Confinement in nanopores can destabilize α-helix folding proteins and stabilize the β structures

Protein folding in confined media has attracted wide attention over the past decade due to its importance in both in vivo and in vitro applications. Currently, it is generally believed that protein stability increases by decreasing the size of the confining medium, if its interaction with the confining walls is repulsive, and that the maximum folding temperature in confinement occurs for a pore size only slightly larger than the smallest dimension of the folded state of a protein. Protein stability in pore sizes, very close to the size of the folded state, has not however received the attention that it deserves. Using detailed, 0.3-ms-long molecular dynamics simulations, we show that proteins with an α-helix native state can have an optimal folding temperature in pore sizes that do not affect the folded-state structure. In contradiction to the current theoretical explanations, we find that the maximum folding temperature occurs in larger pores for smaller α-helices. In highly confined pores the free energy surface becomes rough, and a new barrier for protein folding may appear close to the unfolded state. In addition, in small nanopores the protein states that contain the β structures are entropically stabilized, in contrast to the bulk. As a consequence, folding rates decrease notably and the free energy surface becomes rougher. The results shed light on many recent experimental observations that cannot be explained by the current theories, and demonstrate the importance of entropic effects on proteins' misfolded states in highly confined environments. They also support the concept of passive effect of chaperonin GroEL on protein folding by preventing it from aggregation in crowded environment of biological cells, and provide deeper clues to the α → β conformational transition, believed to contribute to Alzheimer's and Parkinson's diseases. The strategy of protein and enzyme stabilization in confined media may also have to be revisited in the case of tight confinement. For in silico studies of protein folding in confined media, use of non-Go potentials may be more appropriate.     

Excluded volume effects in macromolecular forces and ion-interface interactions

A charged Yukawa liquid confined in a slit nanopore is studied in order to understand excluded volume effects in the interaction force between the pore walls. A previously developed self-consistent scheme [S. Buyukdagli, C. V. Achim, and T. Ala-Nissila, J. Stat. Mech. 2011, P05033] and a new simpler variational procedure that self-consistently couple image forces, surface charge induced electric field, and pore modified core interactions are used to this aim. For neutral pores, it is shown that with increasing pore size, the theory predicts a transition of the interplate pressure from an attractive to a strongly repulsive regime associated with an ionic packing state, an effect observed in previous Monte Carlo simulations for hard core charges. We also establish the mean-field theory of the model and show that for dielectrically homogeneous pores, the mean-field regime of the interaction between the walls corresponds to large pores of size d > 4 ?. The role of the range of core interactions in the ionic rejection and interplate pressure is thoroughly analyzed. We show that the physics of the system can be split into two screening regimes. The ionic packing effect takes place in the regime of moderately screened core interactions characterized with the bare screening parameter of the Yukawa potential b ? 3/l(B), where l(B) is the Bjerrum length. In the second regime of strongly screened core interactions b ? 3/l(B), solvation forces associated with these interactions positively contribute to the ionic rejection driven by electrostatic forces and enhance the magnitude of the attractive pressure. For weakly charged pores without a dielectric discontinuity, core interactions make a net repulsive contribution to the interplate force and also result in oscillatory pressure curves, whereas for intermediate surface charges, these interactions exclusively strengthen the external pressure, thereby reducing the magnitude of the net repulsive interplate force. The pronounced dependence of the interplate pressure and ionic partition coefficients on the magnitude and the range of core interactions indicates excluded volume effects as an important ion specificity and a non-negligible ingredient for the stability of macromolecules in electrolyte solutions.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Stability of a protein tethered to a surface

Surface-tethered proteins are increasingly being used in a variety of experimental situations, and they are the basis for many new technologies. Nevertheless, a thorough understanding of how a surface can impact the native state stability of an attached protein is lacking. In this work, the authors use molecular dynamics simulations of a model beta-barrel protein to investigate how surface tethering influences native state stability. They find that stability, as measured by the folding temperature Tf, can be either increased, decreased, or remain unchanged as a result of tethering. Observed shifts are highly dependent on the location of residue used as the tether point, and stability is influenced by a number of factors, both energetic and entropic. These factors include native state vibrations, loss of bulk unfolded conformations, changes to the unfolded state ensemble, and the emergence of an entropic term not present for the bulk protein. They discuss each of these contributions in detail and comment on their relative importance and connection to experiment.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.     

Contact angles, pore condensation, and hysteresis: insights from a simple molecular model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.     

