Computer simulations of the bacterial cytoplasm

Abstract

Ever since the pioneering work of Minton, it has been recognized that the highly crowded interior of biological cells has the potential to cause dramatic changes to both the kinetics and thermodynamics of protein folding and association events relative to behavior that might be observed in dilute solution conditions. One very productive way to explore the effects of crowding on protein behavior has been to use macromolecular crowding agents that exclude volume without otherwise strongly interacting with the protein under study. An alternative, complementary approach to understanding the potential differences between behavior in vivo and in vitro is to develop simulation models that explicitly attempt to model intracellular environments at the molecular scale, and that thereby can be used to directly monitor biophysical behavior in conditions that accurately mimic those encountered in vivo. It is with studies of this type that the present review will be concerned. We review in detail four published studies that have attempted to simulate the structure and dynamics of the bacterial cytoplasm and that have each explored different biophysical aspects of the cellular interior. While each of these studies has yielded important new insights, there are important questions that remain to be resolved in terms of determining the relative contributions made by energetic and hydrodynamic interactions to the diffusive behavior of macromolecules and to the thermodynamics of protein folding and associations in vivo. Some possible new directions for future generation simulation models of the cytoplasm are outlined.

Introduction

An important current goal in molecular biophysics is to determine the extent to which protein behavior in vitro reflects that occurring in vivo. Thanks in large part to the work of Minton (Zimmerman and Minton 1993; Minton 2001), it is now established that there are good theoretical reasons to anticipate that the highly crowded intracellular environment might significantly alter the thermodynamics and kinetics of biophysical processes such as protein folding, association and diffusion (see, e.g., the reviews of Zhou et al. 2008; Dix and Verkman 2008; Elcock 2010; Gershenson and Gierasch 2011; Mika and Poolman 2011). In order to directly study biophysical behavior in living cells and to thereby bridge the gap in knowledge between the in vitro and in vivo realms, a number of exciting applications of experimental techniques such as hydrogen exchange (Ghaemmaghami and Oas 2001; Wang et al. 2012b), ‘in-cell’ NMR (Reckel et al. 2007; Pielak et al. 2009; Wang et al. 2011; Robinson et al. 2012), and fluorescence (Ignatova and Gierasch 2004; Golding and Cox 2006; Xie et al. 2008; Ebbinghaus et al. 2010; Dhar et al. 2011; Phillip et al. 2012) have been reported. These types of studies have provided unprecedented insights into biophysical behavior in vivo. They also, however, present significant technical challenges in terms of execution, resolution and interpretation (e.g., Serber et al. 2001; Malchus and Weiss 2010; Barnes and Pielak 2011; Crowley et al. 2011; Padilla-Parra and Tramier 2012); in addition, they typically allow only one or a few types of macromolecule to be studied at a time.

In principle, computer simulations of molecular-level models of intracellular environments can provide a useful complement to these experimental techniques. The major potential advantages of such simulations are that (1) many different types of biomolecules can be observed simultaneously (there is no need, for example, to use fluorescent tags), and (2) the impact of the many possible aspects of macromolecular crowding—excluded volume effects, nonspecific energetic interactions, hydrodynamic interactions, and even shape effects—can all be individually assessed by either switching on or off interaction terms or by changing the structural resolution (‘coarse-graining’) of the model. There is therefore significant interest in developing simulation models of intracellular environments, and a handful of simulation studies have already been reported that have attempted to model both the structure and dynamics of the bacterial cytoplasm (Bicout and Field 1996; Ridgway et al. 2008; McGuffee and Elcock 2010; Ando and Skolnick 2010). The cytoplasm of the Gram-negative bacterium Escherichia coli, in particular, has several characteristics that make it an attractive candidate as a ‘model’ intracellular environment: it has a total macromolecular concentration of ∼300–400 g/l (Zimmerman and Trach 1991), its macromolecular and small-solute contents are well characterized (Goodsell 1991; Link et al. 1997; Lopez-Campistrous et al. 2005; Bennett et al. 2009), and 3D structures are readily available for many of the most highly abundant proteins (and RNAs). This review will briefly summarize each of the principal simulation studies of the bacterial cytoplasm published at the time of writing, will outline the advantages and limitations of each study, and will discuss a number of possible future directions. At the outset, it is worth noting that although a large number of simulation studies have already explored the effects of macromolecular crowding on biophysical behavior, for space reasons we will focus here exclusively on studies that have explicitly attempted to simulate the cytoplasm; for the same reason, we do not review interesting simulation studies that have been performed of protein diffusion through static models of the cytoplasm on the scale of entire bacterial cells (Lipkow et al. 2005; Roberts et al. 2009).

