Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism.

We report a 100-million atom-scale model of an entire cell organelle, a photosynthetic chromatophore vesicle from a purple bacterium, that reveals the cascade of energy conversion steps culminating in the generation of ATP from sunlight. Molecular dynamics simulations of this vesicle elucidate how the integral membrane complexes influence local curvature to tune photoexcitation of pigments. Brownian dynamics of small molecules within the chromatophore probe the mechanisms of directional charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore's structural integrity and robust energy conversion. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence molecular-scale insights into the mechanism of cellular aging are inferred. Together, our integrative method and spectroscopic experiments pave the way to first-principles modeling of whole living cells.

Lateral Segregation of Photosystem I in Cyanobacterial Thylakoids.

Photosystem I (PSI) is the dominant photosystem in cyanobacteria and it plays a pivotal role in cyanobacterial metabolism. Despite its biological importance, the native organization of PSI in cyanobacterial thylakoid membranes is poorly understood. Here, we use atomic force microscopy (AFM) to show that ordered, extensive macromolecular arrays of PSI complexes are present in thylakoids from Thermosynechococcus elongatus, Synechococcus sp PCC 7002, and Synechocystis sp PCC 6803. Hyperspectral confocal fluorescence microscopy and three-dimensional structured illumination microscopy of Synechocystis sp PCC 6803 cells visualize PSI domains within the context of the complete thylakoid system. Crystallographic and AFM data were used to build a structural model of a membrane landscape comprising 96 PSI trimers and 27,648 chlorophyll a molecules. Rather than facilitating intertrimer energy transfer, the close associations between PSI primarily maximize packing efficiency; short-range interactions with Complex I and cytochrome b6f are excluded from these regions of the membrane, so PSI turnover is sustained by long-distance diffusion of the electron donors at the membrane surface. Elsewhere, PSI-photosystem II contact zones provide sites for docking phycobilisomes and the formation of megacomplexes. PSI-enriched domains in cyanobacteria might foreshadow the partitioning of PSI into stromal lamellae in plants, similarly sustained by long-distance diffusion of electron carriers.

Multiscale modeling and cinematic visualization of photosynthetic energy conversion processes from electronic to cell scales.

Conversion of sunlight into chemical energy, namely photosynthesis, is the primary energy source of life on Earth. A visualization depicting this process, based on multiscale computational models from electronic to cell scales, is presented in the form of an excerpt from the fulldome show Birth of Planet Earth. This accessible visual narrative shows a lay audience, including children, how the energy of sunlight is captured, converted, and stored through a chain of proteins to power living cells. The visualization is the result of a multi-year collaboration among biophysicists, visualization scientists, and artists, which, in turn, is based on a decade-long experimental-computational collaboration on structural and functional modeling that produced an atomic detail description of a bacterial bioenergetic organelle, the chromatophore. Software advancements necessitated by this project have led to significant performance and feature advances, including hardware-accelerated cinematic ray tracing and instanced visualizations for efficient cell-scale modeling. The energy conversion steps depicted feature an integration of function from electronic to cell levels, spanning nearly 12 orders of magnitude in time scales. This atomic detail description uniquely enables a modern retelling of one of humanity's earliest stories-the interplay between light and life.

Atomic Detail Visualization of Photosynthetic Membranes with GPU-Accelerated Ray Tracing.

The cellular process responsible for providing energy for most life on Earth, namely photosynthetic light-harvesting, requires the cooperation of hundreds of proteins across an organelle, involving length and time scales spanning several orders of magnitude over quantum and classical regimes. Simulation and visualization of this fundamental energy conversion process pose many unique methodological and computational challenges. We present, in two accompanying movies, light-harvesting in the photosynthetic apparatus found in purple bacteria, the so-called chromatophore. The movies are the culmination of three decades of modeling efforts, featuring the collaboration of theoretical, experimental, and computational scientists. We describe the techniques that were used to build, simulate, analyze, and visualize the structures shown in the movies, and we highlight cases where scientific needs spurred the development of new parallel algorithms that efficiently harness GPU accelerators and petascale computers.

Integration of energy and electron transfer processes in the photosynthetic membrane of Rhodobacter sphaeroides.

