Pressure Sensitivity of SynGAP/PSD‐95 Condensates as a Model for Postsynaptic Densities and Its Biophysical and Neurological Ramifications

Abstract Biomolecular condensates consisting of proteins and nucleic acids can serve critical biological functions, so that some condensates are referred as membraneless organelles. They can also be disease‐causing, if their assembly is misregulated. A major physicochemical basis of the formation of biomolecular condensates is liquid–liquid phase separation (LLPS). In general, LLPS depends on environmental variables, such as temperature and hydrostatic pressure. The effects of pressure on the LLPS of a binary SynGAP/PSD‐95 protein system mimicking postsynaptic densities, which are protein assemblies underneath the plasma membrane of excitatory synapses, were investigated. Quite unexpectedly, the model system LLPS is much more sensitive to pressure than the folded states of typical globular proteins. Phase‐separated droplets of SynGAP/PSD‐95 were found to dissolve into a homogeneous solution already at ten‐to‐hundred bar levels. The pressure sensitivity of SynGAP/PSD‐95 is seen here as a consequence of both pressure‐dependent multivalent interaction strength and void volume effects. Considering that organisms in the deep sea are under pressures up to about 1 kbar, this implies that deep‐sea organisms have to devise means to counteract this high pressure sensitivity of biomolecular condensates to avoid harm. Intriguingly, these findings may shed light on the biophysical underpinning of pressure‐related neurological disorders in terrestrial vertebrates.


Introduction
Biological cells need to orchestrate al arge number of biochemicalreactions in as patiotemporally precise manner,which is facilitated by compartmentalization of cellular space. In addition to utilizing "classical" lipid bilayer membranes to achieve compartmentalization (e.g.,p lasma membrane, lysosomes, endoplasmic reticulum, mitochondria), membraneless compartmentsc onsisting of phase-separated liquid-like droplets have attracted significant attention in the last 10 years. [1][2][3][4][5][6][7] Such membraneless compartments-generally referred to as biomolecular condensates-are ubiquitous and central to many cellular processes, including but not limited to cell growth, division, migration, and cell-cell communication. [1,3,8,9] Examples include variousr ibonucleoprotein-enriched cytoplasmic granules, nucleoli, centrosomes,c lusters of proteins involved in signaling, and postsynaptic densities. [6,10,11] One advantage of such membraneless bodies over lipid-bilayer-bound compartments is that their biological function can be switchedo na nd off more rapidly by regulating the liquid-liquid phase separation (LLPS) that underlies the formation and dissolution of the condensed dropletphase.
As LLPSs are generally dependent on temperature, pressure, and cosolutes, biomolecular condensates can contribute toward in vivo responses to environmental stress factors. ModelL LPS systemsi nv itro have been demonstrated to respond to changes in temperature, pH and ionic strength. [5,10,12] By comparison, high hydrostatic pressure (HHP) as as tress factor for biomolecular LLPS is much less explored. [7,[13][14][15] Yet, a large fraction of the earth biosphere thrives under HHP,r eaching pressures up to about 1kbar (100 MPa, % 1000 atm) in the deep sea and even beyond in the sub-seafloorc rust. [16,17] HHP studies on biomolecular condensates are thus necessary for understanding the physical basis of extant life in the deep sea, which might also be the birth place of life on earth. [16] Aside from this direct relevance to deep-sea biology,p ressure serves as au seful physicalp robe of biomolecular interactions. As increasingp ressure favors states with lower volumes, pressuredependence experiments can reveal low-volume configurational states that are functionally important, but difficult to detect under ambient conditions. [18][19][20][21][22][23][24][25] Seekingp rogress in this context, we recently started investigating effects of pressureo n the LLPS of simple one-component protein systems, such as lysozyme, a-elastin, g-crystallin, and the intrinsically disordered region of the DEAD-box helicaseD dx4. [7,[13][14][15] Here, we explore am ore complex aqueous system consisting of two major proteins of the postsynaptic densities in neurons.
