Efficient encapsulation of proteins with random copolymers

Trung Dac Nguyen, Baofu Qiao, and Monica Olvera de la Cruz
PNAS June 26, 2018 115 (26) 6578-6583; published ahead of print June 12, 2018 https://doi.org/10.1073/pnas.1806207115

  1. Contributed by Monica Olvera de la Cruz, May 16, 2018 (sent for review April 12, 2018; reviewed by Andrey V. Dobrynin and Alexander Y. Grosberg)

Significance

Inside cells of living organisms, aggregates rich in disordered proteins organize the local environment to promote cellular functions. These membraneless organelles are able to concentrate enzymes and biomolecules to regulate interactions via the multiple conformations and compositions of disordered proteins. The interior of these organelles seems to behave akin to organic solvents. This opens the possibility of assembling synthetic organelles using random copolymers that mimic disordered proteins to disperse and stabilize enzymatic proteins in different environments, including organic solvents. Here, we demonstrate that random copolymers with solvophobic and solvophilic groups can encapsulate numerous proteins, including Candida antarctica lipase B, subtilisin, cutinase, and pseudolysin, in basically any solvent. These aggregates are promising constituents of synthetic membraneless organelles.

Abstract

Membraneless organelles are aggregates of disordered proteins that form spontaneously to promote specific cellular functions in vivo. The possibility of synthesizing membraneless organelles out of cells will therefore enable fabrication of protein-based materials with functions inherent to biological matter. Since random copolymers contain various compositions and sequences of solvophobic and solvophilic groups, they are expected to function in nonbiological media similarly to a set of disordered proteins in membraneless organelles. Interestingly, the internal environment of these organelles has been noted to behave more like an organic solvent than like water. Therefore, an adsorbed layer of random copolymers that mimics the function of disordered proteins could, in principle, protect and enhance the proteins’ enzymatic activity even in organic solvents, which are ideal when the products and/or the reactants have limited solubility in aqueous media. Here, we demonstrate via multiscale simulations that random copolymers efficiently incorporate proteins into different solvents with the potential to optimize their enzymatic activity. We investigate the key factors that govern the ability of random copolymers to encapsulate proteins, including the adsorption energy, copolymer average composition, and solvent selectivity. The adsorbed polymer chains have remarkably similar sequences, indicating that the proteins are able to select certain sequences that best reduce their exposure to the solvent. We also find that the protein surface coverage decreases when the fluctuation in the average distance between the protein adsorption sites increases. The results herein set the stage for computational design of random copolymers for stabilizing and delivering proteins across multiple media.

The ability to maintain the enzymatic activity of proteins out of their native aqueous medium is crucial for the pharmaceutical and chemical-processing industries. Among the most important reasons to use organic solvents in place of water is to reduce aggregation of hydrophobic reactants and products, to enable reactions that are not favored in water, and to allow for energy-efficient downstream processing with volatile solvents to suppress side reactions caused by water, as well as to prevent microbial growth, to name a few (1). However, in foreign media such as organic and highly polar solvents, proteins are prone to a substantial reduction in their functionalities, as their structure, solubility, and conformational mobility are heavily affected (2⇓–4). Common approaches for stabilizing proteins in nonnative solvents are devoted to mediate protein–solvent interactions such as via protein sequence design, solvent modification, polymer conjugation, reverse micelles, and nanoconfinement (5). However, these methods are often protein- and solvent-specific and yet not cost-effective in retaining protein functions. The challenge here is to encapsulate the proteins with a coating shell that minimizes nonfavorable protein–solvent contacts while preserving the structure and conformational mobility of the proteins.