Dynamic models of the cytoplasm

The first bona fide attempt to perform a computer simulation of the bacterial cytoplasm was reported by Bicout and Field in 1996. Guided by approximate physiological macromolecular concentrations noted in David Goodsell’s influential review (1991), the cytoplasm was modeled as a mixture of three macromolecular components: ribosomes, tRNAs, and proteins. All three components were modeled as spherical particles of appropriate mass and radius, with the heterogeneous protein population modeled as a single type of protein, with a size of 160 kDa and a guessed net charge of −4e. A total of 12 ribosomes, 136 tRNAs and 188 ‘protein’ molecules were simulated in cubic periodic boundary conditions, with dimensions set so that the volume fraction occupied by the macromolecules was 20 %. Interactions between the macromolecules were modeled as a combination of (1) short-range dispersive and steric interactions, and (2) long-range electrostatic interactions, modeled with DLVO (Derjaguin-Landau-Verwey-Overbeek) potentials. Owing to uncertainties in how to treat the charge properties of the ribosomes, three separate simulation models were investigated with the ribosome net charges set to −2, −500, and −1,000e respectively; the net charge on the tRNA molecules was in all cases set to −75e. In order to assess the overall effect of electrostatic interactions on the observed behavior, an additional simulation model was constructed in which the net charges on all molecule types were set to zero.

Having defined the intermolecular potential functions used in each simulation model, the authors used Langevin dynamics techniques to simulate the motion of the cytoplasm macromolecules on a timescale of 7.5 μs. In this simulation approach, the solvent is represented implicitly as a structureless dielectric continuum, and macromolecules move according to a combination of: (1) forces acting on them from interactions with nearby particles, (2) random forces that mimic the effects of collisions with the missing solvent molecules, and (3) frictional forces that are proportional to the particle’s velocity. A variety of structural and dynamic properties of the cytoplasm models were measured by Bicout and Field: these included radial distribution functions for each type of interaction (ribosome–protein, ribosome–tRNA, ribosome–ribosome, etc.), so-called ‘neighborship distribution functions’ (Mazur 1992), structure factors, and long-time translational self-diffusion and collective-diffusion coefficients. The radial distribution functions obtained for the different types of intermolecular interactions exhibited relatively sharp peaks at close separation distances but generally were devoid of peaks at longer separation distances, indicating that the distribution of molecules beyond the first shell of neighbors was essentially homogeneous. This view was reinforced by an analysis of the neighborship distribution functions, which suggested that the molecules of the cytoplasm model were in a random, close-packed state with each protein having, on average, approximately four to six neighbors. With all four simulation models, the long-time translational diffusion coefficient, , of the prototypical protein molecules was slowed to a factor of ∼0.60 to 0.66 relative to the infinite dilution value and was relatively insensitive to the way in which the ribosome’s electrostatic properties were modeled; in an interesting contrast, however, the tRNA value was very sensitive to the ribosome’s charge properties, decreasing from a factor of ∼0.80 (relative to the infinite dilution value) in the absence of electrostatic interactions, to ∼0.48 when the ribosomes were modeled with a net charge of −1,000e.

From subsequent experimental work we now know that the ∼35–40 % decrease in the protein value observed in Bicout and Field’s simulations is much less pronounced than it should be: the experimental of GFP (Green Fluorescent Protein) measured in vivo, for example, is approximately 10-fold lower than that measured in vitro (Elowitz et al. 1999; Mullineaux et al. 2006; Konopka et al. 2006, 2009). This suggests, of course, that something is fundamentally missing from the simulation model (see below), but it is important to stress that, since the experimental data did not exist at the time the study was conducted, the authors could not use this information to guide the parameterization of their simulation model. Literally and figuratively, therefore, the simulations of Bicout and Field were a number of years ahead of their time.

The next reported simulation study of the bacterial cytoplasm, performed by the Ellison group (Ridgway et al. 2008), is notable for using physiological concentrations of macromolecules estimated from their own proteomics studies of E. coli (Lopez-Campistrous et al. 2005), for exploring effects on both diffusion and rates of protein–protein associations, and for the sheer size of the simulations: 1.7 million particles were included in the largest simulation reported. In order to construct their ‘virtual cytoplasm’ model, the authors selected 118 of the most numerous, non-ribosomal proteins and sorted them by mass into groups in 20-kDa increments up to 200 kDa, with proteins that exceeded 200 kDa and ribosomes forming two additional groups. Macromolecules within each group were then modeled—as in the Bicout and Field study—as spherical particles with radii appropriate to the average properties of the macromolecules in the group.

