Protein Solvent Systems Research Articles

Optical Microrheology of Protein Solutions Using Tailored Nanoparticles.

This work represents a critical re-examination of the application of dynamic light scattering (DLS)-based tracer particle microrheology to measure the zero shear viscosity of aqueous solutions of different proteins up to very high concentrations. It is demonstrated that a combination of surface-functionalized tracer particles, the use of the so-called 3D-DLS technique, and carefully chosen parameters for the scattering experiments is essential for a reliable and artifact-free determination of the viscosity of highly diverse protein solutions, while keeping the amount of protein to a minimum. The major challenges that arise in such microrheology experiments with protein solutions are discussed and used as guiding principles for the synthesis of all-purpose tracer particles with optimal size and an efficient surface functionalization, and the choice of the appropriate amount of tracers in the sample. Potential problems arising from depletion attractions between the tracer particles induced by the proteins are addressed, and compelling evidences for the absence of such effects are presented. The validity of the approach is corroborated by the perfect agreement between the zero shear viscosity obtained from 3D-DLS-based microrheology and literature data from classical rheological measurements for two vastly different protein-solvent systems up to concentrations close to the arrest transition.

Solvent-quality-dependent contact formation dynamics in proteins

The mean time of contact formation between two ends of a protein chain shows power law dependence with respect to the number of residues, . Fluorescence quenching measurements based on triplet–triplet energy transfer show variation in the value of scaling exponent α for different protein–solvent systems. This points to the relevance of the protein–solvent interactions (solvent quality) and hydrodynamic interactions in determining the time scale of contact formation. Here, starting from a non-Markovian diffusion equation supplemented with an exponential sink term that accounts for the energy transfer reaction between the donor and acceptor groups, we calculate the mean time of contact formation using the Wilemski–Fixman closure approximation. The non-Markovian diffusion–reaction equation includes the effects of solvent quality and hydrodynamic interaction in a mean-field fashion. It shows that the contact formation dynamics is mainly governed by two time scales, the reciprocal of the intrinsic rate of quenching , and the relaxation time of the coarse-grained residue of size b. A comparison of these two time scales yields reaction-controlled and diffusion-controlled kinetic regimes with different values of the scaling exponents. In between these regimes the increase in the number of residues switches the kinetics from RC at low N to DC at large N. These general results suggest that experimental estimates of the scaling exponents reflect solvent-quality dependence of the RC kinetics.

Including the Dispersion Attraction into Structure-Adapted Fast Multipole Expansions for MD Simulations.

Molecular dynamics (MD) simulations of protein–solvent systems, which are modeled by polarizable or nonpolarizable all-atom force fields and are enclosed by periodic boundaries, require accurate and efficient algorithms for the computation of the long-range interactions. A possible choice is the fast structure-adapted multipole method called SAMMp/RF (Lorenzen et al. J. Chem. Theory Comput. 2012, 8, 3628–3636). It is based on pth order Cartesian Taylor expansions of the electrostatic interactions, on an adaptive and hierarchical decomposition of a macromolecular simulation system into a quaternary tree of nested atom clusters, and on a reaction field (RF) correction originating from a distant dielectric continuum. Here, we substantially extend this method by adding qth order Taylor expansions of the dispersion attraction and by formulating an interaction acceptance criterion for cluster–cluster interactions, which is based on substance-specific accuracy estimates. As a result, we obtain with the default e...

Exploring the multiscale signaling behavior of phototropin1 from Chlamydomonas reinhardtii using a full-residue space kinetic Monte Carlo molecular dynamics technique

