Simulation and modeling of crowding effects on the thermodynamic and kinetic properties of proteins with atomic details

Recent experimental studies of protein folding and binding under crowded solutions suggest that crowding agents exert subtle influences on the thermodynamic and kinetic properties of the proteins. While some of the crowding effects can be understood qualitatively from simple models of the proteins, quantitative rationalization of these effects requires an atomistic representation of the protein molecules in modeling their interactions with crowders. A computational approach, known as postprocessing, has opened the door for atomistic modeling of crowding effects. This review summarizes the applications of the postprocessing approach for studying crowding effects on the thermodynamics and kinetics of protein folding, conformational transition, and binding. The integration of atomistic modeling with experiments in crowded solutions promises new insight into biochemical processes in cellular environments.     

From the test tube to the cell: exploring the folding and aggregation of a beta-clam protein

A crucial challenge in present biomedical research is the elucidation of how fundamental processes like protein folding and aggregation occur in the complex environment of the cell. Many new physico-chemical factors like crowding and confinement must be considered, and immense technical hurdles must be overcome in order to explore these processes in vivo. Understanding protein misfolding and aggregation diseases and developing therapeutic strategies to these diseases demand that we gain mechanistic insight into behaviors and misbehaviors of proteins as they fold in vivo. We have developed a fluorescence approach using FlAsH labeling to study the thermodynamics of folding of a model beta-rich protein, cellular retinoic acid binding protein (CRABP) in Escherichia coli cells. The labeling approach has also enabled us to follow aggregation of a modified version of CRABP and chimeras between CRABP and huntingtin exon 1 with its glutamine repeat tract. In this article, we review our recent results using FlAsH labeling to study in-vivo folding and present new observations that hint at fundamental differences between the thermodynamics and kinetics of protein folding in vivo and in vitro.     

Protein folding in the cell: challenges and progress

It is hard to imagine a more extreme contrast than that between the dilute solutions used for in vitro studies of protein folding and the crowded, compartmentalized, sticky, spatially inhomogeneous interior of a cell. This review highlights recent research exploring protein folding in the cell with a focus on issues that are generally not relevant to in vitro studies of protein folding, such as macromolecular crowding, hindered diffusion, cotranslational folding, molecular chaperones, and evolutionary pressures. The technical obstacles that must be overcome to characterize protein folding in the cell are driving methodological advances, and we draw attention to several examples, such as fluorescence imaging of folding in cells and genetic screens for in-cell stability.     

Chaperonin function--effects of crowding and confinement

Chaperonins assist in the acquisition of native protein structure in the cell by providing a shielded environment for a folding polypeptide chain, generated by the interior surface of their cylindrical structure. The folding chain is isolated from the highly crowded cytoplasm, but at the same time confined within the chaperonin folding cage. Both confinement and macromolecular crowding can affect folding kinetics and yields, the modus operandi of chaperonins and their interaction with their protegés. Recent experimental data, as well as computer simulations, provide increasing evidence that the particular physico-chemical conditions prevailing in the cellular interior have to be taken into account when trying to unravel the processes of cellular protein folding.     

Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.     

Soft interactions and crowding

The intracellular milieu is complex, heterogeneous and crowded—an environment vastly different from dilute solutions in which most biophysical studies are performed. The crowded cytoplasm excludes about a third of the volume available to macromolecules in dilute solution. This excluded volume is the sum of two parts: steric repulsions and chemical interactions, also called soft interactions. Until recently, most efforts to understand crowding have focused on steric repulsions. Here, we summarize the results and conclusions from recent studies on macromolecular crowding, emphasizing the contribution of soft interactions to the equilibrium thermodynamics of protein stability. Despite their non-specific and weak nature, the large number of soft interactions present under many crowded conditions can sometimes overcome the stabilizing steric, excluded volume effect.     

