Mixed Macromolecular Crowding: A Protein and Solvent Perspective.

In the living cell, biomolecules perform their respective functions in the presence of not only one type of macromolecules but rather in the presence of various macromolecules with different shapes and sizes. In this study, we have investigated the effects of five single macromolecular crowding agents, Dextran 6, Dextran 40, Dextran 70, Ficoll 70, and PEG 8000 and their binary mixtures on the modulation in the domain separation of human serum albumin using a Förster resonance energy transfer-based approach and the translational mobility of a small fluorescent probe fluorescein isothiocyanate (FITC) using fluorescence correlation spectroscopy (FCS). Our observations suggest that mixed crowding induces greater cooperativity in the domain movement as compared to the components of the mixtures. Thermodynamic analyses of the same provide evidence of crossovers from enthalpy-based interactions to effects dominated by hard-sphere potential. When compared with those obtained for individual crowders, both domain movements and FITC diffusion studies show significant deviations from ideality, with an ideal solution being considered to be that arising from the sum of the contributions of those obtained in the presence of individual crowding agents. Considering the fact that domain movements are local (on the order of a few angstroms) in nature while translational movements span much larger lengthscales, our results imply that the observed deviation from simple additivity exists at several possible levels or lengthscales in such mixtures. Moreover, the nature and the type of deviation not only depend on the identities of the components of the crowder mixtures but are also influenced by the particular face of the serum protein (either the domain I-II or the domain II-III face) that the crowders interact with, thus providing further insights into the possible existence of microheterogeneities in such solutions.

Introduction

Biochemical studies of macromolecules are often done in dilute solutions where the macromolecular concentration is in the range of 1–10 g/L.[1−4] These dilute environments differ dramatically from the interiors of cells or extracellular matrices of tissues and cartilages where the biological macromolecules are known to function.[4−6] Real biological environments contain a high density of macromolecular solutes (proteins, nucleic acids, polysaccharides, etc.) as a part of the same medium where the test protein locates.[7,8] Depending upon the specific organelle, the total occupancy by macromolecules can be in the range of 5–40% of the available volume, corresponding to 50–400 g/L of the total macromolecular concentration. Traditionally, macromolecular crowding has been explained based on the “excluded volume” effect[1−6] arising from the mutual impenetrability of the involved species, the latter being treated as hard spheres. In this regard, a multitude of processes such as the protein folding–unfolding reaction,[9−11] protein–protein association,[12−14] protein aggregation,[15,16] to name a few, have been shown to be appreciably affected by the presence of macromolecular crowding agents. From the increase in enzymatic activity to the increase in protein–protein association rates and enhancement of aggregation kinetics, synthetic crowding agents have already been reported to exhibit significant influence. Of late, studies using protein-based crowding agents have reported a shift in paradigm where enthalpy-based soft interactions were observed to gain prominence over hard-sphere-based steric interactions.[17−21]

Recent years have seen a considerable increase in the number of reports addressing issues and effects that a crowded milieu can have on biomolecular conformation, dynamics, and diffusion.[22−32] However, one aspect that has received far less attention is the fact that the crowded interior is not composed of only one macromolecule in high concentration but is rather made up of many different kinds of such molecules. Thus, studies in the presence of mixed crowders are essential but are quite rare to come across.[33−38] Using optimum mixtures of Dextran 70 or Ficoll 70 and the protein-based crowder bovine serum albumin during the refolding of lysozyme, it was observed that not only was the refolding yield increased significantly as compared to that of the component crowders, but also the kinetics of the oxidative refolding process of the enzyme was enhanced to a considerable extent.[33] A similar effect on the refolding and kinetics of rabbit muscle creatine kinase was also shown in mixed crowded environments, with calf thymus DNA and Ficoll 70 (or Dextran 70 or PEG 200) forming the binary crowder mixtures.[37] The stability of the lysozyme was found to be increased, while its activity decreased in the presence of mixtures of Dextran 70 and Ficoll 70.[39] An optimum mixing ratio of crowders of different sizes, the latter allowing tunability of the mixture types, has been proposed to have the most stabilizing effect on proteins.[35] Moreover, the nonadditive effect of binary crowder mixtures on protein stability has also been brought to the fore.[36,39] While all these aforementioned reports allude to the advantage that a mixed crowding scenario has in connection with protein refolding and stability and hence the physiological importance of the same, further support of this fact was obtained from a report wherein the mixed crowding system (in an optimized mixing ratio) inhibited the formation of protein (lysozyme) aggregates.[40] Usage of the concept of mixed crowders has been further extended, wherein the stability of the protein chymotrypsin inhibitor 2 (CI2) was monitored in the presence of reconstituted bacterial cytosol. It was observed that contrary to general expectations, the cytosol, which is a mixture of many proteins, destabilized CI2, this phenomenon being attributed to the nonspecific attractive interactions that the test protein experienced in the cytosol.[38]

Keeping the importance of mixed crowding in mind and its relevance to the physiological interior and the paucity of existing studies on the same, we have tried to provide much needed insights into this phenomenon from two different perspectives as follows: (a) conformational modulation of the multidomain protein human serum albumin (HSA) → wherein we have mapped domain movements based on Förster resonance energy transfer (FRET) in the presence of binary mixtures of crowding agents and (b) solvent perspective → where we have monitored the changes in diffusion characteristics of the fluorescent reporter, fluorescein isothiocyanate (FITC) using fluorescence correlation spectroscopy (FCS) in the presence of the same mixtures as used for the FRET study. The binary mixtures of several commonly used synthetic macromolecular crowders (Dextran 6, Dextran 40, Dextran 70, Ficoll 70, and PEG 8000) have been used here as a mimic of the congested cellular interior. The choice of HSA as the protein under study is based on the fact that it is not only a known avid transporter of small molecules and fatty acids (FAs) and hence functionally quite important but also is composed of three domains (I, II, and III) (Figure A). With regards to its physiological function, the binding of ligands to serum protein has been extensively studied in dilute solutions,[41−45] and the protein has also been well-characterized with respect to its structure and dynamics. Recent papers have shown that the structure of HSA is significantly modulated in the presence of crowding agents.[46−48] Keeping in mind the fact that the serum protein undergoes large scale domain movements (angular displacements) when binding to FAs[49,50] and also exhibits allostery on ligand binding,[51,52] understanding and trying to comprehend the manner in which such displacements are affected in a mixed crowding scenario is of immense importance. Indeed, it has been shown that extent of FA binding to HSA and the number of relevant binding sites on the protein are modulated in a crowded environment.[53] Moreover, HSA being quite a large protein, it itself sweeps a considerable volume even in the native state, thereby increasing the chances of it getting perturbed in the presence of the crowders. While the domain movement is quite local in nature, translational diffusion studies as monitored using FCS cover a larger lengthscale over which the reporter diffuses in the mixed crowding environment, thereby allowing us to monitor the extent of complexity “on the offer” under such conditions.

Figure 1

(A) Crystal structure of HSA (PDB ID: 4K2C) with its approximate domain boundaries marked with red circles. For convenience, the fluorophore ligation sites have also been depicted. A schematic of the domain movement has been provided for clarity. (B,C) Variation of interdomain distances for domain I–II and II–III separations, respectively, with increasing crowder concentrations (g/L) [as mentioned in the legend].