Random copolymers have long been recognized as an interesting choice for applications involving pattern recognition of molecules and multifunctional disordered surfaces (6⇓⇓⇓–10). Due to the randomness in their monomer sequence reminiscent of intrinsically disordered proteins (11), this special family of copolymers is expected to allow for unique versatility that helps the surfaces to select the most favorable sequences for adsorption. The phase behavior of random copolymers in solution and in melt (12⇓⇓⇓⇓⇓⇓⇓⇓⇓–22), as well as their adsorption onto numerous surfaces and interfaces (7⇓⇓–10, 23, 24), have been under extensive investigation. Bratko et al. showed that random copolymers recognize disordered surfaces when the statistics characterizing the disordered surfaces and the polymer sequences satisfy certain conditions, so-called statistical pattern matching (7). Srebnik et al. (8) demonstrated that random copolymers in selective solvent undergo a sharp (but continuous) transition from weak to strong adsorption to a surface with disordered adsorption sites when the density of the adsorption sites, or, equivalently, the net adsorption strength, exceeds a certain threshold. The adsorption strength threshold is dependent on the attraction strength between polymer segments, which effectively controls the entropy difference between the nonadsorbed state and adsorbed state. Ge and Rubinstein (23) developed a scaling model for adsorption of a solution of polymers with regularly distributed sticky monomers adsorbed on a flat surface with sticky sites. Their model predicted that at a given bulk density the morphologies of the adsorbed layers, which vary from mushrooms to stretched loops to self-similar carpets, result from the competition between two length scales: the average nearest distance between the sticky sites, l, on the polymer chain, and that between neighboring sticky sites on the substrate, d. Hershkovits et al. proposed a scaling model for adsorption of homopolymers on spherical clusters in a good solvent (25). They showed that the structural properties of the adsorbed polymer layers are influenced by surface curvature when the cluster size is similar to, or smaller than, the polymer radius of gyration. Meenakshisundaram et al. analyzed the effects of copolymer sequences as compatibilizers that adsorb at the liquid–liquid interface of two immiscible homopolymers (24). They found that the monomer sequence specificity of the binary copolymers plays an important role in minimizing the interfacial energy. Given the inherent multicomponent nature in composition and in sequences of random copolymer solutions, it is not clear which sequences adsorb more favorably onto a finite-size patterned substrate with high curvature, like a protein, and the degree of adsorption as the quality of the solvent varies. The above-mentioned studies as well as previous scaling and mean field adsorption models (26⇓⇓⇓⇓⇓–32) cannot readily be extended to describe this random copolymer adsorption process, given that the copolymers should not be too long so that the attraction between the polymers and the protein permits the protein to maintain its structure and functionalities. This constraint generates large fluctuations in the correlations between the disorder quenched in the copolymer sequences and in the protein surface disordered pattern.

It is evident that by varying the volume fraction and composition of the constituent monomers, one can tune the effective attraction between the copolymers and the substrate. Interestingly, recent studies in membraneless organelles, which are spatiotemporal aggregates with high concentrations of disordered proteins (33), demonstrate that disordered proteins hold aggregates of biomolecules including enzymes together in an environment that behaves more like an organic solvent than water (34). Therefore, random copolymer solutions, which contain chains of various compositions and sequences, can be designed to mimic disordered proteins and used to disperse enzymatically active proteins in organic solvents. Recently, Xu and coworkers demonstrated that a special case of random heteropolymers with four different monomers allows for highly effective encapsulation of numerous enzymes (35). The enzymes coated by this type of random heteropolymers are soluble in toluene and retain their enzymatic activity after days. The key challenge for this strategy is to predict the optimal average composition of the monomers that yields maximum surface coverage for a specified protein in a given solvent condition. It is therefore crucial to find the connection between the characteristics of the target protein and the desirable composition of the random copolymers. In the present study, using multiscale modeling and molecular simulation, we investigate the key factors that influence the encapsulation of random binary copolymers for several model proteins. By examining the microscopic details of the adsorbed polymer layers, we find the relationship between the protein surface coverage and adsorption strength, solvent selectivity, and the average composition of the adsorbing monomers. Our study predicts the optimal average composition ϕA* of the adsorbing component that maximizes the protein surface coverage, which is attributed to the delicate interplay between the adsorption strength and solvent selectivity. Importantly, we demonstrate that the random copolymers allow for the host proteins to selectively pick the polymer sequences that minimize the protein exposure to the solvent, in a manner reminiscent of disordered proteins. Finally, we find that the protein–solvent interactions can be effectively mediated by choosing the suitable average composition of the adsorbing random copolymers.

