Helmut Grubmueller

Arginine52 Controls the Photoisomerization Process in Photoactive Yellow Protein

We have performed excited-state dynamics simulations of the Arg52Gln (R52Q) mutant of photoactive yellow protein (PYP). The results of these simulations demonstrate that in the mutant the primary events after photoexcitation are different from those in the wild-type. In the mutant, the chromophore predominantly undergoes single bond photoisomerization, whereas in the wild-type, photoisomerization of the double bond occurs. Furthermore, the excited-state lifetime is around three times longer than in wild-type PYP, which agrees well with recent transient absorption measurements. In 20% of the trajectories, we observe the formation of a photoproduct that has the carbonyl oxygen atom of the chromophore flipped by almost 180°, disrupting the hydrogen bond between the chromophore and the backbone amino group of Cys69. This observation, in combination with the fact that the mutant is photoactive, suggests that the break of the hydrogen bond is the key step in the photoactivation process rather than the double bo...

Linear-Scaling Soft Core Scheme for Alchemical Free Energy Calculations

Alchemical free energy calculations hold the promise of unrivalled quantitative accuracy in the computational study of molecular recognition and related biochemical processes. Although noteworthy successes have been reported, there remains significant room for improvement in algorithm design and sampling methods.We here present an alternative formulation of a soft-core nonbonded potential, designed to be suitable for linear mixing of potential functions. The use of soft-core potentials is essential when considering thermodynamic cycles involving the insertion / removal of atoms from the surroundings. Existing formulations resolve the numerical instabilities that normally accompany linear mixing, but render the mixing of potential functions a non-linear function of the coupling parameter (lambda). Our formulation permits linear mixing while avoiding the numerical instability normally associated with simple scaling of the Lennard-Jones and Coulomb potentials. We demonstrate the advantages of linear mixing with reference to optimisation of free energy estimation, and of protocol design from the perspective of phase space overlap. We assess the performance of protocols based on the linear scaling soft-core potential as applied to the calculation of relative binding free energies for a complex biomolecular system, consisting of a zinc finger protein and a series of bound DNA oligonucleotides.

Bayesian structure determination from sparse single molecule X-ray diffraction images.

X-ray free electron lasers used in single molecule experiments offer new possibilities for molecular structure determination. We propose a Bayesian method capable of extracting structure information from sparse and noisy diffraction images. We investigate two different strategies. In the first, a ‘seed’ model is used to determine the molecular orientation for each of the collected diffraction images, and an improved molecular transform is obtained by averaging those images in three-dimensional reciprocal space. In the second approach, a real space structure model that fits best to the entire set of diffraction images is obtained, thus enabling distinction between different structures.We found that the achievable resolution increases with molecular mass as m1/6, which somehow unexpectedly suggests that, at a given resolution level, structure determination is more challenging for small molecules.As a proof of concept, we have computed the electron density for a glutathione (molecular mass 307 Da) from 20,000 synthetic diffraction images, each with 82 recorded elastically scattered photons, and up to 50% additional background noise. Alternatively, and demonstrating the feasibility of the second approach, the structure of the same molecule was also determined in a Monte Carlo refinement simulation starting from random conformations. Further, the second approach is exemplified for a ribosomal structure (molecular mass about 2.5 MDa). Our results show that it is possible to distinguish between minute structural changes associated with tRNA translocation.Overall, our results suggest that the proposed method allows for structure determination at atomic resolution from sparse and noisy X-ray diffraction images in single molecule experiments for a broad spectrum of molecular masses.

Bayesian Orientation Estimate and Structure Reconstruction from Sparse Single Molecule X-Ray Scattering Images

The use of X-ray free electron lasers in single molecule experiments holds the promise of solving macromolecular structures by ‘sequential crystallography’. To that aim, reliable structure reconstruction from sparse and noisy scattering images with rigorous bounds for the statistical uncertainty is one of the main challenges. We here developed a method to refine a ‘seed’ structure model given a set of scattering patterns, each with only few recorded photons and background noise.Firstly, using a Bayesian approach, the molecular orientation for each of scattering images is determined by calculating the posterior probability distribution, such that the images are further averaged in 3D reciprocal space. This step requires a ‘seed’ model to calculate the probability distribution. To test the validity of the method, the real space electron density is retrieved using a relaxed averaged alternating reflections algorithm.Secondly, the ‘seed’ model is refined in a Monte Carlo simulation. The probability that the model fits to the given set of diffraction images is determined at each iteration so as to find a model with highest probability.Using scattering data for a glutathione molecule obtained in a numerical simulation as a test case, successful reconstruction was demonstrated for 20,000 diffraction patterns corresponding to random orientations and containing an average of 82 photons per image, yielding an effective R-factor of about 0.3. At the level of 100 scattered photons per image, the molecular orientation is determined to 5o accuracy for white background noise of up to 50%, corresponding to a resolution for the glutathione molecule of ca. 0.5A.These results show that the proposed method is robust and enables structure determination from sparse and noisy single molecule x-ray scattering images.