Our results suggest that mixed crowding has the effect of making protein motions more cooperative, thereby having an important effect in the protein folding and denaturation pathways. Thermodynamic analyses based on the cooperative interdomain movements provide a unique insight into the manner in which the individual components of the mixtures affect the serum protein, with features in transitions representing crossovers from soft enthalpy-based interactions to effects dominated by excluded volume-type interactions. Moreover, the nature of the domain movement and modulations in tracer diffusion imply that the mixed crowder solutions deviate appreciably from ideality, with the extent of deviation also depending on the nature of the component macromolecular crowding agents in the mixtures. Finally, with domain movements providing insights into the crowder arrangement in the immediate vicinity of the protein, this in combination with the translation diffusion studies suggest that nonideality exists over several orders of length scales, arguably from angstroms to nanometers, thereby further highlighting the importance of a mixed crowding scenario and its underlying complexity.

Results and Discussion

We have studied a total of seven binary mixtures of some commonly used macromolecular crowders, namely, Dextran 6 in Dextran 40, Dextran 6 in Dextran 70, Dextran 6 in Ficoll 70, Dextran 6 in PEG 8, Dextran 40 in Dextran 70, Dextran 40 in Ficoll 70, and Dextran 70 in Ficoll 70, thereby encompassing a range of shapes and sizes along with differences in the structure of the crowders at the molecular level. These synthetic crowders are not only highly soluble in water but also are neutral by nature. Additionally, these have been proposed to be inert and hence exert their effects mainly through excluded volume. Moreover, the variation in the average molecular weight is synonymous with the variation in the respective sizes of the crowders, thereby allowing us the flexibility of tuning the excluded volume that HSA is exposed to on an individual crowder basis and more so in the binary mixtures. For example, Dextran 6 reportedly has a hydrodynamic radius of ∼1.7 nm, with the larger-sized dextrans, namely, Dextran 40 and Dextran 70, having radii of ∼4.8 and ∼6.8 nm, respectively.[54] While dextrans have often been likened to being rod-like in shape (though reports exist of this crowder behaving more like a random coil), Ficoll 70, having a hydrodynamic radius of ∼5.1 nm,[55,56] has been considered to have a structure that is an intermediate between that of a sphere and a random coil. The choice of PEG 8000, which unlike the aforementioned ones, is not an ideal inert crowding agent as it is known to interact with proteins, was not only because of its molecular weight being similar to that of Dextran 6 but also because of the fact that it is a linear open-chain polymer as opposed to the others that are typically constrained to a certain extent by the cyclic ring systems of the component sugar moieties. Because polymers are known to entangle as a function of concentration, comparison of influence of the mixtures of the different polymers with that of their individual components should provide us insights into the manner in which the different crowders interact with each other and hence allow us to have a better idea about the mixed crowding phenomenon. Thus, the different binary combinations that we have employed in this study not only span different sizes, leading to gradation in packing densities, but also invoke the possibility of probing multiple interactions between the component crowders at the molecular level.

These mixtures were then examined based on their effects on (i) domain separation (r) of the multidomain protein HSA using steady-state FRET and (ii) diffusion of a fluorophore (FITC) using FCS. While the former provides insights into how HSA adjusts and adapts its geometry to reach a stable conformation, the latter throws light onto the manner in which the polymers are entangled. Because FITC is essentially nonperturbing when compared to HSA, with the latter through its hydrophilic–hydrophobic points of contact being able to dictate the crowder assembly around itself,[25] this study stands to provide a detailed insight into the mixed crowding milieu. For FRET studies, HSA was individually labeled covalently either at Cys-34 of domain I by the probe acrylodan (Ac) or at Tyr-411 by p-nitrophenyl anthranilate (NPA). These fluorophores are acceptors of the energy transferred from the donor Trp-214, the lone tryptophan residue of HSA. For FCS measurements, FITC was used as the probe for monitoring changes in its diffusion in the aforementioned mixtures of macromolecular crowding agents.

FRET Analysis of the Domain Movement in HSA

Individual Crowders

The addition of Dextran 6 leads to an increase in the distance between the Trp–Ac FRET pair. As evident from Figure B, the separation (r) between domains I and II increases steadily with the increasing Dextran 6 concentration (∼75–100 g/L), leading to an appreciable decrease in the efficiency of energy transfer. The steepest increase was observed for the 25–100 g/L crowder concentration range, while beyond this, the change was gradual, thereby reflecting on the enhanced restriction in the domain movement of the protein under these conditions, arising understandably from the limited space available to HSA amidst the sea of crowder molecules. On the other hand, for the same concentration range of Dextran 6, domains II and III moved closer to each other (Figure C). In the presence of the crowder Dextran 40, both domains I and III move toward domain II, showing correlated motion, with major portion of the changes having taken place by 75 g/L. Similar to that of Dextran 40, in the presence of Dextran 70 also, the motions of domains I and III remain correlated in that both show a sizeable decrease in the interdomain separation with respect to domain II. While Ficoll 70 brings about the maximum decrease in the distance for domains I and II, it also induces increase in the separation between domains II and III (Figure B,C). Finally, for PEG 8000, we observed increasing interdomain compaction (domains I and II) up to 75 g/L, beyond which the Trp–Ac FRET pair moved farther from one another. However, in the case of domains II–III, just the reverse happened (Figure B,C). Our FRET data thus show that the crowder-induced domain movements of HSA are dependent not only on the concentration of the crowding agent but also on the shape and size of the crowder molecule. These results are in good agreement with our recent report, wherein we had monitored the domain separation as a function of the pH-induced denatured states of HSA.[47]

Mixed Macromolecular Crowding

Figure (panels A and B) and Supporting Information Figures S1–S7 show how the distances between the domains based on the Trp–Ac (domains I and II) and Trp–NPA (domains II and III) FRET pairs are modulated in the presence of the different binary mixtures of crowders used. The total crowder concentration at any given data point was always kept at 200 g/L throughout. On the basis of this, for domains I–II, the interdomain separation undergoes an appreciable increase for the binary mixtures of Dextran 6 with either Dextran 40, Dextran 70, or Ficoll 70. This trend was expected because as shown in Figure B, Dextran 6 increased the separation of domains I and II while the other higher molecular weight crowders induced the domains to approach each other. Thus, in line with the same argument, the “Dextran 40 + Dextran 70” mixture showed very little distance change as one moved from Dextran 70 (200 g/L) only to Dextran 40 (200 g/L). Closer analysis of the two panels of Figure reveals the differences in the manner in which the mixed crowding influences the separation of domains I–II and II–III, an aspect that we have also observed in our recent report,[47] this being directly related to the behavior induced by the individual crowders as mentioned above.