Simulation Model

We briefly present our simulation model of the proteins and random copolymers with the key parameters and relevant terms used throughout the work. Additional details on the simulation procedure and data analysis are given in Materials and Methods and SI Appendix, section I.

Protein.

Fig. 1A shows the all-atom model of the enzyme Candida antarctica lipase B (1TCA) equilibrated in water. Using the shaped-based coarse-graining algorithm mentioned in SI Appendix, we find the coarse-grained (CG) beads for the atoms in the hydrophobic groups and for those in the hydrophilic groups (Fig. 1B and SI Appendix, Fig. S2). The number of the CG beads is chosen so that the distance between the nearest beads of the same type is ∼5.0 Å, as measured by their radial distribution functions. Additionally, we keep the ratio between the numbers of the CG beads in the hydrophilic and hydrophobic groups approximately equal to that between the number of atoms in the respective groups in the all-atom simulation. For instance, our model protein 1TCA is composed of 97 hydrophilic CG beads and 77 hydrophobic CG beads. Without loss in generality, the hydrophilic beads are chosen as adsorption sites (green) for the polymer beads (blue). This coarse-graining procedure is in good agreement with all-atom simulations with regard to the spatial distribution of the hydrophobic and hydrophilic domains (SI Appendix, Fig. S1).

Fig. 1.
Fig. 1.

Models and snapshots. (A) Representative configuration of the protein 1TCA equilibrated in water using all-atom simulations, with hydrophobic (red) and hydrophilic (green) residues. (B) Shaped-based CG model obtained from the all-atom configuration in A and an instance of the random copolymers composed of N=20 beads with a disordered sequence of the bead types (Right). For the protein, the adsorption sites are green beads. For the polymer chains, the adsorbing units (type A) are in blue, and the nonattractive beads (type B) are in orange. Images are created by VMD (36). The nonbonded interactions modeled by the Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) potentials, as well as the bonded interactions (FENE) are described in SI Appendix, section I. The LJ potential captures the tendency of the polymer beads of type A to aggregate to minimize their contacts with the solvent molecules via ε=εpp and the attraction between the polymer beads of type A and the adsorption sites on the protein via ε=εhp, both in unit of kBT. The WCA potential captures the excluded volume interaction between the species and their tendency to segregate. In our CG model, the σ parameter of the LJ and WCA potential corresponds to ∼5.0 Å. (C) Histogram of the adsorbing component fraction, fA, for batches of 50 random copolymer chains. Error bars are the standard deviations from averaging over 20 different batches. The average composition of the random copolymers, ϕA, is given by ϕA=∑fAP(fA)/∑P(fA). (D and E) Representative simulation snapshots for ϕA=0.7 and εpp=0.8: εhp=0.8 (D) and εhp=1.2 (E). The average surface coverages are 40% and 75%, respectively.

Random Copolymers.

We consider a classical model of binary random copolymers composed of two monomer types, A and B (12, 13). For simplicity, we assume that the polymer chains have the same total number of beads, N=20. To model the random composition of the A–B copolymers, we sample the fraction of type A per chain, fA, from a Gaussian distribution, with the mean value of ⟨fA⟩=ϕA and variance σf2=ϕA(1−ϕA)/N. Throughout the present study, the average copolymer composition is defined as the average fraction of type A monomers, ϕA. Fig. 1C shows the representative histograms of the composition of the type A beads in different batches of Nc=50 polymer chains for the average composition ϕA=0.5 (for other values of ϕA, see SI Appendix, Fig. S3). We then shuffle the order of the polymer beads for individual chains to create the sequence disorder. To improve the statistics of our results, we perform up to 10 independent simulations with different sets of random sequences by varying the random seed used for generating the number of A beads for each chain. These additional simulations help ascertain that the equilibrated configurations are not biased by the limited number of the polymers per protein.