Photosynthesis converts absorbed solar energy to a protonmotive force, which drives ATP synthesis. The membrane network of chlorophyll-protein complexes responsible for light absorption, photochemistry and quinol (QH2) production has been mapped in the purple phototrophic bacterium Rhodobacter (Rba.) sphaeroides using atomic force microscopy (AFM), but the membrane location of the cytochrome bc1 (cytbc1) complexes that oxidise QH2 to quinone (Q) to generate a protonmotive force is unknown. We labelled cytbc1 complexes with gold nanobeads, each attached by a Histidine10 (His10)-tag to the C-terminus of cytc1. Electron microscopy (EM) of negatively stained chromatophore vesicles showed that the majority of the cytbc1 complexes occur as dimers in the membrane. The cytbc1 complexes appeared to be adjacent to reaction centre light-harvesting 1-PufX (RC-LH1-PufX) complexes, consistent with AFM topographs of a gold-labelled membrane. His-tagged cytbc1 complexes were retrieved from chromatophores partially solubilised by detergent; RC-LH1-PufX complexes tended to co-purify with cytbc1 whereas LH2 complexes became detached, consistent with clusters of cytbc1 complexes close to RC-LH1-PufX arrays, but not with a fixed, stoichiometric cytbc1-RC-LH1-PufX supercomplex. This information was combined with a quantitative mass spectrometry (MS) analysis of the RC, cytbc1, ATP synthase, cytaa3 and cytcbb3 membrane protein complexes, to construct an atomic-level model of a chromatophore vesicle comprising 67 LH2 complexes, 11 LH1-RC-PufX dimers & 2 RC-LH1-PufX monomers, 4 cytbc1 dimers and 2 ATP synthases. Simulation of the interconnected energy, electron and proton transfer processes showed a half-maximal ATP turnover rate for a light intensity equivalent to only 1% of bright sunlight. Thus, the photosystem architecture of the chromatophore is optimised for growth at low light intensities.

Light harvesting by lamellar chromatophores in Rhodospirillum photometricum.

Purple photosynthetic bacteria harvest light using pigment-protein complexes which are often arranged in pseudo-organelles called chromatophores. A model of a chromatophore from Rhodospirillum photometricum was constructed based on atomic force microscopy data. Molecular-dynamics simulations and quantum-dynamics calculations were performed to characterize the intercomplex excitation transfer network and explore the interplay between close-packing and light-harvesting efficiency.

Perspective on Integrative Simulations of Bioenergetic Domains.

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Förster energy transfer theory as reflected in the structures of photosynthetic light-harvesting systems.

Förster's theory of resonant energy transfer underlies a fundamental process in nature, namely the harvesting of sunlight by photosynthetic life forms. The theoretical framework developed by Förster and others describes how electronic excitation migrates in the photosynthetic apparatus of plants, algae, and bacteria from light absorbing pigments to reaction centers where light energy is utilized for the eventual conversion into chemical energy. The demand for highest possible efficiency of light harvesting appears to have shaped the evolution of photosynthetic species from bacteria to plants which, despite a great variation in architecture, display common structural themes founded on the quantum physics of energy transfer as described first by Förster. Herein, Förster's theory of excitation transfer is summarized, including recent extensions, and the relevance of the theory to photosynthetic systems as evolved in purple bacteria, cyanobacteria, and plants is demonstrated. Förster's energy transfer formula, as used widely today in many fields of science, is also derived.

Photosynthetic vesicle architecture and constraints on efficient energy harvesting.

Photosynthetic chromatophore vesicles found in some purple bacteria constitute one of the simplest light-harvesting systems in nature. The overall architecture of chromatophore vesicles and the structural integration of vesicle function remain poorly understood despite structural information being available on individual constituent proteins. An all-atom structural model for an entire chromatophore vesicle is presented, which improves upon earlier models by taking into account the stoichiometry of core and antenna complexes determined by the absorption spectrum of intact vesicles in Rhodobacter sphaeroides, as well as the well-established curvature-inducing properties of the dimeric core complex. The absorption spectrum of low-light-adapted vesicles is shown to correspond to a light-harvesting-complex 2 to reaction center ratio of 3:1. A structural model for a vesicle consistent with this stoichiometry is developed and used in the computation of excitonic properties. Considered also is the packing density of antenna and core complexes that is high enough for efficient energy transfer and low enough for quinone diffusion from reaction centers to cytochrome bc(1) complexes.

Self-assembly of photosynthetic membranes.

Bacterial photosynthetic membranes, also known as chromatophores, are tightly packed with integral membrane proteins that work together to carry out photosynthesis. Chromatophores display a wide range of cellular morphologies; spherical, tubular, and lamellar chromatophores have all been observed in different bacterial species, or with different protein constituents. Through recent computational modeling and simulation, it has been demonstrated that the light-harvesting complexes abundant in chromatophores induce local membrane curvature via multiple mechanisms. These protein complexes assemble to generate a global curvature and sculpt the chromatophores into various cellular-scale architectures.