Figure 2

Variation of interdomain distances for domain I–II (A) and II–III (B) in mixed macromolecular crowding with the following color codes: “Dextran 6 + Dextran 40” (black); “Dextran 6 + Dextran 70” (red); “Dextran 6 + Dextran 70” (blue); “Dextran 6 + PEG 8” (magenta); “Dextran 40 + Dextran 70” (green); “Dextran 40 + Ficoll 70” (yellow); “Dextran 70 + Ficoll 70” (violet); [along the arrowhead, the increment of the respective crowder indicated for a binary mixture is as follows: Dextran 6 increases along the x-axis in all the four mixtures having this crowder as one of the components; Dextran 70 increases along the x-axis in the “Dextran 70 + Ficoll 70” mixture; Dextran 40 increases along the x-axis in the “Dextran 40 + Ficoll 70” and “Dextran 40 + Dextran 70” mixtures].

To further probe the differences in the mixed crowding scenario, we have plotted the Δr values based on eqs and 16 in the same panel (Figures –5 and Supporting Information Figures S8–S11). As observed from Figure for the “Dextran 6 + Dextran 40” mixture, beyond 75 g/L Dextran 6, a distinct difference is seen between the two Δr trends for domain I–II separation, with the mixture resulting in a larger difference. It was surprising that such an effect was carried on even up till 175 g/L Dextran 6 (and 25 g/L Dextran 40). For a given weight of macromolecular crowding agents, lower the molecular weight of a crowder, higher will be the number density of that crowder. Thus, at 175 g/L Dextran 6, wherein the number density is overwhelmingly more than that of Dextran 40, the mismatch in the Δr values was least expected. In the case of domains II–III (Figure B), domain motion stalls beyond 125 g/L of Dextran 6 and 75 g/L Dextran 40. To further aid our understanding of the data, in the inset to each of the panels of Figure , we have also plotted ΔΔr (defined as ΔΔr = Δrmc – ΣΔr); it is a reflection of deviation from the so-called ideal mixture, the latter being considered equal to the sum of the effects seen for the individual crowder components of the binary mixture. As seen from the inset to Figure A, the deviation is quite high, that is, of the order of 4 Å, and that too at 150 g/L Dextran 6. Under similar circumstances, the deviation is much less for domains II and III, thus further showing the dissimilar nature of interactions for the two domain faces (domains I–II and domains II–III) of HSA with the crowders.

Figure 3

Variation of Δr as a function of the crowder concentration in (A) mixed crowding environment (Δrmc = rmc – r0; eq ) and (B) sum of individual crowders (ΣΔr = Δr + Δr); eq , where C1 and C2 are Dextran 6 and Dextran 40, respectively. [Inset shows the variation of ΔΔr (ΔΔr = Δrmc – ΣΔr)].

Figure 5

Variation of Δr as a function of the crowder concentration in (A) mixed crowding environment (Δrmc = rmc – r0; eq ) and (B) sum of individual crowders (ΣΔr = Δr + Δr); eq , where C1 and C2 are Dextran 40 and Dextran 70, respectively. [Inset shows the variation of ΔΔr (ΔΔr = Δrmc – ΣΔr)].

Similar analyses were also carried out for all the other binary mixtures. For domains I–II, in the presence of the mixtures of “Dextran 6 + Dextran 70” (Supporting Information Figure S8A) and “Dextran 6 + Ficoll 70” (Supporting Information Figure S9A), the agreement between the two Δr values is quite similar. This implies either of the following: (i) Dextran 70 and Ficoll 70 are very similar in their behavior or (ii) Dextran 6 is the main component that decides the profile that we observe. Comparison of the Δr profiles for the Dextran 70 and Ficoll 70 mixture (Figure ) reveals that the effect so observed for the mixture of these high molecular weight crowders is not additive (inset to Figure A), that is, there exists significant differences between the Δrmc values obtained from the mixture and from the sum of the individual crowders (ΣΔr), for domains I and II. This thus suggests that it is Dextran 6 that drives the Δr trends, an aspect that is expected based on the high packing density of Dextran 6 and also its influence being more of the excluded volume type. Furthermore, the “Dextran 40 + Dextran 70” mixture (Figure A) induces a large disparity in the Δr values for domains I and II, with Δrmc being lower than that of ΣΔr implying that the mixture gives rise to a lower change in the interdomain distance as compared to its components when considered together in isolation. The same mixture, however, gives rise to very little difference for domains II and III (Figure B), again hinting at the differences that the two faces of HSA exude. Moreover, for the mixtures involving Dextran 6 as one of its constituents, ΔΔr is positive for the distance between domains I and II while the same is negative for domains II and III, further confirming the dissimilarity between the two HSA faces. For the “Dextran 6 + PEG 8000” mixture (Supporting Information Figure S10), the deviation from so-called ideality peaks at 125 g/L Dextran 6, that is, where the PEG concentration is 75 g/L. Such an effect is reminiscent of the fact that PEG 8000 induces a change in the direction of the domain movement for both the domains (I and III) with respect to domain II, at that concentration (Figure ). Additionally, the large deviation observed for the domain II–III distance with ΔΔr of ∼−6 Å, the maximum observed for the mixtures studied here, can be hypothesized to be arising from the changeover from a predominantly excluded volume type interaction until 125 g/L Dextran 6 (or 75 g/L of PEG 8000) to a competition between the interaction governed by electrostatics between PEG and HSA and excluded volume as exerted by Dextran 6.

Figure 4

Variation of Δr as a function of the crowder concentration in (A) mixed crowding environment (Δrmc = rmc – r0; eq ) and (B) sum of individual crowders (ΣΔr = Δr + Δr); eq , where C1 and C2 are Dextran 70 and Ficoll 70, respectively. [Inset shows the variation of ΔΔr (ΔΔr = Δrmc – ΣΔr)].

A common feature for all the mixtures is that the variation in the interdomain distance r (for the mixtures) is quite cooperative, despite the fact that changes in r for the individual crowders do not show any such trend (Supporting Information Figures S2–S7). To address the cooperative nature of the trends as a function of the mixture composition, we have also analyzed these changes based on existing thermodynamic models (eq –14) for both pairs of domains, I–II and II–III (Supporting Information Figure S12). Depending on the nature of the transitions and the domains involved, the transitions were either fitted to a two-state (eq ) or a three-state (eq ) model. The corresponding free energy (ΔG0(H2O)) changes were thereby obtained from the fits and have been tabulated in Tables and 2. On the basis of our previous hypothesis, the effect of Dextran 6 is predominantly due to that of excluded volume that is entropy-driven, while the large macromolecular crowders such as Dextran 40 or Ficoll 70 show appreciable soft interactions that are enthalpic in origin.[46,47] As evident from the Tables and 2, for domains I and II, the binary mixtures of Dextran 6 with the higher molecular weight crowders induced a three-state transition, while in the case of the domain II–III distance, for the same mixed crowders, the transition was primarily two-state. A similar switch in the nature of transition is also observed for the large molecular weight crowder mixtures but in a reverse manner, that is, the two-state process for domains I and II became three-state in the case of domains II and III. These data thus reveal significant differences in the overall nature of interaction potential presented by the two faces of HSA, which is in agreement with our recent findings.[47]

Table 1

Variation of the Thermodynamic Parameters for Domain I–II Separation in the Mixed Crowding Environmenta

crowding mixture	ΔGIn→10	mIn→1	ΔG2→In0	m2→In	crowding mixture	ΔG1→20	m1→2
Dextran 6 + Dextran 40	11.1	0.14	25.4	0.37	Dextran 6 + PEG 8	15.2	0.13
Dextran 6 + Dextran 70	8.8	0.12	27.6	0.25	Dextran 40 + Dextran 70	4.3	0.08
Dextran 6 + Ficoll 70	12.0	0.10	28.6	0.18	Dextran 40 + Ficoll 70	8.9	0.09
					Dextran 70 + Ficoll 70	7.2	0.05

[ΔG and m having units of kJ mol–1, kJ/(mol M) respectively]. (ΔG was calculated after conversion of g/L to molar concentrations; PEG 8 refers to PEG 8000).

