@article {2020|2075, title = {Characterization of β-turns by electronic circular dichroism spectroscopy: a coupled molecular dynamics and time-dependent density functional theory computational study.}, journal = {Phys Chem Chem Phys}, volume = {22}, year = {2020}, month = {2020 Jan 21}, pages = {1611-1623}, abstract = {

Electronic circular dichroism is one of the most used spectroscopic techniques for peptide and protein structural characterization. However, while valuable experimental spectra exist for α-helix, β-sheet and random coil secondary structures, previous studies showed important discrepancies for β-turns, limiting their use as a reference for structural studies. In this paper, we simulated circular dichroism spectra for the best-characterized β-turns in peptides, namely types I, II, I\&$\#$39; and II\&$\#$39;. In particular, by combining classical molecular dynamics simulations and state-of-the-art quantum time-dependent density functional theory (with the polarizable embedding multiscale model) computations, two common electronic circular dichroism patterns were found for couples of β-turn types (namely, type I/type II\&$\#$39; and type II/type I\&$\#$39;), at first for a minimal di-peptide model (Ace-Ala-Ala-NHMe), but also for all sequences tested with non-aromatic residues in the central positions. On the other hand, as expected, aromatic substitution causes important perturbations to the previously found ECD patterns. Finally, by applying suitable approximations, these patterns were subsequently rationalized based on the exciton chirality rule. All these results provide useful predictions and pave the way for a possible experimental characterization of β-turns based on circular dichroism spectroscopy.

}, keywords = {Circular Dichroism, Computational Chemistry, Computer Simulation, Molecular Dynamics Simulation, Protein Conformation, beta-Strand, Protein Structure, Tertiary}, issn = {1463-9084}, doi = {10.1039/c9cp05776e}, author = {Migliore, Mattia and Bonvicini, Andrea and Tognetti, Vincent and Guilhaudis, Laure and Marc Baaden and Oulyadi, Hassan and Joubert, Laurent and S{\'e}galas-Milazzo, Isabelle} } @article {2019|2081, title = {Visualizing Biological Membrane Organization and Dynamics.}, journal = {J Mol Biol}, volume = {431}, year = {2019}, month = {2019 05 03}, pages = {1889-1919}, abstract = {

Biological membranes are fascinating. Santiago Ram{\'o}n y Cajal, who received the Nobel prize in 1906 together with Camillo Golgi for their work on the nervous system, wrote \"[\…]in the study of this membrane[\…] I felt more profoundly than in any other subject of study the shuddering sensation of the unfathomable mystery of life\". The visualization and conceptualization of these biological objects have profoundly shaped many aspects of modern biology, drawing inspiration from experiments, computer simulations, and the imagination of scientists and artists. The aim of this review is to provide a fresh look on current ideas of biological membrane organization and dynamics by discussing selected examples across fields.

}, keywords = {Animals, Cell Membrane, Humans, Lipid Bilayers, Microscopy, Atomic Force, Microscopy, Electron, Transmission, Molecular Dynamics Simulation}, issn = {1089-8638}, doi = {10.1016/j.jmb.2019.02.018}, author = {Marc Baaden} } @article {2018|2086, title = {Analyzing protein topology based on Laguerre tessellation of a pore-traversing water network.}, journal = {Sci Rep}, volume = {8}, year = {2018}, month = {2018 09 10}, pages = {13540}, abstract = {

Given the tight relation between protein structure and function, we present a set of methods to analyze protein topology, implemented in the VLDP program, relying on Laguerre space partitions built from series of molecular dynamics snapshots. The Laguerre partition specifies inter-atomic contacts, formalized in graphs. The deduced properties are the existence and count of water aggregates, possible passage ways and constrictions, the structure, connectivity, stability and depth of the water network. As a test-case, the membrane protein FepA is investigated in its full environment, yielding a more precise description of the protein surface. Inside FepA, the solvent splits into isolated clusters and an intricate network connecting both sides of the lipid bilayer. The network is dynamic, connections set on and off, occasionally substantially relocating traversing paths. Subtle differences are detected between two forms of FepA, ligand-free and complexed with its natural iron carrier, the enterobactin. The complexed form has more constricted and more centered openings in the upper part whereas, in the lower part, constriction is released: two main channels between the plug and barrel lead directly to the periplasm. Reliability, precision and the variety of topological features are the main interest of the method.

