Identification of an N-terminal inhibitory extension as the primary mechanosensory regulator of twitchin kinase.

Titin-like kinases are an important class of cytoskeletal kinases that intervene in the response of muscle to mechanical stimulation, being central to myofibril homeostasis and development. These kinases exist in autoinhibited states and, allegedly, become activated during muscle activity by the elastic unfolding of a C-terminal regulatory segment (CRD). However, this mechano-activation model remains controversial. Here we explore the structural, catalytic, and tensile properties of the multidomain kinase region of Caenorhabditis elegans twitchin (Fn(31)-Nlinker-kinase-CRD-Ig(26)) using X-ray crystallography, small angle X-ray scattering, molecular dynamics simulations, and catalytic assays. This work uncovers the existence of an inhibitory segment that flanks the kinase N-terminally (N-linker) and that acts synergistically with the canonical CRD tail to silence catalysis. The N-linker region has high mechanical lability and acts as the primary stretch-sensor in twitchin kinase, while the CRD is poorly responsive to pulling forces. This poor response suggests that the CRD is not a generic mechanosensor in this kinase family. Instead, the CRD is shown here to be permissive to catalysis and might protect the kinase active site against mechanical damage. Thus, we put forward a regulatory model where kinase inhibition results from the combined action of both N- and C-terminal tails, but only the N-terminal extension undergoes mechanical removal, thereby affording partial activation. Further, we compare invertebrate and vertebrate titin-like kinases and identify variations in the regulatory segments that suggest a mechanical speciation of these kinase classes.

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.

Mutation of conserved histidines alters tertiary structure and nanomechanics of consensus ankyrin repeats.

The conserved TPLH tetrapeptide motif of ankyrin repeats (ARs) plays an important role in stabilizing AR proteins, and histidine (TPLH)-to-arginine (TPLR) mutations in this motif have been associated with a hereditary human anemia, spherocytosis. Here, we used a combination of atomic force microscopy-based single-molecule force spectroscopy and molecular dynamics simulations to examine the mechanical effects of His → Arg substitutions in TPLH motifs in a model AR protein, NI6C. Our molecular dynamics results show that the mutant protein is less mechanically stable than the WT protein. Our atomic force microscopy results indicate that the mechanical energy input necessary to fully unfold the mutant protein is only half of that necessary to unfold the WT protein (53 versus 106 kcal/mol). In addition, the ability of the mutant to generate refolding forces is also reduced. Moreover, the mutant protein subjected to cyclic stretch-relax measurements displays mechanical fatigue, which is absent in the WT protein. Taken together, these results indicate that the His → Arg substitutions in TPLH motifs compromise mechanical properties of ARs and suggest that the origin of hereditary spherocytosis may be related to mechanical failure of ARs.

Sampling diverse near-optimal solutions via algorithmic quantum annealing.

Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open problems is the lack of ergodicity, or mode collapse, for typical stochastic solvers based on Monte Carlo techniques leading to poor generalization or lack of robustness to uncertainties. Currently, there is no universal metric to quantify such performance deficiencies across various solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems. Among others, it allows benchmarking solver performance by a required time-to-diversity (TTD), a generalization of often used time-to-solution (TTS). We illustrate this metric by comparing the sampling power of various quantum annealing strategies. In particular, we show that the inhomogeneous quantum annealing schedules can redistribute and suppress the emergence of topological defects by controlling space-time separated critical fronts, leading to an advantage over standard quantum annealing schedules with respect to both TTS and TTD for finding rare solutions. Using path-integral Monte Carlo simulations for up to 1600 qubits, we demonstrate that nonequilibrium driving of quantum fluctuations, guided by efficient approximate tensor network contractions, can significantly reduce the fraction of hard instances for random frustrated 2D spin glasses with local fields. Specifically, we observe that by creating a class of algorithmic quantum phase transitions, the diversity of solutions can be enhanced by up to 40% with the fraction of hard-to-sample instances reducing by more than 25%.

Excited state dynamics in photosynthetic reaction center and light harvesting complex 1.