Protein Stability and Folding Kinetics in the Nucleus and Endoplasmic Reticulum of Eucaryotic Cells

We measure the stability and folding relaxation rate of phosphoglycerate kinase (PGK) Förster resonance energy transfer (FRET) constructs localized in the nucleus or in the endoplasmic reticulum (ER) of eukaryotic cells. PGK has a more compact native state in the cellular compartments than in aqueous solution. Its native FRET signature is similar to that previously observed in a carbohydrate-crowding matrix, consistent with crowding being responsible for the compact native state of PGK in the cell. PGK folds through multiple states in vitro, but its folding kinetics is more two-state-like in the ER, so the folding mechanism can be modified by intracellular compartments. The nucleus increases PGK stability and folding rate over the cytoplasm and ER, even though the density of crowders in the nucleus is no greater than in the ER or cytoplasm. Nuclear folding kinetics (and to a lesser extent, thermodynamics) vary less from cell to cell than in the cytoplasm or ER, indicating a more homogeneous crowding and chemical environment in the nucleus.     

Protein homeostasis disorders of key enzymes of amino acids metabolism: mutation-induced protein kinetic destabilization and new therapeutic strategies

Many inborn errors of amino acids metabolism are caused by single point mutations affecting the ability of proteins to fold properly (i.e., protein homeostasis), thus leading to enzyme loss-of-function. Mutations may affect protein homeostasis by altering intrinsic physical properties of the polypeptide (folding thermodynamics, and rates of folding/unfolding/misfolding) as well as the interaction of partially folded states with elements of the protein homeostasis network (such as molecular chaperones and proteolytic machineries). Understanding these mutational effects on protein homeostasis is required to develop new therapeutic strategies aimed to target specific features of the mutant polypeptide. Here, I review recent work in three different diseases of protein homeostasis associated to inborn errors of amino acids metabolism: phenylketonuria, inherited homocystinuria and primary hyperoxaluria type I. These three different genetic disorders involve proteins operating in different cell organelles and displaying different structural complexities. Mutations often decrease protein kinetic stability of the native state (i.e., its half-life for irreversible denaturation), which can be studied using simple kinetic models amenable to biophysical and biochemical characterization. Natural ligands and pharmacological chaperones are shown to stabilize mutant enzymes, thus supporting their therapeutic application to overcome protein kinetic destabilization. The role of molecular chaperones in protein folding and misfolding is also discussed as well as their potential pharmacological modulation as promising new therapeutic approaches. Since current available treatments for these diseases are either burdening or only successful in a fraction of patients, alternative treatments must be considered covering studies from protein structure and biophysics to studies in animal models and patients.     

Intermediates in the folding equilibrium of repeat proteins from the TPR family

In recent decades, advances in computational methods and experimental biophysical techniques have improved our understanding of protein folding. Although some of these advances have been remarkable, the structural variability of globular proteins usually encountered makes it difficult to extract general features of their folding processes. To overcome this difficulty, experimental and computational studies of the folding of repeat (or modular) proteins are of interest. Because their native structures can be described as linear arrays of the same, repeated, supersecondary structure unit, it is possible to seek  a possibly independent behavior of the different modules without taking into account the intrinsic stability associated with different secondary structure motifs. In this work we have used a Monte Carlo-based simulation to study the folding equilibrium of four repeat proteins belonging to the tetratricopeptide repeat family. Our studies provide new insights into their energy profiles, enabling investigation about the existence of intermediate states and their relative stabilities. We have also performed structural analyses to describe the structure of these intermediates, going through the vast number of conformations obtained from the simulations. In this way, we have tried to identify the regions of each protein in which the modular structure yields a different behavior and, more specifically, regions of the proteins that can stay folded when the rest of the chain has been thermally denatured.     

Effects of macromolecular crowding agents on protein folding in vitro and in silico

Proteins fold and function inside cells which are environments very different from that of dilute buffer solutions most often used in traditional experiments. The crowded milieu results in excluded-volume effects, increased bulk viscosity and amplified chances for inter-molecular interactions. These environmental factors have not been accounted for in most mechanistic studies of protein folding executed during the last decades. The question thus arises as to how these effects—present when polypeptides normally fold in vivo—modulate protein biophysics. To address excluded volume effects, we use synthetic macromolecular crowding agents, which take up significant volume but do not interact with proteins, in combination with strategically selected proteins and a range of equilibrium and time-resolved biophysical (spectroscopic and computational) methods. In this review, we describe key observations on macromolecular crowding effects on protein stability, folding and structure drawn from combined in vitro and in silico studies. As expected based on Minton’s early predictions, many proteins (apoflavodoxin, VlsE, cytochrome c, and S16) became more thermodynamically stable (magnitude depends inversely on protein stability in buffer) and, unexpectedly, for apoflavodoxin and VlsE, the folded states changed both secondary structure content and, for VlsE, overall shape in the presence of macromolecular crowding. For apoflavodoxin and cytochrome c, which have complex kinetic folding mechanisms, excluded volume effects made the folding energy landscapes smoother (i.e., less misfolding and/or kinetic heterogeneity) than in buffer.     