}, keywords = {Bacterial Outer Membrane Proteins, Carrier Proteins, Enterobactin, Molecular Dynamics Simulation, Protein Stability, Protein Structure, Secondary, Receptors, Cell Surface, Structure-Activity Relationship, Water}, issn = {2045-2322}, doi = {10.1038/s41598-018-31422-5}, author = {Esque, J{\'e}r{\'e}my and Sansom, Mark S P and Marc Baaden and Oguey, Christophe} } @article {2018|2094, title = {Holding the Nucleosome Together: A Quantitative Description of the DNA-Histone Interface in Solution.}, journal = {J Chem Theory Comput}, volume = {14}, year = {2018}, month = {2018 Feb 13}, pages = {1045-1058}, abstract = {

The nucleosome is the fundamental unit of eukaryotic genome packaging in the chromatin. In this complex, the DNA wraps around eight histone proteins to form a superhelical double helix. The resulting bending, stronger than anything observed in free DNA, raises the question of how such a distortion is stabilized by the proteic and solvent environments. In this work, the DNA-histone interface in solution was exhaustively analyzed from nucleosome structures generated by molecular dynamics. An original Voronoi tessellation technique, measuring the topology of interacting elements without any empirical or subjective adjustment, was used to characterize the interface in terms of contact area and occurrence. Our results revealed an interface more robust than previously known, combining extensive, long-lived nonelectrostatic and electrostatic interactions between DNA and both structured and unstructured histone regions. Cation accumulation makes the proximity of juxtaposed DNA gyres in the superhelix possible by shielding the strong electrostatic repulsion of the charged phosphate groups. Overall, this study provides new insights on the nucleosome cohesion, explaining how DNA distortions can be maintained in a nucleoprotein complex.

}, keywords = {DNA, Histones, Molecular Dynamics Simulation, Nucleosomes, Solutions, Static Electricity}, issn = {1549-9626}, doi = {10.1021/acs.jctc.7b00936}, author = {Elbahnsi, Ahmad and Retureau, Romain and Marc Baaden and Hartmann, Brigitte and Oguey, Christophe} } @article {2018|2087, title = {The major β-catenin/E-cadherin junctional binding site is a primary molecular mechano-transductor of differentiation .}, journal = {Elife}, volume = {7}, year = {2018}, month = {2018 07 19}, abstract = {

, the primary molecular mechanotransductive events mechanically initiating cell differentiation remain unknown. Here we find the molecular stretching of the highly conserved Y654-β-catenin-D665-E-cadherin binding site as mechanically induced by tissue strain. It triggers the increase of accessibility of the Y654 site, target of the Src42A kinase phosphorylation leading to irreversible unbinding. Molecular dynamics simulations of the β-catenin/E-cadherin complex under a force mimicking a 6 pN physiological mechanical strain predict a local 45\% stretching between the two α-helices linked by the site and a 15\% increase in accessibility of the phosphorylation site. Both are quantitatively observed using FRET lifetime imaging and non-phospho Y654 specific antibody labelling, in response to the mechanical strains developed by endogenous and magnetically mimicked early mesoderm invagination of gastrulating embryos. This is followed by the predicted release of 16\% of β-catenin from junctions, observed in FRAP, which initiates the mechanical activation of the β-catenin pathway process.

}, keywords = {Amino Acid Sequence, Animals, Armadillo Domain Proteins, Binding Sites, Cadherins, Cell Differentiation, Drosophila melanogaster, Drosophila Proteins, Fluorescence Resonance Energy Transfer, Mechanotransduction, Cellular, Molecular Dynamics Simulation, Phosphorylation, Protein Binding, Protein Conformation, Proto-Oncogene Proteins pp60(c-src), Sequence Homology, Transcription Factors}, issn = {2050-084X}, doi = {10.7554/eLife.33381}, author = {R{\"o}per, Jens-Christian and Mitrossilis, D{\'e}mosth{\`e}ne and Guillaume Stirnemann and Waharte, Fran{\c c}ois and Brito, Isabel and Fernandez-Sanchez, Maria-Elena and Marc Baaden and Salamero, Jean and Farge, Emmanuel} } @article {2017|2025, title = {Critical structural fluctuations of proteins upon thermal unfolding challenge the Lindemann criterion}, journal = {Proc Natl Acad Sci U S A}, volume = {114}, year = {2017}, month = {Aug}, pages = {9361-9366}, abstract = {

Internal subnanosecond timescale motions are key for the function of proteins, and are coupled to the surrounding solvent environment. These fast fluctuations guide protein conformational changes, yet their role for protein stability, and for unfolding, remains elusive. Here, in analogy with the Lindemann criterion for the melting of solids, we demonstrate a common scaling of structural fluctuations of lysozyme protein embedded in different environments as the thermal unfolding transition is approached. By combining elastic incoherent neutron scattering and advanced molecular simulations, we show that, although different solvents modify the protein melting temperature, a unique dynamical regime is attained in proximity of thermal unfolding in all solvents that we tested. This solvation shell-independent dynamical regime arises from an equivalent sampling of the energy landscape at the respective melting temperatures. Thus, we propose that a threshold for the conformational entropy provided by structural fluctuations of proteins exists, beyond which thermal unfolding is triggered.