Quantitative Membrane Bending Energies at Extreme Curvatures from Molecular Dynamics Simulations

At mesoscopic length scales and small curvatures, Helfrichs well established continuum model [1] provides accurate membrane bending and stretching energies. For the small nanometer scales and extreme curvatures relevant for fundamental biological processes like synaptic fusion and tubulation, however, its validity is unclear. To test whether or not the bending energy remains a harmonic function of curvature, described by a simple bending modulus, we developed and applied a new type of collective umbrella sampling molecular dynamics (MD) simulations.Most MD simulations computing bending moduli are limited to thermally accessible energies (a few kBT) and curvatures. In this limited regime, the harmonic approximation has been repeatedly confirmed. Very few simulation strategies exist to compute bending energies at higher curvatures, due to the inherent difficulty of controlling membrane structures. These simulation studies have generally verified the harmonic bending approximation but were limited by the requirements of a soft coarse grained lipid model[2], and unavoidable coupling between bending and stretching[3]. To overcome these limitations, we have developed a novel approach to control membrane curvature thereby accessing the regime of <10nm curvature radii and ∼50 kBT energies. Our preliminary results show that at high curvatures, moduli have a small positive deviation from the harmonic approximation, that would not be discernible in the flat/thermal regime. As expected, we observe that increasing temperature decreases the elastic moduli and that ethanol and cholesterol act to soften and stiffen membranes, respectively.[1] W. Helfrich, Naturforsch [C] 28, p693 (1973).[2] V.A. Harmandris and M. Deserno, JCP 125, p204905 (2006).[3] W.K. den Otter and W.J. Briels, JCP 118, p4712 (2003).

Protein Classification Based on Physicochemical Descriptors

ystematic and efficient analysis of proteins on the proteome scale requires their classification into meaningful sub groups. Approaches to the problem are either top-down, following the evolutionary pathways (SCOP, CATH) and bottom-up, where structures are compared pairwise and aggregated to clusters (DALI). Here we present a novel way of protein classification based on physicochemical descriptors. Atomistic structures are for classification purpose overly rich in information and we distilled biologically relevant features by projecting from the structure space into a lower dimensional descriptor space. Chosen descriptors fall into three groups, sequence dependent, topology, and overall structure and consist of amino acid distribution, charge, hydrophobicity, average path length, cluster coefficient, helix content, sheet content, solvent accessible surface area, radius of gyration, besides others. All descriptors were corrected for chain length and normalized by the standard deviation.Over 3000 representative and non-redundant structures from the pdb Cluster90 were mapped to descriptor space and clustered. The identified clusters coincide to large extend with those from existing classification methods. Our method provides, unlike others, a direct measure for the distance between any two proteins and is easily expandable by for instance descriptors for molecular dynamics.Nothing about protein structure classification makes sense except in the light of evolution.Valas, R.B., Yang S., and Bourne P.E. Curr Opin Struct Biol 2009 19:329-34Multipolar representation of protein structure.Gramada, A. Bourne P.E. BMC Bioinformatics 2006 7:242

Primary Electronic Response In Biomolecules Exposed To X-ray Laser Radiation

The ultra intense femtosecond X-ray pulses from free electron lasers that are being developed in Hamburg and Stanford hold the promise to obtain X-ray scattering information from single molecules, even from proteins [1]. This technique could enable monitoring ultrafast atomistic dynamics in proteins and other biomolecules at the single molecule level. At such short wavelengths the X-ray photons will eject electrons from the sample. This will lead to a coulomb explosion of the nuclei. Thus it is crucial how much time-resolved structural information can be expected from a single molecule diffraction experiment. To address this question, we have begun to develop a method to simulate the electronic response of biomolecular systems subject to electron emission. Due to their strong binding to the nuclei, the inner shell electrons show significantly larger X-ray cross section than the outer electrons, such that the initial event will be the nearly instantaneous partial removal of the inner shells. The resulting fast re-filling dynamics by electrons of the outer shells will critically determine the atomic dynamics and the pace of the Coulomb explosion.In our simulations, a stochastic criterion is used to generate an initial open shell system based on the cross sections. We use Hartree-Fock level of theory and gaussian basis sets to treat the initial state. The expansion coefficients of the basis functions are taken to be time-dependent. Thus the expansion coefficients are propagated by the time-dependent Schroedinger equation. This time-dependent approach is currently applied to a one dimensional model system. We plan to apply it to real molecular systems. Our goal is to treat systems up to the size of a peptide.[1] R. Neutze, et. al., “Potential for biomolecular imaging with femtosecond X-ray pulses”, Nature, 406, 752 (2000).