Systematic multiscale parameterization of heterogeneous elastic network models of proteins

We present a method to parameterize heterogeneous elastic network models (heteroENMs) of proteins to reproduce the fluctuations observed in atomistic simulations. Because it is based on atomistic simulation, our method allows the development of elastic coarse-grained models of proteins under different conditions or in different environments. The method is simple and applicable to models at any level of coarse-graining. We validated the method in three systems. First, we computed the persistence length of ADP-bound F-actin, using a heteroENM model. The value of 6.1 ± 1.6 μm is consistent with the experimentally measured value of 9.0 ± 0.5 μm. We then compared our method to a uniform elastic network model and a realistic extension algorithm via covariance Hessian (REACH) model of carboxy myoglobin, and found that the heteroENM method more accurately predicted mean-square fluctuations of α-carbon atoms. Finally, we showed that the method captures critical differences in effective harmonic interactions for coarse-grained models of the N-terminal Bin/amphiphysin/Rvs (N-BAR) domain of amphiphysin, by building models of N-BAR both bound to a membrane and free in solution.     

Reaction of the Co(II)-substrate radical pair catalytic intermediate in coenzyme B12-dependent ethanolamine ammonia-lyase in frozen aqueous solution from 190 to 217 K

The decay kinetics of the aminoethanol-generated Co^II-substrate radical pair catalytic intermediate in ethanolamine ammonia-lyase from Salmonella typhimurium have been measured on timescales of <10⁵ s in frozen aqueous solution from 190 to 217 K. X-band continuous-wave electron paramagnetic resonance (EPR) spectroscopy of the disordered samples has been used to continuously monitor the full radical pair EPR spectrum during progress of the decay after temperature step reaction initiation. The decay to a diamagnetic state is complete and no paramagnetic intermediate states are detected. The decay exhibits three kinetic regimes in the measured temperature range, as follows. i), Low temperature range, 190 ≤ T ≤ 207 K: the decay is biexponential with constant fast (0.57 ± 0.04) and slow (0.43 ± 0.04) phase amplitudes. ii), Transition temperature range, 207 < T < 214 K: the amplitude of the slow phase decreases to zero with a compensatory rise in the fast phase amplitude, with increasing temperature. iii), High temperature range, T ≥ 214 K: the decay is monoexponential. The observed first-order rate constants for the monoexponential (k_obs,m) and the fast phase of the biexponential decay (k_obs,f) adhere to the same linear relation on an lnk versus T⁻¹ (Arrhenius) plot. Thus, k_obs,m and k_obs,f correspond to the same apparent Arrhenius prefactor and activation energy (logA_app,f (s⁻¹) = 13.0, E_a,app,f = 15.0 kcal/mol), and therefore, a common decay mechanism. We propose that k_obs,m and k_obs,f represent the native, forward reaction of the substrate through the radical rearrangement step. The slow phase rate constant (k_obs,s) for 190 ≤ T ≤ 207 K obeys a different linear Arrhenius relation (logA_app,s (s⁻¹) = 13.9, E_a,app,s = 16.6 kcal/mol). In the transition temperature range, k_obs,s displays a super-Arrhenius increase with increasing temperature. The change in E_a,app,s with temperature and the narrow range over which it occurs suggest an origin in a liquid/glass or dynamical transition. A discontinuity in the activation barrier for the chemical reaction is not expected in the transition temperature range. Therefore, the transition arises from a change in the properties of the protein. We propose that a protein dynamical contribution to the reaction, which is present above the transition temperature, is lost below the transition temperature, owing to an increase in the activation energy barrier for protein motions that are coupled to the reaction. For both the fast and slow phases of the low temperature decay, the dynamical transition in protein motions that are obligatorily coupled to the reaction of the Co^II-substrate radical pair lies below 190 K.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.     

Synthesis, structure and magnetic studies of two-dimensional network of Cu(II) polymer using malonate and 4,4′-azobispyridine ligands

The malonato-bridged copper(II) complex [Cu(mal)(H₂O)(azpy)_1/2] · H₂O (1) (mal = malonate, azpy = 4,4′-azobispyridine) has been synthesized and characterized by X-ray diffraction. The structure of 1 consists of malonato-bridged uniform copper(II) chains which are covalent connected through azpy to form two-dimensional wavelike network. The magnetic pathway of complex 1 is through a single syn-anti carboxylate bridge connecting equatorial and equatorial positions of adjacent copper(II) atoms, and have the value of the intrachain ferromagnetic coupling (J = 8.73(3) cm⁻¹) and interchain antiferromagnetic coupling (zJ′ = − 1.31(1) cm⁻¹) through a numerical expression for a ferromagnetic uniform chain.     

