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DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals’ affected neighbors, such a spreading process becomes a “complex contagion”. This non-linearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g. for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g. for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary non-linear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of ”selection” (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Saturation and Recurrence of Quantum Complexity in Random Local Quantum Dynamics

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. Published by the American Physical Society 2024

Oszmaniec, Michał (ORCID:0000000249466835)↗

DOE OSTI2024

Dicarbonyl[10,10-dimethyl-5,15-bis(pentafluorophenyl)biladiene]ruthenium(II): discovery of the first ruthenium tetrapyrrole cis -dicarbonyl complex by X-ray and electron diffraction

Dicarbonyl[10,10-dimethyl-5,15-bis(pentafluorophenyl)biladiene]ruthenium(II), [Ru(C 33 H 16 F 10 N 4 )(CO) 2 ] or Ru(CO) 2 [DMBil1], is the first reported ruthenium(II) cis-dicarbonyl tetrapyrrole complex. The neutral complex sports two carbonyls and an oligotetrapyrrolic biladiene ligand. Notably, the biladiene adopts a coordination geometry that is well distorted from square planar and much more closely approximates a seesaw arrangement. Accordingly, Ru(CO) 2 [DMBil1] is not only the first ruthenium cis-dicarbonyl with a tetrapyrrole ligand, but also the first metal biladiene complex in which the tetrapyrrole does not adopt a (pseudo-)square-planar coordination geometry. Ru(CO) 2 [DMBil1] is weakly luminescent, displaying λ em = 552 nm upon excitation at λ ex = 500 nm, supports two reversible 1 e – reductions at –1.45 and –1.73 V (versus Fc + /Fc), and has significant absorption features at 481 and 531 nm, suggesting suitability for photocatalytic and photosensitization applications. While the structure of Ru(CO) 2 [DMBil1] was initially determined by X-ray diffraction, a traditionally acceptable quality structure could not be obtained (despite multiple attempts) because of consistently poor crystal quality. Furthermore, an independent structure obtained from electron diffraction experiments corroborates the structure of this unusual biladiene complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Multivariate analysis: An essential for studying complex glasses

Understanding the impact of individual compositional components on the devitrification of complex multicomponent glasses, for example, 10–50+ oxides, typically requires numerous studies to examine each component's impact. Here we apply exploratory data analysis (EDA) to a heterogeneous data set of silicate glasses to determine the cations’ individual and interacting effects on the crystallization of nepheline (nominally NaAlSiO 4 ). Our data consisted of 795 simulated high-level nuclear waste glasses composed of, on average, 50 oxide components. We determine the interactions in the heterogeneous data that cause deviations from the behavior found in simplified composition studies. Using both univariate and bivariate EDA techniques, we demonstrate the importance of including calculated structural glass parameters on nepheline's devitrification, including field strength, cation-to-anion radius ratio, and single-bond strength. Here, we also show that studies with simplified glass compositions may fall short in generating knowledge directly transferrable to complex glass compositions. The method used in this study has the potential to inform experimental design for simplified compositions (~6+ oxides) that can generate knowledge directly transferrable to complex, multivariable compositions. The observations reported here have broad implications for any study attempting to map the physical properties of a complex glass containing numerous cations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Phylogenomic structure and speciation in an emerging model: the Sphagnum magellanicum complex (Bryophyta)

Sphagnum magellanicum is one of two Sphagnum species for which a reference-quality genome exists to facilitate research in ecological genomics. Phylogenetic and comparative genomic analyses were conducted based on resequencing data from 48 samples and RADseq analyses based on 187 samples. Here, we report that there are four clades/species within the S. magellanicum complex in eastern North America and that the reference genome belongs to Sphagnum divinum . The species exhibit tens of thousands (RADseq) to millions (resequencing) of fixed nucleotide differences. Two species, however, referred to informally as S. diabolicum and S. magni because they have not been formally described, are differentiated by only 100 (RADseq) to 1000 (resequencing) of differences. Introgression among species in the complex is demonstrated using D-statistics and f 4 ratios. One ecologically important functional trait, tissue decomposability, which underlies peat (carbon) accumulation, does not differ between segregates in the S. magellanicum complex, although previous research showed that many closely related Sphagnum species have evolved differences in decomposability/carbon sequestration. Phylogenetic resolution and more accurate species delimitation in the S. magellanicum complex substantially increase the value of this group for studying the early evolutionary stages of climate adaptation and ecological evolution more broadly.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Novel principal component analysis tool based on python for analysis of complex spectra of time-of-flight secondary ion mass spectrometry