Results and Discussion

Fig. 1 D and E shows two representative snapshots for partial and nearly complete coverage of the protein by Nc=50 polymer chains for ϕA=0.7. For εpp=0.8, the attraction between the type A polymer beads is strong compared with the adsorption strength between A and the protein sticky beads, εhp=0.8 (Fig. 1D); the polymer chains therefore collapse into a dense aggregate on the protein surface. For εhp=1.2 (Fig. 1E), the adsorption energy is sufficiently stronger than the attraction between the type A beads, favoring the polymer chains spread all over the protein surface. The two scenarios are reminiscent of the wetting/dewetting phenomena observed in thin film–substrate systems, where the stability of the liquid-like polymer layers is governed by the competition between the polymer–protein and polymer–polymer attractions—that is, εhp and εpp, respectively.

We first analyze the similarity in the monomer sequences of the adsorbed polymer chains. Subsequently, we characterize the correlation between the spatial distribution of protein adsorption sites and the protein surface coverage of the random copolymers. We then report the dependence of the protein surface coverage of the random copolymers on the adsorption energy (εhp) and solvent selectivity (as represented by the attraction between the polymer beads of type A, εpp) for a given value of ϕA. Finally, we examine how the effective protein–solvent interaction is mediated in the presence of the coating polymer layer.

Sequence Similarity Between the Adsorbed Polymer Chains.

To examine whether the protein would favor certain sequences out of the available random sequences, we characterize the correlation in the monomer sequence of the adsorbed polymer chains for the given model protein. We define the order parameters to characterize the similarity between the sequences within the same batch and between those from two batches (Materials and Methods). For ϕA=0.5−0.8, the sequence similarity order parameter for the polymer chains with random sequences within individual batches Sintra ranges from 0.55 to 0.60, which means that the sequences are sufficiently uncorrelated.

Our simulation results reveal that the sequence similarity between the adsorbed chains within the individual batches is well beyond that between all of the chains and the threshold value of 0.6 for close matches. We performed simulation of 20 different batches, each with Nc=50 polymer chains and compute the sequence correlation between the adsorbed chains among the batches Sinter (Fig. 2A). The average value of Sinter is 0.78±0.006, indeed indicating that the adsorbed monomers from any two batches are strongly correlated. We also find that the average similarity order parameter across all of the values of εhp=(0.5−2.0) (Fig. 2B) is Sinter=0.73±0.008, despite the fact that the number of the adsorbed chains nads varies with εhp. As can be seen from Fig. 2C (and SI Appendix, Fig. S3), the sticky fraction of the adsorbed chains, (fA)ads, is different from that of all of the chains. All of these results strongly suggest that certain sequences are more favored to adsorb to the protein than others.

Fig. 2.
Fig. 2.

Sequence similarity analysis. (A) Sequence similarity order parameter between the batches Sinter of the adsorbed chains for εhp=1.0. (B) Sequence similarity order parameter for the adsorbed chains Sinter for different values of εhp. εpp=0.8 and ϕA=0.7. Different polymer batches are used for each value of εhp. A value of S=0.5 corresponds to uncorrelated sequences and S≥0.6 to close matches. (C) Histograms of the sticky component fraction, fA, of all of the chains in a batch and of the adsorbed chains, (fA)ads.

Versatility.

As shown in the work by Panganiban et al. (35), random heteropolymers of the same average composition are able to retain the activity of numerous enzymes in toluene equally efficiently. This is of practical importance because it suggests that the approach is not restricted to specific proteins or solvents, which is advantageous compared with other approaches such as polymer conjugation. Consistent with experimental findings in ref. 35, our simulation results indicate that random copolymers with the same average composition covers the proteins under investigation (Fig. 3A) fairly effectively. For instance, for ϕA=0.7 surface coverage Γ varies from 0.75 to 0.95 for 1TCA and PDB ID codes 1A2Q, 1EZM, 1CEX, and 1UBQ (Fig. 3B). The variation of Γ with ϕA is dependent upon specific proteins. For 1A2Q, there exists an optimal value of ϕA for maximum surface coverage, similar to what was observed with 1TCA. For 1CEX and 1EZM, Γ is consistently high and fairly independent of ϕA.

Fig. 3.
Fig. 3.