Although the macromolecular models used in the study by Ridgway et al. were structurally similar to those used by Bicout and Field, a considerably more simplified description of their intermolecular interactions was employed: only steric (i.e. excluded volume) interactions were monitored. Simplifications were also made to the algorithms used to model the motion of the macromolecules (see below) and to model their association and dissociation reactions; as a result, much of the work was focused on demonstrating the validity of the approximate methods used in the simulations. With the range of applicability of the methods determined, however, the authors were able to perform some very large-scale simulations, with the largest such system having a volume comparable to that of an entire E. coli cell.

One of the primary motivations of the work was to assess the effects of excluded volume interactions on the diffusion of macromolecules in vivo. In order to do this, a simplified algorithm for modeling movement was employed. Molecules were moved one at a time with a uniform step size but in randomly chosen directions, with the probability of each macromolecule being subjected to a trial move at a given timestep being set in such a way that, in a simulation of a single such macromolecule, its diffusion coefficient would reproduce the value expected at infinite dilution. Having conducted a trial move of a particular molecule, potential reactions with neighboring molecules (e.g., association) were determined probabilistically, before a search for steric collisions was carried out. Any trial move that resulted in a steric collision with another molecule was rejected, with the result being that the effective translational diffusion coefficient of the molecule in a crowded system would be reduced relative to its infinite-dilution value.

Simulations of the cytoplasm model were run at volume fractions ranging from 1 to 50 %. Translational diffusion was found to be transiently anomalous, meaning that the computed diffusion coefficients were dependent upon the timescale over which the diffusion was monitored. For the smaller molecules, a clear finite-size effect was also noted at long observation intervals, reflecting the fact that these proteins were able to traverse the entire simulation cell (a 1-μm³ cube with reflecting boundary conditions) over the course of the simulation. More importantly, the authors found that larger macromolecules suffered a greater decrease in their long-time translational diffusion coefficients as the level of crowding increased—presumably because their trial moves were more likely to be rejected due to steric collisions than those of smaller molecules—and found that the value of GFP-sized macromolecules was slowed by only a factor of ∼2 at a volume fraction thought to be representative of that encountered in vivo (34 %). As in the work of Bicout and Field, therefore, the simulations were not able to reproduce the ∼10-fold reduction in translational diffusion observed experimentally for GFP. This led the authors to draw the important conclusion that effects additional to excluded volume effects would be necessary to quantitatively reproduce rates of macromolecular diffusion in vivo.

A second important aspect of the study by Ridgway et al. was to consider the effects of the crowded intracellular environment on the rates of association of the ribonuclease barnase with its protein inhibitor barstar. To model this process, ∼11,000 spheres representing the two proteins were randomly distributed in a box and spheres representing the cytoplasm constituents were added to give additional volume fractions of 30 and 50 %. The reaction probability for the barnase-barstar association was set to unity, meaning that whenever copies of the two proteins came within contact distance they would be assumed to form an (irreversible) complex; this has the effect of modeling the reaction—correctly—as being fully diffusion-limited (Schreiber and Fersht 1996). The authors monitored the ‘survival probability’ of barnase molecules (i.e. the population of uncomplexed molecules) as a function of time during simulations and found that the rate of association with barstar molecules was accelerated at short time scales but decelerated at long time scales. The former effect is presumably due to the rapid association of barnase and barstar molecules that—due to their initially random placement—happen to be close to one another at the beginning of the simulation and that are therefore effectively trapped within a single ‘cage’ formed by their cytoplasmic neighbors. The latter effect must be due to the association of barnase and barstar molecules that are initially more distant from one another and that must, therefore, find each other by slow diffusion through the crowded cytoplasm.

The cytoplasm models of Bicout and Field and Ridgway et al. both approximated all macromolecules as spherical particles. The first cytoplasm model to add structural detail to the macromolecules was reported by McGuffee and Elcock (2010). Here, as in the Ridgway et al. model, quantitative proteomics data were used to select which macromolecules to include in the model and to determine how many copies of each should be added. In this case, 45 of the most abundant proteins identified in the seminal proteomics study carried out by the Church group (Link et al. 1997) were selected for inclusion. To this list were added the large and small ribosomal subunits, three types of tRNA, and the non-E. coli protein GFP, to give a total of 50 different types of macromolecule; all these were represented by atomically-detailed models, either using bona fide E. coli crystal structures, or using homology-modeled structures. In total, 1,000 E. coli macromolecules plus 8 GFP molecules were modeled under periodic boundary conditions at a total macromolecular concentration of 275 g/l.