High hydrostatic pressurei sk nown to affect various biomolecular systems, including lipid membranes, proteins such as enzymes, membrane transporters, the cytoskeleton, and nucleic acidh airpins. [18,19,22,[26][27][28] Depending on the system,p ressures of several hundred to thousand atmospheresa re needed to induce significant conformationala nd,b yi nference, meaningful functional changes.D ifferently,e xposure of vertebrates to high pressure results in severe neurological disorders known as high pressure neurological syndrome (HPNS), [29] which starts to take place already at tens of atmospheres. They consist of altered electroencephalogram (EEG), dizziness, loss of coordination including tremor and convulsions. [30][31][32][33] Althought his syndrome is among the most pressure-sensitivep rocesses known to date, its underlying physiological and biomolecular basis is still largely unknown. What is known so far only is that release of various neurotransmitters is suppresseda nd the function of some receptors and ion channels is perturbed. [30][31][32][33] The molecular effects of pressure on more complex synaptic assemblies, such as the postsynaptic densities, are still terra incognita. [33] Synapses represent au nique typeo fm embrane-semi-enclosed compartment that control signal transmission in all nervouss ystems. Underneath the postsynaptic plasma membraneso ft he synapse resides ap rotein-rich sub-compartment known as postsynaptic density (PSD), an assembly whichi sr esponsible for receiving,i nterpreting, and storageo fs ignals transmitted by presynaptic axonal termini. [6,10,11] PSDs have been shownt ob ec omposed of hundreds of denselyp acked proteins forming large assemblies with af ew hundred nanometer in width and3 0-50 nm in thickness. [34,35] Extensive studies have also revealed numerousp rotein-protein interactions that organize the PSD protein network. [6,11,36] SynGAPa nd PSD-95 are two very abundant proteins existing at an ear stoichiometric ratio in PSD, [37] andm utationso fe ither of SynGAP or PSD-95 are known to cause human psychiatric disorders, such as intellectual disorders (ID) and autism. [38][39][40] SynGAPp redominantly localizes in PSDs through specificallyb inding to PSD-95. [41,42] SynGAP,abrain-specific GTPase-activating protein, forms ap arallel coiled-coil trimer capable of binding to multiple copieso fP SD-95. Importantly,t his multivalent SynGAP/ PSD-95 interaction leads to the formation of liquid-liquid phase separation, both in vitro andi nt he living cell. [6,10,11] The manner in which individual SynGAP and PSD-95 monomers are associated to form higher-order complexes in the LLPS state is not well understood in structural detail.T he amino acid compositions of the part of the molecules known to be involved in the interaction suggest that the favorable contacts may involve ac ombination of hydrophobic and p-related interactions.
To explore apossible role of LLPS in pressure-induced neurological disorder,U V/Vis and fluorescences pectroscopy,t urbidity measurements, light and fluorescencem icroscopy in various high-pressure sample cells were used to study the structure and phase properties of the SynGAP/PSD-95 system, covering ap ressure range up to about1 500 bar.A ss hown below,L LPS of the SynGAP/PSD-95 system is highly pressure sensitive and becomes unstable well below the 1kbar range that can be encountered by organisms in the deep sea.

Results
Concentration and pressure dependence of SynGAP/PSD-95 LLPS SynGAPa nd PSD-95 were prepared following previously described procedures. [6] To prepares amples for the present experiments, SynGAPa nd PSD-95 stock solutions were diluted to the desired concentration with Tris buffer and mixed in ar atio of 1:1. Liquid droplet formation upon entering the LLPS region was examined by monitoring the turbidity (apparent absorption) through light scattering at 400 nm using aU V/Vis spectrometer (Shimadzu UV-1800). The temperature of the sample cell was controlled by an external water thermostat.M easurementswere carriedout at 25 8Cand 37 8C. The pressure-dependent measurements were carriedo ut using ah ome-built highpressureo pticalc ell. [14,15] Sapphire with ad iameter of 20 mm and at hickness of 10 mm was used as the window material. Pressure was applied by using ah igh-pressure hand pump and was measured by apressure sensor.
To reveal the effect of protein concentration on the appearance of LLPS, we first studied the concentrationd ependence of the turbidity upon increasing the concentration of PSD95/ SynGAP (1:1). As seen in Figure 1, we observe the expected increase in turbidity of the solution with increasing concentration of the protein mixture, indicating phase separation and droplet formationa lready at concentrations above 20 mm at 25 8C, in agreement with literature data. [6] Beyondaprotein concentration of 90 mm,t he turbidity reaches ap lateau value, which may indicatem aximal droplet formation.H owever,t he plateau is more likely caused by fusion of droplets and macroscopic phase separation at high protein concentrations, leading to an apparent plateau in light scattering.
