A coarse-grained model of the effective interaction for charged amino acid residues and its application to formation of GCN4-pLI tetramer

ABSTRACT

We present a simple coarse-grained model of the effective interaction for charged amino acid residues, such as Glu and Lys, in a water solvent. The free-energy profile as a function of the distance between two charged amino acid side-chain analogues in an explicit water solvent is calculated with all-atom molecular dynamics simulation and thermodynamic integration method. The calculated free-energy profile is applied to the coarse-grained potential of the effective interaction between two amino acid residues. The Langevin dynamics simulations with our coarse-grained potential are performed for association of a small protein complex, GCN4-pLI tetramer. The tetramer conformation reproduced by our coarse-grained model is similar to the X-ray crystallographic structure. We show that the effective interaction between charged amino acid residues stabilises association and orientation of protein complex. We also investigate the association pathways of GCN4-pLI tetramer.     

A simple coarse-grained model for interacting protein complex

ABSTRACT

We present a simple coarse-grained model in which each amino acid residue is represented by one coarse-grained particle for interacting protein complex. In order to determine the coarse-grained potential function of the interaction between amino acid residues, free energy profile as a function of the distance between amino acid side chains is investigated by using all-atom molecular dynamics simulations with thermodynamic integration method. The Langevin dynamics simulation with Gō-like model and our coarse-grained model reproduces homotetramer complex structure of GCN4-pLI and shows that interaction between hydrophobic amino acid residues promote the association of GCN4-pLI monomers.     

Coarse-grained model of proteins incorporating atomistic detail of the active site

We present a novel approach to explore the conformational space of globular proteins near their native state. It combines the advantages of coarse-grained models with those of all-atoms simulations, required to treat molecular recognition processes. The comparison between calculated structural properties with those obtained with all-atoms molecular dynamics simulations establishes the accuracy of the model. Our method has the potential to be extended to molecular recognition processes in systems whose characteristic size and time scale prevent an analysis based on all-atoms molecular dynamics.     

Pressure stability of insulin: A fourier transform infrared spectroscopy study

High hydrostatic pressure can induce partially unfolded protein conformations that are highly aggregation prone under conditions that normally favour the native state. We investigated the pressure stability of insulin at pH 2 with Fourier transform infrared spectroscopy. We do not observe any cooperative change up to 13 kbar. All spectral changes in the amide I area are fully reversible and are assumed to arise from the elastic effect of pressure, which causes no conformational changes. Moreover, insulin has no higher temperature-induced aggregation tendency when pressure pre-treated.     

Intrinsic Fluorescence of Actin

In this work actin is used to illustrate connection of protein fluorescence characteristics with its structure. On one hand, it has been demonstrated what kind of information about the contribution of each tryptophan residues to the bulk fluorescence spectrum can be obtained from the special analysis of protein three-dimensional structure. On the other hand, potentials of intrinsic fluorescence for elucidation of proteins structure, dynamics and processes of folding-unfolding are shown. In particular, using this method a new essentially unfolded kinetic intermediate state of actin was detected and characterized, and the place of inactivated actin and its kinetic predecessor in the process of folding-unfolding was determined. It has been revealed that inactivated actin is not intermediate state between the native and completely unfolded states, as it has been accepted before, but a result of protein misfolding. On the basis of the obtained data a new model of actin folding-unfolding pathway has been proposed.     

Phase behaviour and interfacial properties of ternary system CO2 + n-butane + n-decane: coarse-grained theoretical modelling and molecular simulations

ABSTRACT

This work illustrates the application of a three-party approach based on theoretical modelling, molecular dynamic (MD) simulations and available experimental data for describing the phase equilibrium and interfacial properties for the ternary system: carbon dioxide + n-butane + n-decane and its corresponding binary sub-systems at 344.3 K. Specifically, a coarse-grained force field is employed for both theoretical predictions and MD. The interfacial region is described by the square gradient theory where the homogenous Helmholtz energy density contribution is provided by the Statistical Associated Fluid Theory equation of state for potentials of variable range for molecules conformed of segments interacting through the Mie potential (SAFT-VR Mie) and MD simulations in the canonical ensemble where the molecules are represented by a coarse-grained Mie force field. The novelty here is that both the theory and the simulations uniquely share the same underlying intermolecular potentials; hence, the experimental data are employed to verify both the theory and simulations. In this schema, the ternary mixture is full predictive as its parameters are only based on pure fluids parameters and binary interactions. It is observed that the phase equilibria and the interfacial properties are equally well represented by the used approach.     

Simulation of dissociation of DNA duplexes attached to the surface

We present Monte Carlo simulations of dissociation of duplexes formed of complementary single-stranded DNAs with one of the strands attached to the surface. To describe the transition from the bound state to the unbound state of two strands located nearby, we use a lattice model taking DNA base-pair interactions and comformational changes into account. The results obtained are employed as a basis for a more coarse-grained model including strand backward association and diffusion resulting in complete dissociation. The distribution of the dissociation time is found to be exponential. This finding indicates that the non-exponential kinetic features observed in the corresponding experiments seem to be related to extrinsic factors, e.g., to the surface heterogeneity.     

