Atomic-level observation of macromolecular crowding effects: escape of a protein from the GroEL cage

PEG-mCherry interactions beyond classical macromolecular crowding

The dense cellular environment influences bio-macromolecular structure, dynamics, interactions, and function. Despite advancements in understanding protein-crowder interactions, predicting their precise effects on protein structure and function remains challenging. Here, we elucidate the effects of PEG-induced crowding on the fluorescent protein mCherry using molecular dynamics simulations and fluorescence-based experiments. We identify and characterize specific PEG-induced structural and dynamical changes in mCherry. Importantly, we find interactions in which PEG molecules wrap around specific surface-exposed residues in a binding mode previously observed in protein crystal structures. Fluorescence correlation spectroscopy experiments capture PEG-induced changes, including aggregation, suggesting a potential role for the specific PEG-mCherry interactions identified in simulations. Additionally, mCherry fluorescence lifetimes are influenced by PEG and not by the bulkier crowder dextran or by another linear polymer, polyvinyl alcohol, highlighting the importance of crowder-protein soft interactions. This work augments our understanding of macromolecular crowding effects on protein structure and dynamics.

Elucidating the novel mechanisms of molecular chaperones by single-molecule technologies

Molecular chaperones play central roles in sustaining protein homeostasis and preventing protein aggregation. Most studies of these systems have been performed in bulk, providing averaged measurements, though recent single-molecule approaches have provided an in-depth understanding of the molecular mechanisms of their activities and structural rearrangements during substrate recognition. Chaperone activities have been observed to be substrate specific, with some associated with ATP-dependent structural dynamics and others via interactions with co-chaperones. This Review aims to describe the novel mechanisms of molecular chaperones as revealed by single-molecule approaches, and to provide insights into their functioning and its implications for protein homeostasis and human diseases.

Globular Proteins and Where to Find Them within a Polymer Brush-A Case Study

Protein adsorption by polymerized surfaces is an interdisciplinary topic that has been approached in many ways, leading to a plethora of theoretical, numerical and experimental insight. There is a wide variety of models trying to accurately capture the essence of adsorption and its effect on the conformations of proteins and polymers. However, atomistic simulations are case-specific and computationally demanding. Here, we explore universal aspects of the dynamics of protein adsorption through a coarse-grained (CG) model, that allows us to explore the effects of various design parameters. To this end, we adopt the hydrophobic-polar (HP) model for proteins, place them uniformly at the upper bound of a CG polymer brush whose multibead-spring chains are tethered to a solid implicit wall. We find that the most crucial factor affecting the adsorption efficiency appears to be the polymer grafting density, while the size of the protein and its hydrophobicity ratio come also into play. We discuss the roles of ligands and attractive tethering surfaces to the primary adsorption as well as secondary and ternary adsorption in the presence of attractive (towards the hydrophilic part of the protein) beads along varying spots of the backbone of the polymer chains. The percentage and rate of adsorption, density profiles and the shapes of the proteins, alongside with the respective potential of mean force are recorded to compare the various scenarios during protein adsorption.

Varying molecular interactions explain aspects of crowder-dependent enzyme function of a viral protease

Biochemical processes in cells, including enzyme-catalyzed reactions, occur in crowded conditions with various background macromolecules occupying up to 40% of cytoplasm's volume. Viral enzymes in the host cell also encounter such crowded conditions as they often function at the endoplasmic reticulum membranes. We focus on an enzyme encoded by the hepatitis C virus, the NS3/4A protease, which is crucial for viral replication. We have previously found experimentally that synthetic crowders, polyethylene glycol (PEG) and branched polysucrose (Ficoll), differently affect the kinetic parameters of peptide hydrolysis catalyzed by NS3/4A. To gain understanding of the reasons for such behavior, we perform atomistic molecular dynamics simulations of NS3/4A in the presence of either PEG or Ficoll crowders and with and without the peptide substrates. We find that both crowder types make nanosecond long contacts with the protease and slow down its diffusion. However, they also affect the enzyme structural dynamics; crowders induce functionally relevant helical structures in the disordered parts of the protease cofactor, NS4A, with the PEG effect being more pronounced. Overall, PEG interactions with NS3/4A are slightly stronger but Ficoll forms more hydrogen bonds with NS3. The crowders also interact with substrates; we find that the substrate diffusion is reduced much more in the presence of PEG than Ficoll. However, contrary to NS3, the substrate interacts more strongly with Ficoll than with PEG crowders, with the substrate diffusion being similar to crowder diffusion. Importantly, crowders also affect the substrate-enzyme interactions. We observe that both PEG and Ficoll enhance the presence of substrates near the active site, especially near catalytic H57 but Ficoll crowders increase substrate binding more than PEG molecules.

