Non-exponentiality in electron transfer kinetics: Static versus dynamic disorder models

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation-in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element, V-el.

A perspective of biological supramolecular electron transfer

Electron transfer is an essential activity in biological systems. The migrating electron originates from water-oxygen in photosynthesis and reverts to dioxygen in respiration. In this cycle two metal porphyrin complexes possessing circular conjugated system and macrocyclic pi-clouds, chlorophyll and hems, play a decisive role in mobilising electrons for travel over biological structures as extraneous electrons. Transport of electrons within proteins (as in cytochromes) and within DNA (during oxidative damage and repair) is known to occur. Initial evaluations did not favour formation of semiconducting pathways of delocalized electrons of the peptide bonds in proteins and of the bases in nucleic acids. Direct measurement of conductivity of bulk material and quantum chemical calculations of their polymeric structures also did not support electron transfer in both proteins and nucleic acids. New experimental approaches have revived interest in the process of charge transfer through DNA duplex. The fluorescence on photoexcitation of Ru-complex was found to be quenched by Rh-complex, when both were tethered to DNA and intercalated in the base stack. Similar experiments showed that damage to G-bases and repair of T-T dimers in DNA can occur by possible long range electron transfer through the base stack. The novelty of this phenomenon prompted the apt name, chemistry at a distance. Based on experiments with ruthenium modified proteins, intramolecular electron transfer in proteins is now proposed to use pathways that include C-C sigma-bonds and surprisingly hydrogen bonds which remained out of favour for a long time. In support of this, some experimental evidence is now available showing that hydrogen bond-bridges facilitate transfer of electrons between metal-porphyrin complexes. By molecular orbital calculations over 20 years ago. we found that "delocalization of an extraneous electron is pronounced when it enters low-lying virtual orbitals of the electronic structures of peptide units linked by hydrogen bonds". This review focuses on supramolecular electron transfer pathways that can emerge on interlinking by hydrogen bonds and metal coordination of some unnoticed structures with pi-clouds in proteins and nucleic acids, potentially useful in catalysis and energy missions.

Direct and sensitized (energy and electron transfer) geometric isomerization of stilbene within zeolites: a comparison between solution and zeolite as reaction media

The trans- and cis-stilbenes upon inclusion in NaY zeolite are thermally stable. Direct excitation and triplet sensitization results in geometric isomerization and the excited state behavior under these conditions are similar to that in solution. Upon direct excitation, a photostationary state consisting of 65% cis and 35% trans isomers is established. Triplet sensitization with 2-acetonaphthone gave a photostationary state consisting of 63% cis and 37% trans isomers. These numbers are similar to the ones obtained in solution. Thus, the presence of cations and the confined space within the zeolite have very little influence on the overall chemistry during direct and triplet sensitization. However, upon electron transfer sensitization with N-methylacridinium (NMA) as the sensitizer within NaY, isomerization from cis-stilbene radical cation to trans-stilbene occurs and the recombination of radical ions results in triplet stilbene. Prolonged irradiation gave a photostationary state (65% cis and 35% trans) similar to triplet sensitization. This behavior is unique to the zeolite and does not take place in solution. Steady state fluorescence measurements showed that the majority of stilbene molecules are close to the N-methylacridinium sensitizer. Diffuse reflectance flash photolysis studies established that independent of the isomer being sensitized only trans radical cation is formed. Triplet stilbene is believed to be generated via recombination of stilbene radical cation and sensitizer radical anion. One should be careful in using acidic HY zeolite as a medium for photoisomerization of stilbenes. In our hands, in these acidic zeolites isomerization dominated the photoisomerization. (C) 2002 Elsevier Science B.V. All rights reserved.

Combined Electron Transfer Dissociation-Collision-Induced Dissociation Fragmentation in the Mass Spectrometric Distinction of Leucine, Isoleucine, and Hydroxyproline Residues in Peptide Natural Products

Distinctions between isobaric residues have been a major challenge in mass spectrometric peptide sequencing. Here, we propose a methodology for distinction among isobaric leucine, isoleucine, and hydroxyproline, a commonly found post-translationally modified amino acid with a nominal mass of 113 Da, through a combined electron transfer dissociation-collision-induced dissociation approach. While the absence of c and z(center dot) ions, corresponding to the Yyy-Xxx (Xxx = Leu, Ile, or Hyp) segment, is indicative of the presence of hydroxyproline, loss of isopropyl (Delta m = 43 Da) or ethyl radicals (Delta m = 29 Da), through collisional activation of z(center dot) radical ions, are characteristic of leucine or isoleucine, respectively. Radical migration processes permit distinctions even in cases where the specific e ions, corresponding to the Yyy-Leu or -Ile segments, are absent or of low intensity. This tandem mass spectrometric (MSn) method has been successfully implemented in a liquid chromatography MSn platform to determine the identity of 23 different isobaric residues from a mixture of five different peptides. The approach is convenient for distinction of isobaric residues from any crude peptide mixture, typically encountered in natural peptide libraries or proteomic analysis.