New scenarios of protein folding can occur on the ribosome

Identifying and understanding the differences between protein folding in bulk solution and in the cell is a crucial challenge facing biology. Using Langevin dynamics, we have simulated intact ribosomes containing five different nascent chains arrested at different stages of their synthesis such that each nascent chain can fold and unfold at or near the exit tunnel vestibule. We find that the native state is destabilized close to the ribosome surface due to an increase in unfolded state entropy and a decrease in native state entropy; the former arises because the unfolded ensemble tends to behave as an expanded random coil near the ribosome and a semicompact globule in bulk solution. In addition, the unfolded ensemble of the nascent chain adopts a highly anisotropic shape near the ribosome surface and the cooperativity of the folding-unfolding transition is decreased due to the appearance of partially folded structures that are not populated in bulk solution. The results show, in light of these effects, that with increasing nascent chain length folding rates increase in a linear manner and unfolding rates decrease, with larger and topologically more complex folds being the most highly perturbed by the ribosome. Analysis of folding trajectories, initiated by temperature quench, reveals the transition state ensemble is driven toward compaction and greater native-like structure by interactions with the ribosome surface and exit vestibule. Furthermore, the diversity of folding pathways decreases and the probability increases of initiating folding via the N-terminus on the ribosome. We show that all of these findings are equally applicable to the situation in which protein folding occurs during continuous (non-arrested) translation provided that the time scales of folding and unfolding are much faster than the time scale of monomer addition to the growing nascent chain, which results in a quasi-equilibrium process. These substantial ribosome-induced perturbations to almost all aspects of protein folding indicate that folding scenarios that are distinct from those of bulk solution can occur on the ribosome.     

Reaction of exciplex formation in the gas phase. The role of weak attractive interactions in the initial state

The reaction of molecular exciplex formation in the gas phase is treated within the framework of the Landau-Zener approximation, with the assumption that the initial state of the reaction has a potential energy curve including both repulsive and attractive interactions. It is found that the introduction of attractive interactions into the initial state (commonly treated as a repulsive state) leads, in the case of dipole-induced-dipole interaction, to a “reverse” temperature dependence of the exciplex formation rate constant.     

Anisotropic dynamics of dipolar liquids in narrow slit pores

We report molecular dynamics simulation results for Stockmayer fluids confined to narrow slitlike pores with structureless, nonconducting walls. The translational and rotational dynamics of the dipolar particles have been investigated by calculating autocorrelation functions, diffusion coefficients, and relaxation times for various pore widths (five or less particle diameters) and directions parallel and perpendicular to the walls. The dynamic properties of the confined systems are compared to bulk properties, where corresponding bulk and pore states at the same temperature and chemical potential are determined in parallel grand canonical Monte Carlo simulations. We find that the dynamic behavior inside the pore depends on the distance from the walls and can be strongly anisotropic even in globally isotropic systems. This concerns especially the particles in the surface layers close to the walls, where the single particle and collective dipolar relaxation resemble that of true two-dimensional dipolar fluids with different in-plane and out-of-plane relaxations. On the other hand, bulklike relaxation is observed in the pore center of sufficiently wide pores.     

Modeling of adsorption in pores with strongly heterogeneous walls: parametric lattice-site wall model

We present results of grand canonical Monte Carlo simulations of adsorption in cylindrical pores with rough surface modeled by a parametric lattice-site approach. The sites are randomly distributed over the pore walls. They could be attractive, neutral or repulsive with respect to the smooth pore model. Each site is characterized by two amplitudes (structural and energetic) which modify locally the structure and energetic properties of the surface. The results presented here show how different parameters of the model affect the mechanism of adsorption and, consequently, the form of the isotherm.     

Solvation force for long-ranged wall--fluid potentials

The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long-ranged wall-fluid potentials decaying as -Az(-p),z--> infinity, for various values of p. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field h=0 by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force f(solv) for the Ising film is repulsive and decays for large wall separations L in the same fashion as the boundary field f(solv) approximately L(-p), whereas for temperatures larger than the bulk critical temperature f(solv) is attractive and the asymptotic decay is f(solv) approximately L(-(p+1)). For the LJ fluid system f(solv) is always repulsive away from the critical region and decays for large L with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behavior of the solvation force.     