}, keywords = {cell thermal stability, Lindemann criterion, Molecular Dynamics Simulation, neutron scattering, protein dynamics}, doi = {10.1073/pnas.1707357114}, author = {Katava, Marina and Guillaume Stirnemann and Zanatta, Marco and Capaccioli, Simone and Pachetti, Maria and Ngai, K L and Sterpone, Fabio and Paciaroni, Alessandro} } @article {2017|2041, title = {Fast coarse-grained model for RNA titration.}, journal = {J Chem Phys}, volume = {146}, year = {2017}, month = {2017 Jan 21}, pages = {035101}, abstract = {

A new numerical scheme for RNA (ribonucleic acid) titration based on the Debye-H{\"u}ckel framework for the salt description is proposed in an effort to reduce the computational costs for further applications to study protein-RNA systems. By means of different sets of Monte Carlo simulations, we demonstrated that this new scheme is able to correctly reproduce the experimental titration behavior and salt pKshifts. In comparison with other theoretical approaches, similar or even better outcomes are achieved at much lower computational costs. The model was tested on the lead-dependent ribozyme, the branch-point helix, and the domain 5 from Azotobacter vinelandii Intron 5.

}, keywords = {Azotobacter vinelandii, Introns, Models, Chemical, Molecular Dynamics Simulation, Monte Carlo Method, Protein Structure, Secondary, Protons, RNA, RNA, Catalytic, Titrimetry}, issn = {1089-7690}, doi = {10.1063/1.4972986}, author = {Barroso da Silva, Fernando Luis and Philippe Derreumaux and Pasquali, Samuela} } @article {2017|2095, title = {Residues of Alpha Helix H3 Determine Distinctive Features of Transforming Growth Factor β3.}, journal = {J Phys Chem B}, volume = {121}, year = {2017}, month = {2017 06 08}, pages = {5483-5498}, abstract = {

Transforming growth factors (TGF-βs) are proteins that regulate cell growth by binding to their receptors. In contrast to transforming growth factor (TGF) β1, TGF-β3 homodimer is believed to exist also in an open conformation, in which both of its monomers are loosely packed against each other. At the origin of this difference is the H3-helix. Its sequence and degree of structuration seem to govern the outcome of TGF dimerization. We docked two monomers of TGF-β3 with intact and altered H3 α-helix against each other using HADDOCK. TGF-β3 monomer with an intact H3-helix exclusively forms closed conformations of homodimer, whereas the open conformation may coexist with the closed one when a part of the H3 α-helix is destabilized. We quantify the difference in its conformational preference for the open versus the closed structure by calculating the binding energy between monomers using the MMPBSA approach. We compare the wild type (wt) TGFβ3/TGFβ1 homodimers in the Protein Data Bank to a swapped mutant where all residues of the H3-helix were mutated to the respective TGFβ1/TGFβ3 sequence. Swapping stabilizes the closed conformation and destabilizes the open conformation of TGFβ3. Further detailed insight is derived from molecular dynamics simulation studies suggesting that Val 61 of the H3-helix may act as an anchor residue for the closed conformation of TGFβ3. Computational alanine scanning mutagenesis confirms that several residues of the H3-helix are the hot residues for the closed conformation of TGFβ3. These observations may bear relevance to general conformational transitions in proteins and specifically in the TGFβ superfamily.

