Effects of macromolecular crowding on protein folding and aggregation studied by density functional theory: dynamics

Proteins from Thermophilic Thermus thermophilus Often Do Not Fold Correctly in a Mesophilic Expression System Such as Escherichia coli

Majority of protein structure studies use Escherichia coli (E. coli) and other model organisms as expression systems for other species' genes. However, protein folding depends on cellular environment factors, such as chaperone proteins, cytoplasmic pH, temperature, and ionic concentrations. Because of differences in these factors, especially temperature and chaperones, native proteins in organisms such as extremophiles may fold improperly when they are expressed in mesophilic model organisms. Here we present a methodology of assessing the effects of using E. coli as the expression system on protein structures. We compare these effects between eight mesophilic bacteria and Thermus thermophilus (T. thermophilus), a thermophile, and found that differences are significantly larger for T. thermophilus. More specifically, helical secondary structures in T. thermophilus proteins are often replaced by coil structures in E. coli. Our results show unique directionality in misfolding when proteins in thermophiles are expressed in mesophiles. This indicates that extremophiles, such as thermophiles, require unique protein expression systems in protein folding studies.

Conformational Dynamics of Glucagon-like Peptide-2 with Different Electric Field

Molecular dynamics (MD) simulation was used to study the influence of electric field on Glucagon-like Peptide-2 (GLP-2). Different electric field strengths (0 V/nm ≤ E ≤ 1 V/nm) were mainly carried out on GLP-2. The structural changes in GLP-2 were analyzed by the Root Mean Square Deviation (RMSD), Root Mean Square Fluctuation (RMSF), Radius of Gyration (Rg), Solvent Accessible Surface Area (SASA), Secondary Structure and the number of hydrogen bonds. The stable α—helix structure of GLP-2 was unwound and transformed into an unstable Turn and Coil structure since the stability of the GLP-2 protein structure was reduced under the electric field. Our results show that the degree of unwinding of the GLP-2 structure was not linearly related to the electric field intensity. E = 0.5 V/nm was a special point where the degree of unwinding of the GLP-2 structure reached the maximum at this electric field strength. Under a weak electric field, E < 0.5 V/nm, the secondary structure of GLP-2 becomes loose, and the entropy of the chain increases. When E reaches a certain value (E > 0.5 V/nm), the electric force of the charged residues reaches equilibrium, along the z-direction. Considering the confinement of moving along another direction, the residue is less free. Thus, entropy decreases and enthalpy increases, which enhance the interaction of adjacent residues. It is of benefit to recover hydrogen bonds in the middle region of the protein. These investigations, about the effect of an electric field on the structure of GLP-2, can provide some theoretical basis for the biological function of GLP-2 in vivo.

Influence of Nonspecific Interactions on Protein Associations: Implications for Biochemistry In Vivo

The cellular interior is composed of a variety of microenvironments defined by distinct local compositions and composition-dependent intermolecular interactions. We review the various types of nonspecific interactions between proteins and between proteins and other macromolecules and supramolecular structures that influence the state of association and functional properties of a given protein existing within a particular microenvironment at a particular point in time. The present state of knowledge is summarized, and suggestions for fruitful directions of research are offered. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Lateral depletion effect on two-dimensional ordering of bacteriorhodopsins in a lipid bilayer: A theoretical study based on a binary hard-disk model

The 2D ordering of bacteriorhodopsins in a lipid bilayer was studied using a binary hard-disk model. The phase diagrams were calculated taking into account the lateral depletion effects. The critical concentrations of the protein ordering for monomers and trimers were obtained from the phase diagrams. The critical concentration ratio agreed well with the experiment when the repulsive core interaction between the depletants, namely, lipids, was taken into account. The results suggest that the depletion effect plays an important role in the association behaviors of transmembrane proteins.