Macromolecular Crowding Is More than Hard-Core Repulsions

Cells are crowded, but proteins are almost always studied in dilute aqueous buffer. We review the experimental evidence that crowding affects the equilibrium thermodynamics of protein stability and protein association and discuss the theories employed to explain these observations. In doing so, we highlight differences between synthetic polymers and biologically relevant crowders. Theories based on hard-core interactions predict only crowding-induced entropic stabilization. However, experiment-based efforts conducted under physiologically relevant conditions show that crowding can destabilize proteins and their complexes. Furthermore, quantification of the temperature dependence of crowding effects produced by both large and small cosolutes, including osmolytes, sugars, synthetic polymers, and proteins, reveals enthalpic effects that stabilize or destabilize proteins. Crowding-induced destabilization and the enthalpic component point to the role of chemical interactions between and among the macromolecules, cosolutes, and water. We conclude with suggestions for future studies. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Crowding affects structural dynamics and contributes to membrane association of the NS3/4A complex

Using molecular dynamics simulations, we describe how crowded environments affect the internal dynamics and diffusion of the hepatitis C virus proteases NS3/4A. This protease plays a key role in viral replication and is successfully used as a target for antiviral treatment. The NS3 enzyme requires a peptide cofactor, called NS4A, with its central part interacting with the NS3 β-sheet, and flexible, protruding terminal tails that are unstructured in water solution. The simulations describe the enzyme and water molecules at atomistic resolution, whereas crowders are modeled via either all-atom or coarse-grained models to emphasize different aspects of crowding. Crowders reflect the polyethylene glycol (PEG) molecules used in the experiments to mimic the crowded surrounding. A bead-shell model of folded coarse-grained PEG molecules considers mainly the excluded volume effect, whereas all-atom PEG models afford more protein-like crowder interactions. Circular dichroism spectroscopy experiments of the NS4A N-terminal tail show that a helical structure is formed in the presence of PEG crowders. The simulations suggest that crowding may assist in the formation of an NS4A helical fragment, positioned exactly where a transmembrane helix would fold upon the NS4A contact with the membrane. In addition, partially interactive PEGs help the NS4A N-tail to detach from the protease surface, thus enabling the process of helix insertion and potentially helping the virus establish a replication machinery needed to produce new viruses. Results point to an active role of crowding in assisting structural changes in disordered protein fragments that are necessary for their biological function.

Modeling Crowded Environment in Molecular Simulations

Biomolecules perform their various functions in living cells, namely in an environment that is crowded by many macromolecules. Thus, simulating the dynamics and interactions of biomolecules should take into account not only water and ions but also other binding partners, metabolites, lipids and macromolecules found in cells. In the last decade, research on how to model macromolecular crowders around proteins in order to simulate their dynamics in models of cellular environments has gained a lot of attention. In this mini-review we focus on the models of crowding agents that have been used in computer modeling studies of proteins and peptides, especially via molecular dynamics simulations.

GroEL Ring Separation and Exchange in the Chaperonin Reaction

The bacterial chaperonin GroEL and its cofactor, GroES, form a nano-cage for a single molecule of substrate protein (SP) to fold in isolation. GroEL and GroES undergo an ATP-regulated interaction cycle to close and open the folding cage. GroEL consists of two heptameric rings stacked back to back. Here, we show that GroEL undergoes transient ring separation, resulting in ring exchange between complexes. Ring separation occurs upon ATP-binding to the trans ring of the asymmetric GroEL:7ADP:GroES complex in the presence or absence of SP and is a consequence of inter-ring negative allostery. We find that a GroEL mutant unable to perform ring separation is folding active but populates symmetric GroEL:GroES₂ complexes, where both GroEL rings function simultaneously rather than sequentially. As a consequence, SP binding and release from the folding chamber is inefficient, and E. coli growth is impaired. We suggest that transient ring separation is an integral part of the chaperonin mechanism.

