Simulation methods for liquid-liquid phase separation of disordered proteins

Abstract

Liquid-liquid phase separation of intrinsically disordered proteins (IDPs) and other biomolecules is a highly complex but robust process used by living systems. Drawing inspiration from biology, phase separating proteins have been successfully utilized for promising applications in fields of materials design and drug delivery. These protein-based materials are advantageous due to the ability to finely tune their stimulus-responsive phase behavior and material properties, and the ability to encode biologically active motifs directly into the sequence. The number of possible protein sequences is virtually endless, which makes sequence-based design a rather daunting task, but also attractive due to the amount of control coming from exploration of this variable space. The use of computational methods in this field of research have come to the aid in several aspects, including interpreting experimental results, identifying important structural features and molecular mechanisms capable of explaining the phase behavior, and ultimately providing predictive frameworks for rational design of protein sequences. Here we provide an overview of computational studies focused on phase separating biomolecules and the tools that are available to researchers interested in this topic.

Introduction

While liquid-liquid phase separation (LLPS) is relatively well-understood, and has been harnessed for many processes, understanding its role in biological systems is still a nascent field. Cells use phase separation to accomplish many diverse functions requiring compartmentalization of specific biomolecules without needing a lipid membrane[1, 2]. This phase separation gives rise to highly concentrated assemblies, termed biomolecular condensates or membraneless organelles, which carry out many important functions, such as concentrating molecules to accelerate reaction rates and sequestering specific molecules from the surrounding solution. Reaction-accelerating membraneless organelles include nuclear puncta which form around superenhancer regions of DNA[3], and the nucleolus[4, 5]. Cells may also use phase separation to respond to various perturbations in their environment, and intracellular conditions. For example, stress granules may assemble through LLPS when the cell undergoes starvation or heat shock[6].

The diverse applications of phase separating biomolecules in the cell have inspired many technological advances in recent years. It has now been well acknowledged that many membraneless organelles are enriched in proteins having intrinsically disordered regions or proteins (IDRs or IDPs)[7], and therefore most applications focus on the use of disordered sequences. By simply modifying the sequence of fully disordered polypeptides, Garica-Quiroz and Chilkoti provide a large library of thermoresponsive phase separating proteins, and characterize the effects of amino acid composition and chain length on IDP phase separation[8•]. Several other groups have encoded functional motifs into protein sequences in order to gain further control of phase separation, and be able to induce desired responses from controllable stimuli such as protease cleaveage[9], light-induced dimerization[10] and chemical-induced cross-linking to form hydrogels[11].

The astronomical number of possible protein sequences allows for versatile selection of peptides with diverse properties, but also provides the nontrivial task of understanding the principles between sequences and phase separation. Computational approaches offer significant benefits in this area, as they provide predictive frameworks and may aid in interpretation of experimental results by directly probing the underlying physics with molecular detail[4, 12, 13•]. Experimental studies and design applications will benefit greatly from knowledge of how phase separation of IDPs can be controlled and finely-tuned through the molecular driving forces and stimulus-responses arising from sequence and composition. Here we provide a summary of the contributions in recent work made by computational methods, and of the appropriate models best-suited for specific tasks.

Spatiotemporal resolutions of simulations

Biomolecular simulations can be conducted using highly diverse models and at different resolutions, each with their own strengths and weaknesses. In general, there is a trade-off between model detail and simulation efficiency, meaning that the greater the accuracy, the smaller the system that can be simulated. An appropriate resolution must be sufficiently detailed in order to accurately capture the properties of interest, while also being computationally tractable. Figure 1 provides a summary of the different spatial resolutions applied to proteins and protein phase separation.

Figure 1:

Overview of simulation resolutions. Higher-resolution techniques give more detailed insight into chemical systems, but are hindered by low computational efficiency, and limits to system sizes which can be studied.