Encapsulation of numerous proteins. (A) CG model of the proteins under investigation: ubiquitin [Protein Data Bank (PDB) ID code 1UBQ], cutinase (PDB ID code 1CEX), pseudolysin (PDB ID code 1EZM), and subtilisin (PDB ID code 1A2Q). (B) Surface coverage as a function of ϕA for εhp=1.2 and εpp=0.8 for the model proteins under investigation. (C) Surface coverage as a function of the variance in the distances between the adsorption sites, sd2, for ϕA=0.7, εhp=1.2 and εpp=0.8.

To better correlate the ability of the random copolymers to encapsulate the proteins with the features of the protein surface, we compute the distance distribution of the protein adsorption sites P(d) (SI Appendix, Fig. S5). The variance in the distances between the adsorption sites, sr2, is given by sd2=⟨d2⟩−⟨d⟩2. Fig. 3C shows that the proteins with smaller values of sd2, i.e., with narrow distance distributions between the adsorption sites (i.e., 1UBQ, 1CEX, and 1EZM), get encapsulated well by the random copolymers for all of the average compositions tested. Meanwhile, for those with broad distance distributions between the adsorption sites, the random copolymers should have an optimal average composition so to maximize the protein surface coverage. This suggests that the distribution of the distance between the adsorption sites, in addition to the size and shape of the proteins, would be important features for designing the encapsulating random copolymers. It is not possible for the short copolymer chains examined here to make a rigorous analysis on the relationship between the average distance between sticky monomers l and the average distance between adsorbing site on the protein d because the fluctuations in both d and l (SI Appendix, Figs. S5 and S6) are very large.

Surface Coverage as a Function of Average Polymer Adsorbing Fraction and Solvent Selectivity.

Large values of ϕA and εpp favor the folding of the polymer chains into few energetically favored conformations. Consequently, the adsorption strength, εhp, should be sufficiently high to unfold the polymer chains or, in other words, to induce the dewetting–wetting transition of the polymer adsorbed layers on the protein surface. We show in Fig. 4 and SI Appendix, Fig. S7 the variation of Γ with respect to ϕA for different values of εpp and εhp. For εpp=0.3 (Fig. 4A), the solvent is good for the polymer A beads, Γ increases monotonously with ϕA for all values of the adsorption strengths εhp. For stronger attractions between the type A beads—that is, when the solvent becomes more unfavorable to those beads, εpp=0.8 (Fig. 4B) and εpp=1.2 (SI Appendix, Fig. S7)—there exists a maximum value of Γ, which monotonously increases with the adsorption strength εhp. Importantly, we observe that the maximum surface coverage shifts to lower values of ϕA as εpp increases. The presence of an optimal ϕA for maximum protein surface coverage at large enough εpp will be explained below, where we analyze the microscopic details of the adsorbed polymer layers.

Fig. 4.
Fig. 4.

Surface coverage Γ as a function of the average adsorbing fraction ϕA for different adsorption strengths, εhp. εpp=0.3 (A) and εpp=0.8 (B). The error bars (Right) are the standard deviations from averaging over 10 uncorrelated configurations.

Multilayer Adsorption Model.

Fig. 5 shows that the surface coverage Γ varies with the adsorption strength, εhp for different values εpp. For all of the values of ϕA studied, Γ increases with εhp until approaching a saturated value Γ∞, which depends on εpp. The inflection point in Γ(εpp), which marks a transition from the weak adsorption to a strong one, shifts to higher values of the adsorption strength εhp as ϕA and εpp increase. This is because the net polymer–protein attraction should be sufficiently strong to overcome the increased attraction between the polymer beads of type A for the polymer chains to fully cover the protein.

Fig. 5.
Fig. 5.

(A–C) Surface coverage Γ as a function of the attraction strength between sticky protein beads and polymer beads, εhp for different values of εpp. ϕA=0.5 (A), ϕA=0.7 (B), and ϕA=0.9 (C). The error bars are the standard deviations from averaging over multiple steady-state snapshots each obtained at the end of the equilibration cycle. (D) Normalized surface coverage Γ*=Γ/Γ∞ as a function of the reduced adsorption energy εhp* for different values of εpp for ϕA=0.7, where εhp*=αεhp+logK (main text). The black curve is the fitting function of the form f(x)=1/(1+exp(−x)).