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a powerful surface analysis tool, which can simultaneously provide elemental, isotopic, and molecular information with part per million (ppm) sensitivity. However, each spectrum may be composed of hundreds of ion signals, which makes the spectra data complex. Principal component analysis (PCA) is a multivariate analysis technique that has been widely used to figure out the variances among samples in ToF-SIMS spectra data analysis and is showing great success in the explanation of complex ToF-SIMS spectra. So far, several software tools have been developed for PCA of ToF-SIMS spectra; however, none of them are freely available. Such a situation leads to some difficulties in extending applications of PCA to various research fields. More importantly, it has long been challenging for common researchers to understand PCA plots and extract chemical differences among samples. In this work, we developed a new and flexible software tool (named “advanced spectra pca toolbox”) based on python for PCA of complex ToF-SIMS spectra along with an easy-to-read manual. It can generate data analysis reports automatically to explain chemical differences among samples, allowing less experienced researchers to easily understand tricky PCA results. Moreover, it is expandable and compatible with artificial intelligence/machine learning functions. Pure goethite and different lignin adsorbed goethite samples were used as a model system to demonstrate our new software tool, proving that our software tool can be readily used in complex spectra data processing. Our new software tool is open-source, convenient, flexible, and expandable. We expect this open-source tool will benefit the ToF-SIMS community.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

As an optical processor, a diffractive deep neural network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees of freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are nonnegative, acting on diffraction-limited optical intensity patterns at the input field of view. Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Attention to quantum complexity

The imminent era of error-corrected quantum computing demands robust methods to characterize quantum state complexity from limited, noisy measurements. We introduce the Quantum Attention Network (QuAN), a classical artificial intelligence (AI) framework leveraging attention mechanisms tailored for learning quantum complexity. Inspired by large language models, QuAN treats measurement snapshots as tokens while respecting permutation invariance. Combined with our parameter-efficient miniset self-attention block, this enables QuAN to access high-order moments of bit-string distributions and preferentially attend to less noisy snapshots. We test QuAN across three quantum simulation settings: driven hard-core Bose-Hubbard model, random quantum circuits, and toric code under coherent and incoherent noise. QuAN directly learns entanglement and state complexity growth from experimental computational basis measurements, including complexity growth in random circuits from noisy data. In regimes inaccessible to existing theory, QuAN unveils the complete phase diagram for noisy toric code data as a function of both noise types, highlighting AI’s transformative potential for assisting quantum hardware.

Kim, Hyejin [Cornell Univ., Ithaca, NY (United Sta↗

DOE OSTI2024

Metal Organic Complexation in Seawater: Historical Background and Future Directions

The speciation of most biologically active trace metals in seawater is dominated by complexation by organic ligands. This review traces the history of work in this area, from the early observations that showed surprisingly poor recoveries using metal preconcentration protocols to the present day, where advances in mass spectroscopy and stable isotope geochemistry are providing new insights into the structure, origin, fate, and biogeochemical impact of organic ligands. Many long-standing hypotheses about the specific biological origin of ligands such as siderophores in seawater are finally being validated. This work has revealed the complexity of organic complexation, with multiple ligands and, in some cases, timescales of ligand exchange that are much slower than originally thought. The influence of organic complexation on scavenging is now a key parameter in biogeochemical models of biologically essential metals, especially iron. New insights about the sources and sinks of ligands are required to enhance the usefulness of these models.