Design of protein-ligand binding based on the molecular-mechanics energy model

While the molecular-mechanics field has standardized on a few potential energy functions, computational protein design efforts are based on potentials that are unique to individual laboratories. Here we show that a standard molecular-mechanics potential energy function without any modifications can be used to engineer protein-ligand binding. A molecular-mechanics potential is used to reconstruct the coordinates of various binding sites with an average root-mean-square error of 0.61 Å and to reproduce known ligand-induced side-chain conformational shifts. Within a series of 34 mutants, the calculation can always distinguish between weak (K_d > 1 mM) and tight (K_d < 10 μM) binding sequences. Starting from partial coordinates of the ribose-binding protein lacking the ligand and the 10 primary contact residues, the molecular-mechanics potential is used to redesign a ribose-binding site. Out of a search space of 2 × 10¹² sequences, the calculation selects a point mutant of the native protein as the top solution (experimental K_d = 17 μM) and the native protein as the second best solution (experimental K_d = 210 nM). The quality of the predictions depends on the accuracy of the generalized Born electrostatics model, treatment of protonation equilibria, high-resolution rotamer sampling, a final local energy minimization step, and explicit modeling of the bound, unbound, and unfolded states. The application of unmodified molecular-mechanics potentials to protein design links two fields in a mutually beneficial way. Design provides a new avenue for testing molecular-mechanics energy functions, and future improvements in these energy functions will presumably lead to more accurate design results.     

Simultaneous true, gated, and coupled electron-transfer reactions and energetics of protein rearrangement

Cytochromes c₆ and f react by three et mechanisms under similar conditions. We report temperature and viscosity effects on the protein docking and kinetics of ³Zncyt c₆ + cyt f(III) → Zncyt c₆⁺ + cyt f(II). At 0.5-40.0 °C, this reaction occurs within the persistent (associated) diprotein complex with the rate constant k^pr and within the transient (collision) complex with the rate constant k^tr. The viscosity independence of k^pr, the donor-acceptor coupling H_ab = (0.5 ± 0.1) cm⁻¹, and reorganizational energy λ = (2.14 ± 0.02) eV indicate true et within the persistent complex. The viscosity dependence of k^tr and a break at 30 °C in the Eyring plot for k^tr reveal mechanisms within the transient complex that are reversibly switched by temperature change. Kramers protein friction parameters differ much for the reactions below (σ = 0.3 ± 0.1, δ = 0.85 ± 0.07) and above (σ = 4.0 ± 0.9, δ = 0.40 ± 0.06) 30 °C. The transient complex(es) undergo(es) coupled et below ca. 30 °C and gated et above ca. 30 °C. Brownian dynamics simulations reveal two broad, dynamic ensembles of configurations “bridged” by few intermediate configurations through which the interconversion presumably occurs.     

Synthesis and characterization of silver(I) derivatives containing acylpyrazolonate and phosphino ligands: X-ray crystal structures of monomeric [Ag(Q)(PPh3)2] and of dimeric [{Ag(Q)(PiBu3)}2] (Q = 1-phenyl-3-methyl-4-tert-butylacetylpyrazolon-5-ato)

New silver(I) acylpyrazolonate derivatives [Ag(Q)], [Ag(Q)(PR₃)]₂ and [Ag(Q)(PR₃)₂] (HQ = 1-R¹-3-methyl-4-R²(CO)pyrazol-5-one, HQ^Bn = R¹ = C₆H₅, R² = CH₂C₆H₅; HQ^CHPh2 = R¹ = C₆H₅, R² = CH(C₆H₅)₂; HQ^nPe = R¹ = C₆H₅, R² = CH₂C(CH₃)₃; HQ^tBu = R¹ = C₆H₅, R² = C(CH₃)₃; HQ^fMe = R¹ = C₆H₄-p-CF₃, R² = CF₃; HQ^fEt = R¹ = C₆H₅, R² = CF₂CF₃; R = Ph or iBu) have been synthesized and characterized in the solid state and solution. The crystal structure of 1-(4-trifluoromethylphenyl)-3-methyl-5-pyrazolone, the precursor of proligand HQ^fMe and of derivatives [Ag(Q^nPe)(PPh₃)₂] and [Ag(Q^nPe)(PiBu₃)]₂ have been investigated. [Ag(Q^nPe)(PPh₃)₂] is a mononuclear compound with a silver atom in a tetrahedrally distorted AgO₂P₂ environment, whereas [Ag(Q^nPe)(PiBu₃)]₂ is a dinuclear compound with two O₂N-exotridentate bridging acylpyrazolonate ligands connecting both silver atoms, their coordination environment being completed by a phosphine ligand.     