Table 2

Variation of Thermodynamic Parameters for Domain II–III Separation in the Mixed Crowding environmenta

crowding mixture	ΔGIn→10	mIn→1	ΔG2→In0	m2→In	crowding mixture	ΔG1→20	m1→2
Dextran 6 + PEG 8	10.4	0.19	30.2	0.21	Dextran 6 + Dextran 40	15.6	0.16
Ficoll 70 + Dextran 70	12.5	0.2	16.7	0.14	Dextran 6 + Dextran 70	6.5	0.07
Dextran 40 + Ficoll 70	15.6	0.29	18.6	0.15	Dextran 6 + Ficoll 70	8.90	0.09
					Dextran 40 + Dextran 70	2.20	0.07

[ΔG and m having units of kJ mol–1, kJ/(mol M) respectively]. (ΔG was calculated after conversion of g/L to molar concentrations; PEG 8 refers to PEG 8000).

The presence of intermediates, we propose, arises from a change in the nature of the interactions of the crowders with the protein. For example, for the domain I–II separation, the presence of the intermediate likely implies a crossover from soft (enthalpy-based) potential to a more hard-sphere-like potential, the latter being the predominant effect as per the classical excluded volume theory. Thus, in cases where the transition from the protein ensemble (M1) in pure crowder 1 to the ensemble existing in the presence of pure crowder 2 (M2) is predominantly two-state, it suggests that either there is no aforementioned crossover observed or that the serum protein is insensitive to the same. The first option is not a viable one because there is no reason to believe that the same binary mixture by itself will be behaving differently for the two sets of domain pairs, I–II and II–III. Taking into account the fact that the domain II–III face is a polar one while that of the I–II face is more on the hydrophobic side, the observed changes in the nature of the transitions match the different interaction potential that these faces exude, as we have alluded to in the previous section based on the ΔΔr values. To explain a bit more clearly, let us consider the example of the binary mixture of Dextran 6 and Ficoll 70. The domain I–II side being predominantly hydrophobic,[47] it exhibits appreciable soft interactions with Ficoll 70 as also shown by the large change in the interdomain distance in the presence of this crowder (Figure A). With Dextran 6 influencing conformational modulations predominantly through excluded volume, the intermediate is a probable signature of this change from hydrophobic influence (soft interactions) to hard-sphere potential. Moreover, for this mixture, ΔG2→In0 is greater than ΔGIn→10, with ΔG2→In0 characterizing the phase where the Dextran 6 concentration increases, that is, excluded volume takes over. Such a profile is maintained throughout for “Dextran 6 + Dextran 40” and “Dextran 6 + Dextran 70” mixtures, with “Dextran 6 + Ficoll 70” exhibiting the largest combined ΔG0 (ΔGIn→10 + ΔG2→In0). The latter can be explained based on the fact that Ficoll 70 shows the maximum soft interactions (hydrophobic in nature) with the protein (as noted from the large distance change for this crowder when probed individually). Using the same approach for domains II–III for these Dextran 6 mixtures, the absence of intermediate (I) is due to the fact that this face being more polar, it does not exhibit extensive interactions with the polymeric backbones of the high molecular weight crowders. In other words, it experiences only one type of interaction, that is, the excluded volume effect, thereby making the transition two-state.

Further support of our hypothesis comes from consideration of the mixtures of high molecular weight crowders of “Dextran 40 + Dextran 70” and “Dextran 70 + Ficoll 70”. Because all these through their extended backbone interact with the serum protein via hydrophobic interactions, the “not-so-polar” face of HSA, as described by domains I–II, is subjected to similar interactions throughout the variation in the binary mixture composition, resulting in a two-state transition. Dextran 70 and 40 are flexible, long-chain polymers of d-glucose with sparse, short branches and are better modeled as rod-like particles. Because of their similar shapes and similar extents of domain movements on an individual basis, the “Dextran 40 + Dextran 70” mixture gives rise to the least domain motion, as evident from Figure . Similarly, the two-state transition for these two domains in presence of the “Dextran 6 + PEG 8000” binary mixture is reasoned out based on the fact that at the high PEG 8 concentration, excluded volume predominates, and the same feature is expected to be in operation for Dextran 6 too.

To get an idea of the dependence of the Gibbs free energy change ∑ΔG (only ΔG to be considered where the transition is two-state) as a function of the total change in the interdomain distance Δr′ (where Δr′ = rcrowder 1(200g/L) – rcrowder 2(200g/L)) at the two extremes of the mixture crowder concentrations, we have plotted ∑ΔG against Δr′ in Figure . For both pairs of domains (I–II and II–III), the variation of free energy change is overall linear, with domains I–II showing better compliance with linearity than II–III. In other words, larger change in free energy is associated with a higher change in the interdomain distance (Δr′). Representative plots of HSA and labeled HSA, based on which FRET efficiency was calculated, have been presented in Supporting Information Figure S13. For domains II–III, the “Dextran 6 + PEG 8000” mixture is a complete outlier, that is, a higher free energy change is associated with a much smaller change in the distance. This is again a reflection of the strong nature of electrostatic interactions that PEG 8000 exhibits with HSA, thereby bringing about a greater change in free energy than what was expected.

Figure 6

ΣΔG (“ΔGIn→10 + ΔG2→In0” for three-state transitions and ΔG1→20 only for transitions that are two-state) as a function of the interdomain distance Δr′ (rcrowder 1(200g/L) – rcrowder 2(200g/L)) for (A) domain I–II and (B) domain II–III movement. The number inside each circle corresponds to the different crowder mixtures as follows: (1) Dextran 6 + Dextran 40, (2) Dextran 6 + Dextran 70, (3) Dextran 6 + Ficoll 70, (4) Dextran 6 + PEG 8000, (5) Dextran 40 + Dextran 70, (6) Dextran 40 + Ficoll 70, and (7) Dextran 70 + Ficoll 70.

FCS Studies of Translational Diffusion

FCS experiments were carried out to measure the diffusion time of the reporter molecule FITC in the presence of various macromolecular crowding agents. FCS is based on the measurement of temporal intensity fluctuations of the relevant fluorophore as it diffuses in and out of the confocal volume[57−60] and subsequently correlating these fluctuations according to the following equationwhere δF(t) = F(t) – ⟨F(t)⟩ is the fluorescence fluctuation, with ⟨F(t)⟩ being the average fluorescence intensity over the defined time period. The decay of the correlation function G(τ) provides us a measure of the timescales involved in processes such as diffusion,[61,62] rotational relaxation,[63] conformational dynamics,[64,65] and triplet-state photo-physics[66,67] that bring about fluctuations in the fluorescence of the fluorophore under investigation.

