Liquid Network Connectivity Regulates the Stability and Composition Of

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BIOPHYSICS AND COMPUTATIONAL BIOLOGY spontaneous liquid–liquid phase separation (LLPS). LLPS is a the constituent biomolecules to the stability and composition of thermodynamic process in which multicomponent cellular mix- the condensates, and to elucidate the physical mechanisms lead- tures minimize their free energy by demixing into a phase where ing to the observed behavior, thereby attaining a thermodynamic the concentration of certain proteins and nucleic acids is greatly description of intracellular LLPS. enhanced over their concentrations elsewhere in the cell (28–33). While the number of possible components of a biomolecular Results and Discussion condensate is potentially very large (ranging from tens to hun- Minimal Coarse-Grained Model for Protein LLPS. Based on the dreds of different types of biomolecules) (34–37), only a fraction dependence of intracellular LLPS on multivalency, stoichiome- of these molecules seem to be essential for their integrity (29, try, and weak biomolecular interactions, we developed a minimal 38, 39). Based on this distinction, Banani et al. (11) proposed coarse-grained model that allows us to simulate multicomponent two broad categories to classify biomolecules inside condensates: mixtures of thousands of interacting multivalent proteins, while “scaffolds” and “clients” (for an excellent review on this sub- varying all of these features (48). Although atomistic descrip- ject see ref. 36). Scaffolds are defined as groups of biomolecules tions are needed to investigate the microscopic determinants of that self-associate through multivalent interactions and sub- LLPS—such as the impact of chemical modifications, specific sequently drive LLPS. In contrast, clients are biomolecules intermolecular interactions, and conformational dynamics—due that are dispensable for the formation of condensates but to the exponential scaling of the search space with protein size are recruited through their interactions with the scaffold (49), sampling the formation of protein condensates atomisti- biomolecules (11). cally is currently unfeasible. Atomistic simulations of relevant The ability of protein scaffolds to drive LLPS depends strongly systems for understanding protein LLPS are scarce and have on their valency (defined as the number of sites or domains they been limited to aggregates of ∼10 to 20 small proteins (e.g., a possess for interactions with other biomolecules) (11, 23, 28, 36, 56-residue peptide) that are formed prior to simulation (50). 40), which in turn is dictated by the amino acid sequence, the Sequence-dependent protein coarse-grained models (note- protein conformational landscape, and the microenvironment. worthy examples are those described in refs. 51–53) can simulate High valencies facilitate multiple protein–protein (11, 28, 40), condensates containing ∼100 copies of the same protein for up protein–RNA (15), or protein–DNA (18, 19) interactions. Other to 10 µs and are ideal for identifying the dependency of LLPS crucial factors include the scaffold–client stoichiometry (11), on amino acid sequence. However, as we move from single- and the ability of biomolecules to bind weakly to one another component protein condensates to multicomponent systems, through nonspecific and promiscuous binding sites (e.g., via important finite-size effects (e.g., those related to the relative charge–charge, dipole–dipole, π–π, and cation–π interactions) number of copies of each component in the system) arise, cre- (23, 27, 41, 42). ating the need to consider much larger numbers of proteins in Multivalency is ubiquitous in the cell and the number of dif- the simulation setup. Hence, to investigate multicomponent con- ferent molecules that can act as scaffolds is large (36). These densates, minimal models that significantly reduce the degrees include multidomain folded proteins [with repeating (28) or of freedom but retain essential physicochemical information are varying domains (18, 19)], proteins mainly formed by intrinsically mandatory (54). disordered regions (IDRs) with multiple binding motifs (29–32, A notable approach to investigate LLPS is the “stickers- 40), proteins combining both well-folded domains and IDRs (18, and-spacers” lattice-based model, which represents multivalent 19, 29, 43), and the combination of RNA-binding proteins and proteins as heteropolymers composed of stickers (LLPS-binding their complementary RNA strands (44–46). Furthermore, a scaf- motifs) and spacers (regions in between stickers). This model fold may constitute a single type of multivalent protein [e.g., the has been successfully used to generate phase diagrams of mul- fused in sarcoma (FUS) protein (43) or the heterochromatin ticomponent systems (55, 56), and predict and rationalize the protein 1 (HP1) (18, 19)] or a mixture of two or more multi- phase behavior of proteins (40, 56). Patchy-particle models rep- valent biomolecules [e.g., the combination of the high-valency resent another class of important minimal models that have engineered proteins poly-SUMO and poly-SIM (11) or the mix- been successfully employed to investigate the phase behavior ture of LAF-1 and RNA found in P granules (29)]. Examples of biomolecules and colloids. These models have been exten- of clients include the set of low-valency (one to three repeats) sively validated to study the phase behavior of DNA constructs versions of poly-SUMO and poly-SIM and the small RNAs that (57) and proteins (58–62), and to assess the role of multiva- dissolve into liquid drops of Ddx4 proteins (47). lency in phase transitions (48, 63, 64). Therefore, they are ideal Deciphering the physical determinants of LLPS of intracellu- for investigating the phase behavior of multicomponent protein lar mixtures is needed to fully understand, and eventually con- mixtures. trol, how a cell organizes its contents in space and time. Missing Accordingly, our model represents each multivalent protein information includes the dependence of molecular mechanisms as a “patchy particle”: a sphere with a few anisotropic attrac- of condensate formation on varying conditions, the fundamen- tive patches on its surface (Fig. 1). Each attractive patch allows tal physical mechanisms that explain the connection between the protein to engage in one orientationally specific interac- multivalency and the stability and composition of condensates tion with another protein, accounting for generic features of with many components, and the molecular link between con- protein–protein interactions, such as electrostatics, hydrogen densate compositional diversity and stability. A key challenge bonding, and hydrophobic attraction. Although our model rep- in obtaining such information, either by experiment or by sim- resents proteins as sticky spheres, it adequately captures the way ulation, is the difficulty in relating the microscopic properties of in which intrinsically disordered proteins interconnect (see Dom- proteins and nucleic acids, and the nature of their interactions, to inant Role of Protein Multivalency in LLPS). In what follows, we the macroscopic characteristics of multicomponent biomolecular define the valency of our proteins as the number of patches on condensates including density, composition, and stability. their surface. In the present work, we combine the simplicity of a minimal To evaluate phase diagrams, we perform MD simulations, coarse-grained protein model with the efficiency of molecular exploiting our continuous patchy-particle potential (48), which dynamics (MD) simulations of continuous potentials, enabling permits long and large simulations. We use the direct coexis- many long simulations on large systems (48). With this approach tence method that involves simulating two different phases—the we are able to compute the phase diagrams of systems containing condensed (protein-enriched) liquid in contact with the diluted thousands of interacting proteins and many different compo- (protein-depleted) liquid—in the same simulation box sepa- nents. Our approach allows us to link microscopic properties of rated by an interface (65–67) (SI Appendix, section III). Strictly