Devising analysis tools for elucidating the regulatory mechanism of complex enzymes has been a challenging task for many decades. It generally requires the determination of the structural-dynamical information of protein solvent systems far from equilibrium over multiple length and time scales, which is still difficult both theoretically and experimentally. To cope with the problem, we introduce a full-residue space multiscale simulation method based on a combination of the kinetic Monte Carlo and molecular dynamics techniques, in which the rates of the rate-determining processes are evaluated from a biomolecular forcefield on the fly during the simulation run by taking into account the full space of residues. To demonstrate its reliability and efficiency, we explore the light-induced functional behavior of the full-length phototropin1 from Chlamydomonas reinhardtii (Cr-phot1) and its various subdomains. Our results demonstrate that in the dark state the light oxygen voltage-2-Jα (LOV2-Jα) photoswitch inhibits the enzymatic activity of the kinase, whereas the LOV1-Jα photoswitch controls the dimerization with the LOV2 domain. This leads to the repulsion of the LOV1-LOV2 linker out of the interface region between both LOV domains, which results in a positively charged surface suitable for cell-membrane interaction. By contrast, in the light state, we observe that the distance between both LOV domains is increased and the LOV1-LOV2 linker forms a helix-turn-helix (HTH) motif, which enables gene control through nucleotide binding. Finally, we find that the kinase is activated through the disruption of the Jα-helix from the LOV2 domain, which is followed by a stretching of the activation loop (A-loop) and broadening of the catalytic cleft of the kinase.

Molecular mechanism of deactivation of C. antarctica lipase B by methanol

The catalytic activity of Candida antarctica lipase B upon alcoholysis of a constant concentration of 15.2% vinyl acetate (vol/vol) and varying concentrations of methanol (0.7–60%) in toluene was determined experimentally by measuring the initial reaction velocity. The molecular mechanism of the deactivation of the enzyme by methanol was investigated by fitting the experimental data to a kinetic model and by molecular dynamics simulations of C. antarctica lipase B in toluene–methanol–water mixtures.The highest catalytic activity (280U/mg) was observed at methanol concentrations as low as 0.7% methanol (vol/vol), followed by a sharp decrease at higher methanol concentrations. For methanol concentrations above 10% (vol/vol), catalytic activity was at 30% of the maximum activity. A variation of water activity in the range 0.02–0.09 had only minor effects. These experimental observations are described by a simple kinetic model using three assumptions: (1) a ping-pong bi–bi mechanism of the enzyme, (2) competitive inhibition by the substrate methanol, and (3) by describing enzyme kinetics by the thermodynamic activities of the substrates rather than by their concentrations. Two equilibrium constants of methanol (KM,MeOH=0.05 and Ki,MeOH=0.23) were derived by modeling methanol binding to the substrate binding site of the lipase in molecular dynamics simulations of protein-solvent systems at atomic resolution.Thus, the sharp maximum of catalytic activity of C. antarctica lipase B at 0.7% methanol is a direct consequence of the fact that methanol–toluene mixtures are far from ideal. Understanding the thermodynamics of solvent mixtures is prerequisite to a quantitative model of enzymatic activity in organic solvents.

A New Approach for Investigating the Molecular Recognition of Protein: Toward Structure-Based Drug Design Based on the 3D-RISM Theory.

A new approach to investigate a molecular recognition process of protein is presented based on the three-dimensional reference interaction site model (3D-RISM) theory, a statistical mechanics theory of molecular liquids. Numerical procedure for solving the conventional 3D-RISM equation consists of two steps. In step 1, we solve ordinary RISM (or 1D-RISM) equations for a solvent mixture including target ligands in order to obtain the density pair correlation functions (PCF) among molecules in the solution. Then, we solve the 3D-RISM equation for a solute-solvent system to find three-dimensional density distribution functions (3D-DDF) of solvent species around a protein, using PCF obtained in the first step. A key to the success of the method was to regard a target ligand as one of "solvent" species. However, the success is limited due to a difficulty of solving the 1D-RISM equation for a solvent mixture, including large ligand molecules. In the present paper, we propose a method which eases the limitation concerning solute size in the conventional method. In this approach, we solve a solute-solute 3D-RISM equations for a protein-ligand system in which both proteins and ligands are regarded as "solutes" at infinite dilution. The 3D- and 1D-RISM equations are solved for protein-solvent and ligand-solvent systems, respectively, in order to obtain the 3D- and 1D-DDF of solvent around the solutes, which are required for solving the solute-solute 3D-RISM equation. The method is applied to two practical and noteworthy examples concerning pharmaceutical design. One is an odorant binding protein in the Drosophila melanogaster , which binds an ethanol molecule. The other is phospholipase A2, which is known as a receptor of acetylsalicylic acid or aspirin. The result indicates that the method successfully reproduces the binding mode of the ligand molecules in the binding sites measured by the experiments.

