Slow Conformational Motions Research Articles

Free Energy Simulations of Receptor-Binding Domain Opening of the SARS-CoV-2 Spike Indicate a Barrierless Transition with Slow Conformational Motions.

Infection by sarbecoviruses begins with the attachment of the homotrimeric viral "spike" protein to the angiotensin-converting enzyme 2 receptor on the surface of mammalian cells. This requires one or more receptor-binding domains (RBDs) to be in the open (up) position. Here, we present the results of long molecular dynamics simulations with umbrella sampling (US) to compute a one-dimensional free energy profile of RBD opening/closing and the associated transition times. After ≃3.58μs of simulation time per US window (∼229 μs in total), which was required to approach trajectory decorrelation, the computed free energy profile was found to be without large barriers. This suggests that the RBD diffuses between the open and closed positions without significant energetic hindrance. This interpretation appears consistent with experiments but is at odds with some previous simulations. Modeling the RBD motion as diffusive dynamics along the computed free energy profile, we find that the overall time required for the transition is only about 2 μs, which is 5 orders of magnitude shorter than experimentally measured transition times. We speculate that the most likely reason for the transition time mismatch is our use of very short glycans, which was required to make the simulations performed here feasible. Despite the long simulation times, the final free energy profile is not fully converged with statistical errors of ≃1.16 kcal/mol, which were found to be consistent with the slow time decay in the autocorrelation of the conformational motions of the protein. The simulation lengths that would be required to obtain fully converged results remain unknown, but the present calculations would benefit from at least an order-of-magnitude extension.

Protein-Bath Coupling of an Internal Reaction Coordinate at Intermediate Time Scales.

Thermally activated barrier-crossing processes are central to protein reaction kinetics. A determining factor for such kinetics is the extent to which the protein's motions are coupled to the surrounding bath. It is understood that slow large-scale conformational motions are strongly coupled to the environment, while fast librational motions are uncoupled. However, less is known about protein-bath coupling of reaction coordinates located on the interior of a protein and with dynamics on intermediate time scales. In this work, we use single molecule 2D fluorescence lifetime correlation spectroscopy to study the microsecond chemical reaction occurring in the chromophore pocket of eGFP. The equilibrium reaction involves a dihedral rotation of a glutamic acid residue and a rearrangement of the local hydrogen-bonding network surrounding the endogenous chromophore, with no accompanying large-scale conformational changes. We observe that the internal chemical reaction is coupled to the solvent viscosity, though the scaling deviates from Kramers' behavior. We attribute this deviation to the internal friction of the protein, which weakens the protein-solvent coupling at high viscosity and intermediate time scales.

ON/OFF Control of the Flipping Motion of Diuranyl Bis(Salophen) Macrocycle by Extremely Strong Binding with Fluoride Ion.

Diuranyl bis(salophen) complex 1 features a relatively slow conformational motion, induced by an intramolecular O═U═O···UO2 binding motif, which interconverts the two nonsymmetric halves of the ligand. This flipping motion, which constitutes one of the fundamental molecular motions, can be completely halted by addition of fluoride anion, which is bound to 1, reaching one of the highest affinities reported to date. This system represents a model to study flipping dynamics in light of the possibility of developing novel types of molecular machines based on it.

The dynamic conformational landscape of the protein methyltransferase SETD8.

Elucidating the conformational heterogeneity of proteins is essential for understanding protein function and developing exogenous ligands. With the rapid development of experimental and computational methods, it is of great interest to integrate these approaches to illuminate the conformational landscapes of target proteins. SETD8 is a protein lysine methyltransferase (PKMT), which functions in vivo via the methylation of histone and nonhistone targets. Utilizing covalent inhibitors and depleting native ligands to trap hidden conformational states, we obtained diverse X-ray structures of SETD8. These structures were used to seed distributed atomistic molecular dynamics simulations that generated a total of six milliseconds of trajectory data. Markov state models, built via an automated machine learning approach and corroborated experimentally, reveal how slow conformational motions and conformational states are relevant to catalysis. These findings provide molecular insight on enzymatic catalysis and allosteric mechanisms of a PKMT via its detailed conformational landscape.