2 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1917569117 Espinosa et al. Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 est f“pcao”poen n te imlclsta are that biomolecules other the and compute proteins not do “spectator” we of that i.e., proteins density separation; interactions the phase on upon intermolecular focuses enriched model are in Our differences (4). components the among by phases controlled specific densities of is similar selection the with where into compositions, phases different demix but liquid systems coexisting such Indeed, different (4). various interac- easily intermolecular LLPS weak undergo of tions distribution exhibit broad that sufficiently components a interacting different many a with and systems phase) (protein-enriched liquid a phase). (protein-depleted of vapor that direct is the implicitly, coexistence represented is solvent our because speaking, occurs separation phase interac- spontaneously. liquid–liquid the value, simulation, critical a the in exceeds If, point strength observed. tion critical longer no the is as separation phase known liquid is curve coexistence the sys- (T demixed in a maximum of The snapshot a tem). (bottom and phase (protein-enriched) liquid condensed (protein-depleted) a protein–protein diluted into stronger demixing favor a represents that of curve, region,” interactions coexistence snapshot coexistence the (top “two-phase below separation region protein–protein the phase The where sustain phase). homogeneous region,” to well-mixed weak “one-phase too of the above are values region is interactions pro- The what curve occur. what for will coexistence for shows demixing the and axis) it axis) (horizontal because (vertical concentration separate tein strength propen- phase the interaction assessing to protein–protein when protein the useful a is of red) in sity (shown curve coexistence The ie phase. given rti ftype of protein sioae al. et Espinosa (V is phase fraction a volume of The volume and the curve. phases of coexistence different proteins: fraction the a the in plot as proteins to defined the information of this (φ) use fractions 1/ε volume of the value sure given a For protein–protein (inverse) (T ture of space (1/ε inter- the strengths protein–protein explore interaction attractive patch diagrams weak Each phase one patches). The in (gray action. engage surface to their protein on the blue sites allows and scaffolds attractive for with (red clients) as cores hard-sphere diagram for (scaffolds as phase Proteins represented typical (Bottom). are strength a clients) interaction of and (inverse) representation the a of and function (Top) a work this in used 1. Fig. proteins (S) Scaffold c iuain n enfil hoyhv eosrtdthat demonstrated have theory mean-field and Simulations

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since , interaction strength, rpia lutaino h iia oregandpoenmodel protein coarse-grained minimal the of illustration Graphical - S-C S-S φ c :Fritrcinsrntslwrta h rtclvle liquid– value, critical the than lower strengths interaction For ): i = critical point:or C T N diluted liquid di i ∝ i stenme est fpoen ftype of proteins of density number the is V l i coexistence region i 1/ε /V and t d prot two-phase = N li Concentration, C −prot i i one-phase region V prot prot stettlnme fpoen ftype of proteins of number total the is i id where , −prot −prot oiotlaxis). horizontal (φ; fractions volume versus ) patches sticky condensate ftopae r eetd emea- we detected, are phases two if , etclai)o qiaetytempera- equivalently or axis) vertical ; V d C i stevlm ftehr oeof core hard the of volume the is t hti cuidby occupied is that ) proteins (C) Client i nta phase. that in C-C attraction attraction protein strong protein weak i na in ii h omto fpoenitroeua otcs(SI contacts intermolecular protein mutations S6 sec- of LLPS-destabilizing Table Appendix , these formation Appendix, (SI that the phase observe condensed valency limit we the tyrosine-to- average V), within the of tion LCD computing number FUS by increasing of Further, with 2 mutations. shrinks (Fig. serine LCD simulations FUS these of tyrosine-to- IV–VI). (71), 14 sections and experiments FUS A–C, Appendix, 7 of with with (SI diagrams Consistent variants phase respectively two the mutations, compute and serine to chains) (52) (80 al. model LCD et protein Dignon residue-resolution employ- of by sequence-dependent begin phosphorylation the We by and 71). ing inhibited (70, is mutations tyrosine- unmodified. LCD tyrosine-to-serine when and FUS 163-residue-long of separates 71)—a separation phase domain Phase that (70, low-complexity segment the FUS of arginine-rich valency, behavior of protein phase in the (LCD) changes on by focus explained we be indeed can cations their by 71). post- proteins 70, 32, of of (28, introduction replacement mutants via or e.g., modifications valency, protein translational protein that conditions the the experi- under reduce LLPS vitro as of likely in inhibition the rises Previously, revealed tem- (40). had proteins ments increased critical artificially domain experiments the is integrated (11, prion-like valence that tightly valency of demonstrated Indeed, with perature 56). recently increases 55, simulations LLPS 40, and the undergo 32, of 30, to 28, nature proteins abil- the chemical of that ity conditions exact suggest 69). experiments intracellular the 68, interactions, 40, protein–protein by of (32, concentration) affected regardless pattern- ion Importantly, and and and pH, acids, temperature, charge) (e.g., amino and protein– of aromaticity, weak ing nature diverse hydrophobicity, specific the by chemically (e.g., determined are by which interactions, stabilized protein are LLPS. in densates Multivalency Protein of Role Dominant of strength therefore the (1/ε is varying interaction temperature. of It protein–protein effect range. inverse the temperature the consider narrow to relevant a more in important molecular operate most simple ically (T The of temperature 1). diagram the is phase (Fig. mixtures the place controlling takes parameter LLPS which under droplets. the outside and inside is similar molecules) be spectator to over- (including likely the proteins that of expect fraction we volume However, all LLPS. in involved actively not alsS n S8 and S7 Tables can Appendix, proteins (SI that net- connectivity” “liquid volume network—the work of condensed-liquid inter- the unit of within establish number protein per average in connections the valency molecular dictates of Valency role behavior: dominant phase the explain further with lations proteins of mixtures the dominant multicomponent investigate valencies. different the to of approximation for behavior reasonable accounts a phase that is results valency model these of minimal Thus, role a 64). 63, that (48, suggest simulations previous with ment i.S1 Fig. Appendix, (SI 2 of valency a where 2 with diagram (Fig. drops proteins phase 3 valency to the protein 5 the in most as from region significantly are the shrinking Fig. with occurs Appendix , proteins LLPS S1), (SI of Table valency the and diagrams in S1 changes phase by influenced observe liquid–liquid We strongly LLPS. protein the in valency that of role dominant this tures from valency odcpe hte ouaino LSb rti modifi- protein by LLPS of modulation whether decipher To conditions the determine to us allow diagrams phase Our u eunedpnetadmnmlcas-rie simu- coarse-grained minimal and sequence-dependent Our ept t ipiiy u iia oregandmdlcap- model coarse-grained minimal our simplicity, its Despite ofimta h iudlqi oxsec region coexistence liquid–liquid the that confirm Right) to ∼6 A–C, ∼4. n,sbeunl,rdc h protein the reduce subsequently, and, ) ,addspern opeeyfor completely disappearing and Left), 4,5,6) oee,clstyp- cells However, 63). 58, (48, ) NSLts Articles Latest PNAS imlclrcon- Biomolecular prot− tafixed a at ) ,i agree- in ), .Higher ). | f10 of 3