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.

Coarse-Grained Models for Protein-Cell Membrane Interactions

The physiological properties of biological soft matter are the product of collective interactions, which span many time and length scales. Recent computational modeling efforts have helped illuminate experiments that characterize the ways in which proteins modulate membrane physics. Linking these models across time and length scales in a multiscale model explains how atomistic information propagates to larger scales. This paper reviews continuum modeling and coarse-grained molecular dynamics methods, which connect atomistic simulations and single-molecule experiments with the observed microscopic or mesoscale properties of soft-matter systems essential to our understanding of cells, particularly those involved in sculpting and remodeling cell membranes.

Protein crowding affects hydration structure and dynamics

The effect of protein crowding on the structure and dynamics of water was examined from explicit solvent molecular dynamics simulations of a series of protein G and protein G/villin systems at different protein concentrations. Hydration structure was analyzed in terms of radial distribution functions, three-dimensional hydration sites, and preservation of tetrahedral coordination. Analysis of hydration dynamics focused on self-diffusion rates and dielectric constants as a function of crowding. The results show significant changes in both structure and dynamics of water under highly crowded conditions. The structure of water is altered mostly beyond the first solvation shell. Diffusion rates and dielectric constants are significantly reduced following linear trends as a function of crowding reflecting highly constrained water in crowded environments. The reduced dynamics of diffusion is expected to be strongly related to hydrodynamic properties of crowded cellular environments while the reduced dielectric constant under crowded conditions has implications for the stability of biomolecules in crowded environments. The results from this study suggest a prescription for modeling solvation in simulations of cellular environments.

Three-dimensional stochastic off-lattice model of binding chemistry in crowded environments

Molecular crowding is one of the characteristic features of the intracellular environment, defined by a dense mixture of varying kinds of proteins and other molecules. Interaction with these molecules significantly alters the rates and equilibria of chemical reactions in the crowded environment. Numerous fundamental activities of a living cell are strongly influenced by the crowding effect, such as protein folding, protein assembly and disassembly, enzyme activity, and signal transduction. Quantitatively predicting how crowding will affect any particular process is, however, a very challenging problem because many physical and chemical parameters act synergistically in ways that defy easy analysis. To build a more realistic model for this problem, we extend a prior stochastic off-lattice model from two-dimensional (2D) to three-dimensional (3D) space and examine how the 3D results compare to those found in 2D. We show that both models exhibit qualitatively similar crowding effects and similar parameter dependence, particularly with respect to a set of parameters previously shown to act linearly on total reaction equilibrium. There are quantitative differences between 2D and 3D models, although with a generally gradual nonlinear interpolation as a system is extended from 2D to 3D. However, the additional freedom of movement allowed to particles as thickness of the simulation box increases can produce significant quantitative change as a system moves from 2D to 3D. Simulation results over broader parameter ranges further show that the impact of molecular crowding is highly dependent on the specific reaction system examined.

Unified regression model of binding equilibria in crowded environments

Molecular crowding is a critical feature distinguishing intracellular environments from idealized solution-based environments and is essential to understanding numerous biochemical reactions, from protein folding to signal transduction. Many biochemical reactions are dramatically altered by crowding, yet it is extremely difficult to predict how crowding will quantitatively affect any particular reaction systems. We previously developed a novel stochastic off-lattice model to efficiently simulate binding reactions across wide parameter ranges in various crowded conditions. We now show that a polynomial regression model can incorporate several interrelated parameters influencing chemistry under crowded conditions. The unified model of binding equilibria accurately reproduces the results of particle simulations over a broad range of variation of six physical parameters that collectively yield a complicated, non-linear crowding effect. The work represents an important step toward the long-term goal of computationally tractable predictive models of reaction chemistry in the cellular environment.