Energy Transfer Dynamics in an RC-LH1-PufX Tubular Photosynthetic Membrane.

Light absorption and the subsequent transfer of excitation energy are the first two steps of the photosynthetic process, carried out by protein-bound pigments, mainly bacteriochlorophylls (BChls), in photosynthetic bacteria. BChls are anchored in light-harvesting (LH) complexes, such as light-harvesting complex I (LH1), which directly associates with the reaction center (RC), forming the RC-LH1 core complex. In Rhodobacter sphaeroides, RC-LH1 core complexes contain an additional protein, PufX, and assemble into dimeric RC-LH1-PufX core complexes. In the absence of light-harvesting complexes II, the former complexes can aggregate into a helically ordered tubular photosynthetic membrane. We examined the excitation transfer dynamics in a single RC-LH1-PufX core complex dimer using the hierarchical equations of motion for dissipative quantum dynamics that accurately, yet computationally costly, treat the coupling between BChls and their protein environment. A widely employed description, generalized Förster theory, was also used to calculate the transfer rates of the same excitonic system in order to verify the accuracy of this computationally cheap method. Additionally, in light of the structural uncertainties in the Rhodobacter sphaeroides RC-LH1-PufX core complex, geometrical alterations were introduced in the BChl organization. It is shown that the energy transfer dynamics is not affected by the considered changes in the BChl organization, and that generalized Förster theory provides accurate transfer rates. An all-atom model for a tubular photosynthetic membrane is then constructed on the basis of electron microscopy data, and the overall energy transfer properties of this membrane are computed.

Structural model and excitonic properties of the dimeric RC-LH1-PufX complex from Rhodobacter sphaeroides.

The light-harvesting apparatus of the purple bacterial photosynthetic unit consists of a pool of peripheral light-harvesting complexes that transfer excitation energy to a reaction center (RC) via the surrounding pigment-protein complex LH1. Recent electron microscopy and atomic force microscopy studies have revealed that RC-LH1 units of Rhodobacter sphaeroides form membrane-bending dimeric complexes together with the polypeptide PufX. We present a structural model for these RC-LH1-PufX dimeric complexes constructed using the molecular dynamics flexible fitting method based on an EM density map. The arrangement of the LH1 BChls displays a distortion near the proposed location of the PufX polypeptide. The resulting atomic model for BChl arrays is used to compute the excitonic properties of the dimeric RC-LH1 complex. A comparison is presented between the structural and excitonic features of the S-shaped dimeric BChl array of Rhodobacter sphaeroides and the circular BChl arrangement found in other purple bacteria.

Determination of Cell Doubling Times from the Return-on-Investment Time of Photosynthetic Vesicles Based on Atomic Detail Structural Models.

Cell doubling times of the purple bacterium Rhodobacter sphaeroides during photosynthetic growth are determined experimentally and computationally as a function of illumination. For this purpose, energy conversion processes in an intracytoplasmic membrane vesicle, the chromatophore, are described based on an atomic detail structural model. The cell doubling time and its illumination dependence are computed in terms of the return-on-investment (ROI) time of the chromatophore, determined computationally from the ATP production rate, and the mass ratio of chromatophores in the cell, determined experimentally from whole cell absorbance spectra. The ROI time is defined as the time it takes to produce enough ATP to pay for the construction of another chromatophore. The ROI time of the low light-growth chromatophore is 4.5-2.6 h for a typical illumination range of 10-100 µmol photons m-2 s-1, respectively, with corresponding cell doubling times of 8.2-3.9 h. When energy expenditure is considered as a currency, the benefit-to-cost ratio computed for the chromatophore as an energy harvesting device is 2-8 times greater than for photovoltaic and fossil fuel-based energy solutions and the corresponding ROI times are approximately 3-4 orders of magnitude shorter for the chromatophore than for synthetic systems.

Overall energy conversion efficiency of a photosynthetic vesicle.

The chromatophore of purple bacteria is an intracellular spherical vesicle that exists in numerous copies in the cell and that efficiently converts sunlight into ATP synthesis, operating typically under low light conditions. Building on an atomic-level structural model of a low-light-adapted chromatophore vesicle from Rhodobacter sphaeroides, we investigate the cooperation between more than a hundred protein complexes in the vesicle. The steady-state ATP production rate as a function of incident light intensity is determined after identifying quinol turnover at the cytochrome bc1 complex (cytb⁢c1) as rate limiting and assuming that the quinone/quinol pool of about 900 molecules acts in a quasi-stationary state. For an illumination condition equivalent to 1% of full sunlight, the vesicle exhibits an ATP production rate of 82 ATP molecules/s. The energy conversion efficiency of ATP synthesis at illuminations corresponding to 1%-5% of full sunlight is calculated to be 0.12-0.04, respectively. The vesicle stoichiometry, evolutionarily adapted to the low light intensities in the habitat of purple bacteria, is suboptimal for steady-state ATP turnover for the benefit of protection against over-illumination.