BIOPHYSICS AND COMPUTATIONAL BIOLOGY A Minimal Coarse-Grained Model Sequence-dependent Coarse-Grained Model

FUS LCD FUS LCD FUS LCD 5-valency protein 4-valency protein 3-valency protein (unmodified) 7 TYR to SER 14 TYR to SER B

C Valency: 5 FUS LCD 1 Valency: 4 7 TYR to SER Valency: 3 1 14 TYR to SER 0.9 +valency 0.95 +valency 0.8 0.9 0.77

0.85 0.6

0.5 0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 3   (g/cm )

Fig. 2. Impact of protein valency modulation in their phase behavior as predicted by the minimal coarse-grained protein model used in this work (A–C, Left) and the realistic residue-resolution sequence-dependent protein model of Dignon et al. (52) (A–C, Right). (A, Left) Schematic illustration of proteins with three different valencies (green, 5-valency; black, 4-valency; and red, 3-valency) modeled as patchy particles. (A, Right) The low-complexity domain (residues 1 to 163) of the human FUS protein (green, unmodiﬁed FUS LCD), FUS LCD with 7 of its tyrosine (TYR) residues mutated to serine (SER) (green with black spheres highlighting the mutated TYR) and with 14 of its TYR residues mutated to SER (green with red spheres highlighting the mutated TYR). (B) Simulation snapshots illustrating the coexistence of condensed and diluted liquid phases. (C, Left) Phase diagrams (inverse protein–protein interaction strengths, 1/εprot−prot , versus volume fraction, φ) for the three minimal proteins. (C, Right) Average valency (SI Appendix, section V) and liquid–liquid phase diagrams (temperature, T, versus density, ρ) for the three FUS LCD proteins studied. The vertical axes in C have been normalized by the critical point of c c the highest-valency protein in each set (Left,1/εS for the 5-valency protein; Right, T for the unmodiﬁed FUS LCD). The black arrows indicate the direction c c toward which the critical parameters (1/εprot−prot or T ) move upon an increase in valency. Error bars in the phase diagrams are of the same size as or smaller than the symbols. Typical statistical uncertainties are provided in SI Appendix, Table S5.

valencies result in more densely connected liquid networks (SI Having confirmed that our minimal model reproduces well the Appendix, Tables S7 and S8) and, as a result, more stable modulation of protein liquid–liquid phase diagrams by multiva- condensates (Fig. 2). lency, in the rest of this work we employ this minimal model Formation of the dense-liquid phase occurs only when pro- to simulate systems containing thousands of proteins, multi- teins are able to interconnect with one another, forming a ple components (i.e., proteins with different valencies), and dynamic percolated network (SI Appendix, Fig. S1). We thus find long timescales to assess both equilibrium properties and the that LLPS occurs when the biomolecules in the condensed phase mechanism of formation of multicomponent condensates. can form a percolating cluster, where all proteins are connected to at least one other protein. Proteins with a valency of 2 cannot Modulation of Stability of Biomolecular Condensates Formed by Scaf- form percolated structures (rather, they form linear chains) and, folds and Different Types of Clients. To elucidate the essential therefore, cannot undergo LLPS on their own (SI Appendix, sec- physical chemistry governing the formation of phase-separated tion I and Fig. S1C). In addition, for the system to be liquid-like cellular compartments, which contain many components (36), rather than gel-like, the interactions among biomolecules must experimental approaches are generally based on the reconstitu- be weak and transient (29, 33, 72). We note that gels are also tion of minimal in vitro representations—using just one or two characterized by a percolated structure, but exhibit local rigid- essential biomolecules (i.e., the scaffolds) (23). It is then highly ity due to the prevalence of long-lived bonds (33, 73). Weak desirable to have rules predicting how the stability and phys- interactions allow proteins to dynamically switch their interac- ical properties of simplified biomolecular condensates change tion to other neighbors (i.e., bind/unbind on short timescales). upon adding more components, thereby approaching the con- Because the attractive molecular connections are weak, having a ditions for condensates inside cells. Accordingly, we employed high number of them per unit of volume (i.e., high connectivity) our minimal model in a series of computer experiments to inves- becomes critical to compensate for the entropy loss upon demix- tigate how the phase diagrams of pure scaffold systems change ing and stabilize biomolecular condensates; hence, there is the upon addition of clients with different characteristics. Through- dominance of multivalency in protein LLPS. out this work, scaffolds represent a single type of protein or