Effects of ether vs. ester linkage on lipid bilayer structure and water permeability

The structure and water permeability of bilayers composed of the ether-linked lipid, dihexadecylphosphatidylcholine (DHPC), were studied and compared with the ester-linked lipid, dipalmitoylphosphaditdylcholine (DPPC). Wide angle X-ray scattering on oriented bilayers in the fluid phase indicate that the area per lipid A is slightly larger for DHPC than for DPPC. Low angle X-ray scattering yields A = 65.1 Å² for DHPC at 48 °C. LAXS data provide the bending modulus, K_C = 4.2 × 10⁻¹³ erg, and the Hamaker parameter H = 7.2 × 10⁻¹⁴ erg for the van der Waals attractive interaction between neighboring bilayers. For the low temperature phases with ordered hydrocarbon chains, we confirm the transition from a tilted L_β′ gel phase to an untilted, interdigitated L_βI phase as the sample hydrates at 20 °C. Our measurement of water permeability, P_f = 0.022 cm/s at 48 °C for fluid phase DHPC is slightly smaller than that of DPPC (P_f = 0.027 cm/s) at 50 °C, consistent with our triple slab theory of permeability.     

An NMR-based docking model for the physiological transient complex between cytochrome f and cytochrome c6

The physiological transient complex between cytochrome f (Cf) and cytochrome c₆ (Cc₆) from the cyanobacterium Nostoc sp. PCC 7119 has been analysed by NMR spectroscopy. The binding constant at low ionic strength is 8 ± 2 mM⁻¹, and the binding site of Cc₆ for Cf is localized around its exposed haem edge. On the basis of the experimental data, the resulting docking simulations suggest that Cc₆ binds to Cf in a fashion that is analogous to that of plastocyanin but differs between prokaryotes and eukaryotes.     

Models with energy penalty on interresidue rotation address insufficiencies of conventional elastic network models

In this study, I present a new elastic network model, to our knowledge, that addresses insufficiencies of two conventional models—the Gaussian network model (GNM) and the anisotropic network model (ANM). It has been shown previously that the GNM is not rotation-invariant due to its energy, which penalizes rigid-body rotation (external rotation). As a result, GNM models are found contaminated with rigid-body rotation, especially in the most collective ones. A new model (EPIRM) is proposed to remove such external component in modes. The extracted internal motions result from a potential that penalizes interresidue stretching and rotation in a protein. The new model is shown to pertinently describe crystallographic temperature factors (B-factors) and protein open↔closed transitions. Also, the capability of separating internal and external motions in GNM slow modes permits reexamining important mechanochemical properties in enzyme active sites. The results suggest that catalytic residues stay closer to rigid-body rotation axes than their immediate backbone neighbors. I show that the cumulative density of states for EPIRM and ANM follow different power laws as functions of low-mode frequencies. When using a cutoff distance of 7.5 Å, The cumulative density of states of EPIRM scales faster than that of all-atom normal mode analysis and slower than that of simple lattices.     

Hydration properties of adenosine phosphate series as studied by microwave dielectric spectroscopy

Hydration properties of adenine nucleotides and orthophosphate (Pi) in aqueous solutions adjusted to pH = 8 with NaOH were studied by high-resolution microwave dielectric relaxation (DR) spectroscopy at 20 °C. The dielectric spectra were analyzed using a mixture theory combined with a least-squares Debye decomposition method. Solutions of Pi and adenine nucleotides showed qualitatively similar dielectric properties described by two Debye components. One component was characterized by a relaxation frequency (f_c = 18.8-19.7 GHz) significantly higher than that of bulk water (17 GHz) and the other by a much lower f_c (6.4-7.6 GHz), which are referred to here as hyper-mobile water and constrained water, respectively. By contrast, a hydration shell of only the latter type was found for adenosine (f_c ~ 6.7 GHz). The present results indicate that phosphoryl groups are mostly responsible for affecting the structure of the water surrounding the adenine nucleotides by forming one constrained water layer and an additional three or four layers of hyper-mobile water.     