Dynamics of dehaloperoxidase-hemoglobin A derived from NMR relaxation spectroscopy and molecular dynamics simulation

Dehaloperoxidase-hemoglobin is the first hemoglobin identified with biologically-relevant oxidative functions, which include peroxidase, peroxygenase and oxidase activities. Herein we report a study of the protein backbone dynamics of DHP using heteronuclear NMR relaxation methods and molecular dynamics (MD) simulations to address the role of protein dynamics in switching from one function to another. The results show that DHP's backbone helical regions and turns have average order parameters of S2 = 0.87 ± 0.03 and S2 = 0.76 ± 0.08, respectively. Furthermore, DHP is primarily a monomer in solution based on the overall tumbling correlation time τm is 9.49 ± 1.65 ns calculated using the prolate diffusion tensor model in the program relax. A number of amino acid residues have significant Rex using the Lipari-Szabo model-free formalism. These include Lys3, Ile6, Leu13, Gln18, Arg32, Ser48, Met49, Thr56, Phe60, Arg69, Thr71 Cys73, Ala77, Asn81, Gly95, Arg109, Phe115, Leu127 and Met136, which may experience slow conformational motions on the microseconds-milliseconds time scale according to the model. Caution should be used when the model contains >4 fitting parameters. The program caver3.0 was used to identify tunnels inside DHP obtained from MD simulation snapshots that are consistent with the importance of the Xe binding site, which is located at the central intersection of the tunnels. These tunnels provide diffusion pathways for small ligands such as O2, H2O and H2O2 to enter the distal pocket independently of the trajectory of substrates and inhibitors, both of which are aromatic molecules.

Relationship between Structural Flexibility and Function in the C-Terminal Region of the Heparin-Binding Domain of VEGF165

Vascular endothelial growth factor (VEGF) is an angiogenic protein with neurotrophic and neuroprotective effects. Previously, we reported that triamterene (Trm) inhibits VEGF-amyloid β (Aβ) interactions without affecting other biological activities of VEGF or Aβ [Jeong, K.-W., et al. (2011) Biochemistry 50, 4843-4854]. We further showed that molecular motions in the N-terminal disordered loop region of the heparin-binding domain (HBD) are important for interaction with Trm. To investigate the importance of motion at the C-terminal domain of HBD, we constructed a binding model of HBD with heparin octasaccharide (HOS) based on measurements of chemical shift changes and docking studies. Furthermore, the dynamic properties of the HBD-HOS and HBD-Trm-HOS complexes were assessed by measuring spin relaxation rates. The results showed that the HOS-binding site is composed of two basic clusters consisting of side chains of residues R13, R14, and K15 and residues K30, R35, and R49. When HOS binds, values for the heteronuclear nuclear Overhauser effect near HOS-binding sites increased dramatically. CPMG (Carr-Purcell-Meiboom-Gill sequence) experiments as well as an R2 relaxation experiment were undertaken to understand millisecond time-scale motions in HBD. There is large relaxation dispersion of residues at Trm- and HOS-binding sites in free HBD. C-Terminal residues such as S34, C48, and D51 near the HOS-binding sites continued to exhibit slow conformational motions in the HBD-Trm complex, while those slow motions disappeared in the bound conformation of HBD with HOS. Collectively, our results demonstrate that the inherent structural flexibilities of the C-terminal region of the HBD are important in the heparin binding process and that Trm does not inhibit VEGF-heparin interactions necessary for the biological activities of VEGF.

The nuclear magnetic resonance relaxation data analysis in solids: General R1/R1ρ equations and the model-free approach

The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the μs time scale is measuring relaxation rate R(1)(ρ). Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spin-lock pulse is used, the spin-lock field can be oriented under an arbitrary angle in respect to B(0). Second, the spin-lock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R(1)(ρ) that would be applicable for any values of the spin-lock frequency, magic angle spinning rate and resonance offset of the spin-lock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R(1)(ρ) experiment using SPINEVOLUTION program. In addition to that, the applicability of the well-known model-free approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30° and 90° cone angles and two-site jump models, it has been demonstrated that the auto-correlation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the model-free approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.

Parallel Generalized Born Implicit Solvent Calculations with NAMD.

Accurate electrostatic descriptions of aqueous solvent are critical for simulation studies of bio-molecules, but the computational cost of explicit treatment of solvent is very high. A computationally more feasible alternative is a generalized Born implicit solvent description which models polar solvent as a dielectric continuum. Unfortunately, the attainable simulation speedup does not transfer to the massive parallel computers often employed for simulation of large structures. Longer cutoff distances, spatially heterogenous distribution of atoms and the necessary three-fold iteration over atom-pairs in each timestep combine to challenge efficient parallel performance of generalized Born implicit solvent algorithms. Here we report how NAMD, a parallel molecular dynamics program, meets the challenge through a unique parallelization strategy. NAMD now permits efficient simulation of large systems whose slow conformational motions benefit most from implicit solvent descriptions due to the inherent low viscosity. NAMD's implicit solvent performance is benchmarked and then illustrated in simulating the ratcheting Escherichia coli ribosome involving ~250,000 atoms.