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Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 sioae al. et Espinosa of excess an to due together) mixed when PRM(H) LLPS undergo in that LLPS of excel- inhibition (SH3) in showing the are experiments trends condensates These with S3B). agreement the Fig. 3B). lent and inside II (Fig. being concentrations section Appendix , clients stability higher (SI high-affinity much condensate the at with the present consistent on is effect sites) difference binding This regardless negligible scaffold–scaffold clients contrast, the a to (i.e., In affinity has clients low surplus. with competing bind in reduc- poorly that 21% are adding (a stoichiometry, clients significant of the becomes when and LLPS) tion) energy favors interaction still protein–protein inter- that weakest inverse the the of strength, value critical action the are in scaffolds reduction the (6.5% excess when in marginal the is It strongly reduces stoichiometry: is by destabilization always influenced Such we 3A). sites (Fig. system, condensates binding of scaffold stability scaffold–scaffold com- pure strong for are the that petitors clients of low-valency introducing those that observe with mixtures scaffold scaffold–scaffold for sites. used scaffold mode, also alternative client-binding at sites binding the at versus of interactions scaffolds effects to the the binding of probed i.e., stoichiometry affinity. we binding addition, the scaffold–client In varied the and also mixtures We scaffold–client self-interact). section not Appendix, (SI do own their the on LLPS I of undergo valency of cannot the valency that lower-than-scaffold 2 vary a and no with proteins (i.e., clients clients—comparing trivalent self-interact are not scaffolds do where the systems they prepared We because interactions). client–client or attractive not divalent because do either are conditions, that any proteins they under their own as their on considered on LLPS are separate undergo contrary, phase the interactions. on scaffold–scaffold can Clients, heterotypic or that homotypic proteins via own different of group etadbn oatraesafl ie,rte hndisrupt diva- than least rather at sites, are that scaffold clients alternate because to is bind This and higher. valency lent a or have clients con- 2 if of of region) stability coexistence for the the used to (widen not increase densates sites affinity can via clients interactions high of scaffold–scaffold recruitment with that inter- find scaffold– bind scaffold–client We for for actions. specific instead sites additional compete but two scaffolds via not which scaffolds sites, do in binding case that the scaffold clients analyze low-valency a we of 3C, recruit stability Fig. the increase In can condensate. clients of recruitment upon which under loss eventually entropy that the enthalpy for in compensate demixing. gains condensate to modest the insufficient in of become results protein– stability it attractive the of because decreases number associations reduced (SI A protein present S8 ). are clients Table connectiv- when the Appendix, network in condensed-liquid (∼37%) the mixed decrease of the marked ity a of notice that 2-valency we for competing with clients), strongly condensate average 3) of 33% the the of (with system of in compare (valency scaffold–client volume and value system unit 3A) pure-scaffold fixed per Fig. the a in connections line of on dashed number focus a we by (shown if Indeed, condensed-liquid the network. reduces in some which interconnections favorable condensate, of of the density the in replacement scaf- valency) to (high–low for ones affinity scaffold– lead used client with binding valency) conditions sites (high–high scaffold–client three interactions same scaffold–scaffold These the the high. 3) via is and scaffolds self-assembly, to valencies, fold bind lower-than-scaffold possess clients clients 2) 1) when addition (74). client monovalent low-affinity a lysozyme, by LLPS (SH3) ihcinsta aeahge-hnsafl aec f4(and 4 of valency higher-than-scaffold a have that clients with ) hncmaigtepaedarm ftevrosclient– various the of diagrams phase the comparing When h etqeto eadesi hte hr r conditions are there whether is address we question next The client upon suppressed significantly is LLPS words, other In 5 2) n nyamdrt upeso f(SH3) of suppression moderate a only and (28), 1 5 hc sahg-fnt ooaetcmeio for competitor monovalent high-affinity a is which , –PRM(N-WASP) 8 ytm(w ihvlnyproteins high-valency (two system 1/ε 5 –PRM prot− 5 ueia auso h rtclpit r ie in given sym- are the points than critical smaller the in or of as provided values size are Numerical same uncertainties the statistical of Typical are bols. diagrams phase the in bars which toward 1/ε direction parameters the critical indicate valencies the addi- arrows higher-than-scaffold upon black with The observed clients diamonds). is competing (magenta condensate strongly the 33% Second, of of interactions. stability sites tion scaffold–client in same binding to increase the alternate significant devoted with a use exclusively scaffolds but scaffold to self-interactions the increase bind scaffolds’ in moderate clients the 33% a These as of First, triangles). strength addition scenarios. (cyan upon clients two observed ing is in stability clients condensate (C of S3 ). in addition Fig. , Appendix by (SI bility phase diluted concentrated are therefore, the clients and, because in densities condensate increases the higher clients from exhibits competing excluded poorly predominantly branch of diluted-liquid proportion the the with as that squares) (black Note the scaffolds clients. 33% of scaffolds versus 67% clients 67% one-half 33% compare with with We triangles) interactions. sites scaffolds (green scaffold–scaffold binding for to same used the bind those using while as that self-interactions, scaffold those the of as strength defined competing Poorly are clients. competing poorly clients LV of addition by condensate lar neato teghue nFg oeaut h oeua ehns of mechanism molecular the evaluate to (B inverse 4 formation. the condensate Fig. of value in squares) constant used (orange the strength illustrates scaffolds interaction line trian- 33% dotted The (purple versus clients. proteins clients 67% scaffold–scaffold and scaffold high-affinity in 67% 33% as strength, with cases: same gles) two the compare with We and sites, interactions. scaf- same to bind the that at those condensate. as folds the clients to competing strongly clients define competing we strongly Throughout, LV adding by (for formation scaffold normalized drop pure the been of have point 1/ε diagrams critical (i.e., system the val- phase over The the as dividing regions. by of shown purposes) coexistence are axes comparison the diagrams vertical of phase the the comparison on in facilitate ues points to data guide the visual valency through joining i.e., a (HV), assessed lines proteins (LV), The clients valency 4. proteins higher-than-scaffold of of or low-valency 2, either types of are valency different i.e., Clients and diagrams. phase 3) liquid–liquid of (valency scaffolds 3. Fig. C B A ouaino tblt fbooeua odnae omdby formed condensates biomolecular of stability of Modulation 0.6 0.8 1.2 0.6 0.8 1.2 0.6 0.8 1.2 8 8 8 1 1 1 .50101 . 0.25 0.2 0.15 0.1 0.05 0 .50101 . 0.25 0.2 0.15 0.1 0.05 0 .50101 . 0.25 0.2 0.15 0.1 0.05 0 S c etblzto fliquid- of Destabilization (A) system). pure 3-valency the for S +LVpoorlycompetingclients(67%) S +LVpoorlycompetingclients(33%) S +HVstronglycompetingclients(33%) S +LVnoncompetingclients(33%) S +LVstronglycompetingclients(67%) S +LVstronglycompetingclients(33%) Scaffolds (S) elgbecag ntesaiiyo biomolecu- a of stability the in change Negligible ) prot c −prot + clients oeuo h diino let.Error clients. of addition the upon move NSLts Articles Latest PNAS nraei odnaesta- condensate in Increase ) al S2. Table Appendix , SI al S5 Table Appendix, SI +clients +clients Vnoncompet- LV | f10 of 5 .

