UKF 1A Grant (December 2007 - March 2010)
|Together with collaborators Christian L. Müller, Ivo F. Sbalzarini, Wilfred F. van Gunsteren and Philippe H. Hünenberger, all at ETH in Zurich, we have finished a study concerning the residual structure of ideal random walks. Ideal random walks are the premier model for studying random, stochastic phenomena in nature such as polymer structure or diffusion of gases. In our study, contrary to typical assumptions, we have shown that ideal random walks exhibit non-homogeneous shape density distributions, and have characterized this non-homogeneity for walks up to length 9 steps using numerical simulations. The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., 1) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk “folds;” 2) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk “states” and associated relative free energies; and 3) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments.
The manuscript with the results was recently published in Journal of Chemical Physics (Müller CL, Sbalzarini IF, van Gunsteren WF, Zagrovic B & Hünenberger PH (2009) “In the eye of the beholder: inhomogeneous distribution of high-resolution shapes within the random-walk ensemble“, Journal of Chemical Physics, 130, 214904).
Image: Density of shapes for a four-node ideal random walk
|Together with the student Tomasz Wlodarski we finished and published the study on the role of induced fit and conformational selection in ubiquitin binding. Specifically, ubiquitin binding has been cited as the premier example of conformational selection. Contrary to this, we showed that the region surrounding the binding site in ubiquitin undergoes conformational changes that are significantly more pronounced compared to the whole molecule on average, hinting at induced fit instead of conformational selection. What is more, we demonstrated that these induced-fit structural adjustments are comparable in magnitude to that of the overall conformational selection.
The manuscript with the results was recently published in the Proceedings of the National Academy of Sciences USA (Wlodarski T & Zagrovic B (2009) “Conformational selection and induced fit mechanism underlie specificity in non-covalent interactions with ubiquitin”, Proceedings of the National Academy of Sciences USA, 106(46), 19346-19351).
Image: Structural adjustments close to the binding site of ubiquitin are statistically different from the adjustments of the structure as a whole.
|Together with the postdoc dr. Daniela Kruschel we have written and published an exhaustive review on the role of conformational averaging in structural biology. Most experimental methods in structural biology provide time- and ensemble-averaged signals and, consequently, molecular structures based on such signals often exhibit only idealized, average features. Second, most experimental signals are only indirectly related to real, molecular geometries, and solving a structure typically involves a complicated procedure, which may not always result in a unique solution. To what extent do such conformationally-averaged, non-linear experimental signals and structural models derived from the accurately represent the underlying microscopic reality? In this review, we critically address the work that has been aimed at studying such questions.
The review has been published in Molecular Biosystems (Kruschel D & Zagrovic B (2009) “Conformational averaging in structural biology: issues, challenges and computational solutions”, Molecular Biosystems, 5(12), 1606-1616).
Image: Different types of ensemble averaging in structural biology
|Together with a PhD student Antonija Kuzmanic, we have finished and published a computational and theoretical study of the crystallographic B-factors and their link with the dynamics of microscopic biomolecular ensembles as captured by pairwise RMSD. First, we provided a mathematical derivation showing that, given a set of conservative assumptions, the root-mean-square pairwise RMSD is directly related to the average RMSF and, consequently, average experimental B-factors. Second, we demonstrated this on structures taken from two sets of MD simulations of the villin headpiece domain (obtained using the Folding@Home distributed computing cluster): native-like and unfolded structures. Our results provide a basis for determining the level of structural diversity of molecular ensembles, as captured by <pRMSD>RMS, directly from experimental B-factors.
The manuscript with the results was recently published in the Biophysical Journal (Kuzmanic A & Zagrovic B (2010) “Determination of ensemble-average pairwise root mean-square deviation from experimental B-factors”, Biophysical Journal, 98(5), 861-871).
Image: Analogy connecting RMSD and RMSF with the radius of gyration
|Together with the student Mario Hlevnjak and collaborator prof. dr. Gordan Zitkovic, we have completed a computational study of the non-specific effects in protein localization and interactions. A binding event between two proteins typically consists of a diffusional search of binding partners for one another, followed by specific recognition of compatible binding sites resulting in the formation of the complex. However, it is unclear how binding partners find each other in the crowded, constantly fluctuating and interaction-rich cellular environment. Here, we showed that, for a large set of high-resolution experimental 3D structures of binary, transient protein complexes from the DOCKGROUND database, the binding partners display a surprising, statistically significant similarity in terms of their total hydration free energies normalized by a size-dependent variable. We propose that colocalization of binding partners, even within individual cellular compartments such as the cytoplasm, may be influenced by their relative hydrophilicity in response to intra-compartmental hydrophilic gradients. The results have been written up and are currently under review in PLOS One.