All the autocorrelation curves were fitted well using eq having a single diffusion time (τD) (Supporting Information Figure S14). FITC in buffer only (i.e., in absence of crowders) gave rise to a diffusion time (τ0) of 130 ± 10 μs. Prior to investigating the diffusion characteristics of mixed crowding agents, the diffusion times of FITC (τD) in the individual crowders were measured as a function of the crowder concentration. To facilitate comparison, we have plotted τD/τ0 against the concentration of the crowding agents, where τD is the diffusion time of FITC in the presence of crowding agents and τ0 is the diffusion time of FITC in a simple buffer. Our FCS measurements show that the diffusion time of FITC increases remarkably in the presence of all the macromolecular crowding agents as a function of the concentration (Supporting Information Figure S15). Data reveal that the increase in the diffusion time of FITC is highest in the presence of Ficoll 70 and lowest in the presence of Dextran 6.

Having performed these experiments in the presence of the individual crowding agents, our main focus was to probe the diffusion behavior of FITC in the presence of mixtures of the same binary crowders that were used for the FRET studies mentioned before. Again, the total crowder concentration was kept at 200 g/L. Figure A shows the changes in diffusion times as a function of the mixture compositions. As expected, in cases where the diffusion times of the individual components differ by a huge margin, the change in the τD/τ0 value is quite steep, as exemplified by the “Dextran 6 + Ficoll 70” mixture. To get further insights from the obtained data, we have also plotted the difference in relative diffusion times obtained from the mixture and the sum of the relative diffusion times obtained from the respective individual crowders in Figure B as follows

Figure 7

(A) Plot of τD/τ0 of FITC vs crowder concentration for the mixed crowders (the concentration of Dextran 6 increases along the x-axis in all the four mixtures having this crowder as one of the components; Dextran 70 increases along the x-axis in the “Dextran 70 + Ficoll 70” mixture; Dextran 40 increases along the x-axis in the “Dextran 40 + Ficoll 70” and “Dextran 40 + Dextran 70” mixtures). (B) plotted as a function of the crowder concentration with the x-axis being identical to that in (A).

These plots provide some very interesting insights into the manner in which the diffusion time of FITC in mixed crowding agents is different from that of the individual crowders. τD/τ0 for a particular concentration of mixed crowding agents is always higher than that of the sum of the individual crowding agents at that concentration, except at the extremes where there is only one crowding agent (Supporting Information Figure S16). Moreover, the disparity in diffusion times of FITC is dependent on the nature of the components of the crowding mixtures. For example, the deviation is maximum for the “Dextran 70 + Ficoll 70” mixture followed by that of “Dextran 40 + Ficoll 70” and “Dextran 40 + Dextran 70” mixtures, with the latter two showing very similar behavior. In other words, the differences are much more pronounced in the case of the larger crowding agent mixtures as compared to those where at least one of the components is Dextran 6 (Supporting Information Figure S16).

The diffusion of a molecule is affected primarily because of changes in the microviscosity arising from the manner in which the macromolecular crowding agents self-assemble/entangle in solution.[68−70] On the basis of the fact that (from and ; Rh is the hydrodynamic radius, D is the diffusion coefficient, and η is the viscosity) and assuming η0, the viscosity of water, to be 1.0 cP at 25 °C, the ratio of the diffusion times provides a direct readout of the intrinsic viscosity, more properly referred to as microviscosity, of the systems having crowding agents, either alone or in mixed form. In other words, our data show that the microviscosity of the mixtures is always higher than the sum of the microviscosities of the individual crowding agents (Figure B) at their respective mixture concentrations. These suggest that the crowder molecules in the mixtures are always present in a more entangled form than that of the individual crowder components, such that the resistance to translation motion so faced by the tracer molecule is higher. Moreover, the deviation from the so-called ideality being more for the high molecular weight crowder mixtures is an indication of the enhanced entanglement among these, an aspect that can be logically deduced from the long polymeric chains of these crowder molecules available for network formation.

A few other interesting features also emerge from a closer analysis of Figure B. For the “Dextran 70 + Ficoll 70” mixture, the aforementioned deviation in microviscosity is maximum at 50 g/L Dextran 70 and 150 g/L Ficoll 70, which signifies that at this point, the entanglement between Dextran 70 and Ficoll 70 is also at its maximum. In other words, for these particular concentrations, the interactions between Dextran 70 and Ficoll 70 are most favorable. Subsequently with the increasing concentration of Dextran 70 and decreasing Ficoll 70, the microviscosity decreases, which suggests that the Dextran 70 polymeric units start entangling among themselves rather than the Ficoll 70 molecules (Figure B). The subsequent decrease in entanglement and hence at higher Dextran 70 concentrations can be attributed to the difference in morphologies of the crowder molecules. Ficoll 70 has been assumed to be more spherical in shape while Dextran 70 is more rod-like. Hence, it is understandable that such a morphological mismatch starts exerting its influence once the Dextran 70 concentration is high enough that self-entanglement becomes thermodynamically more viable. Similarly, for “Dextran 40 + Dextran 70” and “Dextran 40 + Ficoll 70” mixtures, the microviscosity mismatch peaks at 125 and 150 g/L Dextran 40, respectively, with the difference showing a steeper drop beyond that in the presence of Ficoll 70, probably because of the shape mismatch between the two crowding agents. On the other hand, the difference is much less for the mixtures involving Dextran 6 (Supporting Information Figure S16), and the trends in mismatch are also quite similar (Figure B). Because Dextran 6 has been established to be exerting predominantly excluded volume effect, the level of entanglement with all the other crowding agents remains more or less the same. Furthermore, our data suggest that the formation of entanglement between crowder molecules in a binary mixture is more favorable where the sizes, as defined by the average molecular weight, of the crowder molecules are similar.

To further investigate the behavior of mixed crowding agents, we have performed the FCS measurements of FITC in the presence of another set of the binary mixture of macromolecular crowding agents where the crowders have been used in a 50:50 (1:1) ratio for each, the ratio being in terms of the weight of crowder dissolved. For example, a 100 g/L crowding mixture is composed of 50 g/L of each individual crowding agent. Here, we have plotted the τD/τ0 value against each mixed crowding concentration (Figure ). This figure clearly indicates that at higher concentrations, the increasing trend in the τD/τ0 value is higher for the larger crowder mixture, that is, “Ficoll 70 + Dextran 70”, “Ficoll 70 + Dextran 40”, and “Dextran 70 + Dextran 40”, as compared to that observed for the mixtures where D6 is present. These data thus support our previous conclusion that the entanglement between the component crowders is less for the mixture where the difference in size is more, that is, where Dextran 6 is present. Again, we have plotted the τD/τ0 value of the sum of the individual crowding agents and obtained the τD/τ0 value of their mixtures (Supporting Information Figure S17). At higher concentrations, as expected, each mixture shows higher τD/τ0 value than that of the sum of the individual crowding agents, which suggests that under these conditions, the entanglement between crowders is much more pronounced and hence the microviscosities of mixed crowding agents are more than the individual crowding agents. However, the scenario is completely different at lower concentrations, wherein the microviscosity experienced by FITC of the mixed crowding agents is slightly less or almost similar as compared to that observed from the sum of their individual crowding agents. For “Dextran 40 + Dextran 70” and “Ficoll 70 + Dextran 6” mixtures, the microviscosity of the individual crowding components is almost additive upto 100 g/L, whereas the microviscosity of the mixtures are significantly higher than the sum of the individual crowding agents beyond 100 g/L. Thus, at lower concentrations, the individual polymer molecules do not show any cross interactions, resulting in the additivity of the microviscosities. At higher concentrations, the marked deviations in between the two profiles again suggest increased entanglement with the differences being larger wherein Ficoll 70 is one of the constituents (Supporting Information Figure S17A,B). Hence, as evident, the internal architecture of the mixture of crowding agents depends on the nature of the individual crowder components.