Response properties at the dynamic water/dichloroethane liquid–liquid interface

ABSTRACT

We present a novel approach for calculating the static dielectric permittivity profile of a liquid–liquid interface (LLI) from molecular dynamics simulations. To obtain well-defined features, comparable to those observed at solid–liquid interfaces, we find it essential to reference to the instantaneous liquid–liquid interface rather than the more commonly used average Gibbs interface. We provide a coarse-grained approach for the practical definition of the instantaneous interface and present numerical results for the prototypical water/1,2-dichloroethane system. These results show that the parallel components of the dielectric permittivity tensor can be accurately extracted. In contrast, the perpendicular component does not converge to the correct bulk value at large distances from the LLI, highlighting a flaw in the regularly applied coarse-graining procedure.     

Different Conformation of Thiol Protease Inhibitor During Amyloid Formation: Inhibition by Curcumin and Quercetin

Cystatins are thiol proteinase inhibitors ubiquitously present in mammalian body and serve various important physiological functions. In the present study, we examined the effects of acid denaturation on newly identified thiol protease inhibitors from the lungs of Capra hircus (Goat) with a focus on protein conformational changes and amyloid fibril formation. Acid denaturation as studied by CD (Circular Dichroism) and fluorescence spectroscopy showed that purified inhibitor named GLC (Goat Lung Cystatin) populates three partly unfolded species, a native like state at pH?3.0, a partly unfolded intermediate at pH2.0, and unstructured unfolded state at pH?1.0, from each of which amyloid like fibrils grow as assessed by thioflavin T (ThT) spectroscopy. The result showed, native like structure formed at pH?3.0 is more responsive towards amyloid formation when compare to other conformation of proteins. Morphology of the protein species incubated for amyloid process was observed using transmission electron microscopy (TEM). Moreover, anti-fibrillogenic effects of curcumin and quercetin were analysed using ThT binding assay. Curcumin and quercetin produced a concentration dependent decline inThT fluorescence suggesting deaggregation of the fibrils. When added prior to amyloid fibril initiation 50 μM curcumin inhibited amyloid aggregation. However, more quercetin is needed to prevent the same extent of fibrillation. Implications for therapeutics in view of polyphenols as essential nutrients are suggested in lung diseases.     

Dynamics of polyglutamic acids in α-helical and coil states. Comparison with dynamics of some globular proteins. Rayleigh scattering of Mössbauer radiation (RSMR) data

Summary The classical model system poly-L-glutamic acid (poly-Glu), was investigated in a disordered coil state (atpH=7.0) and in helix state (atpH=2.0) by the RSMR technique. By considering that the coil state of poly-Glu models unfolded (random coil) state and α-helix state models the fluctuating secondary structure (during consequent folding of protein), a comparative analysis of the dynamical properties of poly-Glu in different states with the dynamical properties of different proteins in the native state (α-helical myoglobin and HSA, partially β-sheet lysozyme) and in intermediate (molten globule) state (α-lactalbumin) was performed. This comparison brings some unpredicted results: native α-helical proteins behave close to random coil, native partially β-sheet proteins behave close to fluctuating secondary structure (α-helix) and the dynamic behaviour of molten-globule state (partially β-sheet α-lactalbumin) is not different from the behaviour of lysozyme and much more rigid than that of native α-helical proteins. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Pressure-assisted cold unfolding of proteins and its effects on the conformational stability compared to pressure and heat unfolding

Abstract

The pressure-assisted cold unfolding of metmyoglobin was investigated and the cold unfolded state was compared to the heat and pressure unfolded states. Conformationally and mechanistically the pressure and cold unfolding processes are found to be very alike, while the heat unfolding shows some pronounced differences. We also propose a hypothesis on protein aggregation.     

Modeling hydrogen exchange of proteins by a multiscale method

We proposed a practical way for mapping the results of coarse-grained molecular simulations to the observables in hydrogen change experiments. By combining an atomic-interaction based coarse-grained model with an all-atom structure reconstruction algorithm, we reproduced the experimental hydrogen exchange data with reasonable accuracy using molecular dynamics simulations. We also showed that the coarse-grained model can be further improved by imposing experimental restraints from hydrogen exchange data via an iterative optimization strategy. These results suggest that it is feasible to develop an integrative molecular simulation scheme by incorporating the hydrogen exchange data into the coarse-grained molecular dynamics simulations and therefore help to overcome the accuracy bottleneck of coarse-grained models.     

