Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Impact of Spatial Soil and Climate Input Data Aggregation on Regional Yield Simulations

This work was financially supported by the German Federal Ministry of Food and Agriculture (BMEL) through the Federal Office for Agriculture and Food (BLE), (2851ERA01J). FT and RPR were supported by FACCE MACSUR (3200009600) through the Finnish Ministry of Agriculture and Forestry (MMM). EC, HE and EL were supported by The Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (220-2007-1218) and by the strategic funding ‘Soil-Water-Landscape’ from the faculty of Natural Resources and Agricultural Sciences (Swedish University of Agricultural Sciences) and thank professor P-E Jansson (Royal Institute of Technology, Stockholm) for support. JC, HR and DW thank the INRA ACCAF metaprogramm for funding and Eric Casellas from UR MIAT INRA for support. CB was funded by the Helmholtz project “REKLIM—Regional Climate Change”. CK was funded by the HGF Alliance “Remote Sensing and Earth System Dynamics” (EDA). FH was funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under the Grant FOR1695. FE and SS acknowledge support by the German Science Foundation (project EW 119/5-1). HH, GZ, SS, TG and FE thank Andreas Enders and Gunther Krauss (INRES, University of Bonn) for support. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the δ- and ɛ-tautomers of the distal His-64. Vibrational population relaxation times of 335 ± 115 ps for the δ-tautomer and 640 ± 185 ps for the ɛ-tautomer were estimated by using the Landau–Teller model. Normal mode analysis was used to identify those protein residues that act as the primary “doorway” modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the ɛ- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb13CO). From these measurements, a T1 time of 600 ± 150 ps was determined. The simulation and experimental estimates are compared and discussed.

Yeast chorismate mutase in the R state: Simulations of the active site

The isomerization of chorismate to prephenate by chorismate mutase in the biosynthetic pathway that forms Tyr and Phe involves C5—O (ether) bond cleavage and C1—C9 bond formation in a Claisen rearrangement. Development of negative charge on the ether oxygen, stabilized by Lys-168 and Glu-246, is inferred from the structure of a complex with a transition state analogue (TSA) and from the pH-rate profile of the enzyme and the E246Q mutant. These studies imply a protonated Glu-246 well above pH 7. Here, several 500-ps molecular dynamics simulations test the stability of enzyme–TSA complexes by using a solvated system with stochastic boundary conditions. The simulated systems are (i) protonated Glu-246 (stable), (ii) deprotonated Glu-246 (unstable), (iii) deprotonated Glu-246 plus one H2O between Glu-246 and the ether oxygen (unstable), (iv) the E246Q mutant (stable), and (v) addition of OH− between protonated Glu-246 and the ether oxygen. In (v), a local conformational change of Lys-168 displaced the OH− into the solvent region, suggesting a possible rate-determining step that precedes the catalytic step. In a 500-ps simulation of the enzyme complexed with the reactant chorismate or the product prephenate, no water molecule remained near the oxygen of the ligand. Calculations using the linearized Poisson–Boltzmann equation show that the effective pKa of Glu-246 is shifted from 5.8 to 8.1 as the negative charge on the ether oxygen of the TSA is changed from −0.56 electron to −0.9 electron. Altogether, these results support retention of a proton on Glu-246 to high pH and the absence of a water molecule in the catalytic steps.

The Multisubstrate Docking Site of the MET Receptor Is Dispensable for MET-mediated RAS Signaling and Cell Scattering

The scatter factor/hepatocyte growth factor regulates scattering and morphogenesis of epithelial cells through activation of the MET tyrosine kinase receptor. In particular, the noncatalytic C-terminal tail of MET contains two autophosphorylation tyrosine residues, which form a multisubstrate-binding site for several cytoplasmic effectors and are thought to be essential for signal transduction. We show here that a MET receptor mutated on the four C-terminal tyrosine residues, Y1311F, Y1347F, Y1354F, and Y1363F, can induce efficiently a transcriptional response and cell scattering, whereas it cannot induce cell morphogenesis. Although the mutated receptor had lost its ability to recruit and/or activate known signaling molecules, such as GRB2, SHC, GAB1, and PI3K, by using a sensitive association–kinase assay we found that the mutated receptor can still associate and phosphorylate a ∼250-kDa protein. By further examining signal transduction mediated by the mutated MET receptor, we established that it can transmit efficient RAS signaling and that cell scattering by the mutated MET receptor could be inhibited by a pharmacological inhibitor of the MEK-ERK (MAP kinase kinase–extracellular signal-regulated kinase) pathway. We propose that signal transduction by autophosphorylation of the C-terminal tyrosine residues is not the sole mechanism by which the activated MET receptor can transmit RAS signaling and cell scattering.