Similar to the model of Bicout and Field, intermolecular interactions were modeled using a combination of Lennard–Jones potentials and long-range electrostatic interactions. In the model of McGuffee and Elcock, however, these interactions were computed on an atom-by-atom basis with the result that intermolecular interactions could be highly anisotropic, and would naturally reflect effects due to differences in molecular shape and differences in the distributions of hydrophobic and charged residues. For modeling electrostatic interactions, the rapid but accurate Poisson–Boltzmann-based ‘effective charge’ electrostatic model conceived and developed by Gabdoulline and Wade (1996) was used: this model places charges at the positions of all ionizable residues and adjusts their values so as to reproduce the electrostatic potential calculated from a complete all-atom model of the molecule. For modeling short-range hydrophobic interactions, Lennard–Jones potentials were included between pairs of solvent-exposed non-polar atoms; the well depth (ε) assigned to these potentials was made an adjustable parameter and was varied until the long-time translational diffusion coefficient of GFP in dynamics simulations (see below) matched the values measured in vivo. To provide a point of comparison, a simpler, alternative simulation model was also explored in which only steric interactions were modeled. Following McGuffee and Elcock, in what follows the fully parameterized energy model containing hydrophobic, electrostatic, and steric interactions will be termed the ‘full’ energy model, while the model containing only excluded volume interactions will be referred to as the ‘steric’ model.

The motion of the macromolecules was simulated using the Brownian dynamics (BD) algorithm derived by Ermak and McCammon (1978). Key to the feasibility of the study was the use of a modified version of the fast rigid-body BD simulation software originally developed by Gabdoulline and Wade (1997), and very kindly made available to the authors. In line with the results previously obtained by both Bicout and Field (1996) and by Ridgway et al. (2008), BD simulations using the steric model produced a value for GFP that was reduced by only a factor of ∼2 relative to the infinite-dilution value, and which, therefore, was several-fold too high relative to the experimentally measured values. The inclusion of electrostatic interactions between macromolecules caused a further modest decrease in the value (a factor of ∼3 reduction relative to the infinite-dilution value), but it was only when substantial short-range attractive interaction terms between exposed non-polar groups were added that the in vivo value was correctly captured. Interestingly, the optimal value derived for ε was quite similar to that derived in a previous study—performed with the same BD simulation model—aimed at reproducing the osmotic second virial coefficients of single-component protein solutions (McGuffee and Elcock 2006).

With the energy model parameterized, three independent BD simulations of the cytoplasm, differing only in the initial (random) placement of the molecules, were each carried out for 15 μs. Reflecting the idea expressed in the “Introduction”, that simulations can allow many different types of molecules to be studied simultaneously, the BD simulations provided a number of insights into the dynamic behavior of the very different types of molecules included in the model. As was previously seen in the study of Ridgway et al., the translational diffusion coefficients of larger molecules tended be more strongly decreased by immersion in the cytoplasm than did those of smaller molecules, although, interestingly, the correlation between the diffusional slowdown and the molecular weight was noticeably less good in the simulations that used the ‘full’ energy model: this suggests that the sensitivity of a macromolecule’s diffusion coefficient to crowded intracellular conditions may not depend only on its size (see below). Analysis of the intermolecular contacts sampled during the simulations indicated that the population of macromolecules contacting each GFP molecule underwent ∼14 complete exchanges over the 15-μs simulation period. Finally, comparisons of the cytoplasm’s effects on translational and rotational diffusion showed that the two types of motion experienced different effective viscosities: depending on the macromolecule, the effective translational viscosity was found to be ∼1.5–5 times higher than the effective rotational viscosity, which compared quite well with the value of 2.6 obtained from experimental measurements of apomyoglobin diffusion in concentrated solutions of human serum albumin (Zorrilla et al. 2007).

Finally, and perhaps most importantly, the authors used ‘snapshots’ taken from their BD simulations to perform the first calculations of the cytoplasm’s effects on the folding thermodynamics of proteins. In particular, calculations were performed for the two proteins for which experimental thermodynamic data obtained in the cytoplasm of E. coli were then available: these were the N-terminal domain of λ-repressor (λ_6–85) and the cellular retinoic acid binding protein (CRABP). Experimentally, the apparent thermodynamic stability of λ_6–85 has been reported to be essentially the same in vivo as it is in vitro (Ghaemmaghami and Oas 2001); in contrast, the apparent thermodynamic stability of CRABP is somewhat lower in vivo than in vitro (Ignatova and Gierasch 2004; Ignatova et al. 2007). In an attempt to reproduce these results, McGuffee and Elcock calculated the change in the folding thermodynamics expected to result from transferring each protein from dilute solution to the cytoplasm using a variant of the ‘particle-insertion’ method originally derived by Widom (1963) for hard-sphere systems. To determine the thermodynamic consequences of transferring the protein’s folded state to the cytoplasm, the native state structure was randomly inserted into the cytoplasm snapshots millions of times, with the energy of interaction between the protein and its cytoplasmic neighbors computed each time. To determine the thermodynamic consequences of transferring each protein’s unfolded state to the cytoplasm, similar calculations were performed but using an ensemble of 1,000 randomly-generated unfolded state structures generated by software kindly made available to the authors by the Sosnick group (Jha et al. 2005).