Single electron transfer-driven multi-dimensional signal read-out function of TCNQ as an ``off-the-shelf'' detector for cyanide

Herein we report the first applications of TCNQ as a rapid and highly sensitive off-the-shelf cyanide detector. As a proof-of-concept, we have applied a kinetically selective single-electron transfer (SET) from cyanide to deep-lying LUMO orbitals of TCNQ to generate a persistently stable radical anion (TCNQ(center dot-)), under ambient condition. In contrast to the known cyanide sensors that operate with limited signal outputs, TCNQ(center dot-) offers a unique multiple signaling platform. The signal readability is facilitated through multichannel absorption in the UV-vis-NIR region and scattering-based spectroscopic methods like Raman spectroscopy and hyper Rayleigh scattering techniques. Particularly notable is the application of the intense 840 nm NIR absorption band to detect cyanide. This can be useful for avoiding background interference in the UV-vis region predominant in biological samples. We also demonstrate the fabrication of a practical electronic device with TCNQ as a detector. The device generates multiorder enhancement in current with cyanide because of the formation of the conductive TCNQ(center dot-).

Electron transfer statistics and thermal fluctuations in molecular junctions

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects. (C) 2015 AIP Publishing LLC.

Redox-Active Metal-Organic Frameworks: Highly Stable Charge-Separated States through Strut/Guest-to-Strut Electron Transfer

Molecular organization of donor and acceptor chromophores in self-assembled materials is of paramount interest in the field of photovoltaics or mimicry of natural light-harvesting systems. With this in mind, a redox-active porous interpenetrated metal-organic framework (MOF), {Cd(bpdc)(bpNDI)]4.5H(2)ODMF}(n) (1) has been constructed from a mixed chromophoric system. The -oxo-bridged secondary building unit, {Cd-2(-OCO)(2)}, guides the parallel alignment of bpNDI (N,N-di(4-pyridyl)-1,4,5,8-naphthalenediimide) acceptor linkers, which are tethered with bpdc (bpdcH(2)=4,4-biphenyldicarboxylic acid) linkers of another entangled net in the framework, resulting in photochromic behaviour through inter-net electron transfer. Encapsulation of electron-donating aromatic molecules in the electron-deficient channels of 1 leads to a perfect donor-acceptor co-facial organization, resulting in long-lived charge-separated states of bpNDI. Furthermore, 1 and guest encapsulated species are characterised through electrochemical studies for understanding of their redox properties.

Probing Ultrafast Photoinduced Electron Transfer to TiO2 from CdS Nanocrystals of Varying Crystallographic Phase Content

The photoinduced electron transfer processes in a nanoheterostructured semiconductor assembly are complex and depend on various parameters Of the constituents of the assembly. We present here the ultrafast electron transfer characteristics of an assembly comprised of a Wide band semiconductor, titanium dioxide (TiO2), attached to light-harvesting cadmium sulfide (CdS) nanotrystals of varying crystallographic phase content. Quantitative analysis of Synchrotron high-resolution X-ray. diffraction data of CdS nanocrystals precisely reveals the presence of both wurtzite and zinc blende phases in varying amounts. The,estimated content of crystal phases is observed to be strongly dependent on an important synthesis parameter, viz., the ratio of the two solvents. The biphasit nature of CdS influences directly the shape of the nanocrystal at long reaction times as well as the transfer of the photoexcited electrons from the CdS to TiO2 as obtained from transient absorption spectroscopy. A higher amount of zinc blende Phase is observed to be beneficial for fast electron transfer across the CdS-TiO2 interface. The electron transfer rate constant differs by one order of magnitude between the CdS nanocryStals and varies linearly with the fraction of the phases.