Crowding effects on protein association: effect of interactions between crowding agents

The cell cytoplasm is a dense environment where the presence of inert cosolutes can significantly alter the rates of protein folding and protein association reactions. Most theoretical studies focus on hard sphere crowding agents and quantify the effect of excluded volume on reaction rates. In this work the effect of interactions between the crowding agents on the thermodynamics of protein association is studied using computer simulation. Three cases are considered, where the crowding agents are (i) hard spheres, (ii) hard spheres with additional attractive or repulsive interactions, and (iii) chains of hard spheres. Reactants and products of the protein association are modeled as hard spheres. Although crowding effects are sensitive to the shape of the reaction product, in most cases the excess free energy difference between the product and reactants (nonideality factor) is insensitive to the interactions between crowding agents, due to a cancellation of effects. The simulations therefore suggest that the hard sphere model of crowding agents has a surprisingly large regime of validity and should be sufficient for a qualitative understanding of the thermodynamics of crowding effects when the interactions of associating proteins with crowding agents other than excluded volume interactions are not significant.

Models of macromolecular crowding effects and the need for quantitative comparisons with experiment

In recent years significant effort has been devoted to exploring the potential effects of macromolecular crowding on protein folding and association phenomena. Theoretical calculations and molecular simulations have, in particular, been exploited to describe aspects of protein behavior in crowded and confined conditions and many aspects of the simulated behavior have reflected, at least at a qualitative level, the behavior observed in experiments. One major and immediate challenge for the theorists is to now produce models capable of making quantitatively accurate predictions of in vitro behavior. A second challenge is to derive models that explain results obtained from experiments performed in vivo, the results of which appear to call into question the assumed dominance of excluded-volume effects in vivo.

Effects of macromolecular crowding on intracellular diffusion from a single particle perspective

Compared to biochemical reactions taking place in relatively well-defined aqueous solutions in vitro, the corresponding reactions happening in vivo occur in extremely complex environments containing only 60-70% water by volume, with the remainder consisting of an undefined array of bio-molecules. In a biological setting, such extremely complex and volume-occupied solution environments are termed 'crowded'. Through a range of intermolecular forces and pseudo-forces, this complex background environment may cause biochemical reactions to behave differently to their in vitro counterparts. In this review, we seek to highlight how the complex background environment of the cell can affect the diffusion of substances within it. Engaging the subject from the perspective of a single particle's motion, we place the focus of our review on two areas: (1) experimental procedures for conducting single particle tracking experiments within cells along with methods for extracting information from these experiments; (2) theoretical factors affecting the translational diffusion of single molecules within crowded two-dimensional membrane and three-dimensional solution environments. We conclude by discussing a number of recent publications relating to intracellular diffusion in light of the reviewed material.

Reconciling theories of chaperonin accelerated folding with experimental evidence

For the last 20 years, a large volume of experimental and theoretical work has been undertaken to understand how chaperones like GroEL can assist protein folding in the cell. The most accepted explanation appears to be the simplest: GroEL, like most other chaperones, helps proteins fold by preventing aggregation. However, evidence suggests that, under some conditions, GroEL can play a more active role by accelerating protein folding. A large number of models have been proposed to explain how this could occur. Focused experiments have been designed and carried out using different protein substrates with conclusions that support many different mechanisms. In the current article, we attempt to see the forest through the trees. We review all suggested mechanisms for chaperonin-mediated folding and weigh the plausibility of each in light of what we now know about the most stringent, essential, GroEL-dependent protein substrates.

Parameter effects on binding chemistry in crowded media using a two-dimensional stochastic off-lattice model

The intracellular environment imposes a variety of constraints on biochemical reaction systems that can substantially change reaction rates and equilibria relative to an ideal solution-based environment. One of the most notable features of the intracellular environment is its dense macromolecular crowding, which, among many other effects, tends to strongly enhance binding and assembly reactions. Despite extensive study of biochemistry in crowded media, it remains extremely difficult to predict how crowding will quantitatively affect any given reaction system due to the dependence of the crowding effect on numerous assumptions about the reactants and crowding agents involved. We previously developed a two dimensional stochastic off-lattice model of binding reactions based on the Green's function reaction dynamics method in order to create a versatile simulation environment in which one can explore interactions among many parameters of a crowded assembly system. In the present work, we examine interactions among several critical parameters for a model dimerization system: the total concentration of reactants and inert particles, the binding probability upon a collision between two reactant monomers, the mean time of dissociation reactions, and the diffusion coefficient of the system. Applying regression models to equilibrium constants across parameter ranges shows that the effect of the total concentration is approximately captured by a low-order nonlinear polynomial model, while the other three parameter effects are each accurately captured by a linear model. Furthermore, validation on tests with multi-parameter variations reveals that the effects of these parameters are separable from one another over a broad range of variation in all four parameters. The simulation work suggests that predictive models of crowding effects can accommodate a wider variety of parameter variations than prior theoretical models have so far achieved.