The variation of surface coverage with respect to the adsorption energy (Fig. 5 A–C) is reminiscent of the S-shaped adsorption isotherms (i.e., type 5 in the International Union of Pure and Applied Chemistry classification), where the polymer beads of type A of the adsorbed chains act as secondary adsorption sites, leading to the formation of multilayers of adsorbed type A beads. Qi et al. (37) proposed an analytical model for the adsorption of water vapor adsorbing onto activated carbon, where the adsorption capacity is governed by the ratio between the actual partial and saturated partial water vapor pressures. We propose a similar model where the protein surface coverage (Γ) and adsorption energy (εhp) play similar roles to the adsorption capacity and pressure ratio, respectively:∂Γ*∂εhp∼1−Γ*Γ*,(1)where Γ*=Γ/Γ∞ and Γ∞ is the saturated surface coverage. Analogous to the model by Qi et al. (37), our model is based on the following assumptions: (i) The number of secondary adsorption sites is proportional to the amount of polymer chains adsorbed for a specified εhp; (ii) the number of primary adsorption sites is proportional to the remaining adsorption capacity, (Γ∞−Γ); and (iii) the driving force for the change in adsorption capacity with the change in adsorption energy is proportional to the product of (Γ∞−Γ) and Γ. The solution of Eq. 1 has the form of the logistic function:Γ=Γ∞1+K⁡exp(−αεhp),, (2)where α and K are the model parameters. When the datasets in Fig. 5 are fitted against the model given in Eq. 2, the data points collapse nicely into a single curve (Fig. 5D). The fitting parameter K generally increases with εpp for different values of ϕA (SI Appendix, Fig. S8A), corresponding to the shift in the inflection point of the adsorption curves to higher values of εhp, as earlier shown in Fig. 5. Conversely, the fitting parameter α is rather insensitive to εpp and ϕA (SI Appendix, Fig. S8B). The fact that the analytical model is highly consistent with our simulation results suggests that the assumptions made in our model are relevant to the underlying physics of the system of interest. Our supplementary simulations further show that the polymer/protein molar ratio at a given polymer bulk density and temperature, and, thus, the excess chemical potential of the random copolymers in bulk relative to adsorption, influences protein surface coverage up to a certain value (SI Appendix, Fig. S10). We note that as the concentration of proteins and/or polymers increases, highly heterogeneous gel-like structures (34) or macroscopically segregated polymer chains are expected, depending on the relative magnitude of the different interactions. The delicate balance of these competitive effects is evidenced in the transition in the human eye lenses that undergo macroscopic segregation from a homogeneous mixture to insoluble protein aggregates manifested as cataracts (38).

Structural Features of the Adsorbed Polymer Layers.

To elucidate the relationship between the protein surface coverage, Γ, and the average polymer composition, ϕA, adsorption energy, εhp, and solvent selectivity, εpp, we analyze in detail the structural features of the polymer chains that are in contact with the protein surface beads. First, we compute the number of adsorbed polymer chains, nads, which is proportional to the protein surface coverage, Γ, for different values of ϕA and εhp. As shown in Fig. 6A, for a given value of ϕA nads always increases with εhp, which is consistent with Γ(εhp) (Fig. 5). For a given value of εhp, the variation of nads with ϕA depends on εpp. Specifically, for εpp=0.8, nads exhibits a nonmonotonic behavior with respect to ϕA for εhp>0.5. On the one hand, nads is proportional to the energetically favored polymer–protein contacts governed by the adsorption strength. Consequently, nads, and hence Γ, increases with ϕA as expected. On the other hand, nads is associated with the entropic penalty due to the reduced number of polymer conformations in an adsorbed state compared with polymers that are far away from the protein. For sufficiently high values εpp, the polymers in solution adopt a few energetically favorable conformations to maximize the contacts between type A beads such that the entropic penalty due to adsorption becomes small.

Fig. 6.
Fig. 6.

