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Current address: Sloan-Kettering Institute, New York, New York, United States of America

Conceived and designed the experiments: SRM AHE. Performed the experiments: SRM AHE. Analyzed the data: SRM AHE. Wrote the paper: SRM AHE.

The authors have declared that no competing interests exist.

A longstanding question in molecular biology is the extent to which the behavior of macromolecules observed

The interior of a typical bacterial cell is a highly crowded place in which molecules must jostle and compete with each other in order to carry out their biological functions. The conditions under which such molecules are typically studied

While reductionist biophysical studies continue to contribute important insights into the properties and functions of biological macromolecules, research attention is increasingly being directed at uncovering the extent to which behavior observed

An alternative to the use of experimental techniques is to assemble a molecular model of an intracellular environment

Full details of the construction of the model are provided in

Starting from three different randomized initial configurations of the cytoplasm model (all shown in ^{L}_{trans}, of the ‘tracer’ GFP molecules were computed from the BD simulations and compared with previously reported experimental estimates obtained by fluorescence-recovery-after-photobleaching (FRAP) analysis of GFP in the

A comparison of the computed GFP D^{L}_{trans} values obtained with the different energy models is shown in ^{L}_{trans} value is 3–6 times higher than the experimental estimates, and although this value decreases somewhat when electrostatic interactions between macromolecules are added, it remains 2–5 times too high relative to experiment. A more realistic model of macromolecular interactions would allow favorable short-range attractions to occur between exposed hydrophobic atoms and one simple way of approximating such interactions is to use a Lennard-Jones potential, with the well-depth of the potential, ε, being treated as an adjustable parameter (see ^{L}_{trans} values that decrease monotonically as the well-depth, ε, increases in magnitude. The best agreement with experiment is obtained with ε = 0.285 kcal/mol: at this value of ε the computed value of D^{L}_{trans} – which is ∼10% of its value at infinite dilution – is within the experimental error of all

_{trans} values for GFP from BD simulations performed with different energy models; ‘ε’ refers to the well-depth (in kcal/mol) of the Lennard-Jones potential used to describe hydrophobic interactions (see _{trans} values from refs. 14, 15, 16 and 17 respectively. The vertical arrow indicates the energy model selected for further BD simulation.

Having determined that good agreement with experiment could be obtained using a so-called ‘full’ energy model that included steric, electrostatic and short-range attractive hydrophobic interactions, we extended each of three independent simulations performed with this energy model to 20µs (see

An informative, albeit non-quantitative, impression of the simulation behavior can be obtained by viewing movies of the simulations (

We can place these observations on a more quantitative footing, and obtain an indication of the extent of sampling achieved in 15µs of simulation, from the remaining panels of

As might be expected, the average numbers of neighbors that a macromolecule possesses at any instant scales essentially monotonically with its molecular weight: the average number of macromolecules in the immediate neighborhood of a GFP molecule, for example, is only ∼5 while for the 50S ribosomal subunit it is more than 25 (

While it was noted above that the long-time D^{L}_{trans} value of GFP obtained with the ‘full’ energy model is in good agreement with _{trans} values of macromolecules depend on the observation interval, δt, over which their diffusion is monitored (see _{trans} values of the three proteins versus δt for both the ‘full’ and ‘steric’ energy models. The clear variation of D_{trans} with δt seen for all three proteins is indicative of ‘anomalous’ diffusion

_{trans} values for the three most abundant proteins plotted versus observation interval δt; error bars indicate the standard deviation of values obtained from three independent simulations; solid lines represent fits to the data obtained by integrating the analytical functions shown in the next panel. _{trans} values shown in _{mid} = 144ps) plotted for all molecule types versus molecular weight; error bars represent standard deviations from the three independent BD simulations. _{trans} values expressed relative to infinite-dilution values plotted versus molecular weight of each molecule type; asterisk denotes GFP. _{rot} values expressed relative to infinite-dilution values plotted versus molecular weight of each molecule type.