BIOPHYSICS AND COMPUTATIONAL BIOLOGY scaffold–scaffold connections, can facilitate new connections A Well-mixed intial state between distant scaffolds (i.e., scaffold··· client· · · scaffold). In Time this case, connections per unit of volume (estimated at the same fixed value of 1/εprot−prot used above) are 75% more abundant than in the pure scaffold system (SI Appendix, Table S8). An alternative mechanism to increase the stability of a biomolecular condensate is through recruitment of clients that 3 Scaffolds S/C~1 have higher-than-scaffold valencies (Fig. 3C, magenta diamonds) Q 2 Clients and, thereby, enhance the molecular connectivity. Such an 1 increase is limited to scaffold–client ratios that provide sufficient 0 free scaffold sites for client recruitment. Promotion of LLPS by 0 0.2 0.4 0.6 0.8 1 high-valency clients was observed for the (SH3)5–PRM5 mixture L upon addition of heparin—a highly negatively charged polymer that has a higher valency than the scaffolds and binds with high B affinity to PRM5 (74).

Molecular Mechanism of Condensate Formation and Client Recruit- ment. In addition to providing full phase diagrams, our simulations allow us to probe the spatial reorganization of individual 3 =2.22 scaffold and client molecules over time. To this end, we prepared S/C 2 a well-mixed scaffold–client system (Fig. 4A) at a protein–protein Q interaction strength that favors phase separation, and monitor 1 0 how phase separation proceeds (Fig. 4 B and C) to the final 0 0.2 0.4 0.6 0.8 1 equilibrium state (Fig. 4D) by defining two order parameters L (definitions in SI Appendix, section III). One parameter is a “condensation” order parameter [Q X (L)], which we compute C independently for scaffolds (X = S) and clients (X = C ) as a function of their position in the simulation box (in the direction of the largest box dimension, L). Q X (L) = 0 indicates a well- mixed state (as in Fig. 4A), and an increasingly positive value of Q X (L) signals the formation of protein condensation clus- 3 =2.08 ters (Fig. 4B). The ratio of the integrals of Q S (L) over Q C (L) S/C Q 2 with respect to the largest box dimension defines a second order 1 χ parameter, S/C , that probes the change in relative abundance 0 of scaffolds and clients inside the condensation clusters. 0 0.2 0.4 0.6 0.8 1 Starting from a well-mixed fluid (Fig. 4A; χS/C ∼ 1), we L observe that, as time progresses, the concentration of the scaffolds in various regions of the simulation box increases locally D (χS/C increases to 2.22), signaling the formation of nuclei rich in scaffolds (Fig. 4B; the nucleation stage) that will eventually give rise to the condensate (Fig. 4D). After nucleation, the scaffold-rich nuclei increase in size and fuse (Fig. 4C; growth stage), while the condensate begins to sequester clients from the dilute phase (χS/C drops to 2.08). The scaffolds continue 3 =1.28 D S/C to recruit clients until an equilibrium condensate (Fig. 4 ) is Q 2 formed (χS/C decreases further to 1.28). The “scaffolds and 1 clients” model (11) proposes that scaffolds self-associate first and 0 subsequently recruit low-affinity, low-valency clients to excess 0 0.2 0.4 0.6 0.8 1 scaffold sites that are free for binding. Our results support L this mechanism and demonstrate that it also holds for clients that bind with high affinity to the scaffolds. Indeed, as long Fig. 4. Mechanism of formation of a condensate composed of scaffolds as clients are unable to undergo LLPS on their own, their and clients (67% 3-valency scaffolds + 33% 2-valency high-affinity clients) at a value of the normalized inverse interaction strength equal to 0.85 (dashed phase separation will be dependent on the prior nucleation line in Fig. 3A). Each panel gives a plot of the condensation order param- of scaffolds. eter for scaffolds (red), QS(L), and clients (blue), QC (L), versus the direction of the largest dimension, L, of the simulation box, as well as the value of Biomolecular Condensates with Many Components. To investigate the relative enrichment of scaffolds over clients in the newly formed con- the properties of biomolecular condensates as a function of densates χS/C . Simulation snapshots (scaffolds as red spheres and clients as their compositional diversity, we prepared multicomponent mix- blue spheres) for the different stages of the condensate-formation process tures that included six different types of proteins with different are also provided: (A) initial well-mixed configuration, (B) nucleation, (C) growth, and (D) equilibrium condensate. intrinsic abilities to phase separate (Fig. 5 A and B) and that bind to each other with high affinity. Fig. 5C shows that as long as the proteins with the highest single-component critical ous proteins in our example; black squares in Fig. 5C). The c point (in inverse interaction strength 1/εprot−prot or tempera- curve of the binary mixtures lies slightly below that of the c c ture T ∝ εprot−prot) are in excess, the coexistence curves of a six-component mixture, likely because, besides the high-critical- binary (blue diamonds in Fig. 5C) and a six-component (cyan point proteins, the latter includes a fraction of additional pro- triangles in Fig. 5C) mixture nearly coincide with that of the teins (4-valency, selective) that are better at interconnecting pure high-critical-point protein (i.e., the 4-valency promiscu- the liquid network than the proteins added (3-valency, good