}, keywords = {Molecular Dynamics Simulation, Protein Conformation, alpha-Helical, Transforming Growth Factor beta3}, issn = {1520-5207}, doi = {10.1021/acs.jpcb.7b01867}, author = {Nayeem, Shahid M and Oteri, Francesco and Marc Baaden and Deep, Shashank} } @article {2015|1755, title = {How osmolytes influence hydrophobic polymer conformations: A unified view from experiment and theory.}, journal = {Proc. Natl. Acad. Sci. Usa}, volume = {112}, year = {2015}, pages = {9270{\textendash}5}, abstract = {

It is currently the consensus belief that protective osmolytes such as trimethylamine N-oxide (TMAO) favor protein folding by being excluded from the vicinity of a protein, whereas denaturing osmolytes such as urea lead to protein unfolding by strongly binding to the surface. Despite there being consensus on how TMAO and urea affect proteins as a whole, very little is known as to their effects on the individual mechanisms responsible for protein structure formation, especially hydrophobic association. In the present study, we use single-molecule atomic force microscopy and molecular dynamics simulations to investigate the effects of TMAO and urea on the unfolding of the hydrophobic homopolymer polystyrene. Incorporated with interfacial energy measurements, our results show that TMAO and urea act on polystyrene as a protectant and a denaturant, respectively, while complying with Tanford-Wyman preferential binding theory. We provide a molecular explanation suggesting that TMAO molecules have a greater thermodynamic binding affinity with the collapsed conformation of polystyrene than with the extended conformation, while the reverse is true for urea molecules. Results presented here from both experiment and simulation are in line with earlier predictions on a model Lennard-Jones polymer while also demonstrating the distinction in the mechanism of osmolyte action between protein and hydrophobic polymer. This marks, to our knowledge, the first experimental observation of TMAO-induced hydrophobic collapse in a ternary aqueous system.

}, keywords = {Atomic Force, Computer Simulation, Hydrophobic and Hydrophilic Interactions, Mechanical, Methylamines, Methylamines: chemistry, Microscopy, Molecular Dynamics Simulation, Normal Distribution, Polymers, Polymers: chemistry, Polystyrenes, Polystyrenes: chemistry, Protein Binding, Protein Conformation, Protein Folding, Proteins, Proteins: chemistry, Software, Solvents, Solvents: chemistry, Stress, Thermodynamics, Urea, Urea: chemistry, Water, Water: chemistry}, isbn = {1215421109}, issn = {1091-6490}, doi = {10.1073/pnas.1511780112}, url = {http://www.pnas.org/content/112/30/9270}, author = {Mondal, Jagannath and Halverson, Duncan and Li, Isaac T S and Guillaume Stirnemann and Walker, Gilbert C and Berne, Bruce J} } @article {2014|1669, title = {CHARMM36 united atom chain model for lipids and surfactants.}, journal = {J. Phys. Chem. B}, volume = {118}, number = {2}, year = {2014}, month = {jan}, pages = {547{\textendash}556}, publisher = {, Maryland 20742, United States.}, abstract = {Molecular simulations of lipids and surfactants require accurate parameters to reproduce and predict experimental properties. Previously, a united atom (UA) chain model was developed for the CHARMM27/27r lipids (H{\'e}nin, J., et al. J. Phys. Chem. B. 2008, 112, 7008-7015) but suffers from the flaw that bilayer simulations using the model require an imposed surface area ensemble, which limits its use to pure bilayer systems. A UA-chain model has been developed based on the CHARMM36 (C36) all-atom lipid parameters, termed C36-UA, and agreed well with bulk, lipid membrane, and micelle formation of a surfactant. Molecular dynamics (MD) simulations of alkanes (heptane and pentadecane) were used to test the validity of C36-UA on density, heat of vaporization, and liquid self-diffusion constants. Then, simulations using C36-UA resulted in accurate properties (surface area per lipid, X-ray and neutron form factors, and chain order parameters) of various saturated- and unsaturated-chain bilayers. When mixed with the all-atom cholesterol model and tested with a series of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/cholesterol mixtures, the C36-UA model performed well. Simulations of self-assembly of a surfactant (dodecylphosphocholine, DPC) using C36-UA suggest an aggregation number of 53 {\textpm} 11 DPC molecules at 0.45 M of DPC, which agrees well with experimental estimates. Therefore, the C36-UA force field offers a useful alternative to the all-atom C36 lipid force field by requiring less computational cost while still maintaining the same level of accuracy, which may prove useful for large systems with proteins.}, keywords = {analogs /\&/ derivatives/chemistry, chemistry, Cholesterol, Dimyristoylphosphatidylcholine, Lipid Bilayers, Lipids, Micelles, Molecular Dynamics Simulation, Phosphorylcholine, Surface-Active Agents}, doi = {10.1021/jp410344g}, author = {Lee, Sarah and Tran, Alan and Allsopp, Matthew and Lim, Joseph B. and J{\'e}r{\^o}me H{\'e}nin and Klauda, Jeffery B.} } @article {2014|1751, title = {How force unfolding differs from chemical denaturation.}, journal = {Proc. Natl. Acad. Sci. U.s.a}, volume = {111}, year = {2014}, pages = {3413{\textendash}8}, abstract = {