When the interaction of the protein with the cytoplasm environment was assumed to be purely steric in nature—i.e. when only excluded volume interactions were considered—the calculations suggested that the thermodynamic stability of both λ_6–85 and CRABP should be substantially increased in vivo relative to in vitro. Although these predicted increases in stability were entirely in accord with expectations based on conventional macromolecular crowding theory, they were clearly at odds with the experimental results. In contrast, when the protein–cytoplasm interaction energies were calculated using the same ‘full’ energetic model used in the BD simulations—and that correctly reproduced the long-time translational diffusion coefficient of GFP—the cytoplasm’s thermodynamic effects on the two proteins could be reproduced almost quantitatively; in particular, the surprising decrease in the apparent stability of CRABP in vivo was correctly captured by the calculations. An analysis of the distribution of interaction energies obtained from the millions of random insertions showed that the computed destabilization was due to CRABP’s unfolded state structures engaging in more energetically favorable interactions with the cytoplasm.

The authors finished by reporting the results of similar calculations exploring the potential thermodynamic effects of the cytoplasm on the folding thermodynamics of six other E. coli proteins, on the dimerization thermodynamics of 11 other E. coli proteins, and on the assembly thermodynamics of (1) the trimeric polymerization nucleus of the cytoskeletal protein ParM (Garner et al. 2004), and (2) putative, octameric aggregate structures of a SH3 domain (Ding et al. 2002) and RNaseA (Sambashivan et al. 2005). With only one exception—that of the SH3 domain aggregate—the expected stabilization of folding and association predicted when only excluded volume interactions were considered was either partially or completely cancelled out when additional energetic interactions (i.e. electrostatic and hydrophobic interactions) were included.

The study reported by McGuffee and Elcock, which was the first to include structurally detailed macromolecular models, was followed later in the same year by a study carried out by the Skolnick group, which in turn was the first to consider the potential role of hydrodynamic interactions in determining translational diffusion coefficients in vivo (Ando and Skolnick 2010). Fifteen different types of macromolecules (including GFP) were incorporated in the cytoplasm model of Ando and Skolnick, and were represented either by spherical particles, as in the works of Bicout and Field and Ridgway et al., or by more detailed but still coarse-grained models. Amino acid residues were represented by pseudoatoms placed at the positions of the Cα atoms, and nucleotides were represented by three pseudoatoms representing the phosphate, sugar and base groups. The authors first conducted Brownian dynamics simulations using both types of structural models—in the absence of hydrodynamic interactions—with steric interactions being the only form of energetic interaction between the macromolecules. They found that, at concentrations up to 300 g/l, the computed long-time translational diffusion coefficients of the macromolecules were essentially identical using the two levels of structural representation. On this basis, therefore, the authors concluded that it was reasonable, at least with respect to modeling of translational diffusion, to approximate all macromolecules as spherical particles.

The authors then used the much more sophisticated and computationally intensive Stokesian dynamics simulation method developed by the Brady group (Durlofsky et al. 1987; Brady and Bossis 1988) to explore the effects of including intermolecular hydrodynamic interactions on translational diffusion coefficients. The latter were modeled using the Rotne-Prager-Yamakawa formalism for long-range (‘far-field’) hydrodynamic effects (Rotne and Prager 1969; Yamakawa 1970), supplemented—crucially—with so-called ‘lubrication forces’ for short-range interactions (Brady and Bossis 1988; Phillips et al. 1988); it is the inclusion of the latter terms that makes the short-time diffusion coefficients of the macromolecules sensitive to the overall macromolecular concentration. As found in the previous cytoplasm simulation studies—all of which neglected hydrodynamic interactions—the long-time translational diffusion coefficient of GFP was found to be at least three times higher than experiment when only steric interactions were included and when all hydrodynamic interactions were omitted. However, when intermolecular hydrodynamic interactions were added to the model, the authors were able to immediately capture the ∼10-fold decrease in the long-time translational diffusion coefficient of GFP that occurs in vivo, without having to include any attractive interactions between macromolecules. This important result suggests that much of the slow-down in translational diffusion coefficients that occurs in vivo might be attributable to non-specific hydrodynamic interactions between macromolecules.