For both energy models, the plots of α versus δt fit well to an analytical function (solid lines in ^{L}_{trans}, to be estimated (see ^{L}_{trans} values of all molecule types are expressed relative to their translational diffusion coefficients at infinite dilution (D^{0}_{trans}) and plotted versus molecular weight in ^{L}_{trans}/D^{0}_{trans} decreases with increasing molecular weight, which is qualitatively consistent with experimental studies of tracer protein diffusion in simple single-component protein solutions

The rotational motion of macromolecules is also significantly affected by immersion in the cytoplasm model. In the case of the ‘full’ energy model, the rotational behavior can be fit equally well by either a double-exponential function or a model that describes transiently anomalous rotational diffusion ^{S}_{rot} of all molecule types, relative to their rotational diffusion coefficients at infinite dilution, D^{0}_{rot}, in

Notably, a comparison of _{rel}^{T} and η_{rel}^{R} for translational and rotational diffusion respectively). _{rel}^{T}/η_{rel}^{R}, versus molecular weight for all molecule types. For the abundant proteins MetE, TufA, and CspC, and the less abundant GFP, we find the ratio of these relative viscosities, η_{rel}^{T}/η_{rel}^{R}, to be 3.6, 3.0, 3.2 and 2.5, respectively using the ‘full’ model; perhaps surprisingly, similar numbers are also obtained with the ‘steric’ model (_{rel}^{T}/η_{rel}^{R} of 2.6±0.2 obtained from _{rel}^{T}/η_{rel}^{R} of 2.1±0.3 reported for GFP in Chinese hamster ovary cells

In addition to the simulations providing direct views of diffusive motions in the cytoplasm, snapshots extracted from the simulations offer an important opportunity to explore the thermodynamic consequences of the cytoplasm on macromolecular stability. Using a variant of Widom's ‘particle-insertion’ method _{6-85}

We performed thermodynamic calculations under a total of four different scenarios. The first scenario that we examined involved taking cytoplasm snapshots sampled during the ‘steric’ BD simulations, and computing the cytoplasm-interaction energies of the folded and unfolded conformations with the same ‘steric’ energy model: this scenario corresponds to that considered in conventional models of macromolecular crowding effects _{6-85} and CRABP respectively (blue bars in _{6-85} and are qualitatively wrong for CRABP. In a second scenario, we took cytoplasm snapshots sampled during the ‘full’ model BD simulations, but computed the cytoplasm-interaction energies of folded and unfolded conformations using the simpler ‘steric’ energy model. In this case, the differences between the folding free energies _{6-85} and CRABP respectively (cyan bars in _{6-85} and are in qualitative disagreement with experiment for CRABP.

_{6-85}) and CRABP taken from refs _{int}, of the inserted proteins. _{int}, obtained for all non-clashing insertions of the folded and unfolded state conformations of CRABP with snapshots sampled from the ‘full’ model BD simulations; inset shows the same for λ_{6-85}.

A third scenario that we examined involved taking cytoplasm snapshots sampled during the ‘steric’ BD simulations and computing the cytoplasm-interaction energies with the ‘full’ energy model. In this case, the differences between the folding free energies _{6-85} and CRABP respectively (green bars in _{6-85} and CRABP respectively (yellow bars in

Histograms of the computed interaction energies of the folded and unfolded state with the cytoplasm explain why the predictions of the ‘full’ model successfully reproduce experiment, and deviate so significantly from the predictions of the purely steric model: for both proteins, but especially so in the case of CRABP, the unfolded state conformations are computed to have somewhat more favorable energetic interactions with the cytoplasm than the folded state conformations (

To explore the potential generality of this latter result, we performed identical calculations for a number of other monomeric proteins using snapshots taken from the ‘full’ model BD simulations; histograms illustrating the size distributions of the unfolded states of the tested proteins are shown in

We performed similar calculations to explore the potential thermodynamic effects of immersion in the cytoplasm on a variety of protein-protein associations. For the formation of homo-dimeric complexes (