Electron transfer amongst flavo- and hemo-proteins: diffusible species effect the relay processes, not protein-protein binding

Hitherto, electron transfer (ET) between redox proteins has been deemed to occur via donor-acceptor binding, and diffusible reactive species are considered as deleterious side-products in such systems. Herein, ET from cytochrome P450 reductase (CPR, an animal membrane flavoprotein) and horseradish peroxidase (HRP, a plant hemoprotein) to cytochrome c (Cyt c, a soluble animal hemoprotein) was probed under diverse conditions, using standard assays. ET in the CPR-Cyt c system was critically inhibited by cyanide and sub-equivalent levels of polar one-electron cyclers like copper ions, vitamin C/Trolox and superoxide dismutase. In the presence of lipids, inhibition was also afforded by amphipathic molecules vitamin E, palmitoyl-vitamin C and the membrane hemoprotein, cytochrome b(5). Such nonspecific inhibition (by diverse agents in both aqueous and lipid phases) indicated that electron transfer/relay was effected by small diffusible agents, whose lifetimes are shortened by the diverse radical scavengers. When CPR was retained in a dialysis membrane and Cyt c presented outside in free solution, ET was still observed. Further, HRP (taken at nM levels) catalyzed oxidation of a phenolic substrate was significantly inhibited upon the incorporation of sub-nM levels of Cyt c. The findings imply that CPR-Cyt c or HRP-Cyt c binding is not crucial for ET. Further, fundamental quantitative arguments (based on diffusion/collision) challenge the erstwhile protein-protein binding-assisted ET hypothesis. It is proven beyond reasonable doubt that mobile and diffusible electron carriers (ions and radicals) serve as ``redox-relay agents'' in the biological ET models/setup studied.

Preparation, characterization and intramolecular electron-transfer studies of ruthenium-modified cytochromes c

Redox-active ruthenium complexes have been covalently attached to the surface of a series of natural, semisynthetic and recombinant cytochromes c. The protein derivatives were characterized by a variety of spectroscopic techniques. Distant Fe^(2+) - Ru^(3+) electronic couplings were extracted from intramolecular electron-transfer rates in Ru(bpy)_2(im)HisX (where X= 33, 39, 62, and 72) derivatives of cyt c. The couplings increase according to 62 (0.0060) < 72 (0.057) < 33 (0.097) < 39 (0.11 cm^(-1)); however, this order is incongruent with histidine to heme edge-edge distances [62 (14.8) > 39 (12.3) > 33 (11.1) > =72 (8.4 Å)]. These results suggest the chemical nature of the intervening medium needs to be considered for a more precise evaluation of couplings. The rates (and couplings) correlate with the lengths of a-tunneling pathways comprised of covalent bonds, hydrogen bonds and through-space jumps from the histidines to the heme group. Space jumps greatly decrease couplings: one from Pro71 to Met80 extends the σ-tunneling length of the His72 pathway by roughly 10 covalent bond units. Experimental couplings also correlate well with those calculated using extended Hiickel theory to evaluate the contribution of the intervening protein medium.

Two horse heart cyt c variants incorporating the unnatural amino acids (S)-2- amino-3-(2,2'-bipyrid-6-yl)-propanoic acid (6Bpa) and (S)-2-amino-3-(2,2'-bipyrid-4-yl)propanoic acid ( 4Bpa) at position 72 have been prepared using semisynthetic protocols. Negligible perturbation of the protein structure results from this introduction of unnatural amino acids. Redox-active Ru(2,2'-bipyridine)_2^(2+) binds to 4Bpa72 cyt c but not to the 6Bpa protein. Enhanced ET rates were observed in the Ru(bpy)_2^(2+)-modified 4Bpa72 cyt c relative to the analogous His72 derivative. The rapid (< 60 nanosecond) photogeneration of ferrous Ru-modified 4Bpa72 cyt c in the conformationally altered alkaline state demonstrates that laser-induced ET can be employed to study submicrosecond protein-folding events.

Electron transfer in cytochrome c oxidase : the rate of electron equillibration between cytochrome a and copper A

Intramolecular electron transfer in partially reduced cytochrome c oxidase has been studied by means of perturbed equilibrium techniques. We have prepared a three electron reduced, CO inhibited form of the enzyme in which cytochrome a and copper A are partially reduced an in intramolecular redox equilibrium. When these samples were photolyzed using a nitrogen laser (0.6 µs, 1.0 mJ pulses) changes in absorbance at 598 nm and 830 nm were observed which are consistent with a fast electron from cytochrome a to copper A. The absorbance changes at 598 nm have an apparent rate of 17,200 ± 1,700 s^(-1) (1σ), at pH 7.0 and 25.5 °C. These changes were not observed in either the CO mixed valence or CO inhibited fully reduced forms of the enzyme. The rate is fastest at about pH 8.0, and falls off in either direction, and there is a small, but clear temperature dependence. The process was also observed in the cytochrome c -- cytochrome c oxidase high affinity complex.