To visualize the concentration-dependent phase behavior of the SynGAP/PSD-95 system, light microscopy studies were carried out. As depicted in Figure1b, immediately after mixing the two proteins, macroscopic phase droplets are formed in the solution, with droplet diameters up to about 5 mm.W ith time, droplet size increases. Within 15 min, macroscopic phase droplets are formed which sink to the bottom,forming extended liquid-liquid phase separation regionso nt he bottom window surface of the microcopy cell. Figure 2d epicts the phase droplets at different protein concentrations when the objective focal pointo ft he recordedi mages was on the inner window surface. The diameter of the condensed-phase droplets increasesw ithi ncreasing protein concentration. At ac oncentrationo f1 50 mm,apercolating network of the droplet phase has formed, which extends over 100 mm,ascenario which is in accordance with the resultso btained by the turbidity measurements at high protein concentrations. Figure 3s hows the pressure-dependent turbidityd ata of a 50 mm SynGAP/PSD-95 (1:1) solution at two temperatures, 20 8Ca nd 37 8C. 50 mm Tris solution( 100 mm NaCl, 1mm EDTA, 1mm DTT) with ap Ho f7 .8 was used as buffer system. The pressure-dependentU V/Vis data depicted in Figure 3i ndicate that increasing the pressure beyond approximately 600 bar leads to ah omogeneous phase at T = 25 8C, the amount of droplets seemst od ecrease continuously up to that pressure, however.Ascan be seen in Figures 3b,i nthe depressurization direction, the turbidity of the solution increases at about 400 bar,t hat is, the cloud point pressure is shifted to slightly lower pressures. In fact, ac ertain degree of hysteresis is expected for this type of nucleation-induced phase transition. Several pressurization and depressurization cycles reveal that the process is apparently fully reversible.
In addition, pressure-dependent turbidity investigations were carriedo ut at 37 8C, which corresponds to the physiological temperature of humans. No drastic changes in the transition pressures are observed compared to the 25 8Cd ata (Figure 3b), the transition pressures seem to shift only to slightly higherv alues.
To validatet he results obtained from the turbidity measurements, additional pressure-dependentl ight microscopy measurements using ah ome-built opticalp ressure-cellw ith flat diamond windows were carriedo ut, which operates up to about 1500 bar (see Figure S1, Supporting Information). All pressure-  After mixing the two proteins, small phase droplets are immediately formed in the bulk solution with ad iameter smaller  than approximately 5 mm.W ith increasing pressure, the amount of phase droplets in the bulk solution decreases and a homogeneous single-phase region was observed at ap ressure still below 900 bar (Figure 4), in good agreement with the results obtainedb yt he turbidity measurements. In the depressurization direction, the droplet formation could be detected at about 600 bar.F or ab etter and more detailed visualization,w e have added am ovie( Movie 1i nt he Supporting Information) showingi mages upon continuous pressure release of the sampe. Figure 5d epicts the pressure dependence of the droplet formation of SynGAP/PSD-95 at 37 8C. The measurements indicate that increasing the temperature to 37 8Cs hifts the transition pressure to higher values. In the entire pressure range covered (1-1500 bar), some phase droplets were alwayso bserved in the bulk, although their number decreases drastically with increasingp ressure.

Effect of pressure on SynGAP/PSD-95 bindingdetermined by FRET methodology
Fluorescence measurements ( Figure 6) were performed to determinet he effect of hydrostatic pressure on the binding between SynGAPa nd PSD-95. To this end, as eries of solutions containing 2.5 mm of PSD-95 labeled with Alexa 405 (donor) were prepared, and the concentration of SynGAPl abeled with Alexa 488 (acceptor) was varied between 0-14.8 mm.T he concentration of PSD-95 was chosen such that the absorbance at the wavelength of excitation was less than 0.05 so as to avoid inner filter effects. The samples were then excited at 402 nm and the emission spectra were recorded in the range 420-630 nm by using ah igh-pressureq uartz cuvette with ap ath length of 0.4 cm. The spectra were collected at T = 25 8Cand at pressures of 1, 500, 1000, 1500 and 2000 bar.T he extent of binding was evaluated by followingt he increaseo ff luorescence intensity at about5 22 nm due to the Fçrster resonance energy transfer (FRET)b etween the Alex 405-labeled PSD-95 and the Alexa 488-labeled SynGAP.T he binding curvesw ere obtainedb yp lotting F/F 0 as af unction of total SynGAPc oncentration (in mm), in which F 0 and F denote the fluorescence intensities at 522 nm in the absence and in the presenceo f SynGAP, respectively.T he experimental data points were well fitted using a1:1 binding site model.
The dissociation constant, K d ,o btained from the data fitting procedure are reported in Ta ble 1( see also Figure S2 in the Supporting Information for all data). The results indicate that increasing pressure causes the dissociation constant for complex formation to increase slightly,t hat is, pressure disfavors the formation of the SynGAP/PSD-95 complex. This trend is consistentw ith our data on pressure-dependent LLPS;b ut the effect of pressure on the K d is rather small. Hence, it is likely that other effects also play important roles in the marked pressure sensitivity of the LLPS of the SynGAP/PSD-95 system,a s we will discussb elow.