Reduced density profile of small particles near a large particle: Results of an integral equation theory with an accurate bridge function and a Monte Carlo simulation

Solute-solvent reduced density profiles of hard-sphere fluids were calculated by using several integral equation theories for liquids. The traditional closures, Percus-Yevick (PY) and the hypernetted-chain (HNC) closures, as well as the theories with bridge functions, Verlet, Duh-Henderson, and Kinoshita (named MHNC), were used for the calculation. In this paper, a one-solute hard-sphere was immersed in a one-component hard-sphere solvent and various size ratios were examined. The profiles between the solute and solvent particles were compared with those calculated by Monte Carlo simulations. The profiles given by the integral equations with the bridge functions were much more accurate than those calculated by conventional integral equation theories, such as the Ornstein-Zernike (OZ) equation with the PY closure. The accuracy of the MHNC-OZ theory was maintained even when the particle size ratio of solute to solvent was 50. For example, the contact values were 5.7 (Monte Carlo), 5.6 (MHNC), 7.8 (HNC), and 4.5 (PY), and the first minimum values were 0.48 (Monte Carlo), 0.46 (MHNC), 0.54 (HNC), and 0.40 (PY) when the packing fraction of the hard-sphere solvent was 0.38 and the size ratio was 50. The asymptotic decay and the oscillation period for MHNC-OZ were also very accurate, although those given by the HNC-OZ theory were somewhat faster than those obtained by Monte Carlo simulations.

Effects of macromolecular crowding on amyloid beta (16-22) aggregation using coarse-grained simulations

To examine the effect of crowding on protein aggregation, discontinuous molecular dynamics (DMD) simulations combined with an intermediate resolution protein model, PRIME20, were applied to a peptide/crowder system. The systems contained 192 Aβ(16–22) peptides and crowders of diameters 5, 20, and 40 Å, represented here by simple hard spheres, at crowder volume fractions of 0.00, 0.10, and 0.20. Results show that both crowder volume fraction and crowder diameter have a large impact on fibril and oligomer formation. The addition of crowders to a system of peptides increases the rate of oligomer formation, shifting from a slow ordered formation of oligomers in the absence of crowders, similar to nucleated polymerization, to a fast collapse of peptides and subsequent rearrangement characteristic of nucleated conformational conversion with a high maximum in the number of peptides in oligomers as the total crowder surface area increases. The rate of conversion from oligomers to fibrils also increases with increasing total crowder surface area, giving rise to an increased rate of fibril growth. In all cases, larger volume fractions and smaller crowders provide the greatest aggregation enhancement effects. We also show that the size of the crowders influences the formation of specific oligomer sizes. In our simulations, the 40 Å crowders enhance the number of dimers relative to the numbers of trimers, hexamers, pentamers, and hexamers, while the 5 Å crowders enhance the number of hexamers relative to the numbers of dimers, trimers, tetramers, and pentamers. These results are in qualitative agreement with previous experimental and theoretical work.

Effects of crowding on the stability of a surface-tethered biopolymer: an experimental study of folding in a highly crowded regime

The high packing densities and fixed geometries with which biomolecules can be attached to macroscopic surfaces suggest that crowding effects may be particularly significant under these often densely packed conditions. Exploring this question experimentally, we report here the effects of crowding on the stability of a simple, surface-attached DNA stem-loop. We find that crowding by densely packed, folded biomolecules destabilizes our test-bed biomolecule by ∼2 kJ/mol relative to the dilute (noninteracting) regime, an effect that presumably occurs due to steric and electrostatic repulsion arising from compact neighbors. Crowding by a dense brush of unfolded biomolecules, in contrast, enhances its stability by ∼6 kJ/mol, presumably due to excluded volume and electrostatic effects that reduce the entropy of the unfolded state. Finally, crowding by like copies of the same biomolecule produces a significantly broader unfolding transition, likely because, under these circumstances, the stabilizing effects of crowding by unfolded molecules increase (and the destabilizing effects of neighboring folded molecules decrease) as more and more neighbors unfold. The crowding of surface-attached biomolecules may thus be a richer, more complex phenomenon than that seen in homogeneous solution.