Key to efficient harvesting of sunlight in photosynthesis is the first energy conversion process in which electronic excitation establishes a trans-membrane charge gradient. This conversion is accomplished by the photosynthetic reaction center (RC) that is, in case of the purple photosynthetic bacterium Rhodobacter sphaeroides studied here, surrounded by light harvesting complex 1 (LH1). The RC employs six pigment molecules to initiate the conversion: four bacteriochlorophylls and two bacteriopheophytins. The excited states of these pigments interact very strongly and are simultaneously influenced by the surrounding thermal protein environment. Likewise, LH1 employs 32 bacteriochlorophylls influenced in their excited state dynamics by strong interaction between the pigments and by interaction with the protein environment. Modeling the excited state dynamics in the RC as well as in LH1 requires theoretical methods, which account for both pigment-pigment interaction and pigment-environment interaction. In the present study we describe the excitation dynamics within a RC and excitation transfer between light harvesting complex 1 (LH1) and RC, employing the hierarchical equation of motion method. For this purpose a set of model parameters that reproduce RC as well as LH1 spectra and observed oscillatory excitation dynamics in the RC is suggested. We find that the environment has a significant effect on LH1-RC excitation transfer and that excitation transfers incoherently between LH1 and RC.

Juxtaposing density matrix and classical path-based wave packet dynamics.

In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed.

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.

The effect of correlated bath fluctuations on exciton transfer.

Excitation dynamics of various light harvesting systems have been investigated with many theoretical methods including various non-Markovian descriptions of dissipative quantum dynamics. It is typically assumed that each excited state is coupled to an independent thermal environment, i.e., that fluctuations in different environments are uncorrelated. Here the assumption is dropped and the effect of correlated bath fluctuations on excitation transfer is investigated. Using the hierarchy equations of motion for dissipative quantum dynamics it is shown for models of the B850 bacteriochlorophylls of LH2 that correlated bath fluctuations have a significant effect on the LH2→LH2 excitation transfer rate. It is also demonstrated that inclusion of static disorder is crucial for an accurate description of transfer dynamics.

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.

Computing free energy hypersurfaces for anisotropic intermolecular associations.

We previously used an adaptive reaction coordinate force biasing method for calculating the free energy of conformation (Naidoo and Brady, J Am Chem Soc 1999, 121, 2244) and chemical reactions (Rajamani et al., J Comput Chem 2003, 24, 1775) amongst others. Here, we describe a generalized version able to produce free energies in multiple dimensions, descriptively named the free energies from adaptive reaction coordinate forces method. To illustrate it, we describe how we calculate a multidimensional intermolecular orientational free energy, which can be used to investigate complex systems such as protein conformation and liquids. This multidimensional intermolecular free energy W(r, theta(1), theta(2), phi) provides a measure of orientationally dependent interactions that are appropriate for applications in systems that inherently have molecular anisotropic features. It is a highly informative free energy volume, which can be used to parameterize key terms such as the Gay-Berne intermolecular potential in coarse grain simulations. To demonstrate the value of the information gained from the W(r, theta(1), theta(2), phi) hypersurfaces we calculated them for TIP3P, TIP4P, and TIP5P dimer water models in vacuum. A comparison with a commonly used one-dimensional distance free energy profile is made to illustrate the significant increase in configurational information. The W(r) plots show little difference between the three models while the W(r, theta(1), theta(2), phi) hypersurfaces reveal the underlying energetic reasons why these potentials reproduce tetrahedrality in the condensed phase so differently from each.

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.

Light harvesting complex II B850 excitation dynamics.

The dynamics of excitation energy transfer within the B850 ring of light harvesting complex 2 from Rhodobacter sphaeroides and between neighboring B850 rings is investigated by means of dissipative quantum mechanics. The assumption of Boltzmann populated donor states for the calculation of intercomplex excitation transfer rates by generalized Forster theory is shown to give accurate results since intracomplex exciton relaxation to near-Boltzmann population exciton states occurs within a few picoseconds. The primary channels of exciton transfer between B850 rings are found to be the five lowest-lying exciton states, with non-850 nm exciton states making significant contributions to the total transfer rate.

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.

Different Types of Vibrations Interacting with Electronic Excitations in Phycoerythrin 545 and Fenna-Matthews-Olson Antenna Systems.

The interest in the phycoerythrin 545 (PE545) photosynthetic antenna system of marine algae and the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has drastically increased since long-lived quantum coherences were reported for these complexes. For the PE545 complex, this phenomenon is clearly visible even at ambient temperatures, while for the FMO system it is more prominent at lower temperatures. The key to elucidate the role of the environment in these long-lived quantum effects is the spectral density. Here, we employ molecular dynamics simulations combined with quantum chemistry calculations to study the coupling between the biological environment and the vertical excitation energies of the bilin pigment molecules in PE545 and compare them to prior calculations on the FMO complex. It is found that the overall strength of the resulting spectral densities for the PE545 system is similar to the experiment-based counterpart but also to those in the FMO complex. Molecular analysis, however, reveals that the origin for the spectral densities in the low frequency range, which is most important for excitonic transitions, is entirely different. In the case of FMO, this part of the spectral density is due to environmental fluctuations, while, in case of PE545, it is essentially only due to internal modes of the bilin molecules. This finding sheds new light on possible explanations of the long-lived quantum coherences and that the reasons might actually be different in dissimilar systems.