The most detailed resolution is quantum mechanics (QM) which explicitly accounts for electrons and orbitals, and is mostly limited to very small systems, such as short peptide sequences. Hybrid methods such as quantum mechanics/molecular mechanics (QM/MM) may be used to extend the size of the system, however QM regions are still limited to several hundred atoms[14]. One important contribution from QM calculations in the study of disordered proteins has been in constructing classical force field for atomic resolution simulations [15]. QM methods can also be used to improve and extend existing atomistic force fields to include non-canonical amino acids such as those with post-translational modifications[16].

Reducing the level of complexity to classical mechanics, the highest resolution can be achieved by using all-atom simulations with explicit representation of solvent molecules. These simulations have been applied to many biomolecular systems due to their high level of detail, and sufficient computational efficiency to consider a single IDP consisting of several hundred amino acids, or a small assembly of shorter IDPs. Such simulations are able to provide structural characteristics of protein sequences[17] as well as detailed information on inter-residue interactions[18, 19] in good agreement with experimental measurements[20]. Rauscher et al. simulated 27 copies of a 35-residue elastin-like peptide (ELP) for a combined simulation time of 165 μs and verify the proposed liquid-like nature of ELP assemblies, showing that association is driven by nonspecific hydrophobic contacts and hydrogen bonds[18]. To date, this is the only such study for a large assembly of phase separating IDPs at atomic resolution. However, the system size and amount of sampling required to converge on reasonable results are highly cumbersome, and thus, inaccessible to most research groups. One way to reduce this barrier to sampling would be to develop/use atomic resolution force fields with implicit solvent using mean field theory [21].

To further overcome the obstacle of simulating large IDP assemblies, coarse-grained (CG) models are commonly employed in which a group of atoms may be represented collectively as a coarse-grained “bead”[22]. The degree to which a protein can be coarse-grained is flexible, and ranges from multiple beads per amino acid to multiple amino acids per bead[23], following the same trade-off described earlier between model detail and simulation efficiency. CG models commonly account for interactions between protein and solvent molecules implicitly by modifying the protein-protein interactions accordingly, further reducing the computational cost. CG models can also be system specific, being optimized to the experimental data of one particular system[24, 25], or can be more general-purpose, focusing on transferability and applicability to all IDP sequences[26••][27]. Simulations of proteins in CG representation have been successfully applied to the study of IDP phase separation and assembly, including multiple beads per residue[28, 29], single bead per residue[26••][30], and multiple-residues-per-bead[4, 31, 32]. For the purpose of elucidating sequence-encoded phase separation, the balance lies at a single-bead-per-residue (residue-level) model which minimizes the computational cost while explicitly representing amino acid sequences. Dignon et al. proposed a general purpose, residue-level model which considers IDPs as flexible chains, ignoring secondary structure, and accounts for all 20 canonical amino acids based on either amino acid hydrophobicity[26••] or bioinformatics-based contact potentials[33]. This model has successfully been implemented to reproduce sequence-dependent phase behavior of disordered proteins [12, 13•]. This framework also accommodates for introduction of non-canonical amino acids, improved interaction potentials, and imposition of secondary structure either through rigid body constraints, or combined angle and dihedral potentials[26••]. To date, the residue-level CG model is the most detailed model that can practically simulate the IDP phase coexistence.

Considering many of the proteins involved in biomolecular LLPS are intrinsically disordered[1], polymer theories may also be applicable to the problem. Lin et al. combined Flory-Huggins theory with a random phase approximation (RPA) and successfully captured the interactions between charged amino acids[34]. They further saw a strong correlation between the radius of gyration (R_g) of their corresponding critical temperature, observing phase separation for polyampholytic chains with different charge patterning [35]. This observation is similar to the correlations across three characteristic temperatures for a homopolymer in the limit of infinite chain length, including the critical temperature of phase separation (T_c), the Boyle temperature (T_B) at which the second virial coefficient (B₂₂) vanishes and the θ-solvent temperature (T_θ) at which the polymer behaves like a random coil [36, 37]. Dignon et al. further extended the applicability of these correlations by testing over 30 IDP sequences using the aforementioned CG model and demonstrating that the robust relationship between the T_c and T_θ also applies to heteropolymeric sequences of finite chain length[38••]. Such a general correlation increases the applicability of models with different resolutions in that LLPS properties may be inferred from all-atom simulations of a single IDP.