Density functional theory for protein transfer free energy

We cast the problem of protein transfer free energy within the formalism of density functional theory (DFT), treating the protein as a source of external potential that acts upon the solvent. Solvent excluded volume, solvent-accessible surface area, and temperature dependence of the transfer free energy all emerge naturally within this formalism, and may be compared with simplified "back of the envelope" models, which are also developed here. Depletion contributions to osmolyte induced stability range from 5 to 10 kBT for typical protein lengths. The general DFT transfer theory developed here may be simplified to reproduce a Langmuir isotherm condensation mechanism on the protein surface in the limits of short-ranged interactions, and dilute solute. Extending the equation of state to higher solute densities results in non-monotonic behavior of the free energy driving protein or polymer collapse. Effective interaction potentials between protein backbone or side chains and TMAO are obtained, assuming a simple backbone/side chain two-bead model for the protein with an effective 6-12 potential with the osmolyte. The transfer free energy δg shows significant entropy: d(δg)/dT ≈ 20 kB for a 100-residue protein. The application of DFT to effective solvent forces for use in implicit-solvent molecular dynamics is also developed. The simplest DFT expressions for implicit-solvent forces contain both depletion interactions and an "impeded-solvation" repulsive force at larger distances.

Influences of excluded volume of molecules on signaling processes on the biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by monotonically increasing; increasing then decreasing in a bell-shaped curve; or increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.

Cell-free protein expression under macromolecular crowding conditions

Background

Cell-free protein expression (CFPE) comprised of in vitro transcription and translation is currently manipulated in relatively dilute solutions, in which the macromolecular crowding effects present in living cells are largely ignored. This may not only affect the efficiency of protein synthesis in vitro, but also limit our understanding of the functions and interactions of biomolecules involved in this fundamental biological process.

Methodology/Principal Findings

Using cell-free synthesis of Renilla luciferase in wheat germ extract as a model system, we investigated the CFPE under macromolecular crowding environments emulated with three different crowding agents: PEG-8000, Ficoll-70 and Ficoll-400, which vary in chemical properties and molecular size. We found that transcription was substantially enhanced in the macromolecular crowding solutions; up to 4-fold increase in the mRNA production was detected in the presence of 20% (w/v) of Ficoll-70. In contrast, translation was generally inhibited by the addition of each of the three crowding agents. This might be due to PEG-induced protein precipitation and non-specific binding of translation factors to Ficoll molecules. We further explored a two-stage CFPE in which transcription and translation was carried out under high then low macromolecular crowding conditions, respectively. It produced 2.2-fold higher protein yield than the coupled CFPE control. The macromolecular crowding effects on CFPE were subsequently confirmed by cell-free synthesis of an approximately two-fold larger protein, Firefly luciferase, under macromolecular crowding environments.

Conclusions/Significance

Three macromolecular crowding agents used in this research had opposite effects on transcription and translation. The results of this study should aid researchers in their choice of macromolecular crowding agents and shows that two-stage CFPE is more efficient than coupled CFPE.

Barriers to diffusion in dendrites and estimation of calcium spread following synaptic inputs

The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as D(cyto)/D(water) = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5 μm).

A didactic model of macromolecular crowding effects on protein folding

A didactic model is presented to illustrate how the effect of macromolecular crowding on protein folding and association is modeled using current analytical theory and discrete molecular dynamics. While analytical treatments of crowding may consider the effect as a potential of average force acting to compress a polypeptide chain into a compact state, the use of simulations enables the presence of crowding reagents to be treated explicitly. Using an analytically solvable toy model for protein folding, an approximate statistical thermodynamic method is directly compared to simulation in order to gauge the effectiveness of current analytical crowding descriptions. Both methodologies are in quantitative agreement under most conditions, indication that both current theory and simulation methods are capable of recapitulating aspects of protein folding even by utilizing a simplistic protein model.

Macromolecular crowding induces polypeptide compaction and decreases folding cooperativity

A cell's interior is comprised of macromolecules that can occupy up to 40% of its available volume. Such crowded environments can influence the stability of proteins and their rates of reaction. Using discrete molecular dynamics simulations, we investigate how both the size and number of neighboring crowding reagents affect the thermodynamic and folding properties of structurally diverse proteins. We find that crowding induces higher compaction of proteins. We also find that folding becomes less cooperative with the introduction of crowders into the system. The crowders may induce alternative non-native protein conformations, thus creating barriers for protein folding in highly crowded media.