6 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1917569117 Espinosa et al. Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 en r nihdo eltdi odnae 1,4,75). al. 47, et Espinosa (11, condensates the in pro- versus depleted which to condensate or 5D extent the enriched Fig. the assess in are to protein teins measured are a liquid, of diluted diverse concentration more a of for components other its altered composi- marginally swaps in composition. is system increase curve the an coexistence as the against i.e., robust diversity; be tional con- to the a expect landscape for we the phase proteins, Importantly, of high-critical-point points. of stoichiometry critical concentration domi- stant and higher is the properties with condensate microscopic proteins multicomponent the a by of nated 5 behavior Fig. conden- in phase the triangles the of (green stability substantially reach the decreases (to species), sate all proteins of high-critical-point significantly concentrations we of equal when proportion the Notably, of the mixture. are reduce diagrams binary phase the the to in topology) bars Error protein). 4-valency in (the provided mixture are the uncertainties statistical in Typical a protein symbols. at a the by mixture than smaller established equimolar or contacts the as of of for size number value same calculated highest constant were a the liquid) at over diluted critical the form dividing equivalently, the in as pure or, line here versus in proteins) dotted (defined condensate system a 4-valency coefficients by the independent the partitioning depicted in in The for (0.75) as protein set). energy (that defined the interaction a set inverse among (as of the normalized temperature concentration among the critical of value of highest value critical critical ratio the constant highest the over the divided the of of form over change logarithm pure divided of natural in form direction protein pure the each in indicates of is protein temperatures arrow triangles) each black inverted of The (green energy each). in mixture action (16.6% given six-component are proteins second systems all 4-valency these The of 67% for each). concentrations contains (6.6% equal triangles) by (cyan concentrations 1/ε mixture formed equal parameter six-component i.e., at first mixture, change proteins of The equimolar inverse remaining direction proteins. an the the 33% good-topology indicates and represent 3-valency arrow proteins 33% diagrams black The and promiscuous phase system. proteins the a promiscuous such of 4-valency for all 67% shown not in is The mixture. axes (1/ε curve protein. coexistence the scaffold vertical (C a 1/ε 2-valency single-component The of own, parameter their a the characteristics. critical behavior on the of protein and phase LLPS of undergo value the 2.25-valency), the not which critical with do dominates (1/4; (good, the proteins varies and deactivated 2-valency proteins by point temperature 3-valency partially normalized critical of critical site strength the types highest interaction binding how two and showing one selective), region systems with and coexistence tein “M4,” protein largest term 3-valency the we a has (A, which topology), (promiscuous, protein poor proteins promiscuous 4-valency and 4-valency of “M3,” types term two we mixtures: the in teins 5. Fig.

in pure pure in stability

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hs iga fasxcmoetmxuea w ifrn iigcnetain essabnr itr.Tebnr itr bu imns contains diamonds) (blue mixture binary The mixture. binary a versus concentrations mixing different two at mixture six-component a of diagram Phase ) form neprmns attoigcefiins enda h ratio the as defined coefficients, partitioning experiments, In Right Purephasediagrams 1.25 0.75 1 hs eairo imlclrcnestswt pt i ifrn ye fpaesprtn rtis (A, proteins. phase-separating of types different six to up with condensates biomolecular of behavior Phase 00.05

hs igaso h igecmoetpro- single-component the of diagrams Phase (B) mixture. equimolar six-component a of coexistence liquid–liquid showing snapshot Simulation ) Valency: eel togcreainbtentepartitioning the between correlation strong a reveals prot c Promiscous binding lte safnto ftenraie ubro nemlclrpoenpoencnat e ntvlm (I volume unit per contacts protein–protein intermolecular of number normalized the of function a as plotted D) (M4) −prot . 0.15 0.1 4 Six-component proteinmixture stecnetaino h ihs-aec rti ntemxue(nti aeM)icess ueia auso h rtclpoints critical the of values Numerical increases. M4) case this (in mixture the in protein highest-valency the of concentration the as Selective binding 2.25 3 4 prot c attoigcefiin safnto ftenraie rtclpit(rtclivreinter- inverse (critical point critical normalized the of function a as coefficient Partitioning (D) S3 . and S2 Tables Appendix, SI . .5030.35 0.3 0.25 0.2 Valency: 4,promiscous(S) Valency: 2,NoLLPS Valency: 2.25 Valency: 3,poortopology Valency: 3,goodtopology Valency: 4,selective −prot topology (M3) Good stevlnyicess ueia auso hs igecmoetciia onsaegvnin given are points critical single-component these of values Numerical increases. valency the as topology +valency Poor 32 1 weak site C ε Multi-component phasediagrams S 0.75 1.25 /ε 0.5 1 prot 00.05 .Hence, C). −prot Six components(equimolar;M4:~17%) Six components(M4:67%) Two components(M4:67%+M3:33%) One component(M4:100%) = eto VIII section Appendix, (SI pressure finite and 0.8 . 0.15 0.1 c o n d oevr u iuain eelta iia predictive similar 6B). a (Fig. scaffolds that of pure reveal depletion the simulations of the our that to to Moreover, the due respect for system region with scaffold client coexistence significantly inter- the 2-valency shrinks exhibit expected, and mixture As that (3-valency 6A). proteins scaffolds Fig. the client proteins; with of only types as actions act two which and proteins, same evaluat- (4-valency the scaffolds) before by by form as formed systems protein pure mixture of high-valency multicomponent in type equimolar points these an (a.k.a. investigate critical ing own We estimating their unfeasible. which on is LLPS for undergo and not clients) do that interaction species inverse include the of value critical strength). the equivalently, temperatures compo- (or, critical single-component all respective among the and mixture strengths nents) multicomponent binding intermolecular equimolar equal an (with in species of coefficient e n sdsusdaoe utcmoetcnestscnalso can condensates multicomponent above, discussed As s . .5030.35 0.3 0.25 0.2 a t e al S5 . Table Appendix, SI S c (E C. o h -aec rmsuu rti) oeta because that Note protein). promiscuous 4-valency the for omlzdciia onsfrtepoen npr form pure in proteins the for points critical Normalized ) +M4 E D versus criticalpointsofpuresystems Normalized critical point, Liquid networkconnectivity Multi-component composition 0.4 0.2 0.6 0.8 Partitioning coefficient 2 0 3 0 1 1 Normalized criticalpoint,or 00.51 . . . . 1 0.8 0.6 0.4 0.2 0 Left Valency: 2 Valency: 2.25 Valency: 2 Vale perunitofvolume,I/I Normalized intermolecularcontacts ato lutaigtpso pro- of types illustrating Cartoon ) .Tenraiainwsdn by done was normalization The ). poor topology Valency: 3 NSLts Articles Latest PNAS d poor topology Valency: 3 i good topology Valency: 3 l oor to u /I t ncy: 3 e al S2. Table Appendix, SI S Valency: 2.25 d acltdfreach for calculated ) selective Valency: 4 ology l promiscuous Valency: 4 i promiscuous Valency: 4 q u good topology Valency: 3 i selective Valency: 4 se Valen d S s | : f10 of 7

BIOPHYSICS AND COMPUTATIONAL BIOLOGY A Scaffolds Clients (2 types) C Binary phase diagrams S + 1 type of client (3-valency: 33%) S + 1 type of client (3-valency: 50%) Multi-component composition 1 D versus critical points of binary systems Valency 4 32 no client-client interaction 4 Valency: 4 (S) (no LLPS of clients in pure form) 0.75 3 B Multi-component phase diagrams 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 Scaffolds (S) Valency: 3 (C) S + 1 type of client (2-valency: 33%) S + 2 types of clients (67%) Valency: 2 (C) S + 1 type of client (2-valency: 50%); No LLPS 1 1 1