Advanced sampling of phase coexistence

Even with well chosen models, efficient sampling of phase behavior remains a non-trivial task. One classic strategy is to improve sampling by constraining chains of polymers onto a simple lattice. Brute force lattice Monte Carlo simulations have been used at residue-level to study the phase behavior of short polyampholytic sequences to determine the effects of charge patterning on phase separation[39]. Other studies used a much coarser model, representing multi-domain proteins and RNAs as chains of interaction sites on a lattice, and parameterized to specifically capture behaviors observed in experiment[4, 31, 40•]. Representing particles on a lattice, however, will be limited in its ability to capture densities in the condensed phase[41]. Representing chains off-lattice would therefore provide a more accurate representation protein chain, which we find to justify the additional challenge to sampling.

Another common approach for sampling phase coexistence is grand canonical Monte Carlo (GCMC) which involves attempting insertions and deletions of molecules randomly[42]. One weakness of GCMC is that the acceptance probability of inserting into a liquid-density phase drops rapidly as chain length increases, making study of IDPs prohibitive without the use of lattice coordination and/or other enhanced sampling techniques. One such technique is configurational bias Monte Carlo[43], which can be used to find the “holes” in the dense phase. On-lattice GCMC simulations using conformational biasing have been successful for systems of polymers up to 1000 residues[36]. Jacobs et al. utilize on-lattice GCMC with multicanonical biasing, and observed the effects of interaction strengths and number of unique sequences on phase separation, showing that intermolecular interactions have a greater influence than the number of components[44]. Another popular method is Gibbs ensemble Monte Carlo (GEMC), in which particles are modeled in two separate boxes of varying size where particles may be transferred from one to the other, thus yielding two continuous “bulk” phases in coexistence[45].

Another efficient method to simulate the phase behavior is to use a slab geometry, where two coexisting phases are simulated in an elongated simulation box with periodic boundary conditions, having two planar interfaces perpendicular to the elongated axis (Figure 2 inset)[46, 26••][41]. This strategy can be used with virtually any representation of IDPs on- or off-lattice. Dignon et al. demonstrated that the coexistence concentrations from a spherical droplet simulation are consistent with those from the slab geometry and reduce finite size effects seen in the droplet simulations considerably[38••]. Jung et al. have also shown the use of slab geometry on multi-component systems, leading to convergent results in excellent agreement with studies using semi-GCMC and GEMC[46]. These observations suggest that the slab sampling method could be highly beneficial to the study of LLPS of IDPs and other biomolecules.

Figure 2:

Phase coexistence and single-molecule properties are fundamentally related. When the overall protein-protein interaction strength is stronger than the overall interactions between protein and solvent, IDPs will be able to phase separate, and a single IDP chain isolated in solution will become more collapsed. As some control variable decreases the relative interaction strengths, chains become more soluble, and thus will no longer phase separate, while a single chain becomes more extended in solution.

Applications of computational methods

Most computational methods presented so far can possibly, or have been applied to IDP LLPS, however the choice of methods depends on the specific question being addressed. For example, studies focused on the sequence determinants and molecular driving forces of LLPS must either account for sequence explicitly, or through some descriptors such as amino acid composition or patterning. Lin et al. have shown that differences in charge patterning between the sequences can drive drastically different phase separation behaviors using polymer theory[47••], and follow-up studies showed that lattice Monte Carlo[39] and molecular dynamics simulations with slab geometry[41] on the same systems give similar results. Dignon et al. also used a residue-level CG model based on amino acid hydrophobicity and electrostatic interactions to capture the sequence-dependent phase behavior seen in experiment[12, 13•] [26••]. These observations suggest the key roles of amino acid hydrophopicity and charges in determining the LLPS behavior of sequence.