Protein Folding Requires Crowd Control in a Simulated Cell

Macromolecular crowding has a profound effect upon biochemical processes in the cell. We have computationally studied the effect of crowding upon protein folding for 12 small domains in a simulated cell using a coarse-grained protein model, which is based upon Langevin dynamics, designed to unify the often disjoint goals of protein folding simulation and structure prediction. The model can make predictions of native conformation with accuracy comparable with that of the best current template-free models. It is fast enough to enable a more extensive analysis of crowding than previously attempted, studying several proteins at many crowding levels and further random repetitions designed to more closely approximate the ensemble of conformations. We found that when crowding approaches 40% excluded volume, the maximum level found in the cell, proteins fold to fewer native-like states. Notably, when crowding is increased beyond this level, there is a sudden failure of protein folding: proteins fix upon a structure more quickly and become trapped in extended conformations. These results suggest that the ability of small protein domains to fold without the help of chaperones may be an important factor in limiting the degree of macromolecular crowding in the cell. Here, we discuss the possible implications regarding the relationship between protein expression level, protein size, chaperone activity and aggregation.     

Macromolecular crowding compacts unfolded apoflavodoxin and causes severe aggregation of the off-pathway intermediate during apoflavodoxin folding

To understand how proteins fold in vivo, it is important to investigate the effects of macromolecular crowding on protein folding. Here, the influence of crowding on in vitro apoflavodoxin folding, which involves a relatively stable off-pathway intermediate with molten globule characteristics, is reported. To mimic crowded conditions in cells, dextran 20 at 30% (w/v) is used, and its effects are measured by a diverse combination of optical spectroscopic techniques. Fluorescence correlation spectroscopy shows that unfolded apoflavodoxin has a hydrodynamic radius of 37+/-3 A at 3 M guanidine hydrochloride. F?rster resonance energy transfer measurements reveal that subsequent addition of dextran 20 leads to a decrease in protein volume of about 29%, which corresponds to an increase in protein stability of maximally 1.1 kcal mol(-1). The compaction observed is accompanied by increased secondary structure, as far-UV CD spectroscopy shows. Due to the addition of crowding agent, the midpoint of thermal unfolding of native apoflavodoxin rises by 2.9 degrees C. Although the stabilization observed is rather limited, concomitant compaction of unfolded apoflavodoxin restricts the conformational space sampled by the unfolded state, and this could affect kinetic folding of apoflavodoxin. Most importantly, crowding causes severe aggregation of the off-pathway folding intermediate during apoflavodoxin folding in vitro. However, apoflavodoxin can be over expressed in the cytoplasm of Escherichia coli, where it efficiently folds to its functional native form at high yield without noticeable problems. Apparently, in the cell, apoflavodoxin requires the help of chaperones like Trigger Factor and the DnaK system for efficient folding.     

Folding of a model three-helix bundle protein: a thermodynamic and kinetic analysis.

The kinetics and thermodynamics of an off-lattice model for a three-helix bundle protein are investigated as a function of a bias gap parameter that determines the energy difference between native and non-native contacts. A simple dihedral potential is used to introduce the tendency to form right-handed helices. For each value of the bias parameter, 100 trajectories of up to one microsecond are performed. Such statistically valid sampling of the kinetics is made possible by the use of the discrete molecular dynamics method with square-well interactions. This permits much faster simulations for off-lattice models than do continuous potentials. It is found that major folding pathways can be defined, although ensembles with considerable structural variation are involved. The large gap models generally fold faster than those with a smaller gap. For the large gap models, the kinetic intermediates are non-obligatory, while both obligatory and non-obligatory intermediates are present for small gap models. Certain large gap intermediates have a two-helix microdomain with one helix extended outward (as in domain-swapped dimers); the small gap intermediates have more diverse structures. The importance of studying the kinetic, as well as the thermodynamics, of folding for an understanding of the mechanism is discussed and the relation between kinetic and equilibrium intermediates is examined. It is found that the behavior of this model system has aspects that encompass both the "new" view and the "old" view of protein folding.     