This rate is far faster than any rate measured or inferred previously for the cytochrome a -- copper A electron equilibration, but the interpretation of these results is hampered by the fact that the relaxation could only be followed during the time before CO became rebound to the oxygen binding site. The meaning of our our measured rate is discussed, along with other reported rates for this process. In addition, a temperature-jump experiment on the same system is discussed.

We have also prepared a partially reduced, cyanide inhibited form of the enzyme in which cytochrome a, copper A and copper B are partially reduced and in redox equilibrium. Warming these samples produced absorbance changes at 605 nm which indicate that cytochrome a was becoming more oxidized, but there were no parallel changes in absorbance at 830 nm as would be expected if copper A was becoming reduced. We concluded that electrons were being redistributed from cytochrome a to copper B. The kinetics of the absorbance changes at 605 nm were investigated by temperature-jump methods. Although a rate could not be resolved, we concluded that the process must occur with an (apparent) rate larger than 10,000 s^(-1).

During the course of the temperature-jump experiments, we also found that non-redox related, temperature dependent absorbance changes in fully reduced CO inhibited cytochrome c oxidase, and in the cyanide mixed valence enzyme, took place with an (apparent) rate faster that 30,000 s^(-1).

Electrochemical and electron transfer investigations of copper proteins

A study of the pH and temperature dependence of the redox potentials of azurins from five species of bacteria has been performed. The variations in the potentials with pH have been interpreted in terms of electrostatic interactions between the copper site and titrating histidine residues, including the effects of substitutions in the amino acid sequences of the proteins on the electrostatic interactions. A comparison of the observed pH dependences with predictions based on histidine pK_a values known for Pseudomonas aeruginosa (Pae), Alcaligenes denitrificans (Ade), and Alcaligenes faecalis (Afa) azurins indicates that the Pae and Ade redox potentials exhibit pH dependences in line with electrostatic arguments, while Afa azurin exhibits more complex behavior. Redox enthalpies and entropies for four of the azurins at low and high pH values have also been obtained. Based on these results in conjuction with the variable pH experiments, it appears that Bordetella bronchiseptica azurin may undergo a more substantial conformational change with pH than has been observed for other species of azurin.

The temperature dependence of the redox potential of bovine erythrocyte superoxide dismutase (SOD) has been determined at pH 7.0, with potassium ferricyanide as the mediator. The following thermodynamic parameters have been obtained (T = 25°C): E°' = 403±5 mV vs. NHE, ΔG°' = -9.31 kcal/mol, ΔH°' = -21.4 kcal/mol, ΔS°' = -40.7 eu, ΔS°'_(rc) = -25.1 eu. It is apparent from these results that ΔH°', rather than ΔS°', is the dominant factor in establishing the high redox potential of SOD. The large negative enthalpy of reduction may also reflect the factors which give SOD its high specificity toward reduction and oxidation by superoxide.

Preparation and characterization of an intramolecular electron transfer in a pentaammineruthenium derivative of Candida krisei cytochrome c

A semisynthetic binuclear metalloprotein has been prepared by appending the pentaammineruthenium moiety to histidine 39 of the cytochrome c from the yeast Candida krusei. The site of ruthenium binding was identified by peptide mapping. Spectroscopic and electrochemical properties of the derivative indicate the protein conformation is unperturbed by the modification. A preliminary (minimum) rate constant of 170s^(-1) has been determined for the intramolecular electron transfer from ruthenium(II) to iron(III), which occurs over a distance of at least 13Å (barring major conformational changes). Electrochemical studies indicate that this reaction should proceed with a driving force of ~170mV. The rate constant is an order of magnitude faster than that observed in horse heart cytochrome c for intramolecular electron transfer from pentaammineruthenium(II)(histidine 33) to iron(III) (over a similar distance, and with a similar driving force), suggesting a medium or orientation effect makes the Candida intramolecular electron transfer more favorable.

Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.