Geochemistry & Geophysics↗

DOE OSTI2020

Two-Layer Dynamic Recycling Model (2L-DRM): Learning from Moisture Tracking Models of Different Complexity

Atmospheric moisture tracking models are used to identify and quantify sources and sinks of water in the atmospheric branch of the hydrologic cycle. These models are primarily used to investigate the origin of moisture resulting in precipitation for particular regions around the globe. Moisture tracking models vary widely in their level of complexity, depending on the number of physical processes represented. Complex models are comprehensive in their physical representation, but computationally much more expensive than simple models, which only focus on specific physical processes and use simplifying assumptions. We present the mathematical derivation of the new two-layer dynamical recycling model (2L-DRM), a simple analytical moisture tracking model that relaxes the vertically-integrated formulation of the original one-layer DRM (Dominguez et al., 2006). By comparing the simple DRM to a very complex moisture tracking model that uses water vapor tracers embedded within the Weather Research and Forecast regional climate model (WRF-WVT) for the North American Monsoon region, we pinpoint the absence of vertical wind shear as the main deficiency in the simple DRM. When comparing both simple models (DRM and 2L-DRM) to the WRF-WVT (which we treat as ‘truth’), the 2L-DRM better captures the spatial extent, the net amount and the temporal variability of precipitation that originates from oceanic and local terrestrial sources. The 2L-DRM is well suited to study the large-scale climatological sources of moisture, and for these applications, performs on-par with the much more complex and computationally demanding WRF-WVT model.

Dominguez, Francina↗

DOE OSTI2024

X-Band Radar and Surface-Based Observations of Cold-Season Precipitation in Western Colorado’s Complex Terrain

Abstract Hydrologic processes associated with intermountain cold-season precipitation in the Upper Colorado River basin have important impacts on avalanche forecasting and water resource management. However, traditional weather radar networks struggle with observations in this complex terrain. Data collected during the Study of Precipitation, the Lower Atmosphere, and the Surface for Hydrometeorology (SPLASH) and its sister campaign, Surface Atmosphere Integrated Field Laboratory (SAIL) in the East River watershed of western Colorado, are used to examine a multistorm period from 23 December 2021 to 1 January 2022 that contributed 35% of the total winter precipitation in this watershed. Dual-polarization X-band radar and disdrometer measurements show ∼30-mm differences in precipitation amount at two sites in proximity over four distinct storm events within the period. Wind patterns, synoptic forcings, microphysical characteristics of precipitation, and surface meteorology are analyzed to explain the observed spatial variability of cold-season precipitation in complex mountainous terrain. Analysis shows that differences over time within this event are mainly accounted for by synoptic forcings, such as frontal passages; differences between sites are accounted for by the impact of variations in local wind patterns on precipitation microphysics. Patterns of surface precipitation intensity are compared and found to be correlated with X-band radar signatures; a relationship between a strong dendritic growth stage and intense low-density surface precipitation is reinforced by this study. This relationship demonstrates the importance of particle growth mechanisms on surface snowfall patterns in high-altitude complex terrain, underscoring the importance of realistic microphysical parameterizations. Significance Statement The amount and density of snowpack from western Colorado winter storms have significant impacts on water resources in the Upper Colorado River basin. Snowpack characteristics are affected by small-scale differences in how snow forms in the atmosphere. These differences are hard to study in the complex terrain of the Rockies, but data from the SPLASH and SAIL field campaigns allows us to investigate how snow crystal formation and mountain-driven wind patterns affect snow near the surface. Our study finds that snow crystal growth varies over small space and time scales and is likely controlled by the terrain beneath a given location and resultant local wind patterns. These results imply that predicting snowpack in the Rockies requires properly representing local wind patterns and crystal growth processes in models.