Developing working computational models of intracellular environments is one potential route to understanding differences between biomolecular behavior observed

Before considering the strengths and weaknesses of the present model, and the implications of the results reported here, it is important to reiterate that at least two other cytoplasm models have already been reported in the literature. The first such model was described by Bicout and Field _{trans} values measured

A second and much more recent model for the bacterial cytoplasm has been developed by Ellison and co-workers

Relative to these two previous cytoplasm models, therefore, the present approach offers a significant increase in both structural and energetic complexity: all macromolecules are modeled in atomic detail and interact with one another via an energetic model that accounts for the two major types of interaction that drive protein-protein associations (i.e. electrostatic and hydrophobic interactions). It does so, of course, at very significant computational expense: each of the simulations performed with our ‘full’ energy model required more than a year of clock-time to complete. But even with its associated expense it should not be thought that the present model represents the pinnacle of sophistication in terms of its description of reality. Leaving aside the fact that the model is incomplete in terms of the types of macromolecules (and small molecules) that it includes, there are several key assumptions of the modeling that are both important to stress and which represent obvious candidates to address further in future work.

A first simplification of the present approach, and one shared by the previous models described above, is that all macromolecules have here been treated as rigid bodies. This simplification has two consequences. First, it immediately precludes us from making any meaningful attempt to simulate the (presumably very interesting) diffusive behavior of highly flexible macromolecules such as mRNAs and intrinsically unstructured proteins. While this is undoubtedly a limitation, it is to be noted that in terms of their contributions to the overall mass content of the cytoplasm, such molecules play a comparatively minor role

A second, but not unrelated simplification adopted in the present approach concerns the energy model used to describe intermolecular interactions. On the one hand, the model is comparatively sophisticated in that it includes descriptions of electrostatic and hydrophobic interactions, and models both at an atomic, or near-atomic level of resolution: in this respect it is a clear improvement over previous models used to simulate the cytoplasm. On the other hand, the model assumes that electrostatic desolvation effects can be neglected (which may lead to an overestimation of the strength of electrostatic interactions;

In future, it should be possible to increase the sophistication of the energy model without incurring an exorbitant additional computational cost: if one stays with a rigid-body approach, for example, a number of grid-based methods might be used that allow electrostatic desolvation

A third limitation of the present model concerns its very simplified description of macromolecular hydrodynamics. In particular, while the

While simply stating that HI are expensive to calculate does not constitute a compelling reason for leaving them out of the simulations, it is pertinent to note that the omission of HI seems unlikely to be the cause of the gross overestimation of the diffusion coefficient of GFP obtained with the ‘steric’ energy model (_{trans} values over both short _{trans} values at both short

Having produced in the preceding paragraphs a litany of shortcomings of the model one might be tempted to view it as so fundamentally limited that its practical utility is in doubt. Perhaps the strongest argument against such a view comes from the results of the particle-insertion calculations aimed at computing the thermodynamics of protein folding _{6-85}'s relative stability is essentially unchanged. As noted earlier, the experimental CRABP result is inexplicable with conventional macromolecular crowding theory (as exemplified by the results obtained here when the ‘steric’ energy model is used in the particle-insertion calculations) since the dimensions of its unfolded state are greater than those of its native state. Use of the ‘full’ energy model, on the other hand, produces results in close agreement with experiment because it explicitly allows for the two states of the protein to engage in differential, favorable energetic interactions with the rest of the constituents of the cytoplasm. Interestingly, good results are obtained when the ‘full’ energy model is used in the particle-insertion calculations regardless of whether the cytoplasm snapshots were sampled from the ‘steric’ BD simulations or sampled from the ‘full’ BD simulations. Although the most internally consistent approach is obviously to use the same energy model in both the BD simulations and the particle-insertion calculations, the fact that good results can apparently also be obtained using snapshots from the ‘steric’ BD simulations is intriguing since such simulations are much faster to conduct than those using the ‘full’ energy model. Our model's predicted effects on the folding free energies of the six other proteins investigated (

