the proteins. As the applied force increases, ETp via Az changes from temperature-independent to thermally activated at high temperatures. This is in contrast to the Cu-depleted form of Az (apo-Az), where increasing the applied force causes only small quantitative effects, that fit with a decrease in electrode spacing. At low force ETp via holo-Az is temperature-independent and thermally activated via apo-Az. This observation agrees with macroscopic-scale measurements, thus confirming that the difference in ETp dependence on temperature between holo- and apo-Az is an inherent one that may reflect a difference in rigidity between the two forms. An important implication of these results, which depend on CP-AFM measurements over a significant temperature range, is that for ETp measurements on floppy systems, such as proteins, the stress applied to the sample should be kept constant or, at least controlled during measurement.Comment: 24 pages, 6 figures, plus Supporting Information with 4 pages and 2 figure

Taking cues from nature: Hemoglobin catalysed oxygen reduction

We describe experiments which elucidate the reaction mechanism of electrochemical oxygen reduction reaction (ORR) on a glassy carbon electrode modified with hemoglobin in an aqueous environment but with the hemoglobin physically separated from the electrode by a porous Nafion layer. Catalytic amplification of the current signal from the reduction of oxygen in a first electron transfer step is observed in the presence of hemoglobin immobilized within a Nafion coating. An overall four electron ORR mechanism is inferred and validated