Heflin, Stella↗

DOE OSTI2022

Assembly of ordered DNA-curli fibril complexes during Salmonella biofilm formation correlates with strengths of the type I interferon and autoimmune responses

Deposition of human amyloids is associated with complex human diseases such as Alzheimer’s and Parkinson’s. Amyloid proteins are also produced by bacteria. The bacterial amyloid curli, found in the extracellular matrix of both commensal and pathogenic enteric bacterial biofilms, forms complexes with extracellular DNA, and recognition of these complexes by the host immune system may initiate an autoimmune response. Here, we isolated early intermediate, intermediate, and mature curli fibrils that form throughout the biofilm development and investigated the structural and pathogenic properties of each. Early intermediate aggregates were smaller than intermediate and mature curli fibrils, and circular dichroism, tryptophan, and thioflavin T analyses confirmed the establishment of a beta-sheet secondary structure as the curli conformations matured. Intermediate and mature curli fibrils were more immune stimulatory than early intermediate fibrils in vitro . The intermediate curli was cytotoxic to macrophages independent of Toll-like receptor 2. Mature curli fibrils had the highest DNA content and induced the highest levels of Isg15 expression and TNFα production in macrophages. In mice, mature curli fibrils induced the highest levels of anti-double-stranded DNA autoantibodies. The levels of autoantibodies were higher in autoimmune-prone NZBWxF/1 mice than wild-type C57BL/6 mice. Chronic exposure to all curli forms led to significant histopathological changes and synovial proliferation in the joints of autoimmune-prone mice; mature curli was the most detrimental. In conclusion, curli fibrils, generated during biofilm formation, cause pathogenic autoimmune responses that are stronger when curli complexes contain higher levels of DNA and in mice predisposed to autoimmunity.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Uranyl oxalate species in high ionic strength environments: stability constants for aqueous and solid uranyl oxalate complexes

Uranyl ion, UO 2 2+ , and its aqueous complexes with organic and inorganic ligands can be the dominant species for uranium transport on the Earth surface or in a nuclear waste disposal system if an oxidizing condition is present. As an important biodegradation product, oxalate, C 2 O 4 2– , is ubiquitous in natural environments and is known for its ability to complex with the uranyl ion. Oxalate can also form solid phases with uranyl ion in certain environments thus limiting uranium migration. Therefore, the determination of stability constants for aqueous and solid uranyl oxalate complexes is important not only to the understanding of uranium mobility in natural environments, but also to the performance assessment of nuclear waste disposal. In this work, we developed a thermodynamic model for the UO 2 2+ –Na + –H + –Cl – –ClO 4 – –C 2 O 4 2– –NO 3 – –H 2 O system to ionic strength up to ~11 mol•kg –1 . We constrained the stability constants for UO 2 C 2 O 4 (aq) and UO 2 (C 2 O 4 ) 2 2– at infinite dilution based on our evaluation of the literature data over a wide range of ionic strengths up to ~11 mol•kg –1 . We also obtained the solubility constants at infinite dilution for solid uranyl oxalates, UO 2 C 2 O 4 •3H 2 O, based on the solubility data over a wide range of ionic strengths. The developed model will enable for the accurate stability assessment of oxalate complexes affecting uranium mobility under a wide range of conditions including those in deep geological repositories.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Computational Data Associated with the publication: Formation of a Decanuclear Organometallic Dysprosium Complex via a Radical–Radical Cross–Coupling Reaction

Over the years, polynuclear cyclic or torus complexes have attracted increasing interest due to their unique metal topologies and properties. However, the isolation of polynuclear cyclic organometallic complexes is extremely challenging due to their inherent reactivity, which stems from the labile and reactive metal‐carbon bonds. In this study, the pyrazine ligand undergoes a radical‐radical cross‐coupling reaction leading to the formation of a decanuclear [(Cp*)20Dy10(L1)10] ⋅ 12(C7H8) (1; where L1 = anion of 2‐prop‐2‐enyl‐2H‐pyrazine; Cp* = pentamethylcyclopentadienyl) complex, where all DyIII metal centres are bridged by the anionic L1 ligand. Amongst the family of polynuclear Ln organometallic complexes bearing CpR2Lnx units (CpR = substituted cyclopentadienyl), 1 features the highest nuclearity obtained to date. In‐depth computational studies were conducted to elucidate the proposed reaction mechanism and formation of L1, while probing of the magnetic properties of 1, revealed slow magnetic relaxation upon application of a static dc field.