Modulation of calmodulin plasticity by the effect of macromolecular crowding

In vitro biochemical reactions are most often studied in dilute solution, a poor mimic of the intracellular space of eukaryotic cells, which are crowded with mobile and immobile macromolecules. Such crowded conditions exert volume exclusion and other entropic forces that have the potential to impact chemical equilibria and reaction rates. In this article, we used the well-characterized and ubiquitous molecule calmodulin (CaM) and a combination of theoretical and experimental approaches to address how crowding impacts CaM's conformational plasticity. CaM is a dumbbell-shaped molecule that contains four EF hands (two in the N-lobe and two in the C-lobe) that each could bind Ca(2+), leading to stabilization of certain substates that favor interactions with other target proteins. Using coarse-grained molecular simulations, we explored the distribution of CaM conformations in the presence of crowding agents. These predictions, in which crowding effects enhance the population of compact structures, were then confirmed in experimental measurements using fluorescence resonance energy transfer techniques of donor- and acceptor-labeled CaM under normal and crowded conditions. Using protein reconstruction methods, we further explored the folding-energy landscape and examined the structural characteristics of CaM at free-energy basins. We discovered that crowding stabilizes several different compact conformations, which reflects the inherent plasticity in CaM's structure. From these results, we suggest that the EF hands in the C-lobe are flexible and can be thought of as a switch, while those in the N-lobe are stiff, analogous to a rheostat. New combinatorial signaling properties may arise from the product of the differential plasticity of the two distinct lobes of CaM in the presence of crowding. We discuss the implications of these results for modulating CaM's ability to bind Ca(2+) and target proteins.

Macromolecular crowding modulates folding mechanism of alpha/beta protein apoflavodoxin

Protein dynamics in cells may be different from those in dilute solutions in vitro, because the environment in cells is highly concentrated with other macromolecules. This volume exclusion because of macromolecular crowding is predicted to affect both equilibrium and kinetic processes involving protein conformational changes. To quantify macromolecular crowding effects on protein folding mechanisms, we investigated the folding energy landscape of an alpha/beta protein, apoflavodoxin, in the presence of inert macromolecular crowding agents, using in silico and in vitro approaches. By means of coarse-grained molecular simulations and topology-based potential interactions, we probed the effects of increased volume fractions of crowding agents (phi(c)) as well as of crowding agent geometry (sphere or spherocylinder) at high phi(c). Parallel kinetic folding experiments with purified Desulfovibro desulfuricans apoflavodoxin in vitro were performed in the presence of Ficoll (sphere) and Dextran (spherocylinder) synthetic crowding agents. In conclusion, we identified the in silico crowding conditions that best enhance protein stability, and discovered that upon manipulation of the crowding conditions, folding routes experiencing topological frustrations can be either enhanced or relieved. Our test-tube experiments confirmed that apoflavodoxin's time-resolved folding path is modulated by crowding agent geometry. Macromolecular crowding effects may be a tool for the manipulation of protein-folding and function in living cells.

Effect of mixed macromolecular crowding agents on protein folding

In cells, proteins fold and unfold in the presence of macromolecules with various sizes and shapes. Recent experiments by Liang and coworkers (J Biol Chem 2004;279:55109-55116; J Mol Biol 2006;364:469-482) show that protein refolding is enhanced by a mixture of two different crowding agents relative to the individual crowding agents and an optimal mixing ratio exists. Here, we present a theory that predicts the existence of an optimal mixing ratio. The theory is based on models for calculating the changes in the chemical potentials of the folded and unfolded states by a mixture of crowders. The existence of an optimal mixing ratio results from the dependences of these chemical-potential changes on crowder sizes and concentrations, which can be argued to be quite general. We further predict that, for any crowding agent, the stabilizing effect can be optimized both by varying the molecular weight and the mixing ratio of two species with different molecular weights.