Coupling between lysozyme and trehalose dynamics: Microscopic insights from molecular-dynamics simulations

We have carried out molecular-dynamics simulations on fully flexible all-atom models of the protein lysozyme immersed in trehalose, an effective biopreservative, with the purpose of exploring the nature and extent of the dynamical coupling between them. Our study shows a strong coupling over a wide range of temperatures. We found that the onset of anharmonic behavior was dictated by changes in the dynamics and relaxation processes in the trehalose glass. The physical origin of protein-trehalose coupling was traced to the hydrogen bonds formed at the interface between the protein and the solvent. Moreover, protein-solvent hydrogen bonding was found to control the structural relaxation of the protein. The dynamics of the protein was found to be heterogeneous; the motions of surface and core atoms had different dependencies on temperature and, in addition, the surface atoms were more sensitive to the dynamics of the solvent than the core atoms. From the solvent perspective we found that the dynamics near the protein surface showed an unexpected enhanced mobility compared to the bulk. These results shed some light on the microscopic origins of the dynamical coupling in protein-solvent systems.

Comparison of semiempirical and ab initio QM decomposition analyses for the interaction energy between molecules

A decomposition analysis of the interaction energy of molecular complexes using both semiempirical (PM3) and ab initio methods shows major differences. Whereas electrostatic stabilization accounted for a significant part of the interaction by ab initio theory, the electrostatic energy in semiempirical theory was mainly repulsive. This difference has major implications for intuitive models of intermolecular interactions, particularly in light of recent AM1 and PM3 energy decomposition calculations suggesting that charge transfer and polarization provides the binding energy of molecular clusters, including protein-solvent systems.

Meanfield Approach to the Thermodynamics of Protein–Solvent Systems with Application to P53

We present a meanfield theoretical approach for studying protein–solvent interactions. Starting with the partition function of the system, we develop a field theory by introducing densities for the different components of the system. At this point, protein–solvent interactions are introduced following the inhomogeneous Flory–Huggins model for polymers. Finally, we calculate the free energy in a meanfield approximation. We apply this method to study the stability of the tetramerization domain of the tumor suppressor protein p53 when subjected to site-directed mutagenesis. The four chains of this protein are held together by hydrophobic interactions, and some mutations can weaken this bond while preserving the secondary structure of the single protein chains. We find good qualitative agreement between our numerical results and experimental data, thus encouraging the use of this method as a guide in designing experiments.

FAMUSAMM: An algorithm for rapid evaluation of electrostatic interactions in molecular dynamics simulations

Within molecular dynamics simulations of protein–solvent systems the exact evaluation of long-range Coulomb interactions is computationally demanding and becomes prohibitive for large systems. Conventional truncation methods circumvent that computational problem, but are hampered by serious artifacts concerning structure and dynamics of the simulated systems. To avoid these artifacts we have developed an efficient and yet sufficiently accurate approximation scheme which combines the structure-adapted multipole method (SAMM) [C. Niedermeier and P. Tavan, J. Chem. Phys., 101, 734 (1994)] with a multiple-time-step method. The computational effort for MD simulations required within our fast multiple-time-step structure-adapted multipole method (FAMUSAMM) scales linearly with the number of particles. For a system with 36,000 atoms we achieve a computational speed-up by a factor of 60 as compared with the exact evaluation of the Coulomb forces. Extended test simulations show that the applied approximations do not seriously affect structural or dynamical properties of the simulated systems. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1729–1749, 1997

Structural stability of oligomeric proteins: A mean-field theoretical approach

We present a mean-field approach for calculating thermodynamic properties(free energies) of protein–solvent systems. We apply this method to thetumor suppressor protein p53, where we study the stability of itstetramerization domain when subjected to site-directed mutagenesis. Acomparison with experimental results is included.