General random matrix approach to account for the effect of static disorder on the spectral properties of light harvesting systems.

We develop a random matrix model approach to study static disorder in pigment-protein complexes in photosynthetic organisms. As a case study, we examine the ring of B850 bacteriochlorophylls in the peripheral light-harvesting complex of Rhodospirillum molischianum, formulated in terms of an effective Hamiltonian describing the collective electronic excitations of the system. We numerically examine and compare various models of disorder and observe that both the density of states and the absorption spectrum of the model show remarkable spectral universality. For the case of unitary disorder, we develop a method to analytically evaluate the density of states of the ensemble using the supersymmetric formulation of random matrix theory. Succinct formulas that can be readily applied in future studies are provided in an appendix.

Atomic-level structural and functional model of a bacterial photosynthetic membrane vesicle.

The photosynthetic unit (PSU) of purple photosynthetic bacteria consists of a network of bacteriochlorophyll-protein complexes that absorb solar energy for eventual conversion to ATP. Because of its remarkable simplicity, the PSU can serve as a prototype for studies of cellular organelles. In the purple bacterium Rhodobacter sphaeroides the PSU forms spherical invaginations of the inner membrane, approximately 70 nm in diameter, composed mostly of light-harvesting complexes, LH1 and LH2, and reaction centers (RCs). Atomic force microscopy studies of the intracytoplasmic membrane have revealed the overall spatial organization of the PSU. In the present study these atomic force microscopy data were used to construct three-dimensional models of an entire membrane vesicle at the atomic level by using the known structure of the LH2 complex and a structural model of the dimeric RC-LH1 complex. Two models depict vesicles consisting of 9 or 18 dimeric RC-LH1 complexes and 144 or 101 LH2 complexes, representing a total of 3,879 or 4,464 bacteriochlorophylls, respectively. The in silico reconstructions permit a detailed description of light absorption and electronic excitation migration, including computation of a 50-ps excitation lifetime and a 95% quantum efficiency for one of the model membranes, and demonstration of excitation sharing within the closely packed RC-LH1 dimer arrays.

Comparison of the light-harvesting networks of plant and cyanobacterial photosystem I.

With the availability of structural models for photosystem I (PSI) in cyanobacteria and plants it is possible to compare the excitation transfer networks in this ubiquitous photosystem from two domains of life separated by over one billion years of divergent evolution, thus providing an insight into the physical constraints that shape the networks' evolution. Structure-based modeling methods are used to examine the excitation transfer kinetics of the plant PSI-LHCI supercomplex. For this purpose an effective Hamiltonian is constructed that combines an existing cyanobacterial model for structurally conserved chlorophylls with spectral information for chlorophylls in the Lhca subunits. The plant PSI excitation migration network thus characterized is compared to its cyanobacterial counterpart investigated earlier. In agreement with observations, an average excitation transfer lifetime of approximately 49 ps is computed for the plant PSI-LHCI supercomplex with a corresponding quantum yield of 95%. The sensitivity of the results to chlorophyll site energy assignments is discussed. Lhca subunits are efficiently coupled to the PSI core via gap chlorophylls. In contrast to the chlorophylls in the vicinity of the reaction center, previously shown to optimize the quantum yield of the excitation transfer process, the orientational ordering of peripheral chlorophylls does not show such optimality. The finding suggests that after close packing of chlorophylls was achieved, constraints other than efficiency of the overall excitation transfer process precluded further evolution of pigment ordering.

Excitation migration in trimeric cyanobacterial photosystem I.

A structure-based description of excitation migration in multireaction center light harvesting systems is introduced. The description is an extension of the sojourn expansion, which decomposes excitation migration in terms of repeated detrapping and recapture events. The approach is applied to light harvesting in the trimeric form of cyanobacterial photosystem I (PSI). Excitation is found to be shared between PSI monomers and the chlorophylls providing the strongest respective links are identified. Excitation sharing is investigated by computing cross-monomer excitation trapping probabilities. It is seen that on the average there is a nearly 40% chance of excitation cross transfer and trapping, indicating efficient coupling between monomers. The robustness and optimality of the chlorophyll network of trimeric PSI is examined.