Biochemical effects of molecular crowding

Cell cytoplasm contains high concentrations of high-molecular-weight components that occupy a substantial part of the volume of the medium (crowding conditions). The effect of crowding on biochemical processes proceeding in the cell (conformational transitions of biomacromolecules, assembling of macromolecular structures, protein folding, protein aggregation, etc.) is discussed in this review. The excluded volume concept, which allows the effects of crowding on biochemical reactions to be quantitatively described, is considered. Experimental data demonstrating the biochemical effects of crowding imitated by both low-molecular-weight and high-molecular-weight crowding agents are summarized.Translated from Biokhimiya, Vol. 69, No. 11, 2004, pp. 1522–1536.Original Russian Text Copyright © 2004 by Chebotareva, Kurganov, Livanova.     

Molecular crowders and cosolutes promote folding cooperativity of RNA under physiological ionic conditions

Folding mechanisms of functional RNAs under idealized in vitro conditions of dilute solution and high ionic strength have been well studied. Comparatively little is known, however, about mechanisms for folding of RNA in vivo where Mg²⁺ ion concentrations are low, K⁺ concentrations are modest, and concentrations of macromolecular crowders and low-molecular-weight cosolutes are high. Herein, we apply a combination of biophysical and structure mapping techniques to tRNA to elucidate thermodynamic and functional principles that govern RNA folding under in vivo–like conditions. We show by thermal denaturation and SHAPE studies that tRNA folding cooperativity increases in physiologically low concentrations of Mg²⁺ (0.5–2 mM) and K⁺ (140 mM) if the solution is supplemented with physiological amounts (∼20%) of a water-soluble neutral macromolecular crowding agent such as PEG or dextran. Low-molecular-weight cosolutes show varying effects on tRNA folding cooperativity, increasing or decreasing it based on the identity of the cosolute. For those additives that increase folding cooperativity, the gain is manifested in sharpened two-state-like folding transitions for full-length tRNA over its secondary structural elements. Temperature-dependent SHAPE experiments in the absence and presence of crowders and cosolutes reveal extent of cooperative folding of tRNA on a nucleotide basis and are consistent with the melting studies. Mechanistically, crowding agents appear to promote cooperativity by stabilizing tertiary structure, while those low molecular cosolutes that promote cooperativity stabilize tertiary structure and/or destabilize secondary structure. Cooperative folding of functional RNA under physiological-like conditions parallels the behavior of many proteins and has implications for cellular RNA folding kinetics and evolution.     

Entropic stabilization of the folded states of RNA due to macromolecular crowding

We review the effects of macromolecular crowding on the folding of RNA by considering the simplest scenario when excluded volume interactions between crowding particles and RNA dominate. Using human telomerase enzyme as an example, we discuss how crowding can alter the equilibrium between pseudoknot and hairpin states of the same RNA molecule—a key aspect of crowder–RNA interactions. We summarize data showing that the crowding effect is significant only if the size of the spherical crowding particle is smaller than the radius of gyration of the RNA in the absence of crowding particles. The implication for function of the wild type and mutants of human telomerase is outlined by using a relationship between enzyme activity and its conformational equilibrium. In addition, we discuss the interplay between macromolecular crowding and ionic strength of the RNA buffer. Finally, we briefly review recent experiments which illustrate the connection between excluded volume due to macromolecular crowding and the thermodynamics of RNA folding.     

The ankyrin repeat as molecular architecture for protein recognition

The ankyrin repeat is one of the most frequently observed amino acid motifs in protein databases. This protein-protein interaction module is involved in a diverse set of cellular functions, and consequently, defects in ankyrin repeat proteins have been found in a number of human diseases. Recent biophysical, crystallographic, and NMR studies have been used to measure the stability and define the various topological features of this motif in an effort to understand the structural basis of ankyrin repeat-mediated protein-protein interactions. Characterization of the folding and assembly pathways suggests that ankyrin repeat domains generally undergo a two-state folding transition despite their modular structure. Also, the large number of available sequences has allowed the ankyrin repeat to be used as a template for consensus-based protein design. Such projects have been successful in revealing positions responsible for structure and function in the ankyrin repeat as well as creating a potential universal scaffold for molecular recognition.     

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.