Figure 8

Plot of τD/τ0 of FITC vs crowder concentration for the mixed crowders.

Summary and Conclusions

The cellular environment comprises a heterogeneous mixture of proteins, nucleic acids, ribosomes, and carbohydrates (polysaccharides), each of which is likely to affect the folding mechanism of different proteins in its own distinctive fashion.[4,6,22,71−75] The excluded volume theory predicts that a high concentration of “inert” macromolecules should stabilize the compact native state relative to any less compact unfolded or partially folded state of the polypeptide. We extended our idea of mixed macromolecular crowding to study the effects of binary mixtures of crowders on the domain movement of the multidomain protein, HSA, by mapping the changes in interdomain distances. We observe that mixed crowding induces significant cooperativity in the domain motion as compared to that of the individual crowders, a feature that bears tremendous significance with regard to the folding energy landscape of this serum protein in that domain interfaces have been hypothesized to play a critical role in the overall folding of the multidomain protein (see below). Cooperativity in protein folding is associated with the negligible presence of intermediates in between the folded and the unfolded states, that is, the folding–unfolding transition being primarily two-state.[76,77] However, multidomain proteins have been known to exhibit a certain degree of noncooperativity, primarily because of the existence of domains that are capable of folding independently.[77] The presence of cooperativity has been proposed to be advantageous because the absence of partially folded–unfolded states would tend to decrease the chances of that particular protein to aggregate.[78,79] Moreover, as mentioned above, in proteins having multiple domains, the existence of a cooperative transition is often dictated by interactions present at the domain–domain interfaces because it is the magnitude of such forces that primarily make the transitions deviate from an “all or none” (cooperative) process. Thus, in our case, the manner in which the domains move relative to each other as a function of the crowders can be considered to be a strong signature of how well-connected the domain interfaces are, that is, how cooperative the protein is under the given conditions. Thus, the observation that in the presence of the single crowders (Figure ) the domains move rather gradually as the crowder concentration is varied implies that the protein goes through multiple intermediates. On the other hand, crowders are also known to enhance aggregation tendency. Thus, combining this noncooperativity of the domain motion of HSA and aggregation enhancing propensity of the crowders, it seems that in the presence of a single macromolecular crowding agent, the protein is being almost tuned to becoming more aggregation-prone. With the binary crowder mixtures, however, this condition stands quite alleviated as the protein always experiences a high enough crowder concentration, with the only caveat being that the composition changes. Hence, the increase in cooperativity that becomes evident in the mixtures is probably one of the means by which in spite of the high degree of crowding inside the cells, aggregation is less predominant, thereby bringing to the fore one of the advantages that a mixed crowding scenario offers.

Also, a distinct crossover between two different types of forces, namely, entropic and enthalpic, was observed in terms of the presence of intermediate states and increased ΣΔG values. A closer look at Tables and 2 reveals that the obtained three-state transitions and the proposed crossover arises mainly for those mixtures where either the difference in the average molecular weight is high (e.g., “Dextran 6 + Ficoll 70” in Table ) or where there is a considerable difference in the gross architecture of the crowders (e.g., “Dextran 40 + Ficoll 70” and “Dextran 6 + PEG 8” in Table ). It should also be noted that for the three-state transition cases, wherever Dextran 6 is involved, the change in free energy for the second step which occurs when the Dextran 6 concentration is increased, is always on the higher side, a feature that we propose is a signature of the effect of Dextran 6 being predominantly that of excluded volume. This can be attributed to the high packing density of Dextran 6 (arising from it having the least molecular weight among the crowders used in this study), wherein at high concentrations of this crowder, the work done in creating a cavity to house the serum protein is presumably more. Furthermore, the observed switch in the nature of transitions depending on the domain I–II or domain II–III face supports the fact that these two faces of HSA exude different extents of hydrophobic potentials, that is, HSA presents an asymmetric structure disposition. This also points to the fact that the serum protein, with its vast array of amino acids, can direct the arrangement of crowders around itself depending upon the nature of the latter. Moreover, the deviation of the domain separation as observed in the mixtures, from that expected in the case of a strictly ideal solution, is a strong evidence of the nature of entanglement and hence the complexity of the crowded milieu.

To put these results into perspective with regard to the structure of the serum protein, it is known that the binding of FAs to HSA invokes significant conformational changes that involve large-scale domain movements.[42,50,51] Binding of myristate (there are six binding sites of myristate on HSA), a long chain FA, brings about relative rotations of the three domains with these domains themselves undergoing only a modest distortion. For example, domains I and III are displaced to the left, thereby opening the central crevice and increasing the width of the protein, with the latter serving as a possible discriminatory gate for further entry of drugs that are known to bind to the subdomain cavities of HSA. Myristate binding to subdomain IIIA of HSA replaces the interaction in the domain interface between Glu 450 (of subdomain IIIA) and Arg 348 (of subdomain IIB) which have minimal effect on the local structure of the multidomain protein.[50,51] Moreover, FAs also affect binding of ligands such as heme to HSA through an allosteric mechanism that includes subtle movement of several amino acids. Few other studies show that because of the rotation of the domain interfaces of I and III, substantial conformational changes occur in HSA which significantly affect the FA binding in that specific domain of HSA.[42,43,50] Thus, as evident, domain movements play a critical role in the function of the serum protein. Keeping in mind the fact that crowders (whether individual or mixed) affect the relative domain distances considerably, it is thus logical to expect that the same will be modulated extensively in the crowded milieu, with the mixed crowding scenario providing us a closer mimic of the physiological interior.