Bajaj, Neha↗

DOE OSTI2022

Tomographic imaging of atmospheric pressure plasma on complex surfaces

Many plasma types and behaviors such as streamer, arcs, cathode spots, anode spots, ionization waves, and magnetic field interactions create non-symmetric, fully 3D plasma structures. The plasma distribution in 3D space is heavily influenced by complex surfaces and the coupling interactions between plasma properties and the interfacing material properties. For example, ionization waves propagate in directions where ionization rates are highest, leading to complex configurations that are not fully understood or well characterized. Recent advances in laser diagnostics and models have been able to investigate well-controlled idealized plasmas in 2D fashion, but the complex structure in actual plasmas requires a technique than can provide a more complete 3D picture. However, 3D plasma diagnostics do not currently exist. To address this limitation, this activity will leverage available equipment to build a new tomographic optical imaging capability and advance the state-of-the-art in plasma diagnostics to investigate 3D phenomena on complex surfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Project 18-15263 X-ray Studies of Interfacial Molecular Complexes in ALSEP Back-Extraction (Research Performance Final Report)

The objective of the project was to use synchrotron X-rays to measure the molecular-scale organization of extractants, complexants, buffers, and metal ions at the organic-aqueous (liquid-liquid) interface during solvent back-extraction under conditions relevant to ALSEP (Actinide-Lanthanide Separation Process). The capability of X-ray fluorescence near total reflection (XFNTR) was extended to explore the distribution of Eu(III) between the liquid-liquid interface and bulk organic and aqueous phases which contained extractants HDEHP (bis(2-ethylhexyl) phosphoric acid) and HEHEHP (2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester), the complexant DTPA (diethylene triamine pentaacetic acid), and citric and nitric acids. Although an Am-compatible sample cell was developed, extending x-ray measurements of flat liquid-liquid interfaces to the actinide Am(III) did not prove to be possible within constraints imposed by the Advanced Photon Source. However, preliminary measurements with a drop cell may eventually provide a path forward to investigate Am(III) at a liquid interface. It was also demonstrated that competitive binding that occurs during back-extraction of lanthanide ions to either a phosphoric acid extractant (DHDP, di-hexadecyl phosphate) at the liquid interface or to complexant DTPA in the bulk aqueous phase could be reversibly tuned by X-ray exposure. Separately, X-ray measurements from the liquid-vapor interface explored the role of the aqueous solubility of HDEHP and HEHEHP and their interactions with a range of lanthanides and transition metal ions. Finally, the capability of X-ray absorption spectroscopy (EXAFS) was extended to probe metal ion coordination in lanthanide ion-extractant complexes at the liquid-vapor interface. Complementary to the specific interfacial systems studied during this project, the development of x-ray techniques expands our ability to understand ion ordering at liquid interfaces.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Structure-Function and Nearest Neighbor Interactions of the Cytochrome b 6 f Complex

Test prediction from our (i) high resolution (2.5 Å) structure of cyanobacterial cytochrome b 6 f complex (Structure, 22, 1008-1015, 2014), and (ii) analysis of quinone/quinol traffic within the b 6 f complex (Biophys. J., 107, 1620-1628, 2014) concerning the rate-limiting step in the linear (non-cyclic) electron transport chain. It was concluded that it arises from access of plastoquinol, the electron/proton donor, to the high potential electron carriers, i. e., the Fe 2 S 2 and cytochrome f proteins. The directed motion of the quinol proceeds via a narrow channel on the lumen or electrochemically positive, p- (lumen) side of the b 6 f complex which was defined by crystal structures of the b 6 f complex with quinol analogue inhibitors (J. Mol. Biol., 370, 39-52, 2007).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