Density-functional theory for complex fluids

Density-functional theory (DFT) and its variations provide a fruitful approach to the computational modeling of the microscopic structures and phase behavior of soft-condensed matter. The methodology takes deep root in quantum mechanics but shares a mathematical similarity with a number of classical approaches in statistical mechanics. This review discusses different strategies commonly used to formulate the free-energy functional of complex fluids for either phenomena-oriented applications or as a generic description of the thermodynamic nonideality owing to various components of intermolecular forces. We emphasize the connections among different schemes of DFT approximations, their underlying assumptions, and inherent limitations. We also address extensions of equilibrium DFT to phenomenological theories for the dynamic properties of complex fluids and for the kinetics of phase transitions. In addition, we highlight the recent literature concerning applications of DFT to diverse static and time-dependent phenomena in complex fluids.

Effects of macromolecular crowding on biochemical reaction equilibria: a molecular thermodynamic perspective

A molecular thermodynamic model is developed to investigate the effects of macromolecular crowding on biochemical reactions. Three types of reactions, representing protein folding/conformational isomerization, coagulation/coalescence, and polymerization/association, are considered. The reactants, products, and crowders are modeled as coarse-grained spherical particles or as polymer chains, interacting through hard-sphere interactions with or without nonbonded square-well interactions, and the effects of crowder size and chain length as well as product size are examined. The results predicted by this model are consistent with experimentally observed crowding effects based on preferential binding or preferential exclusion of the crowders. Although simple hard-core excluded-volume arguments do in general predict the qualitative aspects of the crowding effects, the results show that other intermolecular interactions can substantially alter the extent of enhancement or reduction of the equilibrium and can even change the direction of the shift. An advantage of the approach presented here is that competing reactions can be incorporated within the model.

The polysaccharide scaffold of PrP 27-30 is a common compound of natural prions and consists of alpha-linked polyglucose

An inert polysaccharide scaffold identified as a 5-15% component of prion rods (PrP 27-30) is unambiguously distinguishable from the N-glycosyl groups and the GPI anchor of PrP, and consists predominantly of 1,4-linked glucose with some branching via 1,4,6-linked glucose. We show that this polysaccharide scaffold is a common secondary component of prions found in hamster full-length PrP(Sc), prion rods and in mouse ScN2a prions from cell culture. The preparation from prion rods was improved, resulting in a polysaccharide scaffold free of remaining infectivity. Furthermore, we determined the stereochemistry of the glycoside linkages as pre-dominantly if not entirely alpha-glycosidic. The origin of the polysaccharide, its interaction with PrP and its potential relation to glycogen and corpora amylacea are discussed.

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.

Density-functional theory for the structures and thermodynamic properties of highly asymmetric electrolyte and neutral component mixtures

Density-functional theory (DFT) is applied to investigate the structural and thermodynamic properties of concentrated electrolyte and neutral component mixtures that are highly asymmetric in terms of both size and charge mimicking a crowded cellular environment. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The direct correlation functions are obtained from the analytical solutions of the mean-spherical approximation. In the context of a primitive model where biomacromolecules are represented by neutral or charged hard spheres and the solvent is represented by a continuous dielectric medium, this DFT is able to take into account both the excluded-volume effects and the long-ranged electrostatic interactions quantitatively. The performance of the theoretical method has been tested with Monte Carlo simulation results from this work and from the literature for the pair correlation functions, excess internal energies, and osmotic coefficients for a wide variety of aqueous dispersions of charged and neutral particles.

Competition between protein folding and aggregation with molecular chaperones in crowded solutions: insight from mesoscopic simulations

The living cell is inherently crowded with proteins and macromolecules. To avoid aggregation of denatured proteins in the living cell, molecular chaperones play important roles. Here we introduce a simple model to describe crowded protein solutions with chaperone-like species based on a dynamic density functional theory. As predicted by others, our simulations show that macromolecular crowding enhances the association of proteins and chaperones. However, when the intrinsic folding rate of the protein is slow, it is possible that crowding also enhances aggregation of proteins. The results of simulation suggest that, when the concentration of the crowding agent is as high as that in the cell, the association of the protein and unbound chaperone becomes correlated with the aggregation process, and that the protein-bound chaperones efficiently destroy the potential nuclei of aggregates and thus prevent the aggregation.