Discussion
As stated above,h ydrostatic pressure is one of the environmental constraints in our biosphere which has had substantial impact upon the evolution of aw ide variety of aquatic organisms. Thought he effect of pressure on simple biomolecular systems, such as lipid bilayers, proteins and nucleic acids, is quite well understood, [18][19][20][21][22][23][24][25][26][27][28] the effect of HHP on more complex biomolecular assembliesi ss till largely unknown. In this study, we explored the effect of pressure on liquid-phased roplets and the LLPS of two major componentso fP SDs. PSDs concentrates and organizes am ultitudeo fp roteins,s erving as as ignaling machinery in response to synaptic activities. [6,10,11] Our results show the LLPS of the SynGAP/PSD-95 model system for PSD is among the most pressure-sensitive biomolecular assemblies identified so far.A ni ncrease of pressure of severalt en-tohundred bars can lead to ad rastic decrease of phase-separated droplets and the disappearance of the phases eparation region at ambient temperature happensa ta round 600 bar.
From ab iophysical perspective, it is particularly interesting that the pairwise interaction betweenS ynGAP and PSD-95 turned out to be rather pressure-insensitive (Table 1), suggest-ing that the binding interface of as ingle SynGAP/PSD-95 complex by itself is largely devoid of empty cavities and hence rather denselyp acked. Indeed, the pairwise complex is pressure stable up to the 2kbar range. Considering that the pressure dependence of pairwise binding is insufficient to account for the pressure sensitivity of SynGAP/PSD-95 droplets, ap lausible physicalr ationalization is that as ignificant larger void (cavity)v olumei naccessible to water molecules is associated with the multiple-molecule interaction network in the condensed phase than the dilute phase of SynGAP/PSD-95. In general, void volume can arise geometrically from imperfect packing in compactc onformational states, [13] as in the folded structures of globular proteins. [21,[43][44][45] Void-volume effects can offer ar ationalizationf or pressure-dependentL LPS of biomolecular condensates as well, wherein the voids are envisioned to be transientw hereas the voids in folded proteins are essentially static. [7,14] We explorev oid-volumee ffects in SynGAP/PSD-95 droplets semi-quantitatively by using an extremelys imple model of SynGAP/PSD-95 phase separation. Given that the interactions between SynGAP and PSD-95 are structurally specific, [6,46] it is more appropriate to use ag elation-type model that entails a specific number of "stickers" for each molecule [47] rather than a Flory-Huggins polymerm odel with nonspecific contact interactions, [48] even though the SynGAP/PSD-95 droplets are liquid-like rather than gel-like. Since both SynGAP (1308 amino acid residues)a nd PSD-95 (721 residues) are largely folded and tend to form complexes with a3:2 stoichiometry, [6] our model considers as ingle generic molecular species with limited structural flexibility and am olecular volume V p which equals to 5000 times that of an amino acid residue ( % 139.6 3 ). [49] Based on the SynGAP/PSD-95 interaction pattern, [46] each of thesegeneric units in our model is assigned four stickers and the pressure-dependent interaction strengths between ap air of stickers are taken to be those given in Ta ble 1. Details of this model,which by itself neglects void-volumeeffects, are provided in the Supporting Information. Results of our analysis are shown in Figure 7.  As surmised, Figure 7a shows that the pressure-dependent K d values in Ta ble 1a fford only av ery limited variation in LLPS propensity (narrow grey band). They do not account for the fact that LLPS is not observed experimentally at about 500 bar and higher (the entire grey band is in the phase-separated regime).T his situation is indicated again by the modelf reeenergy profiles in Figure 7b,w hich are all bimodal with af avored condensed phase. Recognizing that the model does not address void-volume effects, we consider how an auxiliary increase in void volume, dV void ,f rom the dilutet oc ondensed phase would affect phase behaviors. At pressure p, dV void raises the condensed-phase free energy by pdV void relative to that of the dilute phase (dashed arrow in Figure7b). Hence, ap ositive dV void is expected to destabilize condensed droplets. Because phase boundaries are governed by second derivatives of free energy with respect to volumef raction, [50] an exact determination of void-volume effects on phase behaviors would require knowledge of void volume for all protein volume fractions (not merely the difference between the condensed and dilute phases). Nonetheless, rough estimates based only on dV void are possible because, if the free energy of the condensed phase is raised above the barrier