Image: Size-normalized hydration free energy exhibits highest level of matching between binding partners
|Together with the postdoctoral fellow dr. Anton Polyansky, masters student Ruben Zubac, and summer students Tibor Pakozdi and Pawel Janowski, we have started a study concerning the role of conformational entropy in binding interactions and post-translational modifications of proteins. Here, we are using computational simulations to model the binding of calmodulin to six different short peptides, for which there is a wealth of structural and thermodynamic information. In addition, we have evaluated the change in conformational entropy in the course of protein phosphorylation. So far, we have written computer programs in Python for: 1. estimating conformational entropy in proteins using quasi-harmonic and dihedral approaches, 2. estimating solvent entropy using cell theory, and 3. started computer simulations of bound complexes as well as calmodulin free in solution using OPLS-aa force field and Gromacs simulation package. We are currently also applying the developed entropy code to estimation of entropic effects in ubiquitin binding.
Image: Structure of calmodulin (Cook WJ et al. JMB 1988)
|Together with PhD students Drazen Petrov and Mario Hlevnjak, we have continued the computational study of the effects of carbonylation on the stability and dynamics of proteins. Proteins frequently become irreversibly modified by carbonylation, a process of introducing the carbonyl group in a reaction with reactive oxygen species (ROS) such as superoxide, peroxide or ozone. Carbonylation increases with the age of cells and it is associated with ageing and age related disorders such as Alzheimer’s disease, Parkinson’s disease and cancer. We are using the molecular dynamics method to study the stability of carbonylated proteins villin headpiece and ubiquitin. In addition, we have used thermodynamic integration on standard and carbonylated amino acids in order to estimate their solvation free energy, (related to relative hydrophobicity and hydrophilicity). Our results suggest that carbonylation markedly decreases the overall stability of proteins, and that two potential reasons for that may be: 1. a disruption of the balance between hydrophilic and hydrophobic regions in the protein, and 2. disruption of the steric rigidity of the proline residue.
Image: Simulated structure of carbonylated villin headpiece with exposed hydrophobic residues (red)
|Together with a postdoc Daniela Kruschel, we are have continued using molecular dynamics techniques to analyze the dynamics of Rpn13, a novel receptor for ubiquitin on the proteasome. Daniela has run simulations of ubiquitin free in solution, ubiquitin bound to the Pru domain of Rpn13, and the Pru domain alone in solution, and is currently analyzing the simulations. The overarching goal of her project is to provide a dynamic picture behind the static experimental structures of this important binding complex.
Image: Structure of ubiquitin bound to Rpn13 domain of the proteasome (Groll M et al. Nature 2008)
|Together with the summer student Maria Janowska we have carried out and completed a small computational study of the structure and dynamics of a natively unfolded protein Waskott-Aldrich Syndrome Protein (WASP). The project was primarily educational, with potential to grow into a publishable study in the future.
Image: Structure of the GTPase Binding Domain of WASP in Complex with EspFU (Rosen MK et al. Nature 2008)
|Together with the student Omar Awile and collaborators Anita Kriško and Ivo F. Sbalzarini we have completed a study on the role of natively unfolded regions in the enzyme nudix hydrolaze from the bacterium D. radiodurans. The proteome of the radiation and desiccation-resistant bacterium D. radiodurans features a group of proteins that contain significant intrinsically disordered regions that are not present in non-extremophile homologues. Interestingly, this group includes a number of housekeeping and repair proteins such as DNA polymerase III, nudix hydrolase and rotamase. Here, we focus on a member of the nudix hydrolase family possessing low-complexity N and C-terminal tails, which exhibit sequence signatures of intrinsic disorder and have unknown function. We show that the presence of disordered tails significantly decreases the hydration free energy of the whole protein. We hypothesize that the tails increase the chances of the protein to be located in the remaining water patches in the desiccated cell, where it is protected from the desiccation effects and can function normally. The results have been written up in the form of a publication, and will soon be submitted for publication in PLOS Computational Biology.
Image: Simulated structure of a nudix hydrolaze dimer
|Together with diploma student Mijo Simunovic and collaborator Sanja Tomic (Institute Ruder Boskovic, Zagreb) we have started a computational study looking at the thermodynamics od ligand binding to auxin amidohydrolase. The simulations are currently running, and we expect to start preliminary analysis soon.
Image: RMSF of a simulated auxin amidohydrolase with mutation hot-spots indicated by arrows