Other findings from the simulations, while probably more difficult to directly test experimentally, provide examples of the kinds of new information that can be obtained from simulation approaches that attempt to model intracellular environments. Examples include the observation that the immediate neighbors of individual proteins exchange rapidly on a microsecond timescale – even for the very largest macromolecules – and that diffusion is transiently anomalous even on a sub-nanosecond timescale. The latter observation is especially interesting given the current interest in anomalous subdiffusion as an efficient mechanism of search and association in physiological situations

An examination of all of the dynamic and thermodynamic results described above shows, we think, that it is possible to leverage the existing structural biology and quantitative proteomic data to produce a meaningful, working molecular model of the bacterial cytoplasm. The actual simulation model used here has a number of limitations, of course, but continuing increases in computer power and/or the development of faster simulation methodologies, will likely allow many of these drawbacks to be eliminated in the not too distant future. Given the continuing progress in the fields of structural biology and quantitative proteomics it is likely that the same basic approach might be used to model other intracellular environments.

When this work was initiated, the only large-scale quantitative study of the

Of the 50 types of

The total number of molecules in the simulations was set to 1008 (eight copies of GFP and 1000

Structures for all selected proteins were identified by performing a BLAST search

Any sidechains missing from a structure were built in using the molecular modeling program WHATIF

The final stage of preparation for each molecule involved the calculation of electrostatic potential grids; these were computed in all cases by using the APBS software

The BD software used for the simulations is an extension of the methodology developed and tested in our previous work on pure protein solutions

All simulations were performed under periodic boundary conditions

The form of the energy model used to describe intermolecular interactions was identical to that used in our previous work ^{12} and 1/r^{6} terms) was used to provide a simple combined description of steric, van der Waals and hydrophobic interactions. To accelerate the simulations, the combined non-electrostatic interactions were computed only between atom pairs separated by less than 12Å; a list of all such pairs was continually updated every 40 timesteps (i.e. every 100ps). As in our previous work, we treated the strength of these non-electrostatic interactions, which are determined by the well-depth, ε_{LJ}, of the Lennard-Jones potential, as the _{LJ} values: 0.190, 0.285, 0.3325 and 0.380 kcal/mol. Finally, for comparison purposes, two additional sets of three BD simulations were also performed: these were (a) simulations in which the only the repulsive (1/r^{12}-dependent) steric interactions operated (these are the ‘steric’ simulations discussed in the main text) and (b) simulations in which only steric plus electrostatic interactions acted.

The effective translational diffusion coefficients, D_{trans}, of molecules were calculated from the simulations using the Einstein equation:^{2} > is the mean-squared distance traveled by the molecular center of mass in the observation interval, δt; all D_{trans} values reported in Results are mean values for each molecule type averaged over the number of copies of each type. In cases of ‘normal’ diffusion, the computed D_{trans} values are independent of δt; in certain cases of diffusion _{trans} value is dependent on δt, decreasing with increasing δt. A common way of describing anomalous diffusion involves writing it in the form:_{trans} is now written to indicate that it depends on the observation interval and α is the so-called anomalous diffusion (anomality) exponent; α = 1 corresponds to normal diffusion since it leads to D_{trans} being independent of δt, and α<1 indicates anomalous (sub)diffusion. Taking logarithms and differentiating with respect to log (δt) allows us to write:_{trans} values computed over a range of δt values; in practice we computed D_{trans} at δt values of 100, 200, 300, 600, 1000, … ps, and obtained α at the logarithmic mid-point, δt_{mid}, of these time-intervals, δt_{mid} = 141, 245, 424, … ps.