Congruent Docking of Dimeric Kinesin and ncd into Three-dimensional Electron Cryomicroscopy Maps of Microtubule–Motor ADP Complexes

We present a new map showing dimeric kinesin bound to microtubules in the presence of ADP that was obtained by electron cryomicroscopy and image reconstruction. The directly bound monomer (first head) shows a different conformation from one in the more tightly bound empty state. This change in the first head is amplified as a movement of the second (tethered) head, which tilts upward. The atomic coordinates of kinesin·ADP dock into our map so that the tethered head associates with the bound head as in the kinesin dimer structure seen by x-ray crystallography. The new docking orientation avoids problems associated with previous predictions; it puts residues implicated by proteolysis-protection and mutagenesis studies near the microtubule but does not lead to steric interference between the coiled-coil tail and the microtubule surface. The observed conformational changes in the tightly bound states would probably bring some important residues closer to tubulin. As expected from the homology with kinesin, the atomic coordinates of nonclaret disjunctional protein (ncd)·ADP dock in the same orientation into the attached head in a map of microtubules decorated with dimeric ncd·ADP. Our results support the idea that the observed direct interaction between the two heads is important at some stages of the mechanism by which kinesin moves processively along microtubules.

High-Copy Suppressor Analysis Reveals a Physical Interaction between Sec34p and Sec35p, a Protein Implicated in Vesicle Docking

A temperature-sensitive mutant, sec34-2, is defective in the late stages of endoplasmic reticulum (ER)-to-Golgi transport. A high-copy suppressor screen that uses the sec34-2 mutant has resulted in the identification of the SEC34 structural gene and a novel gene called GRP1. GRP1 encodes a previously unidentified hydrophilic yeast protein related to the mammalian Golgi protein golgin-160. Although GRP1 is not essential for growth, the grp1Δ mutation displays synthetic lethal interactions with several mutations that result in ER accumulation and a block in the late stages of ER-to-Golgi transport, but not with those that block the budding of vesicles from the ER. Our findings suggest that Grp1p may facilitate membrane traffic indirectly, possibly by maintaining Golgi function. In an effort to identify genes whose products physically interact with Sec34p, we also tested the ability of overexpressed SEC34 to suppress known secretory mutations that block vesicular traffic between the ER and the Golgi. This screen revealed that SEC34 specifically suppresses sec35-1. SEC34 encodes a hydrophilic protein of ∼100 kDa. Like Sec35p, which has been implicated in the tethering of ER-derived vesicles to the Golgi, Sec34p is predominantly soluble. Sec34p and Sec35p stably associate with each other to form a multiprotein complex of ∼480 kDa. These data indicate that Sec34p acts in conjunction with Sec35p to mediate a common step in vesicular traffic.

Pex17p Is Required for Import of Both Peroxisome Membrane and Lumenal Proteins and Interacts with Pex19p and the Peroxisome Targeting Signal–Receptor Docking Complex in Pichia pastoris