Dynamics of a Heparin-Binding Domain of VEGF165 Complexed with Its Inhibitor Triamterene

Vascular endothelial growth factor (VEGF), which has neurotrophic and neuroprotective effects in addition to its major role in angiogenesis, interacts with Aβ and accumulates in the senile plaques of Alzheimer's disease (AD) patients' brains. It is known that Aβ binds to the heparin-binding domain (HBD) of the 165-amino acid VEGF variant, VEGF(165). In this study, we showed that triamterene (Trm) inhibits VEGF--Aβ interaction without affecting other biological activities of VEGF or Aβ. We investigated the importance of structural and dynamic features of HBD for its molecular-recognition processes. The binding model of HBD and Trm was constructed based on measurements of chemical shift changes and docking study. The results showed that the loop region (S11-L17) and F18 at the beginning of the first β-sheet in the HBD constitute the inhibitor binding site. The N1 atom of pteridine ring of Trm forms hydrogen bonding with backbone amide proton of R13, and the phenyl ring took part in a hydrophobic interaction with the aromatic ring of F18. To investigate the functional importance of the inherent structural flexibility of the HBD in VEGF, the dynamic properties of free HBD and HBD--Trm complex were assessed by measuring spin relaxation rates, and the backbone dynamics were investigated by model-free analysis. The residues in the disordered loop region of the N-terminus exhibited conformational exchanges in free HBD, and flexibility of this loop region decreased dramatically upon binding to Trm, suggesting that Aβ as well as inhibitor may recognize these unique dynamic features of the HBD. Furthermore, C-terminal residues continued to exhibit slow conformational motions, even in the HBD--Trm complex, implying that these motions at the C-terminus of the HBD might be important for interactions with heparin molecules. The flexibility of HBD demonstrated here should be essential for VEGF function and interaction with other protein partners.

Slow conformational motions that favor sub-picosecond motions important for catalysis.

It has been accepted for many years that functionally important motions are crucial to binding properties of ligands in such molecules as hemoglobin and myoglobin. In enzymatic reactions, theory and now experiment are beginning to confirm the importance of motions on a fast (ps) time scale in the chemical step of the catalytic process. What is missing is a clear physical picture of how slow conformational fluctuations are related to the fast motions that have been identified as crucial. This paper presents a theoretical analysis of this issue for human heart lactate dehydrogenase. We will examine how slow conformational motions bring the system to conformations that are distinguished as catalytically competent because they favor specific fast motions.

Conformation-dependent hydride transfer in neuronal nitric oxide synthase reductase domain

Calmodulin (CaM) activates the constitutive isoforms of mammalian nitric oxide synthase by triggering electron transfer from the reductase domain FMN to the heme. This enables the enzymes to be regulated by Ca(2+) concentration. CaM exerts most of its effects on the reductase domain; these include activation of electron transfer to electron acceptors, and an increase in the apparent rate of flavin reduction by the substrate NADPH. It has been shown that the former is caused by a transition from a conformationally locked form of the enzyme to an open form as a result of CaM binding, improving FMN accessibility, but the latter effect has not been explained satisfactorily. Here, we report the effect of ionic strength and isotopic substitution on flavin reduction. We found a remarkable correlation between the rate of steady-state turnover of the reductase domain and the rate of flavin reduction over a range of different ionic strengths. The reduction of the enzyme by NADPH was biphasic, and the amplitudes of the phases determined through global analysis of stopped-flow data correlated with the proportions of enzyme known to exist in the open and closed conformations. The different conformations of the enzyme molecule appeared to have different rates of reaction with NADPH. Thus, proximity of FMN inhibits hydride transfer to the FAD. In the CaM-free enzyme, slow conformational motion (opening and closing) limits turnover. It is now clear that this motion also controls hydride transfer during steady-state turnover, by limiting the rate at which NADPH can access the FAD.

Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis

We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.

The point mutation A34F causes dimerization of GB1

The immunoglobulin-binding domain B1 of streptococcal protein G (GB1), a very stable, small, single-domain protein, is one of the most extensively used models in the area of protein folding and design. Variants derived from a library of randomized hydrophobic core residues previously revealed alternative folds, namely a completely intertwined tetramer (Frank et al., Nat Struct Biol 2002;9:877-885) and a domain-swapped dimer (Byeon et al., J Mol Biol 2003;333:141-152). Here, we report the NMR structure of the single amino acid mutant Ala-34-Phe which exists as side-by-side dimer. The dimer dissociation constant is 27 +/- 4 microM. The dimer interface comprises two structural elements: First, the beta-sheets of the two monomers pair in an antiparallel arrangement, thereby forming an eight-stranded beta-sheet. Second, the alpha-helix is shortened, ending in a loop that engages in intermolecular contacts. The largest difference between the monomer unit in the A34F dimer and the monomeric wild-type GB1 is the dissolution of the C-terminal half of the alpha-helix associated with a pronounced slow conformational motion of the interface loop. This involves a large movement of the Tyr-33 side chain that swings out from the monomer to engage in dimer contacts.