Estimation of protein folding rate from Monte Carlo simulations and entropy capacity

The problem of protein self-organization is one of the most important problems of molecular biology nowadays. Despite the recent success in the understanding of general principles of protein folding, details of this process are yet to be elucidated. Moreover, the prediction of protein folding rates has its own practical value due to the fact that aggregation directly depends on the rate of protein folding. The time of folding has been calculated for 67 proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native states using a Monte Carlo model where each residue is considered to be either folded as in the native state or completely disordered. The times of folding for 67 proteins which reach the native state within the limit of 10(8) Monte Carlo steps are in a good correlation with the experimentally measured folding rate at the mid-transition point (the correlation coefficient is -0.82). Theoretical consideration of a capillarity model for the process of protein folding demonstrates that the difference in the folding rate for proteins sharing more spherical and less spherical folds is the result of differences in the conformational entropy due to a larger surface of the boundary between folded and unfolded phases in the transition state for proteins with more spherical fold. The capillarity model allows us to predict the folding rate at the same level of correlation as by Monte Carlo simulations. The calculated model entropy capacity (conformational entropy per residue divided by the average contact energy per residue) for 67 proteins correlates by about 78% with the experimentally measured folding rate at the mid-transition point.     

Characteristic features of phase diagrams describing condensation of adsorbate in narrow pores

The phase diagrams describing condensation of adsorbate in micro- and mesoporous adsorbents having slit-shaped and cylindrical pores whose size varied from 1 to 20 monolayers were constructed. The study was performed using the lattice-gas model in the quasichemical approximation to take into account the intermolecular interactions. The phase diagrams for various values of the potential arising from different types of adsorbate--adsorbent interaction were analyzed for adsorption of helium, neon, methane, and carbon tetrachloride in graphite pores. Other adsorption systems are considered and the relationship between the pressure and temperature of adsorbate condensation is discussed. A nonmonotonic variation of the critical densities for pore widths from 3 to 10 molecular diameters was found. The pattern of this variation depends on the ratio of the energy of lateral interactions of the adsorbate molecules to the energy of interaction of the adsorbate molecules with pore walls. The critical temperature decreases monotonically with a decrease in the pore width. The stronger the adsorbate interaction with the pore walls, the greater the decrease in the critical temperature.     

Effects of crowding and confinement on the structures of the transition state ensemble in proteins

Characterization of the structures of the transition state ensemble is a key step in describing the folding reaction. Using two variants of a coarse-grained model of the three-stranded beta-sheet WW domain and a fully automated progress variable clustering (PVC) algorithm, we have dissected the effect of macromolecular crowding and confinement on the changes in the transition state structures in comparison to bulk. Each amino acid is represented using a Calpha atom and a side chain. The distance between the Calpha atom and center of mass of the side chain is taken to be its effective van der Waals radius. For the bulk case, we predict using the PVC algorithm, which does not assume knowledge of the underlying folding reaction coordinate, that there are two classes of structures in the transition state ensemble (TSE). The structures in both of the classes are compact. The dominant cluster is more structured than the structures in the less populated class. In accord with bulk experiments, the residues in strands beta2 and beta3 and the interactions at the beta2-beta3 interface are structured. When only excluded volume interactions between the crowding particles and the WW domain are taken into account or when the protein is confined to an inert spherical pore, the overall structure of the TSE does not change dramatically. However, in this entropy dominated regime, the width of the TSE decreases and the structures become more oblate and less spherical as the volume fraction of crowding particle increases or when the pore radius decreases. It suggests that the shape changes, which are computed using the moment of inertia tensor, may represent the slow degrees of freedom during the folding process. When non-native interactions between side chains and interactions with the cavity of the pores are taken into account, the TSE becomes considerably broader. Although the topology in the transition has a fold similar to the native state, the structures are far more plastic than in the bulk. The TSE is sensitive to the size of the pore as well as interactions between the pore and the protein. The differences between the two cases (confinement in an inert pore and when pore-protein interactions are considered) arise due to the increased importance of enthalpic interactions in the transition state as the strength of the protein-pore interaction increases.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Model for the nucleation mechanism of protein folding