Diffusion in the crowded medium is hindered[80] and has often been considered to be anomalous.[81,82] Anomalous diffusion of the subdiffusive type is generally represented by the value of α < 1, where α is the diffusion exponent that characterizes the dependence of the mean-squared displacement of the fluorescent reporter on time (t). Using FCS, it was shown that the value of the exponent deviated progressively from 1 as the crowder concentration was increased. Another FCS study reported that the microviscosity of Ficoll 70 and not bulk viscosity was the prime factor in enhancing actin polymerization.[83] While the aspect of diffusion in the presence of crowders being anomalous is still a matter of debate,[84] the heterogeneity of the crowded milieu has generally been accepted. Thus, the fact that our FCS studies showed that the microviscosities of the mixed crowders and those of the individual components can be quite different not only provides a peek into the underlying heterogeneity of mixed crowding but also gives us a hint as to what the possible factors are that might affect the extent of deviations from the ideality that we have reported in this work. One such factor that stands out is the size of the crowders. Because the deviation is most for the mixtures of the higher molecular weight crowders (e.g., “Dextran 70 + Ficoll 70” mixture), we propose that this arises from extensive interpolymer entanglement of the long chains of the individual crowder molecules. Moreover, the rapid drops in nonideality observed in such cases can be attributed to a type of phase separation or depletion interactions, wherein a higher number of molecules of the same crowder prefer to stay together. Indeed, to get a more comprehensive understanding, such mixtures need to be extensively studied using various approaches. One possible approach would be to have a labeled crowder molecule, such as FITC-labeled Dextran[85] or FITC-labeled Ficoll or labeled PEG serve, as the tracer molecule for FCS experiments and studies involving single particle tracking, with the latter having been shown to provide a better picture of the crowded milieu. A recent paper has revealed how the crowder molecule PEG 10000 labeled with a FRET pair undergoes changes in efficiency arising from modulations in the distance between the donor–acceptor pair in the presence of different crowders and also under intracellular conditions.[86] Using a similar ploy for different crowder molecules will also provide us much needed insights into the mixed crowding scenario that we have dealt with in this paper.[86]

Finally, we would like to make an attempt to correlate the observations that we have obtained from the two different approaches, one being the domain movement using FRET and the other being the translational diffusion through FCS. Though the two approaches used in this study are different in their own respects, in both the cases, significant deviations from ideality were observed, particularly for the mixtures of the larger crowders. The length-scale over which the domain motion of HSA occurs and gets modulated is of the order of a few angstroms and hence focuses more on the microscopic arrangement of the crowders in the immediate proximity of the serum protein. On the other hand, the translation motion involves much larger distances, typically in the range of nanometers and hence can be considered to be more macroscopic relative to the former. This implies that the observed heterogeneity and deviation from simple additivity exists at several lengthscales in such mixtures of macromolecular crowders and is in agreement with previous reports.[36]

To conclude, we have studied the effect of mixed macromolecular crowding agents from two different aspects, namely, the domain movement of the serum protein HSA and the translational diffusion of FITC. The choice of HSA as the test protein was dictated not only by the fact that it has been one of most well-studied proteins with respect to small molecules and FA binding but also by the fact that such noncovalent associations often induce appreciable angular displacements in the serum protein.[87,88] Moreover, previous reports have shown that macromolecular crowding agents have an appreciable influence on the domain movements of HSA.[46,47] Our data show that for both the cases, the effect of mixed macromolecular crowding is nonadditive, that is, it deviates from that of the sum of the individual components of the respective mixtures. This observation is important because it occurs in spite of the fact that the effects of the mixed crowders on the charged protein HSA and the minimally perturbing fluorescent tracer molecule have been shown to be quite different. The enhanced cooperativity in the domain separation in the presence of the mixed crowders also suggests that the observed increase in refolding kinetics and decrease in competing aggregation pathways of previous studies[33,37] might be a direct outcome of such a phenomenon.

Experimental Details

Materials and Method

Essentially, FA-free HSA, FITC, and all the macromolecular crowding agents [Ficoll 70, Dextran 70, Dextran 40, Dextran 6, and polyethylene glycol 8000 (PEG 8)] were purchased from Sigma-Aldrich Chemicals Pvt. Ltd. (USA) and used as received without purification. Sodium phosphate dibasic anhydrous (Na2HPO4), sodium phosphate monobasic anhydrous (NaH2PO4), and sodium carbonate (Na2CO3) and bicarbonate (NaHCO3) were purchased from Merck Specialities Pvt, Ltd. (Mumbai) and used as received. Acrylodan was purchased from Molecular Probes Inc. (Invitrogen, USA), and NPA was obtained from Clearsynth Labs (France). Keeping the overall crowder concentration fixed at 200 g/L, all different binary combinations of individual crowders were prepared, each at the 25 g/L interval. For example, for the “Dextran 6 + Dextran 40” mixture, these two crowders were mixed in the following ratios: 0:200, 25:175, 50:150, 75:125, 100:100, 125:75, 150:50, 175:25, and 200:0 in pH 7.4 phosphate buffer, with the concentrations expressed in grams per liter. Here, for example, 0:200 represents 0 g/L of Dextran 6 and 200 g/L of Dexran 40. Likewise, 75:125 implies 75 g/L of Dextran 6 and 125 g/L of Dexran 40.

Cys-34 and Tyr-411 of HSA were covalently modified using acrylodan and NPA as discussed elsewhere.[46,47] Absorption measurements were performed in a double-beam Shimadzu UV–vis Spectrophotometer (UV-2450, Japan) using 1 cm path length cuvettes. Absorbance values of the protein solutions were measured in the range of 200–600 nm, and molar extinction coefficient values used were as follows: ε277 = 36 500 M–1 cm–1 for HSA, ε365 = 21 000 for acrylodan (Ac), and ε365 = 20 000 M–1 cm–1 for NPA (4-nitrophenyl anthranilate).[88]

Steady-state fluorescence measurements were carried out on an Edinburgh Instruments (UK) fluorescence spectrometer (model: FLS920). The fluorescence spectra of protein samples at different pH buffer solutions in the presence and in the absence of crowders were measured using fluorescence quartz cuvettes. Prior to each experiment, the concentration of every sample was measured using the UV spectrophotometer (model UV-2450, Shimadzu). The fluorescence spectra of the protein samples were recorded at 25 °C, with the temperature being maintained by a Peltier-based controller, and the protein concentration was maintained at 8 μM for all the experiments. The samples were allowed an equilibration time of 12 h (at 4 °C) before acquiring their respective spectra. Samples containing unlabeled HSA were excited at 295 nm, and emission was collected from 310 to 550 nm in 1 nm increments with an integration time of 0.5 s, using a band pass of 4 nm in both the excitation and emission arms of the instrument. To obtain information about domains I and III, acrylodan-labeled HSA (Ac-HSA) and NPA-labeled HSA (NPA-HSA) samples were excited at 365 nm, with emission collected from 380 to 600 nm in 1 nm increments using an integration time of 0.5 s and a band pass of 2 nm in both the excitation and emission arms of the instrument.

For FCS experiments, sodium carbonate–bicarbonate buffer (50 mM) of pH = 9.4 was prepared by dissolving weighed amounts of sodium carbonate and bicarbonate in Millipore water (Elix 3 UV; Millipore, Molsheim, France). pH of the buffer was maintained using a pH meter (Hanna HI 3220). The solutions of macromolecular crowding agents were prepared by dissolving the crowding agents in sodium carbonate–bicarbonate buffer after weighing out the appropriate amounts using a Precisa XB 120A (Sweden) analytical balance to get the desired concentration.