Partitioning coefficient 0 +clients 0.85 0.9 0.95 1 0.75 Order parameter from binary critical points: c 0.75

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Fig. 6. Phase behavior of biomolecular condensates with one type of scaffold and two types of client proteins that do not undergo LLPS in pure form. (A) The scaffold is a 4-valency protein that self-interacts and drives LLPS. The two types of clients are 3-valency and 2-valency proteins that exhibit only scaffold–client interactions (no client–client interactions) and can phase separate only when mixed with the scaffolds. (B) Phase diagram of the equimolar c multicomponent mixture versus that of the pure scaffold. The black arrow indicates the direction toward which the critical parameter 1/εprot−prot moves upon addition of clients. Numerical values of the critical points of these systems are given in SI Appendix, Table S4. (C) Phase diagrams of binary mixtures consisting of the scaffolds and one type of client each (Top, 3-valency clients; Bottom, 2-valency clients) at two different scaffold–client ratios (33% and 50% clients). For each type of client, we define the parameter ∆c as the difference in the normalized critical points of the binary scaffold–client mixture at c c c two client concentrations, i.e., ∆c = εS/(εLow − εHigh), where the subscripts Low and High indicate that the critical point is taken from the low (e.g., 33%) and high (e.g., 50%) client concentrations, respectively. For systems where increasing the client concentrations results in LLPS inhibition (e.g., scaffold–client c c min min mixture with 50% of 2-valency clients), we define ∆c instead as ∆c = εS/(εLow − εLow), where εLow is the lowest temperature or largest protein–protein interaction strength that we can explore without observing gelation. Consistent with this definition, ∆c for the scaffolds is always equal to zero. The c c c c c c c min horizontal dashed lines indicate the values of εS/εLow (red) and εS/εHigh (purple) for the 3-valency clients, and εS/εLow (blue) and εS/εLow (magenta) for the 2-valency clients. The double-headed arrows illustrate the values of ∆c.(D) Partitioning coefficient of the different species in the equimolar mixture versus the order parameter 1 − ∆c determined from the critical points of the different binary mixtures. Error bars in the phase diagrams are of the same size as or smaller than the symbols. Typical statistical uncertainties are provided in SI Appendix, Table S5.

rule—like that postulated above for mixtures of phase-separating multicomponent condensate by estimating the critical parame- proteins—can also be obtained for these scaffold–client mul- ters (temperature, pH, salt concentration, etc.) of the different ticomponent condensates. Clients that cause the least disrup- components in pure form or, when they cannot phase separate tion to the overall connectivity of the multicomponent con- on their own, in binary scaffold–client mixtures. densate are expected to be preferentially partitioned into the The available simulations (48, 63, 64) and our work show condensate. Here, we assess the effect of each client on that the critical point of a system rises as the number of pos- the scaffold connectivity (and, thus, the overall condensate sible of intermolecular connections per unit of volume in the composition) independently. This is achieved by measuring condensed-liquid network increases (Fig. 5E and SI Appendix, critical points of binary mixtures containing only the scaffolds Table S3). We, therefore, suggest that the key physical fac- and one type of client and repeating this measurement for dif- tor governing the stability and composition of a biomolecular ferent scaffold–client mixing ratios (Fig. 6C). Adding a small condensate with many components is the overall ability of the number of clients that marginally disrupt the connectivity (i.e., different components to enhance the molecular connectivity of 3-valency clients) yields binary mixtures (i.e., where the scaf- the condensate. Higher connectivity can be achieved through a folds are in excess) with critical points that lie close to that of higher valency, through an optimal topology [i.e., an angular dis- the pure scaffold system and that decrease only moderately as tribution of patches that favors network formation (48)], or by more clients are added to the mixture (Fig. 6C, Top). In contrast, binding promiscuously rather than selectively. adding clients that substantially disrupt the connectivity (i.e., 2- valency clients) gives rise to much lower binary critical points Conclusions (with excess scaffolds) that decrease substantially (and can even Our simulations indicate that the dominant physical determi- lead to LLPS inhibition) as more clients are added (Fig. 6C, Bot- nant governing the stability of biomolecular condensates in tom). Strikingly, the partitioning coefficient of each client in the general—and of those with many components in particular— multicomponent condensate and an order parameter that quan- is the ability of the components to enhance the connectivity tifies the variation in the critical points of the binary mixtures (i.e., average number of attractive intermolecular interactions (1 − ∆c ) (Fig. 6 C and D) are positively correlated too. Since this per unit volume) of the percolating condensed-liquid network. procedure captures the effect of clients in disrupting connectiv- Valency plays the dominant role in modulating protein LLPS ity of the condensate, it is expected to hold independently of the because it determines the density of intermolecular connections valencies of the clients and of the binding affinities and binding that biomolecules can form to stabilize the condensed liquid. strengths between clients and scaffolds. High molecular connectivity is crucial for the stability of con- These results suggest that proteins with higher single- densates because scaffold–scaffold interactions are required to component critical temperature or with higher binary scaffold– be weak and transient for the condensate to be liquid-like. client critical temperatures are able to form more connections A system will generally experience a loss in the total num- inside the condensed phase and are generally more concentrated ber of available microstates upon demixing (entropy loss), but in the condensate. Hence, we can predict the composition of a dynamic formation and rupture of a large number of weak