Synthesis and crystal structure of a novel three-dimensional supramolecular network containing one-dimensional honeycomb-like channels

A novel supramolecular assembly containing honeycomb-like channels [Cu(mal)(bpy)] · 3H₂O (mal = malate, bpy = 2,2′-bipy) has been synthesized and characterized by elemental analyses, IR, EPR, TG, UV-Vis and single crystal X-ray diffraction. Compound 1 is constructed from spiral-shaped chains via O-H?O hydrogen bonds and π-π stacking interactions. To our knowledge, compound 1 represents the first supramolecular network constructed from the mixed malate and pyridine ligand.     

Substrate water exchange in photosystem II core complexes of the extremophilic red alga Cyanidioschyzon merolae

The binding affinity of the two substrate–water molecules to the water-oxidizing Mn₄CaO₅ catalyst in photosystem II core complexes of the extremophilic red alga Cyanidioschyzon merolae was studied in the S₂ and S₃ states by the exchange of bound ¹⁶O-substrate against ¹⁸O-labeled water. The rate of this exchange was detected via the membrane-inlet mass spectrometric analysis of flash-induced oxygen evolution. For both redox states a fast and slow phase of water-exchange was resolved at the mixed labeled m/z 34 mass peak: k_f = 52 ± 8 s^− 1 and k_s = 1.9 ± 0.3 s^− 1 in the S₂ state, and k_f = 42 ± 2 s^− 1 and k_slow = 1.2 ± 0.3 s^− 1 in S₃, respectively. Overall these exchange rates are similar to those observed previously with preparations of other organisms. The most remarkable finding is a significantly slower exchange at the fast substrate–water site in the S₂ state, which confirms beyond doubt that both substrate–water molecules are already bound in the S₂ state. This leads to a very small change of the affinity for both the fast and the slowly exchanging substrates during the S₂ → S₃ transition. Implications for recent models for water-oxidation are briefly discussed.     

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.     

Hydrogen-bonded supramolecular manganese(II) complexes with network and sheet structures bridged by terephthalate unit

Two 1D complexes [Mn(4- methylpyrazole)₃(H₂O)(tp)]_n (2) and [Mn(4-methylpyrazole)₄(tp)]_n (3) (tp = terephthalate) were synthesized and characterized by means of X-ray analysis and magnetic studies. The molecular structure of 2 reveals that Mn(II) centers with asymmetric coordination surroundings are bridged by crystallographically different tp ligands, forming a 1D chain. The 1D coordination chains are interconnected by hydrogen bonds between free carboxylate oxygen atoms in a chain and hydrogens of pyrazole nitrogen atoms in neighboring chains, leading to a 3D framework. Compound 3 also exhibits a 1D coordination chain which is hydrogen-bonded to adjacent chains, providing a 2D sheet structure. Interestingly, the structures include intra- and interchain hydrogen bonds contributed from N-H groups of the capping 4-methylpyrazole ligands. Magnetic measurements show weak antiferromagnetic interactions with exchange coupling parameters of J = −0.018 cm⁻¹ for 2 and J = −0.062 cm⁻¹ for 3 through the extended tp ligand on the basis of an infinite chain model (H = −J∑S_i · S_i + 1).     

Tensorial elastic network model for protein dynamics: Integration of the anisotropic network model with bond‐bending and twist elasticities

We present a tensorial elastic network model (TNM) to describe the equilibrium fluctuations of proteins near their native fold structure. The model combines the anisotropic network model (ANM), bond bending elasticity, and backbone twist elasticity, and can predict both the isotropic fluctuations, similar to the Gaussian network model (GNM), and anisotropic fluctuations, similar to the ANM. TNM performs equally well for B‐factor predictions as GNM and predicts the anisotropy of B‐factors better than ANM. The model also outperforms the ANM in its predictability of the complete anisotropic displacement parameters. Proteins 2012; © 2012 Wiley Periodicals, Inc.