Restricted Backbone Conformational and Motional Flexibilities of Loops Containing Peptidyl−Proline Bonds Dominate the Enzyme Activity of Staphylococcal Nuclease,

The role of cis-trans isomerizations of peptidyl-proline bonds in the enzyme activity of staphylococcal nuclease (SNase) was examined by mutation of proline residues. The proline-free SNase ([Pro-]SNase), namely, P11A/P31A/P42A/P47T/P56A/P117G-mutant SNase, was adopted for elucidating the correlation between the nuclease activity and the backbone conformational and dynamic states of SNase. The 3D solution structure of [Pro-]SNase has been determined by heteronuclear NMR experiments. Comparing the structure of [Pro-]SNase with the structure of SNase revealed the conformational differences between the two proteins. In the structure of [Pro-]SNase, conformational rearrangements were observed for the loop of residues Ala112-His121 containing a trans Lys116-Gly117 peptide bond and for the C-terminal alpha-helical loop of residues Leu137-Glu142. Mutation of proline at position 117 also caused the conformational rearrangement of the p-loop (Asp77-Leu89), which is remote from the Ala112-His121 loop. The Ala112-His121 loop and p-loop are placed closer to each other in [Pro-]SNase than in SNase. The backbone dynamic features of the omega-loop (Pro42-Pro56) of SNase are different from those of [Pro-]SNase. The backbone of the omega-loop exhibits restricted flexibility with slow conformational exchange motions in SNase, but is highly flexible in [Pro-]SNase. The analysis indicates that the restrained backbone conformation of the Ala112-His121 loop and restricted flexibility of the omega-loop are two dominant factors determining the enzyme activity of SNase. Of the two factors, the former is correlated with the strained cis Lys116-Pro117 peptide bond and the latter is correlated with the cis-trans isomerizations of the His46-Pro47 peptide bond.

Multistate conformational model of a single LH2 complex: Quantitative picture of time-dependent spectral fluctuations

The fluorescence (FL) spectrum of single LH2 complexes fluctuates on a time-scale of seconds in wavelength, spectral shape and intensity [D. Rutkauskas, V. Novoderezhkin, R.J. Cogdell, R. van Grondelle, Biophys. J. 88 (2005) 422]. Here we propose a model capable to explain the statistics of these time-dependent FL-fluctuations. In this model this evolution of the spectra is described in terms of slow conformational motion of the pigment–protein complex inducing random shifts of the site energies. These shifts manifest themselves as inhomogeneous broadening of the bulk spectra and can be directly observed as spectral fluctuations in single molecule experiments. Our model assumes a finite number of conformational sub-states for each pigment of the complex and allows a calculation of the conformational dynamics by introducing phenomenological transfer rates between these sub-states. The simplest version of the model with two conformations for each pigment in enough to explain the fast small-size (±10 nm) fluctuations within the 860–880 nm spectral region. Larger spectral jumps that are observed in the experiment (10–20 nm jumps to the blue and 10–40 nm to the red) can only be reproduced by including additional conformational states. The simplest model includes one more pair of states (producing big red and big blue shifts of the site energies). This four-state model enables us to reproduce quantitatively (i) the distribution of the FL peak positions, (ii) the changes of the width and asymmetry of the FL profiles as a function of the FL peak position, and (iii) distribution of the amplitudes and times of spectral jumps as a function of the initial FL peak position. We classify and describe the dynamic patterns that appear most often in the measured FL traces and in the calculated dynamics. We demonstrate a similarity between the measured and modelled patterns and show how these main types of the dynamics are related to specific changes in the conformational state of the 18 pigments of the LH2-B850 antenna.