Plots of α versus log (δt_{mid}) for macromolecules simulated with both the ‘steric’ and ‘full’ energy models all indicated that α itself was dependent on δt_{mid}, thus signifying that diffusion was _{0} is a constant, _{short} and τ_{long} are, respectively, the timescales over which α first decreases, and then returns to one, with increasing δt. Plots of α versus δt for all molecule types were fit to the above functional form with SigmaPlot _{mid} value up to the first datapoint that had a percent error exceeding ∼25% (obtained by comparing the α values computed from the three independent BD simulations), or that deviated qualitatively from the trend. To ensure that the latter criterion did not drastically affect the results, the fits were repeated retaining even those datapoints that qualitatively deviated; essentially the same behavior was obtained but with slightly greater values of τ_{long}. Regressed values of τ_{short} and τ_{long} are plotted versus molecular weight for all molecule types in

Having fit a function to the observed dependence of α on δt, it was numerically integrated to obtain an extrapolated, asymptotic long-time D_{trans} value using the D_{trans} value at δt = 100ps as the starting point for the integration. The quality of fits of the integrated D_{trans} values (for the most abundant proteins) is indicated by the solid lines in

Effective rotational diffusion coefficients were computed from the time-dependent behavior of the 3×3 rotational matrix recorded every 100ps for every molecule during the simulations. For each of the three rotational axes, an autocorrelation function, θ (δt), was calculated as:_{0} is the value of the autocorrelation function at δt = 0 (always 1), _{rot} is a long-time rotational correlation time (which dominates as δt→∞), and τ_{rel} is the timescale over which a faster, short-time rotational relaxation gives way to the slower rotation characterized by τ_{rot}. The above functional form was fit to computed values of θ for each molecule type over a range of δt values up to 1µs; the r^{2} values for these fits were all in excess of 0.999. An example of such fits for the most abundant proteins is shown in ^{L}_{rot}, is then obtained using the relationship:^{S}_{rot}, is obtained from ^{L}_{rot}/D^{0}_{rot} and D^{S}_{rot}/D^{0}_{rot} obtained with the ‘full’ energy model are plotted for all molecule types versus their molecular weights in

Comparison of the simulated translational and rotational diffusion coefficients with the infinite-dilution values that are input parameters for the simulations provides an indication of the relative viscosities experienced during the two types of motion. From studies of GFP diffusion in Chinese hamster ovary cells, the Verkman group reports _{rel}^{T} = 3.2±0.2, and a relative viscosity experienced by rotational motion, η_{rel}^{R} = 1.5±0.1. Combining these numbers gives a ratio, η_{rel}^{T}/η_{rel}^{R} of 2.1±0.3, indicating that the effective relative viscosity experienced by translational motion is roughly twice that experienced by rotational motion in mammalian cells.

A second estimate of the η_{rel}^{T}/η_{rel}^{R} ratio can be obtained from the work of Zorrilla

The data reported by Zorrilla _{m}, of the protein solution (measured with an Ostwald viscometer). They report that η_{m} fits to the following functional form, η_{m} = η_{0} exp (A_{0} is the viscosity of pure water, ^{−3} ml/mg and B = 1.3×10^{−3} ml/mg for HSA _{0}. Using the data given in Table 2 of ref. 49, the effective viscosity experienced by the _{rel}^{T} = (η_{m}/η_{0})^{1.28}, which from above means that we can write η_{rel}^{T} = 3.155^{1.28} = 4.35; following similar calculations the effective viscosity experienced by the _{rel}^{R} = (η_{m}/η_{0})^{0.44} = 3.155^{0.44} = 1.66. Together, these numbers translate into a value of η_{rel}^{T}/η_{rel}^{R} of 2.6±0.2.