FRET Analysis

Trp–acrylodan and Trp–NPA moieties form an efficient FRET pair and hence allow one to calculate the distance between the two domains of the protein in response to any perturbation (with Trp being in domain II and acrylodan in domain I and NPA in domain III).[47] The efficiency of the energy transfer (E) as a function of distance (r) between two probes can be expressed as followswhere R0 (Förster radius) represents the distance at which energy transfer is 50% efficient, IDA is the intensity of the donor in the presence of the acceptor, and ID is the unquenched donor intensity (i.e., in the absence of the acceptor). The value of R0 (in Å) can be obtained from the equation belowwhere J(λ) is the overlap integral, n is the refractive index of the medium, and κ2 is the orientation factor between the donor and acceptor electronic transition dipole moments. For our study, we have calculated the energy transfer efficiency from the area under the curve of the Trp emission from the labeled and unlabeled proteins.

The value of R0 for the native protein was first calculated in the phosphate buffer and was determined to be ∼28 and ∼23 Å (using the donor quantum yield of 0.14, a J(λ) value of 1.18 × 1014 nm4 M–1 cm–1 for Ac HSA and 8.18 × 1013 nm4 M–1 cm–1 for NPA HSA and with κ2 set to 2/3 and n set to 1.34) for Ac HSA and NPA-HSA, respectively. To make sure that the observed changes in FRET efficiencies were not due to any abrupt modulations in R0 of the donor acceptor pairs, the R0 and J(λ) were also calculated using MATLAB R2013B software for every crowder mixture. Because the labeling efficiency was not 100%, all FRET data (Eobs) included were corrected for the acceptor stoichiometry. The corrected efficiency (Ecor) is given as Ecor = Eobs/fa, where fa is the fraction of the assembly with the acceptor. For simplicity, we have stated the Ecor as E for all the calculations.[89,90]

Thermodynamic Analyses

Depending on the nature of the transition, the distance change “r” during the movement of domains was fit either to a two-state or a three-state model.[91−93] On the basis of this method, we have assumed that the standard free energy of unfolding ΔG1→20 is a linear function of the concentration of the crowder being varied in the binary mixture (eq ). Closer analysis of Figure suggests that for any crowder at a very high concentration (∼150 g/L), there is almost no change in interdomain separation for both the domains. From this observation, we have assumed that for mixed crowding at very high concentrations of any of the component of the binary mixture, the domain motion attains a near saturation, akin to folded and unfolded baselines as used in the denaturation studies of proteins.where ΔG1→20(H2O) is the free energy change for the domain movement in the absence of crowder 2, and m, the slope, is a measure of the dependence of the change in free energy on the crowder Mc. In the following two-state equilibrium, M1 ⇋ M2, M represents the conformational states of the protein in the pure macromolecular crowders, and the subscripts 1 and 2 refer to the individual crowder components of the binary mixture. It should be noted that in eq , Mc is that crowder whose concentration is being varied in the mixture. For example, in the mixture of Dextran 6 and Dextran 40, because the concentration of Dextran 6 is being varied, the Mc refers to the concentration of Dextran 6.

The FRET-based interdomain distance during the domain movement can be expressed in the following mannerwhere r is the measured interdomain distance, r1 and r2 are the distances between the domains of the protein in the crowders M1 and M2, respectively, and X1 and X2 stand for the mole fractions of these states, respectively. Both r1 and r2 were assumed to depend linearly upon the concentration of the varied crowder [Mc] in g/L

Mole fractions (X1, X2) are related to the equilibrium constant by

Considering the fact that the standard free energy change and the equilibrium constant for the two-state process is given bycombining eqs –9, one can express the observed interdomain distance r bywhere R is the gas constant, and T is the temperature in Kelvin. The two-state transitions were fit to eq and from the nonlinear least squares analysis providing the best fits to the data, the values of ΔG1→20(H2O) and m were obtained.

In some cases, a three-state model for unfolding had to be used for a more proper analysis of mixed crowding-induced domain movement profiles for HSA. The equilibrium can be written aswhere M1 and M2 have their meanings as described above, with “MIn” being the intermediate that gets populated at equilibrium. The MI ⇋ MIn and MIn ⇋ M2 equilibria are characterized by the equilibrium constants and and the free energy changes, ΔGIn→10 and ΔG2→In0, respectively.

For the three-state model, r is given by the following equation[91]where Z1 is a parameter that measures the optical characteristics (in this case, the interdomain distance) of the intermediate MI in relation to that of M1 and M2 and is given bywhere rI is the interdomain distance in the intermediate MIn, and r1 and r2 have the usual meaning as mentioned above.

It has been assumed that the free energies of the domain movement of M1 and M2 both show a linear dependence on the crowder concentration.

Here, we would like to point out the essence of the x-axis, for the plots in Figure . In the mixtures containing Dextran 6 and another crowder, the concentration of Dextran 6 has been varied along the x-axis. For example, in the “Dextran 6 + Ficoll 70” mixture, the “zero” reading of the x-axis corresponds to 0 g/L of Dextran 6 and 200 g/L of Ficoll 70. Similarly for the “Dextran 40 + Dextran 70” and “Dextran 40 + Ficoll 70” mixtures, the Dextran 40 concentration has been varied along the x-axis, whereas for “Dextran 70 + Ficoll 70”, the concentration of Dextran 70 has been varied. For better insights, we have also plotted a comparison of Δr, where one of these, Δrmc, is obtained directly from the mixed crowding data as followswhere mc stands for mixed crowding, rmc is the interdomain distance in the mixed crowding environment, and r0 is the corresponding interdomain distance of HSA in buffer only, that is, in the absence of any crowding agent. The other one, more specifically ΣΔr, is the summation obtained from the individual crowders as followswhere Δr has the same meaning as in eq , with mc replaced by either C1(X) or C2(200 – X), with C1(X) representing “X” g/L of crowder 1 and C2(200 – X) representing “200 – X” g/L of the second crowder (crowder 2) in the binary mixture. For example, in the “Dextran 6 + Dextran 40” mixture, ΣΔr at 50 g/L of Dextran 6 corresponds to the sum of Δr values obtained at 50 g/L Dextran 6 and 150 g/L Dextran 40. The comparison of the Δr trends has been provided in Figures –5 (and Supporting Information Figures S1–S4).

Fluorescence Correlation Spectroscopy

FCS measurements were carried out using a custom-built confocal setup based on an inverted microscope (Olympus) platform, equipped with a water immersion objective (NA = 1.2, 60×). The tracer dye, FITC, in different media (with and without crowders) was excited with the 488 nm line of a CW argon-ion laser (Modu-Laser, model: Stellar Pro. Select), with the light being guided onto the dichroic from the laser using a single-mode fiber. The fluorescence from the samples was collected with the same objective and focussed onto an avalanche photodiode (model: SPCM-AQRH-14, Canada) fitted with a 50 μm confocal pinhole. Fluorescent bursts from the molecules diffusing through the confocal volume were collected, and the photons were correlated in the auto-correlation mode using a FLEX correlator card (Flex02-01D/C), Correlator.com, USA). The FCS traces so obtained were analyzed according to the following model[92]where N is the average number of molecules in the confocal volume, τD is the diffusion time of the tracer molecule, ω is the ratio between radial and length of the confocal volume, τtriplet is the triplet lifetime of the fluorophore, and T is the corresponding triplet amplitude.