Finally, the authors also included non-specific attractive forces between macromolecules by filling the surface of each sphere with van der Waals particles and applying a Lennard–Jones potential with a well depth, ε, of 0.37 kcal/mol, to their interactions. The authors found that the sensitivity of the long-time translational diffusion coefficients to the molecular size was much more pronounced when these attractive interactions were included than when hydrodynamic interactions were included, and it was proposed that this might provide a useful route to experimentally determining which of the two potential factors might be most responsible for slowing down diffusion in crowded protein solutions. It is to be noted that this non-specific model of attractive forces differs significantly from that used by McGuffee and Elcock (2010), which assigned attractive forces only to interacting pairs of exposed non-polar groups, and which also explicitly accounted for the electrostatic forces experienced by each charged amino acid and nucleotide residue.

Open questions and outlook

The simulation studies described above have provided a number of insights into the biophysical aspects of macromolecular behavior in the bacterial cytoplasm. It is probably clear, however, that none of the published models can be considered to be the ‘last word’ in terms of modeling the intracellular environment, and that there are a number of outstanding issues that are likely to be worth addressing in future simulation models. One important goal is likely to be the development of simulation models that allow macromolecules to be modeled in complete structural detail while simultaneously including accurate models of both their energetic and hydrodynamic interactions. Such models may enable us, for example, to unambiguously determine the relative extents to which energetic and hydrodynamic interactions are responsible for controlling the diffusive characteristics of macromolecules in vivo.

The view emerging from the Skolnick group’s study is that intermolecular hydrodynamic interactions are responsible for much of the slow-down observed in translational diffusion in vivo. A recent quasielastic neutron scattering study of the diffusion of bovine serum albumin (BSA) at concentrations up to 30 % volume fraction has provided support for this view, and has proposed that hydrodynamic interactions are responsible for an 80 % decrease in BSA’s diffusion coefficient from its value in dilute solution (Roosen-Runge et al. 2011).

But a variety of experimental evidence suggests that hydrodynamic interactions, while very important, are probably only part of the story and that transient energetic interactions of the type accounted for in the study by McGuffee and Elcock are also likely to play an important role in determining diffusive behavior. First, in the first reported study of GFP translational diffusion in live E. coli cells, the Elowitz group (Elowitz et al. 1999) showed that the addition of a 6-residue His-tag to GFP led to a two-fold slowdown of its diffusion in the E. coli cytoplasm; the addition of such a small tag to a 230-residue protein would be expected to make a negligible difference to its hydrodynamic properties. Second, the Pielak group has shown that rotational diffusion of the small protein chymotrypsin inhibitor 2 (CI2) is drastically decreased when high concentrations of proteins such as lysozyme and ovalbumin are added, in contrast to what is seen when more inert macromolecular crowding agents such as Ficoll are added (Wang et al. 2010). Third, the Crowley (Crowley et al. 2011) and Gierasch groups (Wang et al. 2011) have independently shown that comparatively minor mutations of surface residues can control whether a protein is observable or not via in-cell NMR techniques. Importantly, the Crowley group’s study demonstrated a sensitivity to mutations of charged residues—thereby indicating the potential importance of intermolecular electrostatic interactions—while the Gierasch group’s study showed that similar effects could be elicited by mutating exposed non-polar residues, thereby demonstrating the potential importance of intermolecular hydrophobic interactions. Finally, the Gierasch group (Wang et al. 2011) has shown—by studying a variety of artificial fusion proteins of different sizes—that protein size is not the sole determinant of NMR lineshape broadening; even comparatively small proteins can be rendered NMR-invisible due to interactions with cytoplasmic components. None of these results can be explained solely in terms of intermolecular hydrodynamic interactions; they can, however, all be explained by the additional presence of favorable ‘sticky’ energetic interactions between macromolecules.