Helmholtz free energies of atom pair interactions in proteins

Proteins fold to unique three-dimensional structures, but how they achieve this transition and how they maintain their native folds is controversial. Information on the functional form of molecular interactions is required to address these issues. The basic building blocks are the free energies of atom pair interactions in dense protein solvent systems. In a dense medium, entropic effects often dominate over internal energies but free energy estimates are notoriously difficult to obtain. A prominent example is the peptide hydrogen bond (H-bond). It is still unclear to what extent H-bonds contribute to protein folding and stability of native structures. Radial distribution functions of atom pair interactions are compiled from a database of known protein folds. The functions are transformed to Helmholtz free energies using a recipe from the statistical mechanics of dense interacting systems. In particular we concentrate on the features of the free energy functions of peptide H-bonds. Differences in Helmholtz free energies correspond to the reversible work required or gained when the distance between two particles is changed. Consequently, the functions directly display the energetic features of the respective thermodynamic process, such as H-bond formation or disruption. In the H-bond potential, a high barrier isolates a deep narrow minimum at H-bond contact from large distances, but the free energy difference between H-bond contact and large distances is close to zero. The energy barrier plays an intriguing role in H-bond formation and disruption: both processes require activation energy in the order of 2kT. H-bond formation opposes folding to compact states, but once formed, H-bonds act as molecular locks and a network of such bonds keeps polypeptide chains in a precise spatial configuration. On the other hand, peptide H-bonds do not contribute to the thermodynamic stability of native folds, because the energy balance of H-bond formation is close to zero.

Structure and dynamics of the water around myoglobin.

The interplay between simulations at various levels of hydration and experimental observables has led to a picture of the role of solvent in thermodynamics and dynamics of protein systems. One of the most studied protein-solvent systems is myoglobin, which serves as a paradigm for the development of structure-function relationships in many biophysical studies. We review here some aspects of the solvation of myoglobin and the resulting implications. In particular, recent theoretical and simulation studies unify much of the diverse set of experimental results on water near proteins.

Boltzmann's principle, knowledge-based mean fields and protein folding. An approach to the computational determination of protein structures.

The data base of known protein structures contains a tremendous amount of information on protein-solvent systems. Boltzmann's principle enables the extraction of this information in the form of potentials of mean force. The resulting force field constitutes an energetic model for protein-solvent systems. We outline the basic physical principles of this approach to protein folding and summarize several techniques which are useful in the development of knowledge-based force fields. Among the applications presented are the validation of experimentally determined protein structures, data base searches which aim at the identification of native-like sequence structure pairs, sequence structure alignments and the calculation of protein conformations from amino acid sequences.

Statistical mechanics of hydrogen bond networks

The static and dynamic properties of several hydrogen bond network models, based on thesquare ice model of Lieb [Phys. Rev.162, 162 (1967)] are studied. The two dimensionalsquare water (SW) model and the three-dimensioaalbrick water (BW) model were analyzed by means of Monte Carlo simulations. A simplified vesion of SW (simplified square water, SSW) can be solved exactly. All models yield similar thermodynamic results which can be derived-alternatively-from an independent bond approach due to Angell [J. Chem. Phys.75, 3698 (1971)]. We suggest the existence of a universality class of hydrogen bond networks that can be described by this theory, and which may include the liquid state of water. The mean lifetime of a hydrogen bond exhibits an Arrhenius temperature dependence. Comparison with experimental data on water provides an absolute time scale for the Monte Carlo simulations. The possible use of these models in simulations of protein-solvent systems is discussed.

Numerical Calculations of Reaction Fields of Protein-Solvent Systems

A reaction field in a protein molecule due to aqueous solvent, which is polarized by charges of the protein, has been calculated numerically. First, a Poisson equation for a macroscopic dielectric model of a protein in vacuo was solved by the self-consistent boundary method. Next, Poisson and Poisson-Boltzmann equations for the model of a protein in aqueous solvent were solved in the same manner. The reaction field was then obtained by taking the difference between the potentials of these two systems. The results agreed well with those calculated analytically for simple model cases. Applications of the present method of the particle-particle/particle-mesh algorithm were discussed for actual protein-solvent systems.

Numerical Calculations of Electrostatic Potentials of Protein-Solvent Systems by the Self Consistent Boundary Method

A macroscopic dielectric model for a protein-solvent system has been solved by a numerical calculation using a supercomputer. The whole space including a target protein molecule was first divided into lots of cubes, some of which were inside the protein and the others were embedded in the solvent. Poisson equation and Poisson-Boltzmann equation were then numerically solved inside and outside of the protein, respectively. At the artificial boundary far from the protein for the finite difference procedure, neither the potential nor the field was set to be zero, but they were calculated self-consistently from the field and the potential inside the boundary calculated beforehand. The results by this method agreed well with those by the analytical calculations for some simple model cases. The results of actual protein-solvent systems were quantitatively discussed comparing with the experiments.