between the dilutea nd condensed phases,i ti sl ikely that phase separation would no longer occur.B yu sing such an approximate procedure and requiring that no LLPS occurs at 500 bar, dV void as af raction of protein molecular volumei se stimated to be 0.01-0.03 %( DF = 0i ntercepts in Figure 7c). Notably,t hese values are not affected significantly by varying the model parameters N (up to N = 10) and V p (e.g.,d ecreasing V p to that of 2000 residues as for a pairwise SynGAP/PSD-95 complex). In this regard, we also note that if the K d values in Ta ble 1w ere reduced (which is possible because the ITC-measured K d value for p = 1i nF igure 3B of Ref. [6] is about an order of magnitude smaller), aproportionally larger dV void would be estimated. Despite modeling as well as experimental uncertainties noteda nd taking all the above considerations together,w ed eem it likely that void volumes play ak ey role in the pressure sensitivity of the SynGAP/PSD-95 droplets. In this perspective, the condensed droplet phase becomes unstable under highp ressure, in accordance with Le Châtelier's principle, [28] partly because ar eduction of void volumei sa chieved upon dissolutiono ft he droplets and formationo fahomogeneousd ilute phase, which is also favored by ahighermixing entropy. [7] The present estimate of dV void /V p % 0.01-0.03 %i sp hysically plausible as it does not entail creation of large water-inaccessible voids that would be difficult to maintain in the liquid state. In fact, this dV void /V p ratio is far smaller than the dV void /V p % 7% estimated for folded globularp roteins. [45] It would appear, therefore, that the pressure sensitivity of SynGAP/PSD-95 droplets arises not from al arge dV void .R ather,i ti sl ikely ac onsequenceo ft he combined impact of am odest dV void and as et of droplet-forming cohesive interactions (Table1), which are much weaker than the interactions favoring the folded states of globularproteins.

Conclusion
As mentioned above, proper assemblyo fP SDs are critical to neuron function. An intriguing case in point is that down-scaling of PSDs can be induced by sleepi nm ice. [51] Mutations and dysfunction of PSDs are linked to human neuropsychiatric and neurodevelopmental disorders. [29][30][31][32]52] Considering that the nervous system is one of the most sensitivet argets of high pressure, [29,33] it is tantalizing to find that the phase-transition pressureo ft he PSD-mimicking SynGAP/PSD-95 system is about an order of magnitude smaller compared to those typically leadingt op rotein unfolding. [18,28] Although much further effort,s uch as construction of reconstitutedP SDs using more complex in vitro systems, [11] will be neededt oe lucidate the structure-function relation of PSDs, the present observations offer an ovel approach to investigate neurological effects of hydrostatic pressure. If the pressures ensitivity of naturalP SDs Figure 7. Rudimentary estimation of the increase in void/cavity volume associatedwith the formation of the condensed SynGAP/PSD-95 phasebased on aSemenov-Rubinstein-type gelation model. [47] (a) Phasediagrams (coexistence curves) of three alternate formulationsi nwhich N is an effective number of rigidbody units and, hence, al arger N assumes more flexible individual SynGAP andPSD-95 molecules. The grey band marks the rangeo fp airwise dissociation constants in Ta ble1.( b) Pressure-dependent free energyprofiles of the N = 2m odel. The vertical variable is F V (f,p)ÀfF V (1,1)asd efinedint he Supporting Information, in which f= protein volume fraction, F V is free energy per unit volume in units of k B T, k B is Boltzmannc onstant and T = 300 Ki sa bsolutet emperature. It must be noted that phase separation is not affected [48] by any term linearinf. The pink arrowh ighlights destabilizationoft he f % 0.7 condensedphase localminimum as pressure increases (p › ); the purple dashed arrowi ndicates that ahigher void volume can destabilize the condensed phase. (c) DF is the differencei nf ree energy,p er protein complex, between the low-f localm aximum and the high-f local minimum[ corresponding,f or example, to the free energydifference between f% 0.1 and f% 0.7 for the N = 2c ase in (b)] in the presence of ah ypothetical dV void .R esults are reported for p = 500 bar for the three models in (a) using the samecolor code for N. Dashed lines are obtained using as lightly varied definition of the local free energy minima and maxima, as described in the Supporting Information.
are similaro re ven highert han that of the SynGAP/PSD-95 droplets, our findings may help decipher the underlying mechanismsofneurologicaldisorders of vertebrates under pressures that are not much higher than atmospheric pressure at sea level, [33] including onset of high-pressuren eurological syndrome at approximately 10 bar. [29]