Stochastic off-lattice modeling of molecular self-assembly in crowded environments by Green's function reaction dynamics

The environment inside a living cell is dramatically different from that found in in vitro models, presenting a problem for computational models of biochemistry that are only beginning to capture these differences. This deviation between idealized in vitro models and more realistic intracellular conditions is particularly problematic for models of molecular self-assembly, but also specifically hard to address because the large sizes and long assembly times of biological self-assembly systems force the use of highly simplified models. We have developed a prototype of a molecular self-assembly simulator based on the Green's function reaction dynamics (GFRD) model to achieve more realistic models of assembly in the crowded conditions of the cell without unduly sacrificing tractability. We tested the model on a simple representation of dimer assembly in a two-dimensional space. Our simulations verify that the model is computationally efficient, provides a realistic quantitative model of reaction kinetics in uncrowded conditions, and exhibits expected excluded volume effects under conditions of high crowding. This work confirms the effectiveness of the GFRD technique for more realistic coarse-grained modeling of self-assembly in crowded conditions and helps lay the groundwork for exploring the effects of in vivo crowding on more complex assembly systems.

Influence of macromolecular crowding on protein-protein association rates--a Brownian dynamics study

The high total concentration of macromolecules, often referred to as macromolecular crowding, is one of the characteristic features of living cells. Macromolecular crowding influences interactions between many types of macromolecules, with consequent effects on, among others, the rates of reactions occurring in the cell. Simulations to study the influence of crowding on macromolecular association rate were performed using a modified Brownian dynamics protocol. The calculated values of the time-dependent self-diffusion coefficients in different crowding conditions are in a very good agreement with those obtained by other authors. Simulations of the complex formation between the monoclonal antibody HyHEL-5 and its antigen hen egg lysozyme, both represented at atomic level detail, show that the calculated association rates strongly depend on the volume excluded by crowding. The rate obtained for the highest concentration of crowding particles is greater than twofold higher than the rate for proteins without crowding.

Toward realistic modeling of dynamic processes in cell signaling: quantification of macromolecular crowding effects

One of the major factors distinguishing molecular processes in vivo from biochemical experiments in vitro is the effect of the environment produced by macromolecular crowding in the cell. To achieve a realistic modeling of processes in the living cell based on biochemical data, it becomes necessary, therefore, to consider such effects. We describe a protocol based on Brownian dynamics simulation to characterize and quantify the effect of various forms of crowding on diffusion and bimolecular association in a simple model of interacting hard spheres. We show that by combining the elastic collision method for hard spheres and the mean field approach for hydrodynamic interaction (HI), our simulations capture the correct dynamics of a monodisperse system. The contributions from excluded volume effect and HI to the crowding effect are thus quantified. The dependence of the results on size distribution of each component in the system is illustrated, and the approach is applied as well to the crowding effect on electrostatic-driven association in both neutral and charged environments; values for effective diffusion constants and association rates are obtained for the specific conditions. The results from our simulation approach can be used to improve the modeling of cell signaling processes without additional computational burdens.

Tandem mass spectrometry of intact GroEL-substrate complexes reveals substrate-specific conformational changes in the trans ring

It has been suggested that the bacterial GroEL chaperonin accommodates only one substrate at any given time, due to conformational changes to both the cis and trans ring that are induced upon substrate binding. Using electrospray ionization mass spectrometry, we show that indeed GroEL binds only one molecule of the model substrate Rubisco. In contrast, the capsid protein of bacteriophage T4, a natural GroEL substrate, can occupy both rings simultaneously. As these substrates are of similar size, the data indicate that each substrate induces distinct conformational changes in the GroEL chaperonin. The distinctive binding behavior of Rubisco and the capsid protein was further investigated using tandem mass spectrometry on the intact 800-914 kDa GroEL-substrate complexes. Our data suggest that even in the gas phase the substrates remain bound inside the GroEL cavity. The analysis revealed further that binding of Rubisco to the GroEL oligomer stabilizes the chaperonin complex significantly, whereas binding of one capsid protein did not have the same effect. However, addition of a second capsid protein molecule to GroEL resulted in a similar stabilizing effect to that obtained after the binding of a single Rubisco. On the basis of the stoichiometry of the GroEL chaperonin-substrate complex and the dissociation behavior of the two different substrates, we hypothesize that the binding of a single capsid polypeptide does not induce significant conformational changes in the GroEL trans ring, and hence the unoccupied GroEL ring remains accessible for a second capsid molecule.