As noted in the main text, we find that ^{L}_{trans} and the short-time rotational diffusion coefficient, D^{S}_{rot} (see

The intermolecular contacts engaged in by each molecule were recorded every 100ps during the BD simulations and subsequently analyzed to determine: (a) the average number of neighbors of each molecule type at any given time, (b) the number of unique neighbors encountered by each molecule type during the course of the entire simulations, and (c) the rate of dissociation of intermolecular interactions. The definition of ‘neighbor’ was kept somewhat loose in order to detect all molecules in the immediate environment of the molecule being probed: molecules were assigned as neighbors if any of their atoms were within ∼12Å of each other. The rates at which the neighbors of a particular molecule dissociated were obtained from plots of the fraction of its neighbors, initially present at t = 0, that remained after some time t = δt, averaged over all possible initial timepoints. In order to obtain the characteristic neighbor-decay rate for each particular type of molecule, such plots were averaged over all molecules of that type. The resulting plots are found to follow biexponential kinetics: (a) a very fast decay process (τ_{fast}) that typically has an amplitude of ∼0.7 and is due to loss of neighbors that interact only peripherally with the molecule of interest, and (b) a slower decay process (τ_{slow}) that has an average amplitude of ∼0.3 and is due to loss of those neighbors that form

The effects of immersion in the cytoplasm on the thermodynamics of protein folding and protein-protein association were computed using the particle insertion technique first outlined by Widom _{int} is the interaction energy of the molecule with the constituents of the cytoplasm, R is the Gas constant, T is the temperature, and the brackets indicate an average over randomly selected insertion positions and configurations of the cytoplasm environment. In order to assess the likely effects of the cytoplasm on a thermodynamic process (such as protein folding) therefore, separate particle-insertion calculations are required for both the initial state (e.g. unfolded protein) and the final state (e.g. folded protein). Such calculations give the free energy changes for the vertical processes in the thermodynamic cycle shown below:

Calculations of the cytoplasm's thermodynamic effects initially focused on protein folding equilibria. In addition to calculating the folding thermodynamics of six proteins already present in the cytoplasm model (Adk, Bcp, CspC, Efp, GFP and PpiB), we examined two other proteins that have been subject to direct experimental study _{6-85} construct studied experimentally by Ghaemmaghami and Oas _{6-85} was taken from its crystal structure in complex with operator DNA (pdbcode: 1LMB

The unfolded states of all eight proteins were modeled as ensembles of 1000 unfolded conformations generated using the conformational sampling method developed by the Sosnick group

For each protein, a large number of random trial positions were attempted with both the single, folded state structure and the 1000 unfolded state conformations; each trial consisted of a different randomly selected translation and rotation. For the folded state structure, a total of 25 million trials were attempted; for the unfolded state, 250,000 trials were attempted for each of the 1000 conformations (to give a total of 250 million trials for each cytoplasm ‘snapshot’ studied). For each trial position, the interaction energy of the protein with the surrounding cytoplasm was calculated with (a) the ‘full’ energetic model, which includes electrostatic, steric and hydrophobic contributions, and (b) the ‘steric’ energetic model. To simplify the latter calculations, only two possible energies were allowed: the interaction energy, E_{int}, was set to +∞ if any of the protein's atoms came within 4.5Å of any of the cytoplasm atoms, and was set to zero if not; this binary scoring method is effectively identical to that used in most examinations of excluded-volume (crowding) effects. Due to the very significant computational expense associated with the particle-insertion calculations, they were applied only to the final ‘snapshot’ of the three independent BD simulations performed with the ‘full’ and ‘steric’ models. Error bars for all reported free energy changes were therefore calculated as the standard deviation of the computed values obtained from the three different system ‘snapshots’. The total number of unfolded and folded-state trial positions that were accepted and rejected for each protein, for each of the three ‘full’ model cytoplasm ‘snapshots’ are listed in

A very similar protocol was used to calculate the effects of the cytoplasm on a variety of protein association reactions. Calculations on each assembled protein complex were performed exactly as described above. Calculations on each disassembled complex – e.g. two separated protein monomers in the case of a dimerization reaction – were carried out by performing insertions of all components