Structural features of the adsorbed polymer layers. (A) Number of adsorbed polymer chains, nads, as a function of ϕA for different adsorption strengths εhp when εpp=0.8. The error bars are obtained from averaging over 10 steady-state snapshots at the end of the equilibration cycles. (B) Surface area fraction of solvophilic monomers (type B) at the outer layer of the adsorbed polymers for different values of εhp and ϕA for εpp=0.8.

For larger values of ϕA, the thermodynamics of the polymer adsorption in this regime is governed mainly by the energetics of polymer–polymer and polymer–protein interactions. As a result, there exists a threshold value ϕA* (dependent on εpp) above which forming polymer–protein contacts is less energetically favorable than keeping the A beads in an aggregated state. This leads to a decrease in nads (Γ shows similar behavior; Fig. 4B and SI Appendix, Fig. S7) with ϕA for ϕA>ϕA*. The maximum value of nads, and hence of Γ, may therefore be attributed to the competition between the tendency of the polymers to maximize their energetically favored contacts and their tendency to avoid the entropic loss due to confinement to the surface. These qualitative arguments are in agreement with the results of Srebnik et al. (8), who studied adsorption of random copolymers onto a flat surface randomly decorated by adsorption sites. They found that when the polymer intersegment interaction is strong enough, the entropic penalty due to adsorption becomes comparable to, or even smaller than, the energetic gain due to the segment–surface interaction. Our CG model underestimates the complexity in polymer architecture. Thus, it excludes the effects of sequence-dependent persistent lengths as well as small side chains that interact with the protein patterns. However, for architectural details on length scales smaller than the mean distance between the adsorption sites of the proteins, which is ∼3.0 nm in our tested cases, we expect small corrections to the protein surface coverage trends found with our model.

The pair correlation function of the attractive beads on the polymer chains and those on the protein and the radial density profile of the polymer beads (SI Appendix, Fig. S9) further reveal that the adsorbed polymer chains form a multilayer structure and that the polymer layers would behave like a liquid with number density well below 0.4σ−3.

The effective interaction between the protein and the implicit solvent in the presence of the encapsulating random copolymers is characterized by the outer layers of the polymer shell and the fraction of the protein surface that is uncovered. To characterize the effective interaction between the protein and the solvent mediated by the adsorbed polymer layers, we analyze the structural property of the polymer outer layer. Using the same method to estimate the surface coverage, we compute the area fraction, Γp, occupied by the solvophilic polymer beads (i.e., those of type B) at the distance (Rmax−rc) away from the protein center of mass. Rmax is the maximum distance between the polymer beads to the protein center of mass. Fig. 6B shows the variation in Γp with respect to εhp and ϕA. For any given value of εhp, Γp decreases as ϕA increases, which is expected because the fraction of solvophilic beads decreases. For a given value of ϕA, we observe that increasing εhp leads to a slight increase in Γp, and that Γp is strongly correlated with the fraction of the solvophilic beads ϕB=1−ϕA for εhp<1.2. This is interesting because it is suggested that the phase behavior of the proteins coated by the random polymers resembles that of the random copolymers at the given ϕA.

Conclusions

Random copolymers with two types of monomers appear to possess interesting capabilities of reducing the unfavorable exposure of the enzymes to the foreign media. Using CG simulations, we show here (i) that the sequence randomness of the random copolymers with only two components, solvophobic and solvophilic, enables the proteins to selectively pick the most favorable copolymer sequences; (ii) that the random copolymers encapsulate the proteins with a narrow distribution of the adsorption sites equally well regardless of their average composition; and (iii) that the average adsorption fraction, adsorption strength, and solvent selectivity are the key factors determining the encapsulation of a given protein by random copolymers. By examining the structural features of the adsorbed polymer layers, we have demonstrated that the effective protein–solvent interaction can be mediated by tailoring the average polymer composition. Our findings strongly suggest the possibility of designing random copolymers to stabilize proteins in foreign environments, leading to the fabrication of synthetic aggregates structurally similar to cellular membraneless organelles (34). We envision that polymer architecture, monomer chemistry, and charge polydispersity would introduce additional flexibility toward mimicking disordered proteins. Other potential applications of such rationally designed random copolymers can be neutralizing toxic agents (35) or viruses (39) and stabilizing proteins in healthy fats (40).