Atomically detailed simulations of concentrated protein solutions: the effects of salt, pH, point mutations, and protein concentration in simulations of 1000-molecule systems

An ability to accurately simulate the dynamic behavior of concentrated macromolecular solutions would be of considerable utility in studies of a wide range of biological systems. With this goal in mind, a Brownian dynamics (BD) simulation method is reported here that allows systems to be modeled that comprise in excess of 1000 protein molecules, all of which are treated in atomic detail. Intermolecular forces are described in the method using an energy function that incorporates electrostatic and hydrophobic interactions and that is calibrated to reproduce experimental thermodynamic information with a single adjustable parameter. Using the method, BD simulations have been performed over a wide range of pH and ionic strengths for three proteins: hen egg white lysozyme (HEWL), chymotrypsinogen, and T4 lysozyme. The simulations reproduce experimental trends in second virial coefficients (B(22)) and translational diffusion coefficients, correctly capture changes in B(22) values due to single amino acid substitutions, and reveal a new explanation for the difficulties reported previously in the literature in reproducing B(22) values for protein solutions of very low ionic strength. In addition, a strong correlation is found between a residue's probability of being involved in a protein-protein contact in the simulations and its probability of being involved in an experimental crystal contact. Finally, exploratory simulations of HEWL indicate that the simulation model also gives a promising description of behavior at very high protein concentrations (approximately 250 g/L), suggesting that it may provide a suitable computational framework for modeling the complex behavior exhibited by macromolecules in cellular conditions.

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.

Modeling 2D and 3D diffusion

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.

The influence of macromolecular crowding on HIV-1 protease internal dynamics

High macromolecular concentrations, or crowded conditions, have been shown to affect a wide variety of molecular processes, including diffusion, association and dissociation, and protein folding and stability. Here, we model the effect of macromolecular crowding on the internal dynamics of a protein, HIV-1 protease, using Brownian dynamics simulations. HIV-1 protease possesses a pair of flaps which are postulated to open in the early stages of its catalytic mechanism. Compared to low concentrations, close-packed concentrations of repulsive crowding agents are found to significantly reduce the fraction of time that the protease flaps are open. Macromolecular crowding is likely to have a major effect on in vivo enzyme activity, and may play an important regulatory role in the viral life cycle.

Fluorescence correlation spectroscopy simulations of photophysical phenomena and molecular interactions: a molecular dynamics/monte carlo approach

Fluorescence correlation spectroscopy (FCS) is being applied increasingly to study diffusion and interactions of fluorescently labeled macromolecules in complex biological systems. Fluctuations in detected fluorescence, deltaF(t), are expressed as time-correlation functions, G(tau), and photon-count histograms, P(k;DeltaT). Here, we developed a generalized simulation approach to compute G(tau) and P(k;DeltaT) for complex systems with arbitrary geometry, photophysics, diffusion, and macromolecular interactions. G(tau) and P(k;DeltaT) were computed from deltaF(t) generated by a Brownian dynamics simulation of single-molecule trajectories followed by a Monte Carlo simulation of fluorophore excitation and detection statistics. Simulations were validated by comparing analytical and simulated G(tau) and P(k;DeltaT) for diffusion of noninteracting fluorophores in a three-dimensional Gaussian excitation and detection volume. Inclusion of photobleaching and triplet-state relaxation produced significant changes in G(tau) and P(k;DeltaT). Simulations of macromolecular interactions and complex diffusion were done, including transient fluorophore binding to an immobile matrix, cross-correlation analysis of interacting fluorophores, and anomalous sub- and superdiffusion. The computational method developed here is generally applicable for simulating FCS measurements on systems complicated by fluorophore interactions or molecular crowding, and experimental protocols for which G(tau) and P(k;DeltaT) cannot be computed analytically.

Protein self-association in the cell: a mechanism for fine tuning the level of macromolecular crowding?

A new role for protein self-association in the cell is discussed. An argument is advanced that when cellular protein is in its associated state the excluded volume component of the solution is minimized. Conversely, when cellular protein is in its dissociated state the excluded volume component of the solution is maximized. For proteins that make up a substantial fraction of the intracellular protein concentration, control of the self-association event thus presents itself as a means of regulating cellular processes that are influenced by different levels of volume exclusion. In this communication we examine how the control of protein association/dissociation might influence one such important process, namely the folding of a protein to a compact state.