Pichia pastoris PEX17 was cloned by complementation of a peroxisome-deficient strain obtained from a novel screen for mutants disrupted in the localization of a peroxisomal membrane protein (PMP) reporter. PEX17 encodes a 267-amino-acid protein with low identity (18%) to the previously characterized Saccharomyces cerevisiae Pex17p. Like ScPex17p, PpPex17p contains a putative transmembrane domain near the amino terminus and two carboxyl-terminal coiled-coil regions. PpPex17p behaves as an integral PMP with a cytosolic carboxyl-terminal domain. pex17Δ mutants accumulate peroxisomal matrix proteins and certain integral PMPs in the cytosol, suggesting a critical role for Pex17p in their localization. Peroxisome remnants were observed in the pex17Δ mutant by morphological and biochemical means, suggesting that Pex17p is not absolutely required for remnant formation. Yeast two-hybrid analysis demonstrated that the carboxyl terminus of Pex19p was required for interaction with Pex17p lacking the carboxyl-terminal coiled-coil domains. Biochemical evidence confirmed the interaction between Pex19p and Pex17p. Additionally, Pex17p cross-linked to components of the peroxisome targeting signal–receptor docking complex, which unexpectedly contained Pex3p. Our evidence suggests the existence of distinct subcomplexes that contain separable pools of Pex3p, Pex19p, Pex17p, Pex14p, and the peroxisome targeting signal receptors. These distinct pools may serve different purposes for the import of matrix proteins or PMPs.

Three-dimensional modeling of and ligand docking to vitamin D receptor ligand binding domain

The ligand binding domain of the human vitamin D receptor (VDR) was modeled based on the crystal structure of the retinoic acid receptor. The ligand binding pocket of our VDR model is spacious at the helix 11 site and confined at the β-turn site. The ligand 1α,25-dihydroxyvitamin D3 was assumed to be anchored in the ligand binding pocket with its side chain heading to helix 11 (site 2) and the A-ring toward the β-turn (site 1). Three residues forming hydrogen bonds with the functionally important 1α- and 25-hydroxyl groups of 1α,25-dihydroxyvitamin D3 were identified and confirmed by mutational analysis: the 1α-hydroxyl group is forming pincer-type hydrogen bonds with S237 and R274 and the 25-hydroxyl group is interacting with H397. Docking potential for various ligands to the VDR model was examined, and the results are in good agreement with our previous three-dimensional structure-function theory.

Folding simulations of a three-stranded antiparallel β-sheet peptide

Protein folding is a grand challenge of the postgenomic era. In this paper, 58 folding events sampled during 47 molecular dynamics trajectories for a total simulation time of more than 4 μs provide an atomic detail picture of the folding of a 20-residue synthetic peptide with a stable three-stranded antiparallel β-sheet fold. The simulations successfully reproduce the NMR solution conformation, irrespective of the starting structure. The sampling of the conformational space is sufficient to determine the free energy surface and localize the minima and transition states. The statistically predominant folding pathway involves the formation of contacts between strands 2 and 3, starting with the side chains close to the turn, followed by association of the N-terminal strand onto the preformed 2–3 β-hairpin. The folding mechanism presented here, formation of a β-hairpin followed by consolidation, is in agreement with a computational study of the free energy surface of another synthetic three-stranded antiparallel β-sheet by Bursulaya and Brooks [(1999) J. Am. Chem. Soc. 121, 9947–9951]. Hence, it might hold in general for antiparallel β-sheets with short turns.

Substrate recruitment to cyclin-dependent kinase 2 by a multipurpose docking site on cyclin A

An important question in the cell cycle field is how cyclin-dependent kinases (cdks) target their substrates. We have studied the role of a conserved hydrophobic patch on the surface of cyclin A in substrate recognition by cyclin A-cdk2. This hydrophobic patch is ≈35Å away from the active site of cdk2 and contains the MRAIL sequence conserved among a number of mammalian cyclins. In the x-ray structure of cyclin A-cdk2-p27, this hydrophobic patch contacts the RNLFG sequence in p27 that is common to a number of substrates and inhibitors of mammalian cdks. We find that mutation of this hydrophobic patch on cyclin A eliminates binding to proteins containing RXL motifs without affecting binding to cdk2. This docking site is critical for cyclin A-cdk2 phosphorylation of substrates containing RXL motifs, but not for phosphorylation of histone H1. Impaired substrate binding by the cyclin is the cause of the defect in RXL substrate phosphorylation, because phosphorylation can be rescued by restoring a cyclin A–substrate interaction in a heterologous manner. In addition, the conserved hydrophobic patch is important for cyclin A function in cells, contributing to cyclin A’s ability to drive cells out of the G1 phase of the cell cycle. Thus, we define a mechanism by which cyclins can recruit substrates to cdks, and our results support the notion that a high local concentration of substrate provided by a protein–protein interaction distant from the active site is critical for phosphorylation by cdks.