While phase separation properties such as critical points and coexistence densities may be quantified by using CG simulations, the particular protein-protein interactions and sequence dependence may still be studied on a smaller scale using more detailed models. This has motivated the search for correlations between single-chain properties and phase behaviors. The correlation between T_c and T_θ as discussed previously considers that as intramolecular interactions which cause chain compaction become weaker, the corresponding intermolecular interactions driving phase separation decrease in a similar manner[38••] (Figure 2). Rauscher et al. determined single chain configurations in the condensed phase, and saw that chains are more extended when phase separated than in bulk solution[18], indicating that self-solvation is preferred over aqueous solvation. Ryan et al. find that post-translational modifications of hnRNPA2 causing reducion of phase separation also result in a reduction of atomistic interactions, and overall increase in R_g[13•]. Another example from Zhao et al. used single chain simulations of ELPs and observed a collapse upon heating[48•], in accordance with the propensity of these peptides to phase separate upon heating, having a lower critical solution temperature (LCST) phase behavior[8•].

Simulations with explicit representation of amino acid sequences can also give good insights into relevant features within protein sequences that may be of particular interest. For example, Dignon et al. identified a particular region of LAF-1 RGG domain which is particularly prone to forming intermolecular contacts using their residue-level CG model[26••]. Identification of such regions using CG models can be useful and can be further studied with higher resolution CG or atomic models (Figure 3). All-atom simulations may also be used to identify different types of interactions stabilizing LLPS such as hydrogen bonds, hydrophobic contacts, and π-interactions[18, 13•], and to identify regions prone to form secondary structures[49, 17].

Figure 3:

CG simulations allow for efficient characterization of intermolecular contacts to identify important regions of the sequence. These regions can then be examined in greater detail using higher resolution CG or all-atom simulations to determine the specific interactions stabilizing the condensed phase.

Conclusions and outlook

Simulations have proven greatly helpful in the study of biomolecular phase separation. For a question of particular interest, the balance between the resolution of the model and its computational efficiency should be carefully considered. All-atom explicit solvent simulations remain the most accurate representation applicable to IDPs, but are limited to studies of relatively small systems. We find residue-level CG models to be the most promising resolution as they explicitly represent the specific amino acid sequence and are efficient enough to directly observe phase coexistence. Simple homopolymer models also have contributed to understanding the underlying physics and in bridging the gap between different spatiotemporal resolutions and with experiments.

We anticipate an increase in the use of CG simulations as the applicable models and methods continue to improve, and as the field of IDP LLPS progresses toward maturity. CG models can be improved to account for LCST peptides, such as ELPs by modifying the interaction strengths of beads as temperature increases[50]. CG models which capture secondary structure may also be of great value in directly probing the contribution of structural motifs to the association which drives LLPS, and also the effects of high concentration on secondary structure.

Both computational and experimental researchers may take advantage of the correlation between T_θ, T_B and T_c, to screen large numbers of IDP sequences and to predict or design sequences with desired compactness and association probability, and consequently controllable liquid-liquid phase behavior. The correlation between the Boyle temperature T_B and T_c provides additional utility in that sequences with short unique motifs, which may not be well-represented by a single-chain simulation as self-interaction of such a short region would not be captured, can still be studied using relatively small system sizes. In addition, calculating second virial coefficients between different interacting biomolecules (e.g. IDPs and nucleic acids) may prove useful in predicting multi-component phase behavior. Insights drawn from large-scale CG simulations may guide the more detailed accurate virial coefficients determined using all-atom simulations.

Finally for the purpose of elucidating molecular interactions driving IDP association and LLPS, all-atom explicit solvent simulations remain the gold standard even though convergent phase behaviors are almost impossible to achieve. Improvement to sampling or simulation methods might pave the way toward the use of all-atom simulations to directly investigate IDP LLPS.