Effect of unfolding on the thickness of the hydration layer of a protein

Properties of water in the hydration layer around a protein is intimately correlated with its function. A knowledge of the thickness of the hydration layer is important to understand its role in guiding the folding-unfolding of the protein. We have performed atomistic molecular dynamics simulations of the folded native and a partially unfolded molten globule structure of the villin headpiece subdomain or HP-36 in aqueous solution to estimate the effect of unfolding on the thickness of hydration layer around different segments of the protein. In particular, several dynamic properties of water around different segments of the folded native and the unfolded structure have been calculated by varying the thickness of the hydration layers. It is found that unfolding of a segment of the protein is correlated with the dynamics of water around it, i.e., within the first hydration layer. The effect of unfolding on water properties has been found to diminish when water molecules present beyond the first hydration layer were included in the calculations.      

Gauge theory picture of an ordering transition in a dimer model

We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3D XY model. The continuous nature of the transition is confirmed by a flowgram analysis.     

A study of Barstar folding events using boundary value simulations

From extensive biophysical studies of protein folding, two competing mechanisms emerged: hydrophobic collapse and the framework model. Our protein of choice is Barstar—a barnase inhibitor. The approximation algorithm we used to study Barstar folding trajectories is called SDEL—stochastic difference equation in length. Using the native structure as the final boundary value and a collection of unfolded structures as the varying initial boundary value, SDEL calculates an ensemble of least action pathways between these boundaries. The results are atomically detailed folding pathways, with as many intermediate structures as you request in the input. We generated 12 pathways, starting from a structurally wide selection of unfolded conformations. Using the protein's radius of gyration as our primary reaction coordinate, we tracked H-bonds, dihedral angles, native and non-native contacts, and energy along the folding pathways. This paper will follow our findings, with special emphasis on pinpointing hydrophobic collapse as a more appropriate mechanism for Barstar. Comparison with pathway predictions for Barstar using experimental techniques will also be discussed.     

Liquid–vapour transition of the long range Yukawa fluid

Two liquid state theories, the self-consistent Ornstein–Zernike equation (SCOZA) and the hierarchical reference theory (HRT) are shown, by comparison with Monte Carlo simulations, to perform extremely well in predicting the liquid–vapour coexistence of the hard-core Yukawa (HCY) fluid when the interaction is long range. The long range of the potential is treated in the simulations using both an Ewald sum and hyperspherical boundary conditions. In addition, we present an analytical optimized mean field theory which is exact in the limit of an infinitely long-range interaction. The work extends a previous one by C. Caccamo, G. Pellicane, D. Costa, D. Pini, and G. Stell, Phys. Rev. E 60, 5533 (1999) for short-range interactions.     

Variational Quantum Algorithms for the Steady States of Open Quantum Systems

The solutions of the problems related to open quantum systems have attracted considerable interest.We propose a variational quantum algorithm to find the steady state of open quantum systems.In this algorithm,we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation,which can be efficiently evaluated with quantum circuits.We then optimize the parameters of the quantum circuit to find the steady state.Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels.The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%.This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.     

Entanglement renormalization

We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.     

Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect

ABSTRACT

We present a simple coarse-grained model with the molecular crowding effect in solvent to investigate the structure and dynamics of protein complexes including association and/or dissociation processes and investigate some physical properties such as the structure and the reaction rate from the viewpoint of the hydrophobic intermolecular interactions of protein complex. In the present coarse-grained model, a function depending upon the density of hydrophobic amino acid residues in a binding area of the complex is introduced, and the function involves the molecular crowding effect for the intermolecular interactions of hydrophobic amino acid residues between proteins. We propose a hydrophobic intermolecular potential energy between proteins by using the density-dependent function. The present coarse-grained model is applied to the complex of cytochrome f and plastocyanin by using the Langevin dynamics simulation to investigate some physical properties such as the complex structure, the electron transfer reaction rate constant from plastocyanin to cytochrome f and so on. We find that for proceeding the electron transfer reaction, the distance between metals in their active sites is necessary within about 18 Å. We discuss some typical complex structures formed in the present simulation in relation to the molecular crowding effect on hydrophobic interactions.     

Tethered polyelectrolytes under the action of an electrical field

For a polyelectrolyte undergoing electrophoretic motion, it is predicted (D. Long, J.L. Viovy, A. Ajdari, Phys. Rev. Lett. 76, 3858 (1996); D. Long, A. Ajdari, Electrophoresis 17, 1161 (1996)) that the mechanical force necessary to stall the molecule is substantially smaller than the sum of electrical forces applied on all monomers. In fact, it should be proportional to its hydrodynamic friction coefficient and therefore to the size of its conformation. In our work we examine this prediction using coarse-grained molecular-dynamics simulations in which we explicitly include the polymer, the solvent, the counterions and salt. The electrophoretic mobility of polyelectrolytes is evaluated, the mechanical force necessary to keep the molecules tethered is measured and the resulting anisotropic polymer conformations are observed and quantified. Our results corroborate Long et al.'s prediction.