Dimerization equilibria were investigated by performing separate particle-insertion calculations on the dimeric forms and the monomeric forms; for such calculations it was assumed that no structural change (e.g. unfolding) occurs when the two monomers are separated. The trimerization equilibrium of ParM was investigated in analogous fashion, by performing calculations on a trimer extracted from the ParM filament model (pdbcode: 2QU4 _{α} atoms so complete backbone coordinates were first constructed using the SABBAC webserver _{α}-only model we were unable to add sidechains in such a way that the assembled aggregate model was free of internal steric clashes; this, however, does not significantly affect our ability to estimate the model's interaction with the cytoplasm environment. As with the RNaseA amyloid model, it would be inappropriate to assume that the conformations of unaggregated monomeric units are identical to those found in the amyloid model; instead therefore the conformation of the monomeric SH3 domain was taken from the crystal structure (pdbcode: 1NLO

Two movies, each showing 1.8µs of simulation, are provided as separate Quicktime .mov files.

Views of the three independent system setups before and after 15µs of BD simulation with the ‘full’ energy model. 50S and 30S ribosomal subunits can be identified by the green/yellow of their RNA and the blue and red (respectively) of their proteins. This figure was prepared with VMD

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Total system energy and its electrostatic and hydrophobic components, plotted versus simulation time; the vertical dashed line indicates the beginning of the production simulation.

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Histogram of cytoplasm-interaction energies, E_{int}, obtained for all non-clashing insertions of the aggregated and non-aggregated states of the SH3 domain.

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Time constant for the exponential describing the descent to the minimal value of the anomality exponent, α, plotted for all molecule types versus molecular weight.

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Time constant for the exponential describing the return to normal rotational diffusion plotted for all molecule types versus molecular weight; note that for the ‘steric’ model rotational diffusion is essentially normal at almost all observation intervals examined.

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Plot showing the quality of fit of a two-exponential decay function to the autocorrelation function describing rotational motion for the three most abundant proteins in the model. Symbols indicate the simulation data; lines indicate the two-exponential fit.

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Ratio of the short-time and long-time rotational diffusion coefficients to the infinite-dilution value plotted for the ‘full’ model for all molecule types versus molecular weight.

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Plot showing the quality of fit of a two-exponential decay function to the function describing the loss of neighbors for five selected molecule types. Symbols indicate the simulation data; lines indicate the two-exponential fit

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Plot showing the quality of fit of a 3-Gaussian distribution to the cytoplasm-interaction energy distributions obtained for non-clashing insertions of the IcdA protein in dimeric and monomeric states; note that the y-axis is on a logarithmic scale.

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Ordered list of all those proteins identified and quantified in Table 4 of Link et al.

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Alphabetically-ordered list of the macromolecules present in our cytoplasm model showing the pdbcode of their originating structures, the infinite-dilution translational and rotational diffusion coefficients

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Details of the particle-insertion calculations of the folding equilibria of 8 different proteins, listed in order of increasing protein chain length. Results are shown only for insertions into ‘snapshots’ (A, B, C) taken from BD simulations performed with the ‘full’ energy model. The total numbers of attempted insertions for the folded and unfolded states (for each ‘snapshot’) are 25 million and 250 million respectively. ΔGWidom and ΔΔG are insertion free energies obtained using the ‘steric’ energy model: these numbers can be obtained directly from knowledge of the number of attempted and successful insertions listed in this table.

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Details of the particle-insertion calculations of the association equilibria of 14 different proteins. ‘Process’ refers to the stoichiometry of the association process examined: 1→2 denotes that the equilibrium is between two monomers and one dimer, 4→8 denotes that the equilibrium is between two tetramers and one octamer etc. As in

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Cytoplasm Full Energy Model. 1.8 microseconds of simulation carried out with the ‘full’ energy model.

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Cytoplasm Steric Energy Model. 1.8 microseconds of simulation carried out with the ‘steric’ energy model.

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The authors are grateful to Drs. Abhishek Jha, Joe De Bartolo and Prof. Tobin Sosnick for generous help with the RCG unfolded-state modeling software, and to Dr. Feng Ding for very kindly making available the structural model of the SH3 amyloid octamer.

^{rd}edition.