The FMO complex in a glycerol-water mixture.

Experimental findings of long-lived quantum coherence in the Fenna-Matthews-Olson (FMO) complex and other photosynthetic complexes have led to theoretical studies searching for an explanation of this unexpected phenomenon. Extending in this regard our own earlier calculations, we performed simulations of the FMO complex in a glycerol-water mixture at 310 K as well as 77 K, matching the conditions of earlier 2D spectroscopic experiments by Engel et al. The calculations, based on an improved quantum procedure employed by us already, yielded spectral densities of each individual pigment of FMO, in water and glycerol-water solvents at ambient temperature that compare well to prior experimental estimates. Due to the slow solvent dynamics at 77 K, the present results strongly indicate the presence of static disorder, i.e., disorder on a time scale beyond that relevant for the construction of spectral densities.

Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers.

Calculating the evolution of an open quantum system, i.e., a system in contact with a thermal environment, has presented a theoretical and computational challenge for many years. With the advent of supercomputers containing large amounts of memory and many processors, the computational challenge posed by the previously intractable theoretical models can now be addressed. The hierarchy equations of motion present one such model and offer a powerful method that remained under-utilized so far due to its considerable computational expense. By exploiting concurrent processing on parallel computers the hierarchy equations of motion can be applied to biological-scale systems. Herein we introduce the quantum dynamics software PHI, that solves the hierarchical equations of motion. We describe the integrator employed by PHI and demonstrate PHI's scaling and efficiency running on large parallel computers by applying the software to the calculation of inter-complex excitation transfer between the light harvesting complexes 1 and 2 of purple photosynthetic bacteria, a 50 pigment system.

Hydration-determined orientational preferences in aromatic association from benzene dimer free energy volumes.

In this study of the thermodynamics of benzene association in water, we show that although the potential energy and enthalpy play an important role in the association of benzene dimers, they do not determine the relative orientation of these molecules on close contact in solution. We observe a large variation in the configurations that contribute to the vacuum (i.e., solvent-free) minimum free energy wells of the benzene contact pair. In water, fewer and smaller minimum free energy wells are observed. On examination, we find that fewer close contact configurations of benzene dimers populate these wells and that they are more energetically distinct from each other (compared with the vacuum case). The edge-over-edge configuration is most likely in solution and appears to evolve from the entropically favored side-by-side solvent shared configuration. Therefore, the relative orientation of the benzene molecules (i.e., parallel displaced, T-shaped, etc.) on association is a result of maximizing the contribution of the benzene-benzene entropy of association, to the solution free energy.

Structural Characterization of λ-Repressor Folding from All-Atom Molecular Dynamics Simulations.

The five-helix bundle λ-repressor fragment is a fast-folding protein. A length of 80 amino acid residues puts it on the large end among all known microsecond folders and its size poses a computational challenge for molecular dynamics (MD) studies. We simulated the folding of a novel λ-repressor fast-folding mutant (λ-HG) in explicit solvent using an all-atom description. By means of a recently developed tempering method, we observed reversible folding and unfolding of λ-repressor in a 10-microsecond trajectory. The folding kinetics was also investigated through a set of MD simulations run at different temperatures that together covered more than 125 microseconds. The protein was seen to fold into a native-like topology at intermediate temperature and a slow-folding pathway was identified. The simulations suggest new experimental observables for better monitoring the folding process, and a novel mutation expected to accelerate λ-repressor folding.

Molecular origin of the hierarchical elasticity of titin: simulation, experiment, and theory.

This review uses the giant muscle protein titin as an example to showcase the capability of molecular dynamics simulations. Titin is responsible for the passive elasticity in muscle and is a chain composed of immunoglobulin (Ig)-like and fibronectin III (FN-III)-like domains, as well as PEVK segments rich in proline (P), glutamate (E), valine (V), and lysine (K). The elasticity of titin is derived in stages of extension under increasing external force: Ig domain straightening occurs first (termed tertiary structure elasticity), followed by the extension of the disordered PEVK segments. At larger extension and force, Ig domains unfold one by one (termed secondary structure elasticity). With the availability of crystal structures of single and connected Ig domains, the tertiary and secondary structure elasticity of titin was investigated through molecular dynamics simulations, unveiling the molecular origin of titin's elasticity.