Space in systems biology of signaling pathways--towards intracellular molecular crowding in silico

How cells utilize intracellular spatial features to optimize their signaling characteristics is still not clearly understood. The physical distance between the cell-surface receptor and the gene expression machinery, fast reactions, and slow protein diffusion coefficients are some of the properties that contribute to their intricacy. This article reviews computational frameworks that can help biologists to elucidate the implications of space in signaling pathways. We argue that intracellular macromolecular crowding is an important modeling issue, and describe how recent simulation methods can reproduce this phenomenon in either implicit, semi-explicit or fully explicit representation.

Specificity in lipases: a computational study of transesterification of sucrose

Computational conformational searches of putative transition states of the reaction of sucrose with vinyl laurate catalyzed by lipases from Candida antarctica B and Thermomyces lanuginosus have been carried out. The dielectric of the media have been varied to understand the role of protein plasticity in modulating the observed regioselective transesterification. The binding pocket of lipase from Candida adapts to the conformational variability of the various substates of the substrates by small, local adjustments within the binding pocket. In contrast, the more constrained pocket of the lipase from Thermomyces adapts by adjusting through concerted global motions between subdomains. This leads to the identification of one large pocket in Candida that accommodates both the sucrose and the lauroyl moieties of the transition state, whereas in Thermomyces the binding pocket is smaller, leading to the localization of the two moieties in two distinct pockets; this partly rationalizes the broader specificity of the former relative to the latter. Mutations have been suggested to exploit the differences towards changing the observed selectivities.

Mixed macromolecular crowding accelerates the oxidative refolding of reduced, denatured lysozyme: implications for protein folding in intracellular environments

The oxidative refolding of reduced, denatured hen egg white lysozyme in the presence of a mixed macromolecular crowding agent containing both bovine serum albumin (BSA) and polysaccharide has been studied from a physiological point of view. When the total concentration of the mixed crowding agent is 100 g/liter, in which the weight ratio of BSA to dextran 70 is 1:9, the refolding yield of lysozyme after refolding for 4 h under this condition increases 24% compared with that in the presence of BSA and 16% compared with dextran 70. A remarkable increase in the refolding yield of lysozyme by a mixed crowding agent containing BSA and Ficoll 70 is also observed. Further folding kinetics analyses show that these two mixed crowding agents accelerate the oxidative refolding of lysozyme remarkably, compared with single crowding agents. These results suggest that the stabilization effects of mixed macromolecular crowding agents are stronger than those of single polysaccharide crowding agents such as dextran 70 and Ficoll 70, whereas the excluded volume effects of mixed macromolecular crowding agents are weaker than those of single protein crowding agents such as BSA. Both the refolding yield and the rate of the oxidative refolding of lysozyme in these two mixed crowded solutions with suitable weight ratios are higher than those in single crowded solutions, indicating that mixed macromolecular crowding agents are more favorable to lysozyme folding and can be used to simulate the intracellular environments more accurately than single crowding agents do.

Loops, linkages, rings, catenanes, cages, and crowders: entropy-based strategies for stabilizing proteins

A protein molecule exists in either a compact folded state or a variable and open unfolded state. Since the unfolded state is favored by chain entropy, restricting its entropy is an attractive mechanism for shifting the equilibrium toward the folded state. A number of entropy-based strategies have been engineered or used by natural proteins to increase the folding stability: (a) shortening of loop lengths, (b) covalent linkage of dimeric proteins, (c) backbone cyclization, (d) catenation, (e) spatial confinement, and (f) macromolecular crowding. Theoretical analyses demonstrate the importance of accounting for consequences on the folded as well as the unfolded state and provide guidance for further exploitation of these stabilization strategies.

Macromolecular crowding: qualitative and semiquantitative successes, quantitative challenges

The concept of excluded volume and the theory of effects of excluded volume on the equilibria and rates of macromolecular reactions in fluid media containing high total concentrations of macromolecules ('crowded' media) are summarized. Reports of experimental studies of crowding effects published during the last year are tabulated. Limitations of current excluded volume theory are discussed, and a determination is made of conditions under which this theory may and may not be validly applied. Recently suggested novel approaches to quantitative analysis of crowding phenomena, which may help to overcome some of the limitations of current theory, are summarized.