Materials and Methods

Simulation Method.

For the CG models, we simulate a single protein located at the center of the simulation box surrounded by Nc=50 polymer chains with implicit solvent at constant volume and temperature using molecular dynamics simulation. The protein and the polymer chains are coupled with the Langevin thermostat, which incorporates the effects of the counterions and solvent molecules through the random and drag forces exerting on individual CG beads. We assume that the protein maintains its overall structure upon polymer adsorption and that the protein beads are subject to thermal fluctuations induced by implicit solvent molecules. To capture these effects, we only consider the adsorption energy εhp from 0.5−2.5 (in units of kBT) and tether the protein CG beads to their initial positions (as obtained from the all-atom configuration) by harmonic springs with stiffness of k=100ε/σ. The reduced temperature T*=kBT/ε=1.0 is fixed, where ε=1 is the energy well depth of the WCA potential. The distance unit is the length scale of the potential σ=1. The time unit is defined as τ=σm/ε, where m=1 is the mass of the CG beads. The time step is chosen to be Δt=0.005τ. More information can be found in SI Appendix, section I.

Polymer Sequence Similarity Analysis.

We use the Python module difflib (41) for convenience reasons. The similarity order parameter s for two sequences varies from zero for two completely different sequences to one for identical sequences. According to ref. 41, a value of sij > 0.6 means two sequences i and j are close matches. Because the sequence-matcher kernel is not communicative (i.e., si,j≠sj,i), we define the sequence similarity order parameter S as Sij≡(si,j+sj,i)/2 to enforce symmetry Sij=Sji. To quantify the sequence randomness within a given batch B, we define the intrabatch sequence similarity order parameter Sintra as Sintra(B)=⟨Sij⟩i<j, where the bracket indicates the average over all of the distinct pairs (i,j) within the batch. Using this measure, we find that the similarity order parameter for the random copolymers within a batch of 50 chains is ∼0.5. We define the interbatch order parameter Sinter as: Sinter(B1,B2)=⟨max(Sij)⟩i∈B1,j∈B2, where the bracket indicates the average over all of the distinct pairs from two batches B1 and B2. Here, the average is performed over the maximum values to ensure that Sinter(Bk,Bk)=1.

Surface Coverage Estimate.

We estimate the protein surface coverage Γ from particle-based molecular simulation data as follows. First, the protein beads that interact with the polymer beads (i.e., within the LJ cutoff rc=3.0σ) are identified. The maximum distance from the protein beads to the center of mass of the protein rmax is then calculated. Next, we construct a spherical shell of radius (rmax+rc) centered at the protein center of mass and divide the spherical surface into Ncells with equal areas via a triangular geodesic mesh so that the dimension of each cell is approximately σ. The polymer beads that are within the spherical volume are then binned into the cells based on their coordinates. The ratio between the number of the occupied cells and the total number of cells Ncells gives the approximate measure of surface coverage Γ.

Acknowledgments

T.D.N. thanks M. Tasinkevych and G. Vernizzi for helpful comments and discussion. The research was supported by Department of Energy Award DE-FG02-08ER46539 and the Sherman Fairchild Foundation. T.D.N. was supported by the Midwest Integrated Center for Computational Materials (MICCoM).

Footnotes

  • ↵1To whom correspondence should be addressed. Email: m-olvera{at}northwestern.edu.

  • Author contributions: T.D.N. and M.O.d.l.C. designed research; T.D.N. and B.Q. performed research; T.D.N., B.Q., and M.O.d.l.C. analyzed data; and T.D.N., B.Q., and M.O.d.l.C. wrote the paper.

  • Reviewers: A.V.D., University of Akron; and A.Y.G., Center for Soft Matter Research, New York University.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1806207115/-/DCSupplemental.

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Efficient encapsulation of proteins with random copolymers
Trung Dac Nguyen, Baofu Qiao, Monica Olvera de la Cruz
Proceedings of the National Academy of Sciences Jun 2018, 115 (26) 6578-6583; DOI: 10.1073/pnas.1806207115
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