Induced fit DNA recognition by a minor groove binding analogue of Hoechst 33258: fluctuations in DNA A tract structure investigated by NMR and molecular dynamics simulations

NMR analysis and molecular dynamics simulations of d(GGTAATTACC)2 and its complex with a tetrahydropyrimidinium analogue of Hoechst 33258 suggest that DNA minor groove recognition in solution involves a combination of conformational selection and induced fit, rather than binding to a preorganised site. Analysis of structural fluctuations in the bound and unbound states suggests that the degree of induced fit observed is primarily a consequence of optimising van der Waals contacts with the walls of the minor groove resulting in groove narrowing through: (i) changes in base step parameters, including increased helical twist and propeller twist; (ii) changes to the sugar–phosphate backbone conformation to engulf the bound ligand; (iii) suppression of bending modes at the TpA steps. In contrast, the geometrical arrangement of hydrogen bond acceptors on the groove floor appears to be relatively insensitive to DNA conformation (helical twist and propeller twist). We suggest that effective recognition of DNA sequences (in this case an A tract structure) appears to depend to a significant extent on the sequence being flexible enough to be able to adopt the geometrically optimal conformation compatible with the various binding interactions, rather than involving ‘lock and key’ recognition.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.

Stimulation of phosphatidylinositol 3-kinase by fibroblast growth factor receptors is mediated by coordinated recruitment of multiple docking proteins

The docking protein FRS2 is a major downstream effector that links fibroblast growth factor (FGF) and nerve growth factor receptors with the Ras/mitogen-activated protein kinase signaling cascade. In this report, we demonstrate that FRS2 also plays a pivotal role in FGF-induced recruitment and activation of phosphatidylinositol 3-kinase (PI3-kinase). We demonstrate that tyrosine phosphorylation of FRS2α leads to Grb2-mediated complex formation with the docking protein Gab1 and its tyrosine phosphorylation, resulting in the recruitment and activation of PI3-kinase. Furthermore, Grb2 bound to tyrosine-phosphorylated FRS2 through its SH2 domain interacts primarily via its carboxyl-terminal SH3 domain with a proline-rich region in Gab1 and via its amino-terminal SH3 domain with the nucleotide exchange factor Sos1. Assembly of FRS2α:Grb2:Gab1 complex induced by FGF stimulation results in activation of PI3-kinase and downstream effector proteins such as the S/T kinase Akt, whose cellular localization and activity are regulated by products of PI3-kinase. These experiments reveal a unique mechanism for generation of signal diversity by growth factor-induced coordinated assembly of a multidocking protein complex that can activate the Ras/mitogen-activated protein kinase cascade to induce cell proliferation and differentiation, and PI3-kinase to activate a mediator of a cell survival pathway.

Electrostatic steering and ionic tethering in enzyme–ligand binding: Insights from simulations

To bind at an enzyme’s active site, a ligand must diffuse or be transported to the enzyme’s surface, and, if the binding site is buried, the ligand must diffuse through the protein to reach it. Although the driving force for ligand binding is often ascribed to the hydrophobic effect, electrostatic interactions also influence the binding process of both charged and nonpolar ligands. First, electrostatic steering of charged substrates into enzyme active sites is discussed. This is of particular relevance for diffusion-influenced enzymes. By comparing the results of Brownian dynamics simulations and electrostatic potential similarity analysis for triose-phosphate isomerases, superoxide dismutases, and β-lactamases from different species, we identify the conserved features responsible for the electrostatic substrate-steering fields. The conserved potentials are localized at the active sites and are the primary determinants of the bimolecular association rates. Then we focus on a more subtle effect, which we will refer to as “ionic tethering.” We explore, by means of molecular and Brownian dynamics simulations and electrostatic continuum calculations, how salt links can act as tethers between structural elements of an enzyme that undergo conformational change upon substrate binding, and thereby regulate or modulate substrate binding. This is illustrated for the lipase and cytochrome P450 enzymes. Ionic tethering can provide a control mechanism for substrate binding that is sensitive to the electrostatic properties of the enzyme’s surroundings even when the substrate is nonpolar.