Given that it seems likely that future simulations of the cytoplasm will need to include accurate descriptions of both energetic and hydrodynamic interactions, it is worth considering whether aspects of the different simulation models used by the Elcock and Skolnick groups might be usefully combined in a computationally efficient manner. In fact, a recent report from the Wade group provides a good example of how this might be done. In a way similar to that reported by the Elcock group (McGuffee and Elcock 2006)—and which in turn was based on the original work of Gabdoulline and Wade (1997)—Mereghetti et al. (2010) have parameterized an energy model for rigid-body interactions of atomically detailed protein models that reproduces osmotic second virial coefficient data for three types of protein. Importantly, their energy model includes contributions describing direct electrostatic (Gabdoulline and Wade 1996), electrostatic desolvation (Elcock et al. 1999), and hydrophobic desolvation effects (Gabdoulline and Wade 2009), and so provides a more comprehensive description of the principal factors governing the strengths of macromolecular interactions than that used by McGuffee and Elcock (2010). More recently, the same authors (Mereghetti and Wade 2012) have extended their BD simulation method to account in a fast but approximate way for the effects of intermolecular hydrodynamic interactions. Specifically, building on a mean-field approach first suggested by Heyes (1995), the authors use the local volume fraction occupied by neighboring macromolecules to rescale the short-time translational and rotational diffusion coefficients that are employed to propagate motion of each macromolecule. While such an approach does not explicitly account for the correlated motions that occur between macromolecules when hydrodynamic interactions are included—and that were nicely highlighted in the Skolnick group’s study (Ando and Skolnick 2010)—it does successfully capture the overall slow-down in diffusion that such interactions cause: in simulations of a number of highly concentrated protein systems the Wade group’s BD method successfully reproduced the concentration dependences of both translational and rotational diffusion. Given the very fast nature of such calculations it is quite possible that this same simulation approach would be applicable to very large-scale simulations, such as of the bacterial cytoplasm.

One area where such an approach might be especially useful is in modeling the rates of protein–protein association events in vivo. As noted above, the study by Ridgway et al. (2008) represented an important first step in this direction by modeling the association of barnase and barstar, but involved considerable simplifications in the modeling both of the proteins and their interactions. Interestingly, the Wade group’s effective charge model (Gabdoulline and Wade 1996), and its implementation within Brownian dynamics simulations, was first validated by accurately computing the association rate constants of a wide range of barnase–barstar mutants (Gabdoulline and Wade 1997). Extending such studies to model the association as it might occur in vivo, therefore, is an interesting next step to take, especially as experimental data on rates of protein–protein associations in vivo—at least in human cells (Phillip et al. 2012)—have recently become available. Finally, such studies would represent a nice extension of a number of interesting previous simulation studies examining rates of associations using more simplified models of crowded solutions (Sun and Weinstein 2007; Wieczorek and Zielenkiewicz 2008; Kim and Yethiraj 2009).

All of the simulation methods described thus far have involved rigid-body models of macromolecules. A logical next step, of course, would be to include internal flexibility in some or all of the macromolecules, as this would enable the in vivo diffusion of mRNAs and intrinsically disordered proteins to be modeled in a meaningful way. One potential application of such an extended simulation model would be to attempt to explain the interesting recent report from the Pielak group showing that the relative translational diffusion coefficients of the disordered 14-kDa protein α-synuclein and the folded 7.4-kDa protein CI2 can become switched in magnitude depending on whether diffusion is monitored in dilute solution or in solutions crowded with either proteins, such as lysozyme, or with conventional crowding agents such as Ficoll (Wang et al. 2012a).

A significant challenge for simulations pursuing that objective is that accurately modeling the diffusional properties of flexible protein models requires the inclusion of intramolecular hydrodynamic interactions. It has been shown previously that the omission of such interactions can result in translational and rotational diffusion coefficients that are massively underestimated (Frembgen-Kesner and Elcock 2009). Unfortunately, incorporating hydrodynamic interactions in a rigorous way is computationally very expensive: the Cholesky decomposition method normally used for the calculation of correlated random displacements of particles scales as O(N ³), with N being the number of particles. Because of this, interest is likely to continue in the development of parallelized Cholesky solvers (Hogg 2008), in the development of alternative methods for computing the correlated displacements that scale more favorably with increasing numbers of particles (Fixman 1986; Ando et al. 2012), and in the development of methods that seek to avoid the expense of such calculations entirely (e.g., Geyer and Winter 2009).

One way to mitigate the expense of such calculations would be to decrease the level of structural resolution in the models. The simulations performed by the Skolnick group (Ando and Skolnick 2010) have already indicated that, if one neglects anisotropic energetic interactions between macromolecules, then simple spherical models can be sufficient, at least from the point of view of modeling translational diffusion. An alternative might be to use somewhat more detailed structural models that retain the overall shapes of the molecules while decreasing the number of particles to be simulated (e.g., Wriggers et al. 1999; Chu and Voth 2006; Arkhipov et al. 2006, 2008; Frembgen-Kesner and Elcock 2010). Efforts to develop these kinds of models for the bacterial cytoplasm have recently been reported by the Cheung group (Wang and Cheung 2012). If fast enough, such models might enable the gap that currently exists between the timescales accessible to simulation and experiment to be eliminated, which in turn might enable important insights to be obtained into the timescales over which anomalous diffusion is likely to persist in vivo (Weiss et al. 2004; Golding and Cox 2006; Dix and Verkman 2008; Malchus and Weiss 2010); it is to be noted, after all, that each of the simulation studies of the cytoplasm that have addressed diffusional aspects has noted the presence of transient anomalous diffusion (Ridgway et al. 2008; McGuffee and Elcock 2010; Ando and Skolnick 2010).