Single-molecule force spectroscopies are remarkable tools for studying protein folding and unfolding, but force unfolding explores protein configurations that are potentially very different from the ones traditionally explored in chemical or thermal denaturation. Understanding these differences is crucial because such configurations serve as starting points of folding studies, and thus can affect both the folding mechanism and the kinetics. Here we provide a detailed comparison of both chemically induced and force-induced unfolded state ensembles of ubiquitin based on extensive, all-atom simulations of the protein either extended by force or denatured by urea. As expected, the respective unfolded states are very different on a macromolecular scale, being fully extended under force with no contacts and partially extended in urea with many nonnative contacts. The amount of residual secondary structure also differs: A significant population of $\alpha$-helices is found in chemically denatured configurations but such helices are absent under force, except at the lowest applied force of 30 pN where short helices form transiently. We see that typical-size helices are unstable above this force, and $\beta$-sheets cannot form. More surprisingly, we observe striking differences in the backbone dihedral angle distributions for the protein unfolded under force and the one unfolded by denaturant. A simple model based on the dialanine peptide is shown to not only provide an explanation for these striking differences but also illustrates how the force dependence of the protein dihedral angle distributions give rise to the worm-like chain behavior of the chain upon force.

}, keywords = {Chemical, Hydrogen-Ion Concentration, Models, Molecular Dynamics Simulation, Protein Conformation, Protein Denaturation, Protein Folding, Protein Unfolding, Ubiquitin, Ubiquitin: chemistry, Urea, Urea: chemistry}, issn = {1091-6490}, url = {http://www.ncbi.nlm.nih.gov/pubmed/24550471}, author = {Guillaume Stirnemann and Kang, Seung-gu and Zhou, Ruhong and Berne, Bruce J} } @article {2014|1717, title = {Lipid concentration and molar ratio boundaries for the use of isotropic bicelles.}, journal = {Langmuir}, volume = {30}, number = {21}, year = {2014}, month = {jun}, pages = {6162{\textendash}6170}, publisher = {Department of Chemistry, Universit{\'e} du Qu{\'e}bec {\`a} Montr{\'e}al and Centre Qu{\'e}b{\'e}cois sur les Mat{\'e}riaux Fonctionnels , P.O. Box 8888, Downtown Station, Montreal, Canada H3C 3P8.}, abstract = {Bicelles are model membranes generally made of long-chain dimyristoylphosphatidylcholine (DMPC) and short-chain dihexanoyl-PC (DHPC). They are extensively used in the study of membrane interactions and structure determination of membrane-associated peptides, since their composition and morphology mimic the widespread PC-rich natural eukaryotic membranes. At low DMPC/DHPC (q) molar ratios, fast-tumbling bicelles are formed in which the DMPC bilayer is stabilized by DHPC molecules in the high-curvature rim region. Experimental constraints imposed by techniques such as circular dichroism, dynamic light scattering, or microscopy may require the use of bicelles at high dilutions. Studies have shown that such conditions induce the formation of small aggregates and alter the lipid-to-detergent ratio of the bicelle assemblies. The objectives of this work were to determine the exact composition of those DMPC/DHPC isotropic bicelles and study the lipid miscibility. This was done using (31)P nuclear magnetic resonance (NMR) and exploring a wide range of lipid concentrations (2-400 mM) and q ratios (0.15-2). Our data demonstrate how dilution modifies the actual DMPC/DHPC molar ratio in the bicelles. Care must be taken for samples with a total lipid concentration <=250 mM and especially at q \~{} 1.5-2, since moderate dilutions could lead to the formation of large and slow-tumbling lipid structures that could hinder the use of solution NMR methods, circular dichroism or dynamic light scattering studies. Our results, supported by infrared spectroscopy and molecular dynamics simulations, also show that phospholipids in bicelles are largely segregated only when q > 1. Boundaries are presented within which control of the bicelles{\textquoteright} q ratio is possible. This work, thus, intends to guide the choice of q ratio and total phospholipid concentration when using isotropic bicelles.}, keywords = {chemistry, Circular Dichroism, Detergents, Dimyristoylphosphatidylcholine, Fourier Transform Infrared, Light, Lipid Bilayers, Magnetic Resonance Spectroscopy, Materials Testing, Micelles, Molecular Dynamics Simulation, Phospholipid Ethers, Phospholipids, Radiation, Scattering, Solutions, Spectroscopy, Temperature}, doi = {10.1021/la5004353}, author = {Beaugrand, Ma\"{\i}wenn and Arnold, Alexandre A. and J{\'e}r{\^o}me H{\'e}nin and Warschawski, Dror E. and Williamson, Philip T F. and Marcotte, Isabelle} } @article {2014|1598, title = {A predicted binding site for cholesterol on the GABAA receptor.}, journal = {Biophys. J.}, volume = {106}, number = {9}, year = {2014}, month = {may}, pages = {1938{\textendash}1949}, publisher = {Department of Physics, Rutgers University-Camden, Camden, New Jersey; Center for Computational and Integrative Biology, Rutgers University-Camden, Camden, New Jersey. Electronic address: Grace.Brannigan@rutgers.edu.}, abstract = {Modulation of the GABA type A receptor (GABAAR) function by cholesterol and other steroids is documented at the functional level, yet its structural basis is largely unknown. Current data on structurally related modulators suggest that cholesterol binds to subunit interfaces between transmembrane domains of the GABAAR. We construct homology models of a human GABAAR based on the structure of the glutamate-gated chloride channel GluCl of Caenorhabditis elegans. The models show the possibility of previously unreported disulfide bridges linking the M1 and M3 transmembrane helices in the α and γ subunits. We discuss the biological relevance of such disulfide bridges. Using our models, we investigate cholesterol binding to intersubunit cavities of the GABAAR transmembrane domain. We find that very similar binding modes are predicted independently by three approaches: analogy with ivermectin in the GluCl crystal structure, automated docking by AutoDock, and spontaneous rebinding events in unbiased molecular dynamics simulations. Taken together, the models and atomistic simulations suggest a somewhat flexible binding mode, with several possible orientations. Finally, we explore the possibility that cholesterol promotes pore opening through a wedge mechanism.}, keywords = {Amino Acid, Binding Sites, Caenorhabditis elegans Proteins, chemistry, chemistry/metabolism, Chloride Channels, Cholesterol, GABA-A, Humans, Hydrogen Bonding, Ivermectin, metabolism, Molecular Docking Simulation, Molecular Dynamics Simulation, Porosity, Protein Binding, Protein Conformation, Receptors, Sequence Homology, Substrate Specificity}, doi = {10.1016/j.bpj.2014.03.024}, author = {J{\'e}r{\^o}me H{\'e}nin and Salari, Reza and Murlidaran, Sruthi and Grace Brannigan} } @article {2013|1752, title = {Elasticity, structure, and relaxation of extended proteins under force.}, journal = {Proc. Natl. Acad. Sci. U.s.a}, volume = {110}, year = {2013}, pages = {3847{\textendash}52}, abstract = {