A nucleation-like pathway of protein folding involves the formation of a cluster containing native residues that grows by including residues from the unfolded part of the protein. This pathway is examined by using a heteropolymer as a protein model. The model heteropolymer consists of hydrophobic and hydrophilic beads with fixed bond lengths and bond angles. The total energy of the heteropolymer is determined by the pairwise repulsive/attractive interactions between nonlinked beads and by the contribution from the dihedral angles involved. The parameters of these interactions can be rigorously defined, unlike the ill-defined surface tension of a cluster of protein residues that constitutes the basis of a previous nucleation model. The main idea underlying the new model consists of averaging the dihedral potential of a selected residue over all possible configurations of all neighboring residues along the protein chain. The resulting average dihedral potential depends on the distance between the selected residue and the cluster center. Its combination with the average pairwise potential of the selected residue and with a confining potential caused by the bonds between the residues leads to an overall potential around the cluster that has a double-well shape. Residues in the inner (closer to the cluster) well are considered as belonging to the folded cluster, whereas those in the outer well are treated as belonging to the unfolded part of the protein. Transitions of residues from the inner well into the outer one and vice versa are considered as elementary emission and absorption events, respectively. The double-well character of the potential well around the cluster allows one to determine the rates of both emission and absorption of residues by the cluster using a first passage time analysis. Once these rates are found as functions of the cluster size, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein. The model allows one to evaluate the size of the nucleus and the protein folding time. The latter is evaluated as the sum of the times necessary for the first nucleation event to occur and for the nucleus to grow to the maximum size (of the folded protein). Depending on the diffusion coefficients of the native residues in the range from 10(-6) to 10(-8) cm2/s, numerical calculations for a protein of 2500 residues suggest that the folding time ranges from several seconds to several hundreds of seconds.     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Adsorption of Fluids in Pores Formed between Two Hard Cylinders

We study adsorption in pores with curved hard walls that are made of two uniaxial cylinders by using a density functional approach. Two cases are considered: adsorption of hard spheres and adsorption of a Lennard-Jones fluid. In the case of hard spheres, we perform a comparison with the results of grand canonical ensemble Monte Carlo data. This comparison indicates that the applied approach is capable of reproducing the fluid structure quite satisfactorily. For hard spheres, we also make a comparison of the total adsorption effect (expressed as the average density of a confined fluid) inside pores with curved walls with that evaluated for a slitlike pore. We have found that the differences between adsorption in pores with curved walls and in slits with the same wall-to-wall distance are quite low. The calculations for the Lennard-Jones fluid have been concerned with the investigation of the capillary evaporation and with the evaluation of phase diagrams for different pores, including slitlike pores. We have found that the curvature of the pore walls shifts the transition toward lower values of the chemical potential and increases slightly the value of the critical temperature in comparison with the values obtained for a slitlike pore. Copyright 2000 Academic Press.     

Electrostatic Interaction and Partitioning of Ion-Penetrable Spheres

Electrostatic interaction between two ion-penetrable spheres near a horizontal plate or in a slit pore is investigated theoretically. The orientation of the line connecting the two particle centers can be arbitrary relative to the plate(s). The electrostatic interaction energy and force on each particle are obtained analytically by the method of images. Emphasis is placed on the effect of the presence of the second particle, compared to the case of a single particle or the case without any plate(s). It is found that the horizontal electrical force on each particle is always repulsive. This repulsive force is enhanced by the plate(s) of constant surface charge density, while it is reduced by the plate(s) of constant surface potential. The electrostatic interaction together with the steric effect is used to determine the partition coefficient for the case of a slit pore, correct to O(C(infinity)), where C(infinity) is the volume fraction of particles in the bulk solution. The positive correction coefficient is larger for conducting plates than for insulating plates. Copyright 2001 Academic Press.     

Fast folding of a four-helical bundle protein

The FK506-FKBP12 binding-domain of the kinase FRAP (FRB) forms a classic up-down four-helical bundle. The folding pathway of this protein has been investigated using a combination of equilibrium and kinetic studies. The native state of the protein is stable with respect to the unfolded state by some 7 kcal mol(-1) at pH 6.0, 10 degrees C. A kinetic analysis of unfolding and refolding rate constants as a function of chemical denaturant concentration suggests that an intermediate state may be populated during folding at low concentrations of denaturant. The presence of this intermediate state is confirmed by refolding experiments performed in the presence of the hydrophobic dye 8-anilinonaphthalene-1 sulfonate (ANS). ANS binds to the partially folded intermediate state populated during the folding of FRB and undergoes a large change in fluorescence that can be detected using stopped-flow techniques. Analysis of the kinetic data suggests that the intermediate state is compact and it may even be a misfolded species that has to partially unfold before it can reach the transition state. Folding and unfolding rate constants in water are approximately 150-200 s(-1) and 0.005-0.06 s(-1), respectively, at neutral pH and 10 degrees C. The folding of FRB is somewhat slower than for other all-helical proteins, probably as a consequence of the formation of a metastable intermediate state. The folding rate constant in the absence of any populated intermediate can be estimated to be 8800 s(-1). Despite the presence of an intermediate state, which effectively slows folding, the protein still folds rapidly with a half-life of 5 ms at 10 degrees C. The dependence of the rate constants on denaturant concentration indicates that the transition state for folding is compact with some 80% of the surface area exposed in the unfolded state buried in the transition state. Data presented for FRB is compared with kinetic data obtained for other all-helical proteins.