Collective Langevin dynamics of conformational motions in proteins

Functionally relevant slow conformational motions of proteins are, at present, in most cases inaccessible to molecular dynamics (MD) simulations. The main reason is that the major part of the computational effort is spend for the accurate description of a huge number of high frequency motions of the protein and the surrounding solvent. The accumulated influence of these fluctuations is crucial for a correct treatment of the conformational dynamics; however, their details can be considered irrelevant for most purposes. To accurately describe long time protein dynamics we here propose a reduced dimension approach, collective Langevin dynamics (CLD), which evolves the dynamics of the system within a small subspace of relevant collective degrees of freedom. The dynamics within the low-dimensional conformational subspace is evolved via a generalized Langevin equation which accounts for memory effects via memory kernels also extracted from short explicit MD simulations. To determine the memory kernel with differing levels of regularization, we propose and evaluate two methods. As a first test, CLD is applied to describe the conformational motion of the peptide neurotensin. A drastic dimension reduction is achieved by considering one single curved conformational coordinate. CLD yielded accurate thermodynamical and dynamical behaviors. In particular, the rate of transitions between two conformational states agreed well with a rate obtained from a 150 ns reference molecular dynamics simulation, despite the fact that the time scale of the transition (approximately 50 ns) was much longer than the 1 ns molecular dynamics simulation from which the memory kernel was extracted.

Energy transfer in photosynthesis: experimental insights and quantitative models

We overview experimental and theoretical studies of energy transfer in the photosynthetic light-harvesting complexes LH1, LH2, and LHCII performed during the past decade since the discovery of high-resolution structure of these complexes. Experimental findings obtained with various spectroscopic techniques makes possible a modelling of the excitation dynamics at a quantitative level. The modified Redfield theory allows a precise assignment of the energy transfer pathways together with a direct visualization of the whole excitation dynamics where various regimes from a coherent motion of delocalized exciton to a hopping of localized excitations are superimposed. In a single complex it is possible to observe the switching between these regimes driven by slow conformational motion (as we demonstrate for LH2). Excitation dynamics under quenched conditions in higher-plant complexes is discussed.

Functional conformational motions in the turnover cycle of cholesterol oxidase.

Reexamining experimental data of single-molecule fluorescence correlation spectroscopy for cholesterol oxidase, we find that the existing Michaelis-Menten models with dynamical disorder cannot explain strong correlations between subsequent turnover cycles revealed in the diagonal feature in the joint statistical distribution of adjacent "on" times of this enzyme. We suggest that functional conformational motions representing ordered sequences of transitions between a set of conformational substates are involved, along with equilibrium conformational fluctuations in the turnover cycle of cholesterol oxidase. A two-channel model of single-enzyme dynamics, including a slow functional conformational motion in one of the channels, is proposed that allows us to reproduce such strong correlations.

Molecular Dynamics Study on the Effect of Chain Branching on the Physical Properties of Lipid Bilayers: Structural Stability

In general, bilayers composed of branch-chained lipid molecules are known to have high stability and low ion permeability. To understand how chain branching affects bilayer properties on a molecular level, two molecular dynamics (MD) simulations of lipid bilayers have been undertaken in the isothermal−isobaric ensemble. The first MD simulation was carried out on the straight-chained DPPC bilayer, and the second was carried out on the branch-chained DPhPC bilayer. Chain branching reduced segmental order of the lipid chain. This would be closely related to a high gauche probability at the dihedrals in the vicinity of tert-carbons; these dihedrals brought about the chain bending at the branched segments. Due to the characteristic conformation of the branched chain, some different effects were observed: First, the probability of parallel orientation of the two chains in a lipid was reduced; second, a chain caught between the two chains of the neighboring lipid in the same leaflet of the bilayer was frequently observed. As a consequence, the branched chain showed a much lower overall rate of trans−gauche isomerization than its straight counterpart. In conclusion, the high structural stability of the branched DPhPC bilayer is attributable mainly to the slow conformational motion of the hydrophobic chain, which is clearly correlated with the observed chain “entrapment” between the lateral neighboring lipid molecules.

Slow filament dynamics and viscoelasticity in entangled and active actin networks.

This paper deals with correlations between the viscoelastic impedance of entangled actin networks and the slow conformational dynamics and diffusive motions of single filaments. The single filament dynamics is visualized and analysed by analysing the Brownian motion of attached colloidal beads, which enables independent measurements of characteristic viscoelastic response times such as the entanglement and reptation times. We further studied the frequency-dependent viscoelastic impedance of active actin-heavy-meromyosin II networks by magnetic-tweezers microrheometry to gain insight into the effect of such highly dynamic and force-generating crosslinkers (exhibiting bond lifetimes of less than 1 s) on the rheological properties. We show that at high frequencies (higher than 1 Hz) the viscoelastic loss modulus is slightly increased relative to the entangled network (associated with an increase in the energy dissipated during mechanical excitations), while at low frequencies the plateau of the impedance spectrum becomes more pronounced as a consequence of the cross-linking of the network and the suppression of the terminal regime. Our data provide evidence that the myosin motor protein may play a role as softener of the actin cortex, enabling the adaptive reduction of the yield stress of cells and thus facilitating cellular deformations.