8 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1917569117 Espinosa et al. Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 sioae al. et Espinosa oiinldvriyo h odnaei nrae tteexpense the at increased is condensate com- the the of if diversity However, the positional effect. increasing minor (i.e., a proteins has diversity) different compositional concentration of multitude scaffold com- a protein the for additional ponents the as of long one substituting As constant, remains scaffolds. the binding of scaffold–scaffold affinity) and conden- topology, valency, 67 % multicomponent (e.g., (e.g., scaffolds properties of of excess diagrams major an a with phase play sates the scaffolds the Indeed, of valency role. of and Because with concentration connectivity. condensate the physical intermolecular this, biomolecular the its a is i.e., of components apply; many stability rules the same of the determinant that see we condensate, favors valencies alternate higher-than-scaffold to have bind conden- or compartmentalization. that scaffolds triggers clients on adding sites interactions whereas dissolution, scaffold–scaffold posttranslational sate for of that activation/enhancement clients means the compete compartments low-valency high-affinity by or liquid Introducing interactions clients modifications. their scaffold–client of of by employed introduction of stability be the the could is we modulate increases that Hence, mechanism to scaffolds general stability. cells the a condensate than that and suggest valencies connectivity higher scaffold the with clients introduction Similarly, of condensate. new the within create connections den- they of the sity increase if effectively condensates can and of bridges scaffold–client–scaffold clients) stability the used (noncompeting increase not notably interactions sites through scaffold–scaffold scaffolds to for of bind contrast, because that number In clients is volume. the low-valency unit This reduce per rises. interconnections clients scaffold–scaffold concentration low-valency client and competing which the scaffolds destabilization, strongly as LLPS compet- to enhanced substantial (strongly affinity induce is sites can high clients) binding with ing scaffold–scaffold Low- bind for stability. that compete condensate inter- clients transform scaffold–client valency significantly via recruitment condensates can that to actions find clients We grow. low-valency they sub- of as mul- and clients pure interactions) that recruit of scaffold–scaffold sequently demonstrate work clusters by simulations forming the (sustained our by scaffolds with nucleate (11), Consistent condensates al. ticomponent clients. et introducing Banani of by con- is biomolecular multicomponent densates of stability the fine-tuning of condensates. phase-separated dynamically their to interac- cells of by stability the used the mechanisms control and/or key scaffold the of of of modulation one is that valency valency suggesting the scaffolds, of of strength result tion can increase/decrease variants their an by in scaffolds mod- of chemical replacement posttranslational or vivo, ifications In gain. enthalpic implies higher connectivity a higher making favorable; loss, thermodynamically such for LLPS compensate can intermolecular gain) small (enthalpy separation at interactions scaffold–scaffold attractive .Y hn .P rnwne iudpaecnesto ncl hsooyaddisease. and physiology cell in condensation phase Liquid Brangwynne, P. C. Shin, Y. 8. Iyer K. M. mammals. many in 7. RNAs regulatory with Small Makunin, V. systems I. Mattick, S. biological J. 6. in transitions Phase Ponomarenko A. E. Frenkel, 5. D. Jacobs, M. W. 4. of J F. thousands Weber, A. of C. Hyman, A. mixture A. functional 3. A cells: living Alberts, B. of 2. cytoplasm The Sear, P. R. 1. sw nraetenme fcmoet fabiomolecular a of components of number the increase we As way alternative an scaffolds, of properties the varying Besides Science Genet. Nat. (2005). R121–R132 Chem. Anal. J. components. Biol. Dev. Cell Rev. 2015). 6, ed. NY, York, New components. af32(2017). eaaf4382 357, h adcp fln ocdn Nsi h ua transcriptome. human the in RNAs noncoding long of landscape The al., et oeua ilg fteCell the of Biology Molecular 9–0 (2015). 199–208 47, ipy.J. Biophys. Matter Condens. Phys. J. – (2016). 1–6 2016, 95 (2014). 39–58 30, h ieo h ua rtoe h it n depth. and width The proteome: human the of size The al., et 8–9 (2017). 683–691 112, lce,Lqi-iudpaesprto nbiology. in separation phase Liquid-liquid ulicher, ¨ 38–39 (2005). S3587–S3595 17, GradSine alradFacsGroup, Francis and Taylor Science, (Garland r oiae ythe by dominated are ) u.Ml Genet. Mol. Hum. Annu. Int. 14, 6 .G al h etnilo h aa body. epigenetic Cajal the and of Post-transcriptional centennial The granules: Gall, RNA G. J. Kedersha, 16. ribonucleoprotein N. stabilizes scaffold Anderson, F-actin P. nuclear 15. A Brangwynne, P. C. Feric, M. 14. condensates: Biomolecular Rosen, Brangwynne P. K. C. M. 12. Hyman, A. A. Banani F. S. Lee, 11. O. H. Banani, F. S. 10. 3 .J oe,M .Fize,Ctpamcrbncepoen(N)bde n their and bodies (RNP) ribonucleoprotein Cytoplasmic Fritzler, J. M. Moser, J. J. 13. h abig ir2sse prtdb h nvriyo Cambridge of University by the EPSRC EP/P020259/1. provided by Grant by funded Capital resources Tier-2 (http://www.hpc.cam.ac.uk operated ), using Service Research system Computing performed Ekins Research Tier-2 been Roger Cambridge has College the Emmanuel work an This from (EPSRC) Oppen- Fellowship. is the Council and A.G. from Research Fellowship Sustainability. funding Sciences heimer acknowledges of Physical J.R.E. Physics and (EP/N509620/1). Research the Engineering studentship Advanced for an an Program by research is Winton funded 2020 R.C.-G. the Horizon 803326). from Union (Grant Fellow European program the innovation Euro- under the and from Council funding Research received has pean project pro- This sequence-dependent model. their coarse-grained of tein implementation the with help invaluable ACKNOWLEDGMENTS. Appendix Availability. Data in provided are details simulation and Appendix coexistence analyses, direct the the model, method, protein simulation multivalent minimal the of details Full Methods and Materials cells. inside LLPS and of misregulation controlling—regulation useful eventually are understanding—and and biomolecules, for constituent the micro- of the phase properties to relating scopic mixtures picture intracellular multicomponent mechanistic of current behavior Our the and condensates. expand formation biomolecular findings between multicomponent equilibrium of the dissolution shift that features ular of of points those systems. reduced-component critical from measured predict condensates easily can multicomponent that highly in models inaccessible opportu- concentrations developing present higher for ideas at nities These appear condensate. to Proteins multicomponent sys- expected the components). reduced of be of experiments would the types tems in two points critical or higher one yielding of systems composed simpler much (i.e., multicomponent of points highly critical within measuring con- by interest relative condensates of the predict proteins can words, of one other centration experiments In in components. that many propose with we condensate a different in the thermodynamic of species a composition as relative sys- the considered predicting single-component be for parameter can either mixtures) (i.e., binary or systems tems simplified points highly critical the of Therefore, sim- mixtures. coeffi- of scaffold–client points partitioning binary critical ple the their with correlate mixtures multicomponent can in cients we clients, points. for a critical Similarly, single-component find their we mul- and a own, mixture in their coefficients ticomponent partitioning on their separate between correlation phase Indeed, clear can concentrations. higher which in scaffolds, connectivity present for the are increase condensate can the that of species multicomponent is, inside That composition condensates. their determines also be tions can stability condensate the significantly. concentration, reduced scaffold the of .A .Hmn .Smn,Byn i n ae-hs rniin ncells. in transitions water-phase and oil Beyond Simons, K. 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