Force spectroscopies have emerged as a powerful and unprecedented tool to study and manipulate biomolecules directly at a molecular level. Usually, protein and DNA behavior under force is described within the framework of the worm-like chain (WLC) model for polymer elasticity. Although it has been surprisingly successful for the interpretation of experimental data, especially at high forces, the WLC model lacks structural and dynamical molecular details associated with protein relaxation under force that are key to the understanding of how force affects protein flexibility and reactivity. We use molecular dynamics simulations of ubiquitin to provide a deeper understanding of protein relaxation under force. We find that the WLC model successfully describes the simulations of ubiquitin, especially at higher forces, and we show how protein flexibility and persistence length, probed in the force regime of the experiments, are related to how specific classes of backbone dihedral angles respond to applied force. Although the WLC model is an average, backbone model, we show how the protein side chains affect the persistence length. Finally, we find that the diffusion coefficient of the protein{\textquoteright}s end-to-end distance is on the order of 10(8) nm(2)/s, is position and side-chain dependent, but is independent of the length and independent of the applied force, in contrast with other descriptions.

}, keywords = {Atomic Force, Biophysical Phenomena, Computer Simulation, Elasticity, Mechanical, Microscopy, Models, Molecular, Molecular Dynamics Simulation, Proteins, Proteins: chemistry, Stress, Ubiquitin, Ubiquitin: chemistry}, issn = {1091-6490}, url = {http://www.pnas.org/content/early/2013/02/13/1300596110.abstract}, author = {Guillaume Stirnemann and Giganti, David and Fernandez, Julio M and Berne, B J} }