An additional important application of a flexible simulation model would be to explicitly model the dynamic process of protein folding in vivo. Molecular simulations of protein folding processes in crowded solutions of inert spheres were first reported by the Cheung and Thirumalai groups (Cheung et al. 2005; Cheung and Thirumalai 2007; Stagg et al. 2007), and provided a number of interesting insights into the effects of excluded volume interactions on the thermodynamics and kinetics of folding. An important goal for the future will be to extend such studies to consider how a protein’s folding behavior in vivo might be affected by the presence of accurately modeled favorable energetic interactions with surrounding macromolecules. One indication of the potential importance of such interactions was already provided by McGuffee and Elcock’s calculations of protein folding thermodynamics in the bacterial cytoplasm: excluded volume interactions alone were insufficient to explain the experimentally observed changes in thermodynamic stabilities of proteins in the cytoplasm of E. coli, and, in fact, led to qualitatively incorrect results in the case of CRABP. Interestingly, the apparent decrease in the stability of CRABP observed in vivo (Ignatova and Gierasch 2004; Ignatova et al. 2007) does not appear to be unique to either this protein or to the cytoplasm of E. coli: in-cell NMR experiments performed in the cytoplasm of human cells have indicated that the 76-residue protein ubiquitin is also less stable in vivo than in vitro (Inomata et al. 2009).

It is worth noting, of course, that the thermodynamic stabilities measured in vivo are apparent quantities, not rigorous thermodynamic measurements, and might well be complicated by factors such as rates of protein synthesis and degradation, as well as binding to chaperones. While one very interesting current direction is the development of chemical kinetics models that can simultaneously account for all of these processes (Powers et al. 2012), it is important to note that decreases in protein stability due to interactions with other proteins have also been shown much more directly in vitro in a series of elegant studies performed by the Pielak group. In particular, Miklos et al. (2011) used H/D exchange techniques to show that CI2 is mildly destabilized in the presence of 100 g/l solutions of lysozyme or BSA, even though it is significantly stabilized in the presence of the more conventional crowding agent polyvinylpyrrolidone (PVP). More recently, the same group has used similar techniques to explore the enthalpic and entropic contributions to the stability of ubiquitin in solutions of lysozyme and BSA (Wang et al. 2012b), and again concluded that weak chemical (i.e. energetically favorable) interactions could be as important, or more important, than excluded volume interactions in determining the effects of macromolecular crowding on protein stability. Since there is, therefore, both in vitro and in vivo evidence that the thermodynamic stabilities of proteins can be decreased in the presence of high concentrations of other proteins, we think that this reinforces the idea that future simulation models of the cytoplasm will need to accurately account for the presence of favorable energetic interactions between macromolecules in addition to their hydrodynamic interactions.

Finally, as available computer power continues to increase, it will become increasingly feasible to incorporate explicit treatments of the solvent into simulations of intracellular environments. In fact, a number of steps in this direction have already been reported. First, explicit-solvent molecular dynamics (MD) simulations of concentrated solutions of the small proteins villin and protein G have been reported, showing that the self-diffusion and dielectric response of water is likely to be significantly decreased under the crowded conditions encountered in vivo (Harada et al. 2012). Second, a series of large-scale MD simulations of the behavior of CI2 in 100 g/l solutions of lysozyme and BSA have been reported that go a considerable way toward explaining the H/D exchange studies reported for the same systems by the Pielak group (Feig and Sugita 2012). Finally, based on recently measured metabolomic data (Bennett et al. 2009), interesting explicit-solvent MD simulations of the E. coli cytosol (i.e. the non-macromolecular component of the cellular interior) have even been conducted (Cossins et al. 2011). Given these recent studies, therefore, it seems reasonable to expect that large-scale, explicit-solvent MD simulations of all-atom cytoplasm models might also not be too far away.

Abbreviations

Long-time translational diffusion coefficient

GFP

Green fluorescent protein

CI2

Chymotrypsin inhibitor 2

E. coli

Escherichia coli

BD

Brownian dynamics

λ_6–85

N‐terminal domain of λ-repressor

CRABP

Cellular retinoic acid binding protein